4.1: Simultaneous linear equations and symmetry
Problem 92 Dad took our new baby to the clinic to be weighed. But the baby would not stay still and caused the needle on the scales to wobble. So Dad held the baby still and stood on the scales, while nurse read off their combined weight: 78kg. Then nurse held the baby, while Dad read off their combined weight: 69kg. Finally Dad held the nurse, while the baby read off their combined weight: 137kg. How heavy was the baby?
The situation described in Problem 92 is representative of a whole class of problems, where the given information incorporates a certain symmetry, which the solver would be wise to respect. Hence one should hesitate before applying systematic brute force (as when using the information from one weighing to substitute for one of the three unknown weights – a move which effectively reduces the number of unknowns, but which fails to respect the symmetry in the data).
A similar situation arises in certain puzzles like the following.
Problem 93 Numbers are assigned (secretly) to the vertices of a polygon. Each edge of the polygon is then labelled with the sum of the numbers at its two end vertices.
(a) If the polygon is a triangle ABC , and the labels on the three sides are c (on AB ), b (on AC ), and a (on BC ), what were the numbers written at each of the three vertices?
(b) If the polygon is a quadrilateral ABCD, and the labels on the four sides are w (on AB), x (on BC), y (on CD ), and z (on DA ), what numbers were written at each of the four vertices?
(c) the polygon is a pentagon ABCDE, and the labels on the five sides are d (on AB ), e (on BC ), a (on CD ), b (on DE ), and c (on EA ), what numbers were written at each of the five vertices?
In case any reader is inclined to dismiss such problems as “artificial puzzles”, it may help to recall two familiar instances (Problems 94 and 96 ) which give rise to precisely the above situation.
Problem 94 In the triangle ABC with sides of lengths a (opposite A ), b (opposite B ), and c (opposite C ), we want to locate the three points where the incircle touches the three sides - at point P (on BC ), Q (on CA ), and R (on AB ). To this end, let the two tangents to the incircle from A (namely AQ and AR) have length x, the two tangents from B (namely BP and BR) have length y, and the two tangents from C (namely CP and CQ) have length z . Find the values of x, y, z in terms of a, b, c.
The second instance requires us first to review the basic properties of midpoints in terms of vectors.
Problem 95
(a) Write down the coordinates of the midpoint M of the line segment joining Y = (a, b) and Z = (c, d). Justify your answer.
(b) Position a general triangle XYZ so that the vertex X lies at the origin (0,0). Suppose that Y then has coordinates (a, b) and Z has coordinates (c, d). Let M be the midpoint of XY , and N be the midpoint of XZ . Prove the Midpoint Theorem, namely that
“ MN is parallel to YZ and half its length”.
 Prove that PQRS is always a parallelogram.
Problem 96
(a) Suppose you know the position vectors p, q, r corresponding to the midpoints of the three sides of a triangle. Can you reconstruct the vectors x, y, z corresponding to the three vertices?
(b) Suppose you know the vectors p, q, r, s corresponding to the midpoints of the four sides of a quadrilateral. Can you reconstruct the vectors w, x, y, z corresponding to the four vertices?
(c) Suppose you know the vectors p, q, r, s, t corresponding to the midpoints of the five sides of a pentagon. Can you reconstruct the vectors v, w, x, y, z corresponding to the five vertices?
The previous five problems explore a common structural theme - namely the link between certain sums (or averages) and the original, possibly unknown, data. However this algebraic link was in every case embedded in some practical, or geometrical, context. The next few problems have been stripped of any context, leaving us free to focus on the underlying structure in a purely algebraic, or arithmetical, spirit.
Problem 97 Solve the following systems of simultaneous equations.
(a) (i) x + y = 1, y + z = 2, x + z = 3
(ii) uv = 2, vw = 4, uw = 8
(b) (i) x + y = 2, y + z = 3, x + z = 4
(ii) uv = 6, vw = 10, uw = 15
(iii) uv = 6, vw = 10, uw = 30
(iv) uv = 4, vw = 8, uw = 16
Problem 98 Use what you know about solving two simultaneous linear equations in two unknowns to construct the general positive solution to the system of equations:
Interpret your result in the language of Cramer’s Rule. (Gabriel Cramer (1704–1752)).
Problem 99
(a) For which values b , c does the following system of equations have a unique solution?
(b) For which values a, b, c does the following system of equations have a unique solution?


7.1: Prelude to Work and Kinetic Energy
In this chapter, we discuss some basic physical concepts involved in every physical motion in the universe, going beyond the concepts of force and change in motion, which we discussed in Motion in Two and Three Dimensions and Newton’s Laws of Motion. These concepts are work, kinetic energy, and power. We explain how these quantities are related to one another, which will lead us to a fundamental relationship called the work-energy theorem. In the next chapter, we generalize this idea to the broader principle of conservation of energy.
The application of Newton’s laws usually requires solving differential equations that relate the forces acting on an object to the accelerations they produce. Often, an analytic solution is intractable or impossible, requiring lengthy numerical solutions or simulations to get approximate results. In such situations, more general relations, like the work-energy theorem (or the conservation of energy), can still provide useful answers to many questions and require a more modest amount of mathematical calculation. In particular, you will see how the work-energy theorem is useful in relating the speeds of a particle at different points along its trajectory, to the forces acting on it, even when the trajectory is otherwise too complicated to deal with. Thus, some aspects of motion can be addressed with fewer equations and without vector decompositions.


12.9: Islamic Golden Age Umayyad Mosque (715 CE)
-
- Last updated
- Save as PDF
The Islamic Umayyad Mosque sits in the city center of Old Damascus. The original temple was known for its beauty and size, the largest temple in Roman Syria, dedicated to the god Jupiter. By the end of the 4th century, it was converted into a Christian church and associated with Saint John the Baptist based on the legend his head (also known as a relic) buried inside the church. The area was conquered in 634 CE, then came under Muslim rule and in 700 CE the Umayyad caliph al-Walid I proclaimed: “Inhabitants of Damascus, four things give you a marked superiority over the rest of the world: your climate, your water, your fruits, and your baths. To these, I wanted to add a fifth: this mosque”. The construction of the Umayyad Mosque (7.14) was started in 706 CE and completed in 715 CE and dedicated to the people of Damascus for worship.
People from all over the region were employed to build the mosque, and the labor force grew to 12,000 workers, the old Christian church demolished to make way for the new mosque. Byzantine artisans created the mosaic art depicting buildings and landscapes in tile and glass, a universal art form throughout the Mediterranean structures.
In the eastern section of the mosque, the Dome of the Clock (7.15) added in 780 CE, and nine years later, the Dome of the Treasury (7.16) was incorporated. Over the years and throughout various wars and rulers, the mosque fell into disrepair. In 1082 CE, the new rulers began repairing the mosque with additional support pillars and an updated, more massive central dome. Throughout the next centuries, the mosque experienced cycles of damage and rebuilding, creating the structure we see today.
Four walls enclose the mosque built in the shape of a rectangle, 97 meters by 156 meters, and in the northern part of the complex, a large courtyard. Stone columns support the arcades around the courtyard with a pillar between every two columns. The southern section of the mosque contains three arcades creating the sanctuary, two types of stone columns support the arcades; level one has large semi-circular arches and level two made of double arches. The entire face of the courtyard and the arcades covered with glass mosaics (7.17), colored marble, and gold gilding. It was the most extensive mosaic wall ever created at the time. Only some of the original embellishment remains (7.18), but over the centuries, different rulers have added to the patterned embellishments seen today.
There are three minarets in the complex, the Minaret of the Bride (7.19) first constructed about 800 CE, added to and repaired over the centuries. Today, the minaret is divided into two sections; the oldest and the lower part is square and built from large blocks, the upper part made of sculptured stone. The minaret has 160 steps that are leading to the top. The Minaret of Jesus (7.20) sits on the main body of the large blocks formed in the shape of a square with an octagonal spire on the top. It is the tallest minaret and started at the same time as the Minaret of the Bride but not completed until 1247. The Minaret of Qaitbay (7.21) was not built until 1488 and is octagonal in shape.
The building is one of the few mosques that have maintained its basic shape and architect since it was started in the 8th century, becoming a model for other mosques throughout the Middle East. However, today much of the mosque has been destroyed in the war in Syria.


2.5.0: Quadratic Equations (Exercises)
For the following exercises, solve the quadratic equation by factoring.
40. \(2 x^{2}-7 x-4=0\)
41. \(3 x^{2}+18 x+15=0\)
42. \(25 x^{2}-9=0\)
43. \(7 x^{2}-9 x=0\)
For the following exercises, solve the quadratic equation by using the square-root property.
44. \(x^{2}=49\)
45. \((x-4)^{2}=36\)
For the following exercises, solve the quadratic equation by completing the square.
46. \(x^{2}+8 x-5=0\)
47. \(4 x^{2}+2 x-1=0\)
For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution.
48. \(2 x^{2}-5 x+1=0\)
49. \(15 x^{2}-x-2=0\)
For the following exercises, solve the quadratic equation by the method of your choice.
50. \((x-2)^{2}=16\)
51. \(x^{2}=10 x+3\)


15.2: Introduction to Integrating Source Material
What you’ll learn to do: synthesize outside sources with your own writing through effective quoting, paraphrasing, and summarizing
Well-integrated source material can build the strength of your argument, but integrating sources is a difficult task. Incorporating someone else’s ideas and words into your own writing can be confusing. Fortunately, certain strategies can help—this section will help you learn to integrate sources smoothly using a strategy known as the “source sandwich.” You’ll learn the best ways to include a quote from another source as well as how to integrate paraphrased and summarized passages alongside your own words.
You are the ultimate author of your text, so your words and ideas should make up the bulk of your writing. Using other sources effectively, however, allows you to place your writing into a broader conversation and thus to strengthen and enhance the credibility of your work.
Contributors and Attributions
- Outcome: Integrating Source Material. Provided by : University of Mississippi. License : CC BY: Attribution
- Image of office supplies. Authored by : Tim Gouw. Provided by : Pexels. Located at : www.pexels.com/photo/school-supplies-office-pens-53874/. License : Other . License Terms : www.pexels.com/license/


6.20: Putting It Together- The Writing Process
This module has demonstrated a very broad concept of the writing process, and in some senses a generic one. The next step for you, as a writer, is to visualize and customize your own personal process. Find out what works best for you—do you prefer outlining? Mapping? Fast drafts? Slow drafts? No matter your preferences, you’ll find that good writing is a process. It takes time, planning, and multiple iterations before resulting in a polished piece.
Try to identify a metaphor for your writing process. In the example below, Pat Thomson describes the value such a metaphor can give you. In this case, she’s describing writing her Ph.D. thesis:
When I was just beginning to write my own thesis I thought about it as a jigsaw. I just had to put all the little pieces together. At some point I had one of those aha moments when I realized that a jigsaw was a very unhelpful metaphor—a jigsaw has an original somewhere, it is about producing a predetermined image, and it already has set of relationships and a defined set of edges. My thesis and its authoring was actually nothing like this.
I decided I needed to rethink what I was doing. To help me do this I needed a new metaphor. I came to think that a more helpful approach to my thesis was thinking of it as making a patchwork quilt.
I had lots of pieces of stuff that I’d made up, hacked out, into some kind of shape. Some of the pieces were new material and others were made from second hand bits I’d found lying around (in books).  Even though there was a recommended size, there was still the possibility of approaching the shape somewhat creatively. There was certainly plenty of opportunity for putting the separate pieces together in different ways. It all depended on the effect I was trying to achieve. As long as I had a good backing, and the stitching firmly anchored the result of my more creative handiwork to the backing, then there were quite a few possible variations in patterning available.
This was a metaphor which worked for me at the time. It put me in control of the process. It meant I spent time thinking about the structure of the text, and where the various pieces might go. There were many possible quilts to be made. I played with various options—what if this chapter was about this and that one about that—how did it compare to all the other possible theses that I could write?
Thomson uses the patchwork quilt metaphor as descriptive of her process, and it also helps her define what her role in writing should be. Can you envision similar metaphors for yourself? Does writing a paper feel like creating a new galaxy to you? Does it seem like preparing for and undertaking a big trip to a foreign land? You can decide, and in doing so, you empower yourself to become a more confident writer.
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- What Is Academic Writing?. Authored by : L. Lennie Irvin. Provided by : Writing Spaces. Located at : http://writingspaces.org/ . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Image of I'm Smart. Authored by : Steven Depolo. Located at : https://flic.kr/p/7RxBE3 . License : CC BY: Attribution
- Image of quilt. Authored by : Littlelixie. Located at : https://flic.kr/p/pFKPAY . License : CC BY-NC: Attribution-NonCommercial
- a metaphor for the thesis. Authored by : Pat Thomson. Located at : https://patthomson.net/2013/01/07/a-metaphor-for-the-thesis/ . Project : Patter. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike


Skip to main content
11: Batteries And Power Systems
-
-
Last updated
-
-
Save as PDF
-
-
-
11.1: Electron Activity in Chemical Reactions
-
So far in our discussions on electricity and electric circuits, we have not discussed in any detail how batteries function. Rather, we have simply assumed that they produce constant voltage through some sort of mysterious process. Here, we will explore that process to some degree and cover some of the practical considerations involved with real batteries and their use in power systems.
-
-
11.2: Battery Construction
-
The word battery simply means a group of similar components. In military vocabulary, a “battery” refers to a cluster of guns. In electricity, a “battery” is a set of voltaic cells designed to provide greater voltage and/or current than is possible with one cell alone.
-
-
11.3: Battery Ratings
-
Because batteries create electron flow in a circuit by exchanging electrons in ionic chemical reactions, and there is a limited number of molecules in any charged battery available to react, there must be a limited amount of total electrons that any battery can motivate through a circuit before its energy reserves are exhausted. Battery capacity could be measured in terms of total number of electrons, but this would be a huge number. We could use the unit of the coulomb (equal to 6.25 x 1018 ele
-
-
11.4: Special-purpose Batteries
-
Back in the early days of electrical measurement technology, a special type of battery known as a mercury standard cell was popularly used as a voltage calibration standard. The output of a mercury cell was 1.0183 to 1.0194 volts DC (depending on the specific design of cell), and was extremely stable over time. Advertised drift was around 0.004 percent of rated voltage per year. Mercury standard cells were sometimes known as Weston cells or cadmium cells.
-
-
11.5: Practical Considerations - Batteries
-
When connecting batteries together to form larger “banks” (a battery of batteries?), the constituent batteries must be matched to each other so as to not cause problems.


17.8: The Control- and Involvement-Oriented Approaches to Planning and Controlling
- Differentiate between the execution of the planning and controlling activities under control- and involvement-oriented management practices.
Planning and controlling are approached with distinctive differences under control-oriented and involvement-oriented approaches to management. In the mechanistic organization, both activities tend to be lodged with management in the organizational hierarchy, often above the point in the organization where the plans are being carried out. The hierarchy plays an active role in both the planning and controlling process, and the employee is often a passive player carrying out the planning directives and the target of the control activity.
The organic organization, with its involvement-oriented management practices, places the employee as an active player in both the planning and controlling activity. Management’s role becomes one of a consultant, facilitator, enabler, philosopher, teacher, coach, and resource provider as employees take on active roles in planning and controlling and in assuming responsibility for the execution of both activities.
Upper-level managers assume responsibility for planning and controlling their units while employees assume the right and responsibility for planning and controlling at their job level. As upper-level managers carry out their planning and controlling activities, they do so by soliciting input from those below them in the organizational hierarchy.
Systems such as MBO are much more likely to characterize the planning and controlling process in involvement-oriented organizations than in control-oriented organizations. Control in high-involvement organizations is diffused through many groups and is commonly focused on task accomplishment and overcoming obstacles, with a de-emphasis on fixing blame with a particular individual for performance failures. In many control-oriented management systems, the reins of control are firmly held by the hierarchy, and the activities of individuals are carefully controlled. Performance failures, therefore, tend to become focused on the individual who fails to perform.
Finally, mechanistic organizations are more likely to create large planning departments and to centralize the planning function with specialists. As organizations confront increasing environmental or technology-induced uncertainty, rapid environmental change, and turbulence, planning and controlling move closer to the point in the organization where the plans are implemented and carried out on a day-to-day basis. In place of hierarchy-based control, organizations rely more on professional employees and groups of employees to control their own actions as they execute organizational plans.
MANAGING CHANGE
Blockchain and Managing Currency Fluctuations
When a business goes from being local, even if local is defined as a whole country, to being a global business, a whole new set of constraints is presented and must be controlled and planned. Traditionally, currency fluctuations can be one of the more interesting if not daunting elements of global business. Modern technology, however, has taken that challenge one step further.
The impact of currency fluctuations on profitability is discussed in economics, finance, and various accounting texts. What currency should be used to buy inventory? To sell inventory? How do puts and calls mitigate currency fluctuations? Is the added expense worth covering the potential loss? These are all questions businesses must consider when moving into a global market. When Tata Consultancy Services, India’s largest software services exporter, reported first-quarter results that were below expectations in the first quarter of 2017, much of the blame was laid on currency fluctuations, which accounted for 80 basis points of the drop in profitability (Alawadhi 2017).
But starting in 2009, financial transactions, including global financial transactions, became a little more complicated. Or did they? Bitcoin emerged in 2009 from an unknown source only known as Satoshi Nakamoto (The Economist Explains 2015). Built on what is called blockchain technology, Bitcoin and other cryptocurrencies (jargon for digital assets that are secured by cryptography) are a technological unknown in the future of exchange and financing. The technology behind blockchain and the resulting assets is complicated but not necessary to understand the potential effects of the technology. Effectively, Bitcoin is a “peer-to-peer electronic cash system that uses a distributed ledger to bypass central control systems for transactions” (Pepijn 2017). As peer-to-peer transactions, cryptocurrencies bypass the normal channels, such as banks and credit card processors. Theoretically, this lowers transaction costs for both the buyer and the seller. Blockchain, which can include assets beyond currency, also allows firms to raise funds directly from investors, bypassing investment bankers and venture capitalists. According to the Financial Post , “High levels of encryption protect the transaction by validating the parties involved and by preventing hacking, erasure or amendments” (Francis 2017).
Bitcoin uses blockchain technology to maintain a record of its currency ecosystem. The viability of blockchain technology as a thing in itself should not be confused with Bitcoin’s price volatility, which has seen its price increase (and decrease) by several orders of magnitude. Shady bitcoin exchanges and a shifting regulatory landscape, a result of governments attempting to regulate the very concept of a means of exchange, have produced enormous swings up and down (Crypto Investor 2017).
But however volatile the new currencies, blockchain technology is seeing other, relatively sane applications. Isabel Cooke at Barclays has already used “distributed ledger technology,” or blockchain technology, to process a trade finance transaction in the real world: “Our pilot trade brought the sign-off time from ten days to four hours. It reduced costs, added transparency, decreased risk and looked to improve the customer experience” (Why blockchain is ‘difficult and exciting’ 2017). With an immutable, public ledger to work from, “Creating a really clear audit trail across organizations provides real value – whether that’s with land registration or trade finance. If we have a shared view of data on ledgers, we can then build business logic on top of that, and that can apply to interest rates swaps or smart contracts within the investment bank” (Crypto Investor 2017).
So are blockchains and cryptocurrencies the wave of the future or just a modern financial bubble or threat to global financial security? Some industry writers say that the decentralization and lower costs of the technology are necessary and will launch even more industries (Pepijn 2017). Even governments and central banks are looking at the potential benefits and costs savings of an electronic currency. According to investment banker Alex Tapscott, if the Bank of England replaced 30 percent of the traditional British currency with digital money, he thinks it would add 3 percent to British GDP. The expectation is that digital currency would lower consumer prices and increase sellers’ profits. And the encryption technology would prevent counterfeiting, fraud, or tampering (Francis 2017).
In a perfect world, exchanges in a global currency, such as the blockchain-based cryptocurrencies, could sidestep currency fluctuations. In the real world, however, the wild value fluctuations of cryptocurrencies mean blockchain technology has a way to go before delivering on that possibility, if it ever does.
Alawadhi, Neha. 2017. “Currency fluctuations and BFSI, retail sluggishness hurt TCS's Q1 show.” Moneycontrol.com. http://www.moneycontrol.com/news/bus...w-2325575.html
Crypto Investor. 2017. “Bitcoin: Three Ways the Bubble Could Pop.” Medium.com, September 15, 2017<EMAIL_ADDRESS>Economist Explains, The. 2015. “Who is Satoshi Nakamoto?” The Economist, November 2, 1015. https://www.economist.com/blogs/econ...ist-explains-1
Francis, Diane. 2017. “Why the smart money is betting on blockchain.” Financial Post. business.financialpost.com/di...-on-blockchain
Pepijn, Daan. 2017. “With smart controls and contracts, blockchain tech is bridging the real and virtual worlds.” The Next Web. thenextweb.com/contributors/...#.tnw_oDCnSKF2
“Why blockchain is ‘difficult and exciting.’” 2017. Barclays, May 16, 2017. www.home.barclays/news/2017/...lockchain.html
- What other applications can you see for blockchain technology? Would they reduce costs?
- What drawbacks or potentials risks do you see in blockchain technology?
- Do you think blockchain technology could be used to offset currency fluctuations? Would this likely increase or decrease the risk?
- Why would governments be suspicious of cryptocurrencies and consider regulating or outlawing them? Have any governments done so to date?
- Describe the execution of the planning and controlling activities under control- and involvement-oriented management practices.


2.5: Checklist- Administer IV Push Medications
*Disclaimer: Always follow agency policy and manufacturer recommendations
Checklist: Administer IV Push Medications [1] , [2] , [3] , [4]
- Verify the provider’s order.
- Review the patient’s medical record for factors that increase the patient’s risk of adverse reactions and toxicity to the prescribed medication. Check for allergies or any other contraindication to the prescribed medication. Verify when the last dose of this medication was administered, the indication for this medication for this patient, and related pre-administration assessments, vital signs, lab results, or other clinical data.
- Gather and prepare the necessary equipment: syringe, medication, saline flush, antiseptic pads, and needle/vial access device.
- If medication preparation is required, do so in a designated clean, quiet environment away from sinks using the aseptic non-touch technique (ANTT). [5]
- Check the expiration date on the medication. If it’s expired, return it to the pharmacy and obtain new medication. Inspect the medication for discoloration or compromised integrity.
- Verify the medication can be given by bolus based on agency policy.
- Confirm the following information in a drug reference guide: appropriate dosage, need for dilution or reconstitution, compatibility with running IV fluids and medications, rate of administration, action of medication, potential adverse effects, antidote, and patient education.
- Perform hand hygiene.
- Confirm patient identity using at least two patient identifiers and ask about allergies.
- Provide privacy.
- Explain the procedure to the patient. Provide education regarding the medication, its purpose, and potential side effects.
- Perform necessary pre-administration assessments in accordance with the type of medication being given.
- Raise the bed to waist level when providing care.
- Perform hand hygiene and put on gloves. Adhere to standard aseptic non-touch technique (ANTT) when preparing medication, administering IV push medication, flushing, and locking venous access devices. [6]
- If the medication is not in a prefilled syringe and dilution is required, dilute it and draw it up in a syringe using sterile technique. Do not dilute or reconstitute IV push medications by drawing up the contents in a commercially prefilled saline flush syringe. [7] Only dilute medications when recommended by the manufacturer, supported by evidence in peer-reviewed biomedical literature, or in accordance with approved agency guidelines.
- Check the rights of medication administration X 3 while preparing the medication. When performing three checks, check against the provider order, check as you are reaching for the medication, and check right before administering the medication.
- Prepare one medication syringe at a time. Label all IV push medication syringes unless they are prepared at the bedside and immediately administered. Never pre-label an empty syringe in advance of its use. [8]
- If continuous running IV fluid is compatible with the medication, pause the infusion. Trace the IV line from the patient to its point of origin and use the port closest to the patient and clamp the line.
- If a saline lock is in place, unclamp the catheter.
- Perform a vigorous mechanical scrub of the needleless connector for at least five seconds using 70% alcohol or an alcohol-based chlorhexidine solution and then allow the connector to dry completely. Do not fan or wave over the site.
- Assess the venous access device prior, during, and after administering IV push medication for signs and symptoms of complications, such as pain, infiltration, phlebitis, or extravasation.
- Assess for patency using a single-use 10-mL syringe with 0.9% normal saline. While maintaining the sterility of the syringe tip, attach the syringe to the needleless connector port. Slowly aspirate for blood return. Patency is determined by evidence of brisk, bright red blood return, although blood return is not always present. Slowly inject preservative-free normal saline solution into the catheter. Never forcibly flush a venous access catheter. Remove and discard the syringe. [9]
- Perform a second vigorous mechanical scrub of the needleless connector with a new swab for at least five seconds and allow it to dry completely.
- Maintaining the sterility of the syringe tip, attach the medication syringe to the needleless connector of the venous access device. Administer the medication at the recommended rate of administration according to the MAR, drug reference guide, or manufacturer using a watch or clock with a second hand. Remove and discard the syringe.
- Perform a third vigorous mechanical scrub of the needleless connector with a new swab for at least five seconds and allow it to dry completely.
- Maintaining the sterility of the syringe tip, attach a prefilled 10-mL syringe containing preservative-free 0.9% normal saline to the needleless connector and flush at the same rate of administration as the medication. The volume of the flush should be twice the internal catheter volume (i.e., a J-loop would be 2 mL and extension tubing would be 4 mL). Continue to flush at a slow, steady pace to clear the line, typically another 2 to 7 mL. [10]
- If continuous IV fluids are present, unclamp the tubing and resume the infusion. If locking the venous access device, follow agency policy regarding the sequence of flushing, clamping, and disconnecting the syringe.
- Discard used supplies in appropriate receptacles.
- Remove and discard the gloves.
- Perform hand hygiene.
- Return the bed to the lowest position. Provide for patient safety and comfort.
- Evaluate patient response to the medication and monitor for adverse reactions based on the onset and peak of the prescribed medication. Instruct the patient to call the nurse if feeling any adverse effects.
- Document the administration of the medication per agency policy.
View a YouTube video [11] showing an instructor demonstration of this skill:
- Dorn, L. (2022). IV push evidence-based practice checklist . qsen.org/iv-push-evidence-based-practice-checklist/ ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications . https://www.ismp.org/guidelines/iv-push ↵
- Clinical skills: Essentials collection (1st ed.). (2021). Elsevier. ↵
- Lippincott procedures. http://procedures.lww.com ↵
- Gorski, L. A., Hadaway, L., Hagle, M. E., Broadhurst, D., Clare, S., Kleidon, T., Meyer, B. M., Nickel, B., Rowley, S., Sharpe, E., & Alexander, M. (2021). Infusion therapy standards of practice (8th ed.). Journal of Infusion Nursing: The Official Publication of the Infusion Nurses Society, 44 (1S Suppl 1), S1–S224. https://doi.org/10.1097/NAN.0000000000000396 ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications. https://www.ismp.org/guidelines/iv-push ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications. https://www.ismp.org/guidelines/iv-push ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications. https://www.ismp.org/guidelines/iv-push ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications. https://www.ismp.org/guidelines/iv-push ↵
- Institute for Safe Medication Practices. (2015). Safe practice guidelines for adult IV push medications . https://www.ismp.org/guidelines/iv-push ↵
- Chippewa Valley Technical College. (2023, January 5). Administering IV push medications [Video]. YouTube. Video licensed under CC BY 4.0 . https://youtu.be/4w9JndX9-uI ↵


10.5: The Matrix Exponential via Eigenvalues and Eigenvectors
In this module we exploit the fact that the matrix exponential of a diagonal matrix is the diagonal matrix of element exponentials. In order to exploit it we need to recall that all matrices are almost diagonalizable. Let us begin with the clean case: if \(A\) is n-by-n and has \(n\) distinct eigenvalues, \(\lambda_{j}\), and therefore \(n\) linear eigenvectors, \(s_{j}\), then we note that
\[\forall j, j \in \{1, \cdots, n\} : (As_{j} = \lambda_{j}s_{j}) \nonumber\]
maybe written as
\[A = S \Lambda S^{-1} \nonumber\]
where \(S = \begin{pmatrix} {s_{1}}&{s_{2}}&{\cdots}&{s_{n}} \end{pmatrix}\) is the full matrix of eigenvectors and \(\Lambda = diag (\lambda_{1}, \lambda_{2}, \cdots, \lambda_{n}\) is the diagonal matrix of eigenvalues. One cool reason for writing \(A\) as in Equation is that
\[A^2 = S \Lambda S^{-1} S \Lambda S^{-1} = S \Lambda^{2} S^{-1} \nonumber\]
and, more generally
\[A^k = S \Lambda^{k} S^{-1} \nonumber\]
If we now plug this into the definition in The Matrix Exponential as a Sum of Powers, we find
\[e^{At} = Se^{\Lambda t} S^{-1} \nonumber\]
where \(e^{\Lambda t}\) is simply
\[diag (e^{\lambda_{1}t}, e^{\lambda_{2}t}, \cdots, e^{\lambda_{1}t}) \nonumber\]
Let us exercise this on our standard suite of examples.
If
\[A = \begin{pmatrix} {1}&{0}\\ {0}&{2} \end{pmatrix} \nonumber\]
then
\[S = I \Lambda = A \nonumber\]
and so \(e^{At} = e^{\Lambda t}\)
As a second example let us suppose
\[A = \begin{pmatrix} {0}&{1}\\ {-1}&{0} \end{pmatrix} \nonumber\]
and compute, in matlab,
>> [S, Lam] = eig(A) S = 0.7071 0.7071 0 + 0.7071i 0 - 0.7071i Lam = 0 + 1.0000i 0 0 0 - 1.0000i >> Si = inv(S) Si = 0.7071 0 - 0.7071i 0.7071 0 + 0.7071i >> simple(S*diag(exp(diag(Lam)*t))*Si) ans = [ cos(t), sin(t)] [-sin(t), cos(t)]
If
\[A = \begin{pmatrix} {0}&{1}\\ {0}&{0} \end{pmatrix} \nonumber\]
then matlab delivers
>> [S, Lam] = eig(A) S = 1.0000 -1.0000 0 0.0000 Lam = 0 0 0 0
So zero is a double eigenvalue with but one eigenvector. Hence SS is not invertible and we can not invoke. The generalization is often called the Jordan Canonical Form or the Spectral Representation. The latter reads
\[A = \sum_{j=1}^{h} \lambda_{j}P_{j}+D_{j} \nonumber\]
where the \(\lambda_{j}\) are the distinct eigenvalues of \(A\) while, in terms of the resolvent \(R(z) = (zI-A)^{-1}\)
\[P_{j} = \frac{1}{2 \pi i} \int R(z) dz \nonumber\]
is the associated eigen-projection and
\[D_{j} = \frac{1}{2 \pi i} \int R(z)(z-\lambda_{j}) dz \nonumber\]
is the associated eigen-nilpotent. In each case, \(C_{j}\) is a small circle enclosing only \(\lambda_{j}\)
Conversely we express the resolvent
\[R(z) = \sum_{j=1}^{h} \frac{1}{z-\lambda_{j}}P_{j}+\sum_{k=1}^{m_{j}-1}\frac{1}{(z-\lambda_{j})^{k+1}}D^{k}_{j} \nonumber\]
where
\[m_{j} = \dim (\mathscr{R}(P_{j})) \nonumber\]
with this preparation we recall Cauchy's integral formula for a smooth function f
\[f(a) = \frac{1}{2\pi i} \int \frac{f(z)}{z-a} dz \nonumber\]
where \(C(a)\) is a curve enclosing the point \(a\)
\[f(A) = \frac{-1}{2\pi i} \int f(z)R(z) dz \nonumber\]
where \(C(r)\) encloses ALL of the eigenvalues of \(A\). For \(f(z) = e^{zt}\) we find
\[e^{At} = \sum_{j=1}^{h} e^{\lambda_{j}t} (P_{j}+\sum_{k=1}^{m_{j}-1} \frac{t^k}{k!}D^{k}_{j}) \nonumber\]
with regard to our example we find, \(h=1, \lambda_{1}=0, P_{1}=I, m_{1}=2, D_{1}=A\) so
\[e^{At} = I+tA \nonumber\]
Let us consider a slightly bigger example, if
\[A = \begin{pmatrix} {1}&{1}&{0}\\ {0}&{1}&{0}\\ {0}&{0}&{2} \end{pmatrix} \nonumber\]
then
>> R = inv(s*eye(3)-A) R = [ 1/(s-1), 1/(s-1)^2, 0] [ 0, 1/(s-1), 0] [ 0, 0, 1/(s-2)]
and so \(\lambda_{1} = 1\) and \(\lambda_{2} = 2\) while
\[P_{1} = \begin{pmatrix} {1}&{0}&{0}\\ {0}&{1}&{0}\\ {0}&{0}&{0} \end{pmatrix} \nonumber\]
and so \(m_{1} = 2\)
\[D_{1} = \begin{pmatrix} {0}&{1}&{0}\\ {0}&{0}&{0}\\ {0}&{0}&{0} \end{pmatrix} \nonumber\]
and
\[P_{2} = \begin{pmatrix} {0}&{0}&{0}\\ {0}&{0}&{0}\\ {0}&{0}&{1} \end{pmatrix} \nonumber\]
and \(m_{2}=1\) and \(D_{2}=0\)
\[e^{At} = e^{t}(P_{1}+tD_{1})+e^{2t}P_{2} \nonumber\]
\[\begin{pmatrix} {e^t}&{te^t}&{0}\\ {0}&{e^t}&{0}\\ {0}&{0}&{e^{2t}} \end{pmatrix} \nonumber\]


6.1: Sources and Information Needs
This section and the section on Types of Sources work together. That’s because knowing the kinds of information in each category of sources will help you choose the right kind of information to meet each of your information needs. And some of those needs are very specific.
Information needs are why you require sources. Meeting those needs is what you will do with sources as you complete your research project.
Here are those needs:
- To learn more background information.
- To answer your research question(s).
- To convince your audience that your answer is correct or, at least, the most reasonable answer.
- To describe the situation surrounding your research question for your audience and explain why it’s important.
- To report what others have said about your question, including any different answers to your research question.
The verbs in the list of information needs above tell you exactly how you’ll use sources to carry out your research and create your final product: to learn, answer, convince, describe, and report. But you won’t be doing any of that alone.
Your sources will give you information with which to reason. They’ll also give you direct quotes and information to summarize and paraphrase as you create your final product. In other words, your sources will support you every step of the way during your research project.
Needs and Final Products
Background information may seldom appear directly in any final product. But meeting each of the other information needs will result in written sections of a research paper. For final products other than papers, you’ll have the same needs and will use sources to meet them. But not all needs will result in a section of your final product.


Skip to main content
SECTION 10.5 PROBLEM SET: CHAPTER REVIEW
-
Is the matrix given below a transition matrix for a Markov chain? Explain.
-
\(\left[\begin{array}{ccc}
.1 & .4 & .5 \\
.5 & -.3 & .8 \\
.3 & .4 & .3
\end{array}\right]\)
-
\(\left[\begin{array}{ccc}
.2 & .6 & .2 \\
0 & 0 & 0 \\
.3 & .4 & .5
\end{array}\right]\)
-
A survey of computer buyers indicates that if a person buys an Apple computer, there is an 80% chance that their next purchase will be an Apple, while owners of a Windows computer will buy an Windows computer again with a probability of .70. The buying habits of these consumers are represented in the transition matrix below.
-
Find the probability that a present owner of an Apple computer will buy a Windows computer as his next computer.
-
Find the probability that a present owner of an Apple computer will buy a Windows computer as his third computer.
-
Find the probability that a present owner of a Windows computer will buy a Windows computer as his fourth computer.
-
Professor Trayer either teaches Finite Math or Statistics each quarter. She never teaches Finite Math two consecutive quarters, but if she teaches Statistics one quarter, then the next quarter she will teach Statistics with a 1/3 probability.
-
Write a transition matrix for this problem.
-
If Professor Trayer teaches Finite Math in the Fall quarter, what is the probability that she will teach Statistics in the Winter quarter.
-
If Professor Trayer teaches Finite Math in the Fall quarter, what is the probability that she will teach Statistics in the Spring quarter.
-
Determine whether the following matrices are regular Markov chains.
-
\(\left[\begin{array}{ll}
1 & 0 \\
.3 & .7
\end{array}\right]\)
-
\(\left[\begin{array}{lll}
.2 & .4 & .4 \\
.6 & .4 & 0 \\
.3 & .2 & .5
\end{array}\right]\)
-
The transition matrix for switching academic majors each quarter by students at a university is given below, where Science, Business, and Liberal Arts majors are denoted by S, B, and A, respectively.
-
Find the probability of a science major switching to a business major during their first quarter.
-
Find the probability of a business major switching to a Liberal Arts during their second quarter.
-
Find the probability of a science major switching to Liberal Artsr during their third quarter.
-
John Elway, the football quarterback for the Denver Broncos, called his own plays.  The transition matrix for his plays is given in the following table, where P represents a pass and H a handoff.
-
If John Elway threw a pass on the initial play, what is the probability that he handed handoff on the two plays later?
-
Determine the long term play distribution.
-
Company I, Company II, and Company III compete against each other, and the transition matrix for people switching from company to company each year is given below.
-
If the initial market share is 20% for Company I, 30% for Company II and 50% for Company III, what will the market share be after the next year?
-
If this trend continues, what is the long range expectation for the market?
-
Given the following absorbing Markov chain.
-
Identify the absorbing states.
-
Write the solution matrix.
-
Starting from state 4, what is the probability of eventual absorption in state 1?
-
Starting from state 3, what is the probability of eventual absorption in state 2?
-
A mouse placed in the maze moves from room to room randomly. From any room, the mouse will choose a door to the next room with equal probabilities. Once it reaches room 1, it finds food and never leaves that room. And when it reaches room 6, it is trapped and cannot leave that room. What is the probability that the mouse will end up in room 1 if it was initially placed in room 3?
-
What is the probability that the mouse will end up in room 6 if it was initially in room 2?


1.5E: Exercises - Fitting Linear Models to Data
Exercise \(\PageIndex{1}\)
In Europe and Asia, m-commerce is popular. M-commerce users have special mobile phones that work like electronic wallets as well as provide phone and Internet services. Users can do everything from paying for parking to buying a TV set or soda from a machine to banking to checking sports scores on the Internet. For the years 2000 through 2004, what was the relationship between the year and the number of m-commerce users? Construct a scatter plot and find the linear regression model that best fits the data. Let \(x =\) the year and let \(y =\) the number of m-commerce users, in millions.
| \(x\) (year) | \(y\) (# of users) |
|---|---|
| 2000 | 0.5 |
| 2002 | 20.0 |
| 2003 | 33.0 |
| 2004 | 47.0 |
Exercise \(\PageIndex{2}\)
A random sample of 11 statistics students produced the following data, where \(x\) is the Unit 1 Exam score out of 80, and \(y\) is the Final Exam score out of 200.
| \(x\) (Unit 1 Exam score) | \(y\) (Final Exam score) |
|---|---|
| 65 | 151 |
| 67 | 133 |
| 71 | 185 |
| 71 | 163 |
| 66 | 126 |
| 75 | 198 |
| 67 | 153 |
| 70 | 163 |
| 71 | 159 |
| 69 | 151 |
| 69 | 159 |
A random student earned a 58 on the Unit 1 Exam. If that student follows the class trend, what would you expect this student to earn on the final exam?
Exercise \(\PageIndex{3}\)
SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table show different depths with the maximum dive times in minutes. Use your calculator to find the linear regression line and predict the maximum dive time for 110 feet.
| \(X\) (depth in feet) | \(Y\) (maximum dive time) |
|---|---|
| 50 | 80 |
| 60 | 55 |
| 70 | 45 |
| 80 | 35 |
| 90 | 25 |
| 100 | 22 |
Exercise \(\PageIndex{4}\)
Amelia plays basketball for her high school. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data. She has a goal of playing in college and needs to score 40 points in a game to be considered for the college team. Based on the trend, how many hours each week should she practice her jump shot?
| \(X\) (hours practicing jump shot) | \(Y\) (points scored in a game) |
|---|---|
| 4 | 13 |
| 6 | 18 |
| 7 | 22 |
| 9 | 27 |
| 11 | 30 |


2.5: Multicultural Teams
-
- Last updated
- Save as PDF
What are some challenges and best practices for managing and working with multicultural teams?
As globalization has increased over the last decades, workplaces have felt the impact of working within multicultural teams. The earlier section on team diversity outlined some of the highlights and benefits of working on diverse teams, and a multicultural group certainly qualifies as diverse. However, there are some key practices that are recommended to those who are leading multicultural teams so that they can parlay the diversity into an advantage and not be derailed by it.
People may assume that communication is the key factor that can derail multicultural teams, as participants may have different languages and communication styles. In the Harvard Business Review article “Managing Multicultural Teams,” the authors point out four key cultural differences that can cause destructive conflicts in a team. 12 The first difference is direct versus indirect communication . Some cultures are very direct and explicit in their communication, while others are more indirect and ask questions rather than pointing our problems. This difference can cause conflict because, at the extreme, the direct style may be considered offensive by some, while the indirect style may be perceived as unproductive and passive-aggressive in team interactions.
The second difference that multicultural teams may face is trouble with accents and fluency . When team members don’t speak the same language, there may be one language that dominates the group interaction—and those who don’t speak it may feel left out. The speakers of the primary language may feel that those members don’t contribute as much or are less competent. The next challenge is when there are differing attitudes toward hierarchy . Some cultures are very respectful of the hierarchy and will treat team
members based on that hierarchy. Other cultures are more egalitarian and don’t observe hierarchical differences to the same degree. This may lead to clashes if some people feel that they are being disrespected and not treated according to their status. The final difference that may challenge multicultural teams is conflicting decision-making norms . Different cultures make decisions differently, and some will apply a great deal of analysis and preparation beforehand. Those cultures that make decisions more quickly (and need just enough information to make a decision) may be frustrated with the slow response and relatively longer thought process.
These cultural differences are good examples of how everyday team activities (decision-making, communication, interaction among team members) may become points of contention for a multicultural team if there isn’t adequate understanding of everyone’s culture. The authors propose that there are several potential interventions to try if these conflicts arise. One simple intervention is adaptation , which is working with or around differences. This is best used when team members are willing to acknowledge the cultural differences and learn how to work with them. The next intervention technique is structural intervention , or reorganizing to reduce friction on the team. This technique is best used if there are unproductive subgroups or cliques within the team that need to be moved around. Managerial intervention is the technique of making decisions by management and without team involvement. This technique is one that should be used sparingly, as it essentially shows that the team needs guidance and can’t move forward without management getting involved. Finally, exit is an intervention of last resort, and is the voluntary or involuntary removal of a team member. If the differences and challenges have proven to be so great that an individual on the team can no longer work with the team productively, then it may be necessary to remove the team member in question.
There are some people who seem to be innately aware of and able to work with cultural differences on teams and in their organizations. These individuals might be said to have cultural intelligence . Cultural intelligence is a competency and a skill that enables individuals to function effectively in cross-cultural environments. I develops as people become more aware of the influence of culture and more capable of adapting their behavior to the norms of other cultures. In the IESE Insight article entitled “Cultural Competence: Why It Matters and How You Can Acquire It” (Lee and Liao, 2015), the authors assert that “multicultural leaders may relate better to team members from different cultures and resolve conflicts more easily.13 Their multiple talents can also be put to good use in international negotiations.” Multicultural leaders don’t have a lot of “baggage” from any one culture, and so are sometimes perceived as being culturally neutral. They are very good at handling diversity, which gives them a great advantage in their relationships with teammates.
In order to help employees become better team members in a world that is increasingly multicultural, there are a few best practices that the authors recommend for honing cross-cultural skills. The first is to “broaden your mind”—expand your own cultural channels (travel, movies, books) and surround yourself with people from other cultures. This helps to raise your own awareness of the cultural differences and norms that you may encounter. Another best practice is to “develop your cross-cultural skills through practice” and experiential learning. You may have the opportunity to work or travel abroad—but if you don’t, then getting to know some of your company’s cross-cultural colleagues or foreign visitors will help you to practice your skills. Serving on a cross-cultural project team and taking the time to get to know and bond with your global colleagues is an excellent way to develop skills. In my own “past life,” I led a global human resources organization, and my team included employees from China, India, Brazil, Hungary, the Netherlands, and the United States. We would have annual meetings as a global HR team, and it was so rewarding to share and learn about each other’s cultures. We would initiate the week with a gift exchange in a “show and tell” format from our various countries, so that everyone would learn a little bit more about the cultures in which our fellow colleagues were working.  You first may have to juggle time zone differences to find an adequate meeting time that suits all team members. (I used to have a team call with my Chinese colleagues at 8 p.m. my time, so that I could catch them at 8 a.m. in China the next day!) Language challenges can also pose a problem. In many countries, people are beginning to learn English as one of the main business languages. However, as I have experienced, people don’t always speak their language the same way that you might learn their language in a book. There are colloquialisms, terms, and abbreviations of words that you can’t learn in a classroom—you need to experience how people speak in their native countries.
You also need to be open-minded and look at situations from the perspective of your colleagues’ cultures, just as you hope they will be open-minded about yours. This is referred to as cultural intelligence. Whenever I would travel globally to visit my colleagues in other countries, I would see foods, traditions, situations, and behaviors that were very “foreign” to me. Although my first response to experiencing these might be to think “wow, that’s strange,” I would try to think about what some of my global colleagues find “foreign” when they come to visit me in the United States. For example, my travel to China would put me in contact with chicken feet, a very popular food in China and one that I dislike immensely. Whenever I was offered chicken feet, I would turn them down in the most polite way possible and would take another food that was offered instead. I started to wonder about what my Chinese colleagues thought about the food when they’d come to visit me in the United States. Every year, I would host a global HR meeting in the United States, and a bit part of that meeting was the camaraderie and the sharing of various meals together. When I asked my Chinese colleagues what foods they thought were unpleasant, they mentioned cheese and meat. I was surprised about the meat, and when I asked, they said that it wasn’t the meat itself necessarily, but it was the giant portions of meat that Americans will eat that, to them, is pretty unappetizing. Again, it is so important to check yourself and your own culture every so often, and to think about those elements that we take for granted (e.g., gigantic meat portions) and try to look at them from the eyes of another culture. It really makes us smarter and better partners to our global colleagues around the world.
In the HBR article “Getting Cross-Cultural Teamwork Right,” the author states that three key factors—mutual learning, mutual understanding, and mutual teaching—build trust with cross-cultural colleagues as you try to bridge cultural gaps. With mutual learning, global colleagues learn from each other and absorb the new culture and behaviors through listening and observation. In mutual understanding, you try to understand the logic and cultural behaviors of the new culture to understand why people are doing what they do. This, of course, requires suspending judgment and trying to understand and embrace the differences. Finally, mutual teaching involves instructing and facilitating. This means trying to bridge the gap between the two cultures and helping yourself and others see where different cultures are coming from in order to resolve misunderstandings.
Understanding and finding common ground with your global colleagues isn’t easy, and it takes patience and continuous improvement. In the end, however, I think that you will find it one of the most rewarding and enlightening things you can do. The more we work to close the multicultural “gap” and make it a multicultural advantage, the better off we will be as professionals and as people.
Discussion Questions
- What are some multicultural experiences that you’ve had in which you feel that there was a very wide gap between you and an individual from another culture? How did you handle it?
- Has economic globalization helped people to bridge these cultural gaps? Why or why not?
Once you have a sense of the different cultures and have started to work on developing your cross-cultural skills, another good practice is to “boost your cultural metacognition” and monitor your own behavior in multicultural situations. When you are in a situation in which you are interacting with multicultural individuals, you should test yourself and be aware of how you act and feel. Observe both your positive and negative interactions with people, and learn from them. Developing “ cognitive complexity ” is the final best practice for boosting multicultural skills. This is the most advanced, and it requires being able to view situations from more than one cultural framework. In order to see things from another perspective, you need to have a strong sense of emotional intelligence, empathy, and sympathy, and be willing to engage in honest communications.
In the Harvard Business Review article “Cultural Intelligence,” the authors describe three sources of cultural intelligence that teams should consider if they are serious about becoming more adept in their cross-cultural skills and understanding. These sources, very simply, are head, body, and heart . One first learns about the beliefs, customs, and taboos of foreign cultures via the head . Training programs are based on providing this type of overview information—which is helpful, but obviously isn’t experiential. This is the cognitive component of cultural intelligence. The second source, the body , involves more commitment and experimentation with the new culture. It is this physical component (demeanor, eye contact, posture, accent) that shows a deeper level of understanding of the new culture and its physical manifestations. The final source, the heart , deals with a person’s own confidence in their ability to adapt to and deal well with cultures outside of their own. Heart really speaks to one’s own level of emotional commitment and motivation to understand the new culture.
The authors have created a quick assessment to diagnose cultural intelligence, based on these cognitive, physical, and emotional/motivational measures (i.e., head, body, heart).
Please refer to Table \(\PageIndex{1}\) for a short diagnostic that allows you to assess your cultural intelligence.
| Give your responses on a 1 to 5 scale where 1 means you strongly disagree and 5 that you strongly agree | |
|---|---|
| Before I interact with people from a new culture, I wonder to myself what I hope to achieve | |
|
If I encounter something unexpected while working in a new culture I use that experience to build new ways
to approach other cultures in the future |
|
| I plan on how I am going to relate to people from a different culture before I meet them | |
| When I come into a new cultural situation I can immediately sense whether things are going will or if things are going wrong | |
| Add your total from the four questions above | |
| Divide the total by four. This is your Cognitive Cultural Quotient | |
| It is easy for me to change my body language (posture or facial expression) to suit people from a different culture | |
| I can change my expressions when a cultural encounter requires it | |
| I can easily change the way I act when a cross cultural encounter seems to require it | |
| Add your total from the four questions above | |
| Divide the total by four. This is your Cognitive Physical Quotient | |
|
I have confidence in my ability to deal well with people from different cultures than mine |
|
| I am certain that I can befriend people of different cultural backgrounds than mine | |
| I can adapt to the lifestyles of a different culture with relative ease | |
| I am confident in my ability to deal with an unfamiliar cultural situation or encounter | |
| Add your total from the four questions above | |
| Divide the total by four. This is your This is your Emotional Motivational Cognitive Quotient |
Generally, scoring below 3 in any one of the three measures signals an area requiring improvement.
Averaging over 4 displays strength in cultural intelligence
Adapted from "Cultural Intelligence" Earley and Mosakowski, Harvard Business Review, October 2004
Table \(\PageIndex{1}\)
Cultural intelligence is an extension of emotional intelligence. An individual must have a level of awareness and understanding of the new culture so that he can adapt to the style, pace, language, nonverbal communication, etc. and work together successfully with the new culture. A multicultural team can only find success if its members take the time to understand each other and ensure that everyone feels included. Multiculturalism and cultural intelligence are traits that are taking on increasing importance in the business world today. 14 By following best practices and avoiding the challenges and pitfalls that can derail a multicultural team, a team can find great success and personal fulfillment well beyond the boundaries of the project or work engagement.
concept check
- What are some of the challenges of a multicultural team?
- Explain the cultural intelligence techniques of head, body, and heart.


4.7: Find better coverage
Most of the time, you won’t be able to determine the reliability of a claim or statement based on how it is covered in a single source. To get a better understanding of your topic and ensure that the information you’re using is reliable, try to find better coverage. This can take many forms: you might find better coverage through sources that are more detailed, varied, authoritative, or recent. Even if you think your original source is good, verifying what you’ve found with additional sources will strengthen your research.
Lateral reading
Rather than assuming the information presented within a single article provides a full picture of your topic, read multiple sources and examine how they support or contradict your original source. This is called lateral reading , going beyond your original source to explore how the same topic is discussed by others. [1] The primary purpose of reading laterally is to quickly determine whether the original information you found is true. It’s more than just fact-checking, though; this process can also uncover better information if the source you started with is not as reliable as you had hoped.
Here is an example of reading laterally in action. You may find a news article that asserts “coffee reduces your risk of getting cancer.” Seek out additional sources to determine whether there is any research that backs up that claim. Open up a new browser window and search for the phrase “coffee and cancer risk.” This may reveal if other news sites are reporting the same information, and how they have interpreted the results. Sometimes, multiple news sources will post or broadcast the same story word-for-word. Just because a story is shared widely doesn’t mean that it is accurate, and it doesn’t tell you where the data came from. Keep searching to find a better source. “After verifying, refuting, or otherwise contextualizing the data in question, you’d return to the original text and continue reading.” [2] If you find that the information is being misrepresented or if you cannot find anything to back up the claim, don’t use your original source. Instead, look for new sources on your topic that do a better job of supporting their claims.
Navigating around paywalls
In the past, we encouraged using Wikipedia or Google for quick fact-checking and investigation. However, lateral reading may require more extensive searching because many reliable sources can only be accessed through subscriptions. As an ISU student, you can use the library’s article indexes and databases to access many of these subscription-based materials for free.
Let’s say you’re looking to verify a news story; you find another article on the topic but the newspaper’s website won’t let you read the entire article without subscribing. In cases like this, check if the ISU Library subscribes to that newspaper through a database like Access World News, or if there is access directly, as for the New York Times . The best way to find this information for many local and major newspapers is to check the Newspapers Library Guide .
Alternatively, your professor may provide a link to an article that you need to read, but that leads to a paywall. You can use the search techniques for tracking back a citation from Chapter 3 to find the article you need, or use a tool like LibKey Nomad. LibKey Nomad is a browser extension that enables one-click access to the full text of articles from publishers, Google, Wikipedia, and more, without needing to start at the library website. Visit the LibKey Nomad Library Guide to learn more about this tool.
This process works for any source you want to learn more about. Another benefit of reading laterally is that you may encounter additional sources that will better inform your project and support your argument.
How algorithms affect what you find
Another reason library search tools may be useful for finding better coverage is to avoid the heavy bias built into the search algorithms used by Google and other web search engines. These tools change your search results based on your personal search history, online activity, and location and are affected by algorithmic bias. Unlike the other types of bias we mentioned in the last section, algorithmic bias can be difficult to detect: algorithms may appear to be objective because they are based on data, but the ways that data is gathered, used, or manipulated often reflects the biases of the algorithm’s creators and users. “In search engines, for example, algorithmic bias can create search results that reflect racist, sexist, or other social biases, despite the presumed neutrality of the data.” [3]
Your results are skewed by what Google thinks you want, based on what it “knows” about you. This may change what results are displayed but, more importantly, it determines the order they’re listed in. If you and another person search for the same thing, what is displayed first for each of you may be different.
Don’t let Google decide for you what is and isn’t relevant for your needs. Use a tool that is less likely to use your browsing history to inform what it retrieves for you, such as DuckDuckGo . Everyday tips like clearing your search history and cookies can also lessen these algorithms’ effect on your search results. Alternatively, library databases don’t base their recommendations on who they think you are, but on your actual search terms. Using these can work in your favor, especially for coursework.
- News Literacy Project. (n.d.). Expand your view with lateral reading . Retrieved August 16, 2021 from https://newslit.org/tips-tools/expand-your-view-with-lateral-reading/ ↵
- Heick, T. (n.d.). What's the difference between lateral reading and vertical reading? TeachThought . Retrieved from https://www.teachthought.com/literacy/how-res-ding-different-future-literacy/ ↵
- Butler, W.D., Sargent, A., and Smith, K. (2020). Algorithmic bias. In Introduction to College Research . Retrieved from https://introtocollegeresearch.pressbooks.com/chapter/algorithmic-bias/ ↵


13.4: The Ford-Fulkerson Labeling Algorithm
In this section, we outline the classic Ford-Fulkerson labeling algorithm for finding a maximum flow in a network. The algorithm begins with a linear order on the vertex set which establishes a notion of precedence . Typically, the first vertex in this linear order is the source while the second is the sink. After that, the vertices can be listed in any order. In this book, we will use the following convention: the vertices will be labeled with capital letters of the English alphabet and the linear order will be ,\((S,T,A,B,C,D,E,F,G,…)\), which we will refer to as the pseudo-alphabetic order . Of course, this convention only makes sense for networks with at most 26 vertices, but this limitation will not cramp our style. For real world problems, we take comfort in the fact that computers can deal quite easily with integer keys of just about any size.
Before providing a precise description of the algorithm, let's take a minute to consider a general overview. In carrying out the labeling algorithm, vertices will be classified as either labeled or unlabeled . At first, we will start with only the source being labeled while all other vertices will be unlabeled. By criteria yet to be spelled out, we will systematically consider unlabeled vertices and determine which should be labeled. If we ever label the sink, then we will have discovered an augmenting path, and the flow will be suitably updated. After updating the flow, we start over again with just the source being labeled.
This process will be repeated until (and we will see that this always occurs) we reach a point where the labeling halts with some vertices labeled (one of these is the source) and some vertices unlabeled (one of these is the sink). We will then note that the partition \(V=L \cup U\) into labeled and unlabeled vertices (hence our choice of \(L\) and \(U\) as names) is a cut whose capacity is exactly equal to the value of the current flow. This resolves the debate from earlier in the chapter and says that the maximum flow/minimum cut question is more like antichains and partitioning into chains than clique number and chromatic number. In particular, the labeling algorithm will provide a proof of the following theorem:
Let \(G=(V,E)\) be a network. If \(v_0\) is the maximum value of a flow and \(c_0\) is the minimum capacity \(c_0\) of a cut, then \(v_0=c_0\) .
We're now ready to describe the Ford-Fulkerson labeling algorithm in detail.
Labeling the Vertices
Vertices will be labeled with ordered triples of symbols. Each time we start the labeling process, we begin by labeling the source with the triple \((∗,+,∞)\) . The rules by which we label vertices will be explicit.
Potential on a Labeled Vertex
Let \(u\) be a labeled vertex. The third coordinate of the label given to \(u\) will be positive real number—although it may be infinite. We call this quantity the potential on \(u\) and denote it by \(p(u)\) . (The potential will serve as the amount that the flow can be updated by.) Note that the potential on the source is infinite.
First Labeled, First Scanned
The labeling algorithm involves a scan from a labeled vertex \(u\) . As the vertices are labeled, they determine another linear order. The source will always be the first vertex in this order. After that, the order in which vertices are labeled will change with time. But the important rule is that we scan vertices in the order that they are labeled—until we label the sink. If for example, the initial scan—always done from the source—results in labels being applied to vertices \(D, G\) and (M\), then we next scan from vertex \(D\) . If that scan results in vertices \(B, F, G\) and \(Q\) being labeled, then we next scan from \(G\) , as it was labeled before \(B\) , even though \(B\) precedes \(G\) in the pseudo-alphabetic order. This aspect of the algorithm results in a breadth-first search of the vertices looking for ways to label previously unlabeled vertices.
Never Relabel a Vertex
Once a vertex is labeled, we do not change its label. We are content to label previously unlabeled vertices—up until the time where we label the sink. Then, after updating the flow and increasing the value, all labels, except of course the special label on the source, are discarded and we start all over again.
Labeling Vertices Using Forward Edges
Suppose we are scanning from a labeled vertex \(u\) with potential \(p(u)>0\) . From \(u\) , we consider the unlabeled neighbors of \(u\) in pseudo-alphabetic order. Now suppose that we are looking at a neighbor \(v\) of \(u\) with the edge \((u,v)\) belonging to the network. This means that the edge is directed from \(u\) to \(v\). If \(e=(u,v)\) is not full, then we label the vertex \(v\) with the triple \((u,+,p(v))\) where \(p(v)=min\{p(u),c(e)−ϕ(e)\}\) . We use this definition since the flow cannot be increased by more than the prior potential or the spare capacity on \(e\) . Note that the potential \(p(v)\) is positive since a is the minimum of two positive numbers.
Labeling Vertices Using Backward Edges
Now suppose that we are looking at a neighbor \(v\) of \(u\) with the edge \((v,u)\) belonging to the network. This means that the edge is directed from \(v\) to \(u\) . If \(e=(v,u)\) is used, then we label the vertex \(v\) with the triple \((u,−,p(v))\) where \(p(v)=min\{p(u),ϕ(e)\}\) . Here \(p(v)\) is defined this way since the flow on \(e\) cannot be decreased by more than \(ϕ(e)\) or \(p(u)\) . Again, note that the potential \(p(v)\) is positive since \(a\) is the minimum of two positive numbers
What Happens When the Sink is Labeled?
The labeling algorithm halts if the sink is ever labeled. Note that we are always trying our best to label the sink, since in each scan the sink is the very first vertex to be considered. Now suppose that the sink is labeled with the triple \((u,+,a)\) . Note that the second coordinate on the label must be \(+\) since all edges incident with the sink are oriented towards the sink.
We claim that we can find an augmenting path \(P\) which results in an increased flow with \(δ=a\) , the potential on the sink. To see this, we merely back-track. The sink \(T\) got its label from \(u=u_1, u_1\) got its label from \(u_2\) , and so forth. Eventually, we discover a vertex \(u_m\) which got its label from the source. The augmenting path is then
\(P=(S,u_m,u_{m−1},…,u_1,T)\).
The value of \(δ\) for this path is the potential \(p(T)\) on the sink since we've carefully ensured that
\(p(u_m) \geq p(u_{m-1}) \geq \cdot \cdot \cdot \geq p(u_1) \geq p(T)\).
And if the Sink is Not Labeled?
On the other hand, suppose we have scanned from every labeled vertex and there are still unlabeled vertices remaining, one of which is the sink. Now we claim victory. To see that we have won, we simply observe that if \(L\) is the set of labeled vertices, and \(U\) is the set of unlabeled vertices, then every edge \(e=(x,y)\) with \(x \in L\) and \(y \in U\) is full, i.e., \(ϕ(e)=c(e)\) . If this were not the case, then \(y\) would qualify for a label with \(x\) as the first coordinate. Also, note that \(ϕ(y,x)=0\) for every edge \(e\) with \(x \in L\) and \(y \in U\) . Regardless, we see that the capacity of the cut \(V=L \cup U\) is exactly equal to the value of the current flow, so we have both a maximum flow and minimum cut providing a certificate of optimality.


22.2: The Lungs
Learning Objectives
- Describe the overall function of the lung
- Summarize the blood flow pattern associated with the lungs
- Outline the anatomy of the blood supply to the lungs
- Describe the pleura of the lungs and their function
A major organ of the respiratory system, each lung houses structures of both the conducting and respiratory zones. The main function of the lungs is to perform the exchange of oxygen and carbon dioxide with air from the atmosphere. To this end, the lungs exchange respiratory gases across a very large epithelial surface area—about 70 square meters—that is highly permeable to gases.
Gross Anatomy of the Lungs
The lungs are pyramid-shaped, paired organs that are connected to the trachea by the right and left bronchi; on the inferior surface, the lungs are bordered by the diaphragm. The diaphragm is the flat, dome-shaped muscle located at the base of the lungs and thoracic cavity. The lungs are enclosed by the pleurae, which are attached to the mediastinum. The right lung is shorter and wider than the left lung, and the left lung occupies a smaller volume than the right. The cardiac notch is an indentation on the surface of the left lung, and it allows space for the heart (Figure \(\PageIndex{1}\)). The apex of the lung is the superior region, whereas the base is the opposite region near the diaphragm. The costal surface of the lung borders the ribs. The mediastinal surface faces the midline.
Each lung is composed of smaller units called lobes. Fissures separate these lobes from each other. The right lung consists of three lobes: the superior, middle, and inferior lobes. The left lung consists of two lobes: the superior and inferior lobes. A bronchopulmonary segment is a division of a lobe, and each lobe houses multiple bronchopulmonary segments. Each segment receives air from its own tertiary bronchus and is supplied with blood by its own artery. Some diseases of the lungs typically affect one or more bronchopulmonary segments, and in some cases, the diseased segments can be surgically removed with little influence on neighboring segments. A pulmonary lobule is a subdivision formed as the bronchi branch into bronchioles. Each lobule receives its own large bronchiole that has multiple branches. An interlobular septum is a wall, composed of connective tissue, which separates lobules from one another.
Blood Supply and Nervous Innervation of the Lungs
The blood supply of the lungs plays an important role in gas exchange and serves as a transport system for gases throughout the body. In addition, innervation by the both the parasympathetic and sympathetic nervous systems provides an important level of control through dilation and constriction of the airway.
Blood Supply
The major function of the lungs is to perform gas exchange, which requires blood from the pulmonary circulation. This blood supply contains deoxygenated blood and travels to the lungs where erythrocytes, also known as red blood cells, pick up oxygen to be transported to tissues throughout the body. The pulmonary artery is an artery that arises from the pulmonary trunk and carries deoxygenated, arterial blood to the alveoli. The pulmonary artery branches multiple times as it follows the bronchi, and each branch becomes progressively smaller in diameter. One arteriole and an accompanying venule supply and drain one pulmonary lobule. As they near the alveoli, the pulmonary arteries become the pulmonary capillary network. The pulmonary capillary network consists of tiny vessels with very thin walls that lack smooth muscle fibers. The capillaries branch and follow the bronchioles and structure of the alveoli. It is at this point that the capillary wall meets the alveolar wall, creating the respiratory membrane. Once the blood is oxygenated, it drains from the alveoli by way of multiple pulmonary veins, which exit the lungs through the hilum .
Nervous Innervation
Dilation and constriction of the airway are achieved through nervous control by the parasympathetic and sympathetic nervous systems. The parasympathetic system causes bronchoconstriction , whereas the sympathetic nervous system stimulates bronchodilation . Reflexes such as coughing, and the ability of the lungs to regulate oxygen and carbon dioxide levels, also result from this autonomic nervous system control. Sensory nerve fibers arise from the vagus nerve, and from the second to fifth thoracic ganglia. The pulmonary plexus is a region on the lung root formed by the entrance of the nerves at the hilum. The nerves then follow the bronchi in the lungs and branch to innervate muscle fibers, glands, and blood vessels.
Pleura of the Lungs
Each lung is enclosed within a cavity that is surrounded by the pleura. The pleura (plural = pleurae) is a serous membrane that surrounds the lung. The right and left pleurae, which enclose the right and left lungs, respectively, are separated by the mediastinum. The pleurae consist of two layers. The visceral pleura is the layer that is superficial to the lungs, and extends into and lines the lung fissures (Figure \(\PageIndex{2}\)). In contrast, the parietal pleura is the outer layer that connects to the thoracic wall, the mediastinum, and the diaphragm. The visceral and parietal pleurae connect to each other at the hilum. The pleural cavity is the space between the visceral and parietal layers.
The pleurae perform two major functions: They produce pleural fluid and create cavities that separate the major organs. Pleural fluid is secreted by mesothelial cells from both pleural layers and acts to lubricate their surfaces. This lubrication reduces friction between the two layers to prevent trauma during breathing, and creates surface tension that helps maintain the position of the lungs against the thoracic wall. This adhesive characteristic of the pleural fluid causes the lungs to enlarge when the thoracic wall expands during ventilation, allowing the lungs to fill with air. The pleurae also create a division between major organs that prevents interference due to the movement of the organs, while preventing the spread of infection.EVERYDAY CONNECTION
The Effects of Second-Hand Tobacco Smoke
The burning of a tobacco cigarette creates multiple chemical compounds that are released through mainstream smoke, which is inhaled by the smoker, and through sidestream smoke, which is the smoke that is given off by the burning cigarette. Second-hand smoke, which is a combination of sidestream smoke and the mainstream smoke that is exhaled by the smoker, has been demonstrated by numerous scientific studies to cause disease. At least 40 chemicals in sidestream smoke have been identified that negatively impact human health, leading to the development of cancer or other conditions, such as immune system dysfunction, liver toxicity, cardiac arrhythmias, pulmonary edema, and neurological dysfunction. Furthermore, second-hand smoke has been found to harbor at least 250 compounds that are known to be toxic, carcinogenic, or both. Some major classes of carcinogens in second-hand smoke are polyaromatic hydrocarbons (PAHs), N-nitrosamines, aromatic amines, formaldehyde, and acetaldehyde.
Tobacco and second-hand smoke are considered to be carcinogenic. Exposure to second-hand smoke can cause lung cancer in individuals who are not tobacco users themselves. It is estimated that the risk of developing lung cancer is increased by up to 30 percent in nonsmokers who live with an individual who smokes in the house, as compared to nonsmokers who are not regularly exposed to second-hand smoke. Children are especially affected by second-hand smoke. Children who live with an individual who smokes inside the home have a larger number of lower respiratory infections, which are associated with hospitalizations, and higher risk of sudden infant death syndrome (SIDS). Second-hand smoke in the home has also been linked to a greater number of ear infections in children, as well as worsening symptoms of asthma.
Chapter Review
The lungs are the major organs of the respiratory system and are responsible for performing gas exchange. The lungs are paired and separated into lobes; The left lung consists of two lobes, whereas the right lung consists of three lobes. Blood circulation is very important, as blood is required to transport oxygen from the lungs to other tissues throughout the body. The function of the pulmonary circulation is to aid in gas exchange. The pulmonary artery provides deoxygenated blood to the capillaries that form respiratory membranes with the alveoli, and the pulmonary veins return newly oxygenated blood to the heart for further transport throughout the body. The lungs are innervated by the parasympathetic and sympathetic nervous systems, which coordinate the bronchodilation and bronchoconstriction of the airways. The lungs are enclosed by the pleura, a membrane that is composed of visceral and parietal pleural layers. The space between these two layers is called the pleural cavity. The mesothelial cells of the pleural membrane create pleural fluid, which serves as both a lubricant (to reduce friction during breathing) and as an adhesive to adhere the lungs to the thoracic wall (to facilitate movement of the lungs during ventilation).
Review Questions
Q. Which of the following structures separates the lung into lobes?
A. mediastinum
B. fissure
C. root
D. pleura
Answer: B
Q. A section of the lung that receives its own tertiary bronchus is called the ________.
A. bronchopulmonary segment
B. pulmonary lobule
C. interpulmonary segment
D. respiratory segment
Answer: A
Q. The ________ circulation picks up oxygen for cellular use and drops off carbon dioxide for removal from the body.
A. pulmonary
B. interlobular
C. respiratory
D. bronchial
Answer: C
Q. The pleura that surrounds the lungs consists of two layers, the ________.
A. visceral and parietal pleurae.
B. mediastinum and parietal pleurae.
C. visceral and mediastinum pleurae.
D. none of the above
Answer: A
Critical Thinking Questions
Q. Compare and contrast the right and left lungs.
A. The right and left lungs differ in size and shape to accommodate other organs that encroach on the thoracic region. The right lung consists of three lobes and is shorter than the left lung, due to the position of the liver underneath it. The left lung consist of two lobes and is longer and narrower than the right lung. The left lung has a concave region on the mediastinal surface called the cardiac notch that allows space for the heart.
Q. Why are the pleurae not damaged during normal breathing?
A. There is a cavity, called the pleural cavity, between the parietal and visceral layers of the pleura. Mesothelial cells produce and secrete pleural fluid into the pleural cavity that acts as a lubricant. Therefore, as you breathe, the pleural fluid prevents the two layers of the pleura from rubbing against each other and causing damage due to friction.
Glossary
- bronchoconstriction
- decrease in the size of the bronchiole due to contraction of the muscular wall
- bronchodilation
- increase in the size of the bronchiole due to contraction of the muscular wall
- cardiac notch
- indentation on the surface of the left lung that allows space for the heart
- hilum
- concave structure on the mediastinal surface of the lungs where blood vessels, lymphatic vessels, nerves, and a bronchus enter the lung
- lung
- organ of the respiratory system that performs gas exchange
- parietal pleura
- outermost layer of the pleura that connects to the thoracic wall, mediastinum, and diaphragm
- pleural cavity
- space between the visceral and parietal pleurae
- pleural fluid
- substance that acts as a lubricant for the visceral and parietal layers of the pleura during the movement of breathing
- pulmonary artery
- artery that arises from the pulmonary trunk and carries deoxygenated, arterial blood to the alveoli
- pulmonary plexus
- network of autonomic nervous system fibers found near the hilum of the lung
- visceral pleura
- innermost layer of the pleura that is superficial to the lungs and extends into the lung fissures