5.xx: Enantiomers and Diastereomers
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Objective
After completing this section, you should be able to discuss how the results of work carried out by Biot and Pasteur contributed to the development of the concept of the tetrahedral carbon atom.
Because enantiomers have identical physical and chemical properties in achiral environments, separation of the stereoisomeric components of a racemic mixture or racemate is normally not possible by the conventional techniques of distillation and crystallization. In some cases, however, the crystal habits of solid enantiomers and racemates permit the chemist (acting as a chiral resolving agent) to discriminate enantiomeric components of a mixture. As background for the following example, it is recommended that the section on crystal properties be reviewed.
Tartaric acid, its potassium salt known in antiquity as "tartar", has served as the locus of several landmark events in the history of stereochemistry. In 1832 the French chemist Jean Baptiste Biot observed that tartaric acid obtained from tartar was optically active, rotating the plane of polarized light clockwise (dextrorotatory). An optically inactive, higher melting, form of tartaric acid, called racemic acid was also known. A little more than a decade later, young Louis Pasteur conducted a careful study of the crystalline forms assumed by various salts of these acids. He noticed that under certain conditions, the sodium ammonium mixed salt of the racemic acid formed a mixture of enantiomorphic hemihedral crystals; a drawing of such a pair is shown on the right. Pasteur reasoned that the dissymmetry of the crystals might reflect the optical activity and dissymmetry of its component molecules. After picking the different crystals apart with a tweezer, he found that one group yielded the known dextrorotatory tartaric acid measured by Biot; the second led to a previously unknown levorotatory tartaric acid, having the same melting point as the dextrorotatory acid. Today we recognize that Pasteur had achieved the first resolution of a racemic mixture, and laid the foundation of what we now call stereochemistry.
Optical activity was first observed by the French physicist Jean-Baptiste Biot. He concluded that the change in direction of plane-polarized light when it passed through certain substances was actually a rotation of light, and that it had a molecular basis. His work was supported by the experimentation of Louis Pasteur. Pasteur observed the existence of two crystals that were mirror images in tartaric acid, an acid found in wine. Through meticulous experimentation, he found that one set of molecules rotated polarized light clockwise while the other rotated light counterclockwise to the same extent. He also observed that a mixture of both, a racemic mixture (or racemic modification ), did not rotate light because the optical activity of one molecule canceled the effects of the other molecule. Pasteur was the first to show the existence of chiral molecules.
Exercise \(\PageIndex{1}\)
When you have one enantiomer that rotates plane polarized light clockwise, why does a racemic mixture of that compound not rotate plane polarized light?
- Answer
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Since a racemic mixture consists of equal amounts of both enantiomers, one enantiomer will rotate plane polarized light clockwise, while the other enantiomer will rotate plane polarized light counterclockwise an equal amount, causing them to cancel out, and the racemic mixture being not optically active.


9.4: Liquid and Solid Mixtures of Nonelectrolytes
Homogeneous liquid and solid mixtures are condensed phases of variable composition. Most of the discussion of condensed-phase mixtures in this section focuses on liquids. The same principles, however, apply to homogeneous solid mixtures, often called solid solutions. These solid mixtures include most metal alloys, many gemstones, and doped semiconductors.
The relations derived in this section apply to mixtures of nonelectrolytes—substances that do not dissociate into charged species. Solutions of electrolytes behave quite differently in many ways, and will be discussed in the next chapter.
9.4.1 Raoult’s law
In 1888, the French physical chemist François Raoult published his finding that when a dilute liquid solution of a volatile solvent and a nonelectrolyte solute is equilibrated with a gas phase, the partial pressure \(p\A\) of the solvent in the gas phase is proportional to the mole fraction \(x\A\) of the solvent in the solution: \begin{equation} p\A=x\A p\A^* \tag{9.4.1} \end{equation} Here \(p\A^*\) is the saturation vapor pressure of the pure solvent (the pressure at which the pure liquid and pure gas phases are in equilibrium).
Consider the solvent , A, of a solution that is dilute enough to be in the ideal-dilute range. In this range, the solvent fugacity obeys Raoult’s law, and the partial molar quantities of the solvent are the same as those in an ideal mixture. Formulas for these quantities were given in Eqs. 9.4.8–9.4.13 and are collected in the first column of Table 9.2. The formulas show that the chemical potential and partial molar entropy of the solvent, at constant \(T\) and \(p\), vary with the solution composition and, in the limit of infinite dilution (\(x\A\ra 1\)), approach the values for the pure solvent. The partial molar enthalpy, volume, internal energy, and heat capacity, on the other hand, are independent of composition in the ideal-dilute region and are equal to the corresponding molar quantities for the pure solvent.
Next consider a solute , B, of a binary ideal-dilute solution. The solute obeys Henry’s law, and its chemical potential is given by \(\mu\B = \mu\xbB\rf + RT\ln x\B\) (Eq. 9.4.24) where \(\mu\xbB\rf\) is a function of \(T\) and \(p\), but not of composition. \(\mu\B\) varies with the composition and goes to \(-\infty\) as the solution becomes infinitely dilute (\(x\A\ra 1\) and \(x\B\ra 0\)).
For the partial molar entropy of the solute, we use \(S\B=-\pd{\mu\B}{T}{p,\allni}\) (Eq. 9.2.48) and obtain \begin{equation} S\B = -\Pd{\mu\xbB\rf}{T}{\!p} - R \ln x\B \tag{9.4.36} \end{equation} The term \(-\pd{\mu\xbB\rf}{T}{p}\) represents the partial molar entropy \(S\xbB\rf\) of B in the fictitious reference state of unit solute mole fraction. Thus, we can write Eq. 9.4.36 in the form \begin{gather} \s{ S\B = S\xbB\rf - R \ln x\B } \tag{9.4.37} \cond{(ideal-dilute solution} \nextcond{of a nonelectrolyte)} \end{gather} This equation shows that the partial molar entropy varies with composition and goes to \(+\infty\) in the limit of infinite dilution. From the expressions of Eqs. 9.4.27 and 9.4.28, we can derive similar expressions for \(S\B\) in terms of the solute reference states on a concentration or molality basis.
The relation \(H\B = \mu\B + TS\B\) (from Eq. 9.2.46), combined with Eqs. 9.4.24 and 9.4.37, yields \begin{equation} H\B = \mu\xbB\rf + TS\xbB\rf = H\xbB\rf \tag{9.4.38} \end{equation} showing that at constant \(T\) and \(p\), the partial molar enthalpy of the solute is constant throughout the ideal-dilute solution range. Therefore, we can write \begin{gather} \s{ H\B = H\B^{\infty} } \tag{9.4.39} \cond{(ideal-dilute solution} \nextcond{of a nonelectrolyte)} \end{gather} where \(H\B^{\infty}\) is the partial molar enthalpy at infinite dilution. By similar reasoning, using Eqs. 9.2.49–9.2.52, we find that the partial molar volume, internal energy, and heat capacity of the solute are constant in the ideal-dilute range and equal to the values at infinite dilution. The expressions are listed in the second column of Table 9.2.
When the pressure is equal to the standard pressure \(p\st\), the quantities \(H\B^{\infty}\), \(V\B^{\infty}\), \(U\B^{\infty}\), and \(C_{p,\tx{B}}^{\infty}\) are the same as the standard values \(H\B\st\), \(V\B\st\), \(U\B\st\), and \(C_{p,\tx{B}}\st\).


9.8: End of Chapter Problems
Amino acids
1. For the four amino acids below:
Ile
Arg
Asn
Glu
a. What is the net charge of each amino acid at physiological pH?
b. What is the classification of each amino acid?
2. Identify an amino acid that has in its side chain a (an) --------------.
a. thiol
b. phenol
c. sulfide
d. alcohol
e. amide
f. aromatic ring
3. Which nonpolar amino acid has a side chain that can participate in hydrogen bonding?
Polypeptides
1. Draw the tripeptide Asp-Val-Ser. Label the terminuses in this tripeptide.
2. List all of the possible polypeptides that can be formed from the three amino acids, cysteine (Cys), leucine (Leu), and arginine (Arg).
3. Which of the 20 amino acids can participate in a disulfide bridge? What level of protein structure involves this covalent bonds between two sulfur atoms?
Protein structure
1. What is the primary (1 o ) structure of a protein
2. Describe the two types of secondary (2 o ) structure of proteins.
3. Describe the tertiary structure of a protein. What are the chemical bonds or IMF's responsible for maintaining the 3 o structure?
4. Describe the quaternary structure of hemoglobin. What are the chemical bonds or IMF's responsible for maintaining the 4 o structure?
5. Name pairs of amino acids that have side chains that can participate in salt bridge formation at pH=7?
6. a. Draw the polypeptide fragment shown below in its line bond formula or condensed structural formula at the physiological pH = 7.
Leu-Ala-Trp-Phe-Gly
b. Label C-terminus & N-terminus of the polypeptide fragment. Circle the peptide bonds.
c. In an aqueous environment, will the peptide fragment more likely be buried inside or located on the surface? Why?
d. What is most likely to change the biological activity: Replacement of the Leu with Ile residue or the replacement of Leu with Glu? Please discuss why.
7. What distinguishes a protein:
a. that has a 4 o structure from one that does not?
b. a simple protein form a conjugated (complex) protein?
Denaturation
1. What is denaturation? List some of the ways to denaturation a protein.
2. Discuss what happens when a native protein is subjected to the following agents? Identify the IMF's or chemical bonds that are disrupted.
a. Alcohol
b. Soaps and detergents
c. Changes in pH
d. Heavy metal ions such as Pb 2 +
e. Heat or Agitation
3. True or False: A denatured globular protein -------------.
a. contains no peptide bond
b. has an abnormal 1 o structure
c. is biologically inactive
Digestion of Proteins
1. What part of the digestive system is involved in the digestion of proteins?
2. Name the functional group hydrolyzed when a protein undergoes digestion.
3. Name an enzyme that catalyzes the digestion of proteins.
4. What products are formed when a protein undergoes digestion?


20.3E: Antigen-Presenting Cells
Antigen presentation is a process by which immune cells capture antigens and then enable their recognition by T cells.
- Describe the role of antigen-presenting cells
Key Points
- The host’s cells express “self” antigens that identify them as such. These antigens are different from those in bacteria (“non-self” antigens) and in virus-infected host cells (“missing-self”).
- Antigen presentation consists of pathogen recognition, phagocytosis of the pathogen or its molecular components, processing of the antigen, and then presentation of the antigen to naive T cells.
- The T cell receptor is restricted to recognizing antigenic peptides only when bound to appropriate molecules of the major histocompatibility complex (MHC), also known in humans as human leukocyte antigen (HLA).
- Helper T cells recieve antigens from MHC II on an APC, while cytotoxic T cells recieve antigens from MHC I. Helper T cells present their antigen to B cells as well.Dendritic cells, B cells, and macrophages play a major role in the innate response, and are the primary antigen-presenting cells (APC).
- APCs use toll-like receptors to identify PAMPS and DAMPs, which are signs of an infection and may be processed into antigen peptides if phagocytized. Most APCs cannot tell the difference between different types of antigens like B and T cells can.
Key Terms
- damage-associated molecular pattern : Protein or nucleic acid based signs of pathogen induced damage. Protein DAMPs may be phagocytized and processed for antigen presentation.
- cytotoxic : A population of T cells specialized for inducing the deaths of other cells.
Antigen presentation is a process in the body’s immune system by which macrophages, dendritic cells and other cell types capture antigens, then present them to naive T-cells. The basis of adaptive immunity lies in the capacity of immune cells to distinguish between the body’s own cells and infectious pathogens. The host’s cells express “self” antigens that identify them as belonging to the self. These antigens are different from those in bacteria (“non-self” antigens) or in virally-infected host cells (“missing-self”). Antigen presentation broadly consists of pathogen recognition, phagocytosis of the pathogen or its molecular components, processing of the antigen, and then presentation of the antigen to naive (mature but not yet activated) T cells. The ability of the adaptive immune system to fight off pathogens and end an infection depends on antigen presentation.
Antigen Presenting Cells
Antigen Presenting Cells (APCs) are cells that capture antigens from within the body, and present them to naive T-cells. Many immune system cells can present antigens, but the most common types are macrophages and dendritic cells, which are two types of terminally differentiated leukocytes that arise from monocytes. Both of these APCs perform many immune functions that are important for both innate and adaptive immunity, such as removing leftover pathogens and dead neutrophils after an inflammatory response. Dendritic cells (DCs) are generally found in tissues that have contact with the external environment (such as the skin or respiratory epithelium) while macrophages are found in almost all tissues. Some types of B cells may also present antigens as well, though it is not their primary function.
APCs phagocytize exogenous pathogens such as bacteria, parasites, and toxins in the tissues and then migrate, via chemokine signals, to lymph nodes that contain naive T cells. During migration, APCs undergo a process of maturation in which they digest phagocytized pathogens and begin to express the antigen in the form of a peptide on their MHC complexes, which enables them to present the antigen to naive T cells. The antigen digestion phase is also called “antigen processing,” because it prepares the antigens for presentation. This MHC:antigen complex is then recognized by T cells passing through the lymph node. Exogenous antigens are usually displayed on MHC Class II molecules, which interact with CD4+ helper T cells.
This maturation process is dependent on signaling from other pathogen-associated molecular pattern (PAMP) molecules (such as a toxin or component of a cell membrane from a pathogen) through pattern recognition receptors (PRRs), which are received by Toll-like receptors on the DC’s body. They may also recognize damage-associated molecular pattern (DAMP) molecules, which include degraded proteins or nucleic acids released from cells that undergo necrosis. PAMPs and DAMPS are not technically considered antigens themselves, but instead are signs of pathogen presence that alert APCs through Toll-like receptor binding. However if a DC phagocytzes a PAMP or DAMP, it could be used as an antigen during antigen presentation. APCs are unable to distinguish between different types of antigens themselves, but B and T cells can due to their specificity.
Antigen Presentation
T cells must be presented with antigens in order to perform immune system functions. The T cell receptor is restricted to recognizing antigenic peptides only when bound to appropriate molecules of the MHC complexes on APCs, also known in humans as Human leukocyte antigen (HLA).
Several different types of T cell can be activated by APCs, and each type of T cell is specially equipped to deal with different pathogens, whether the pathogen is bacterial, viral or a toxin. The type of T cell activated, and therefore the type of response generated, depends on which MHC complex the processed antigen-peptide binds to.
MHC Class I molecules present antigen to CD8+ cytotoxic T cells, while MHC class II molecules present antigen to CD4+ helper T cells. With the exception of some cell types (such as erythrocytes), Class I MHC is expressed by almost all host cells. Cytotoxic T cells (also known as TC, killer T cell, or cytotoxic T-lymphocyte (CTL)) are a population of T cells that are specialized for inducing the death of other cells. Recognition of antigenic peptides through Class I by CTLs leads to the killing of the target cell, which is infected by virus, intracytoplasmic bacterium, or are otherwise damaged or dysfunctional. Additionally, some helper T cells will present their antigen to B cells, which will activate their proliferation response.
Antigen presentation : In the upper pathway; foreign protein or antigen (1) is taken up by an antigen-presenting cell (2). The antigen is processed and displayed on a MHC II molecule (3), which interacts with a T helper cell (4). In the lower pathway; whole foreign proteins are bound by membrane antibodies (5) and presented to B lymphocytes (6), which process (7) and present antigen on MHC II (8) to a previously activated T helper cell (10), spurring the production of antigen-specific antibodies (9).
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28.4: Summary
28.1 Clinical Judgment Measurement Model
Historically, nursing was often viewed as a task-oriented career, but in recent years, the profession has grown in terms of autonomy and clinical judgment. Some of this growth was due to the development of the CJMM, a tool designed to measure critical thinking and clinical judgment in nursing students. This tool allows educators to assess the development of nursing student’s critical thinking skills to help ensure they are ready to practice as a nurse after graduation. This tool involves several steps that have expanded upon the traditional nursing process model, making it an excellent framework to guide new nurses in making clinical judgment calls in practice.
28.2 Developing Critical Thinking Skills
Nursing involves several types of thinking, of which one of the most important is critical thinking. Critical thinking involves applying knowledge to make care decisions that reflect evidence-based practice and consider patient preferences. Thinking is a subconscious process, but there are several models that have been developed to focus upon developing more improved thinking skills. Specifically, the 4-Circle CT model demonstrates characteristics that are vital to develop critical thinking skills. The development of critical thinking skills is especially important within nursing because nurses are constantly making clinical judgment calls when caring for sick patients.


9.12: Identifying Training Gaps
- Discuss how to identify training gaps
A training gap exists when there is a variance between desired/required behavior or performance and actual behavior or performance. This gap can occur on an individual, team or organizational level. This gap can reflect a lack of hard or soft skills, a lack of understanding of job expectations, industry knowledge, cultural norms or other issues. Hard skills are job-specific or functional skills—for example, cloud-based computing skills or knowledge of human resource-related laws and practices. Soft skills are bigger-picture capabilities that range from adaptability, curiosity and empathy to communication and critical thinking.
The training needs assessment process can be broken down into the following 6 steps: [1]
- Establish clear expectations. In order to accurately evaluate performance—and, therefore, accurately identify any training needs—job expectations must be clearly established and understood. Given this, job descriptions should be reviewed periodically to ensure performance requirements are current and include the desired/required performance.
- Measure performance. Measuring performance not only establishes an objective point of reference, it creates an opportunity to discuss the instances of unsatisfactory performance and identify and document any issues and associated training or other actions. what training or other action is warranted. Identification of training needs and an associated training plan should also be incorporated in periodic reviews.
- Solicit input on training needs. The individuals who are doing the work have a particularly relevant perspective on training needs are perhaps the best source of information on short-term training needs. Surveying employees individually or conducting focus groups are a couple of ways of obtaining input. In order to get a complete picture, managers should also be asked for input on individual and team training requirements. Use of 360 degree reviews, where employees—including management—are reviewed by their staff, peers and their manager—may also highlight training gaps. Soliciting input also encourages conversations about and progress on training and development broadly—an expectation of both employers and employees.
- Support career development. Ask employees to rate their satisfaction with training and development opportunities and how existing policies and programs might be improved. Provide resources and support to help employees create self-directed development plans, in addition to the plans incorporated in their reviews. Identifying career interests and goals is valuable input into the overall organizational development plan.
- Conduct an organizational resource analysis. Conduct an overall analysis of human resources roles and requirements relative to the organization’s strategies and objectives to identify broad (for example, industry-specific) and position or job category-specific (including reskilling/upskilling) training needs and any resource requirements or redundancies. It may also be useful to convene a round-table group(s) to discuss the results of the organizational analysis, validate training needs and identify any additional issues or opportunities.
- Establish a coaching and mentoring program. As discussed in the onboarding section, coaching and mentoring is an organizational best practice that is associated with high-performance. Mentors can support employee personal and career development and be another point of perspective on training gaps.
-
Jones, Melissa. "
How to Identify Employee Training and Development Needs
." breathe. August 22, 2018. Accessed July 18, 2019. ↵
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9.7: Exercise- Deciding Which ICs to Exclude
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IC 1 is clearly capturing most of the blink activity, and we established in the previous chapter that blinks are both a major source of noise and a confound in the MMN experiment. It’s therefore clear that we should exclude this IC when we reconstruct the EEG data from the ICs. But what about the other ICs?
To answer this question, we need to go back to the three issues described at the beginning of the previous chapter. First, does the artifactual activity create substantial noise that degrades our data quality? Second, does the artifactual activity vary across groups or conditions, creating a confound? Third, does the artifactual activity indicate a problematic change in the sensory input (e.g., because the direction of gaze has changed)? The third issue is mainly relevant for visual experiments, so we won’t worry about it for the MMN.
In the chapter on artifact rejection, we addressed the issue of noise by looking at whether the SME was improved by rejection. We addressed the issue of noise by looking at the averaged ERPs, especially when we inverted the artifact rejection process and included only the trials that were marked for rejection. We can use the same two approaches with artifact correction.
We already assessed the effects of blink rejection and correction on the SME for our first pass at the ICA decomposition earlier in this chapter, and we found that correction improved the SME. Now let’s assess the effects of correcting for horizontal eye movements by excluding IC 13. Specifically, we'll compare excluding only blinks with excluding both blinks and horizontal eye movements. First, make two copies of the dataset with our improved ICA decomposition ( 10_MMN_preprocessed_transferredICAweights ). Then apply EEGLAB > Tools > Remove components from data as in the earlier exercise to remove the blink IC from one dataset and to remove both the blink and horizontal eye movement ICs from the other dataset. You should then create averaged ERPs for these two datasets (which will require adding an EventList, running BINLISTER, and epoching the data). Make sure to specify a custom data quality window of 125-225 ms. Before averaging, use EEGLAB > ERPLAB > Preprocess EEG > Selective Electrode Interpolation to interpolate F7 and PO4 (Channels 3 and 24), excluding the bipolar EOG channels (32 and 33).
If you look at the SME values for FCz in the 125-225 ms time range, you’ll see that eliminating the horizontal eye movement IC had virtually no impact on the data quality. This is consistent with what we saw with artifact rejection in the previous chapter. Horizontal eye movements just don’t have much impact on midline electrode sites, and most of the eye movements occurred during the break periods.
We also need to consider whether the horizontal eye movements were a confound. With artifact rejection, we did this by making averages from only the trials marked with artifacts. Here, we’ll conduct an analogous procedure, in which we reconstruct the data only from the eye movement component (IC 13) and then make averaged ERPs. To do this, select the dataset with the transferred weights ( 10_MMN_preprocessed_transferredICAweights ), select EEGLAB > Tools > Remove components from data , leave the List of component(s) to remove from data field blank, and enter 13 into the field labeled Or list of components to retain . Name the resulting dataset 10_MMN_preprocessed_IC13only . If you scroll through this dataset, you’ll see how the eye movement potentials spread to the other scalp sites (see, e.g., the highlighted time period in Screenshot 9.8.). These potentials are largest at the lateral frontal electrodes but can also be seen at posterior scalp sites (e.g., P7 and P8). However, the positive and negative sides of the dipole largely cancel out at the midline sites (e.g., Fz, FCz, Cz).
Now go through the steps needed to create averaged ERPs from this dataset, and then plot the resulting ERPs. You should see that the EEG channels are essentially flat lines. (There is some activity in the bipolar channels, but these are the original waveforms, not reconstructed from IC 13.) From these flat ERP waveforms, which should solely reflect the horizontal eye movements, we can conclude that the horizontal eye movements were not a meaningful confound. In other words, the fact that the averaged ERPs were largely flat in the EEG channels indicates that any horizontal eye movements were approximately equally likely to be leftward and rightward, resulting in opposite-polarity EOG signals that canceled out in the averages. And the fact that there was no difference between standards and deviants, especially at the key FCz site, indicates that there were no meaningful differences in horizontal eye movements between standards and deviants that could confound our MMN results.
So, should we correct for the horizontal eye movements by excluding IC 13 when we reconstruct the EEG data? Probably not. There is little to be gained, and given that ICA is imperfect and IC 13 may contain brain activity mixed with the horizontal eye movements, we have more to lose than to gain. However, IC 13 didn’t produce much activity in the ERPs when we looked only at this IC, so removing it will also have little impact. Before making a final decision about this, I would want to see how horizontal eye movements impact the data in the other participants. If they’re generally not a problem, I would not correct for them. But if they seem problematic (in terms of data quality and/or confounding activity) in several of the participants, I would probably correct for them in all participants (for the sake of consistency).
We also need to consider whether to exclude IC 16, which has a blink-like scalp distribution and shows small deflections for each blink. Repeat the series of steps you conducted for IC 13 but use IC 16 instead. That is, assess the SME values after excluding both IC 16 and IC 1 with the SME values after excluding only IC 1, and then look at the averaged ERPs after reconstructing the data from only IC 16. When I did this, I found that excluding both IC 16 and IC 1 led to a tiny improvement in SME compared to excluding only IC 1, and I found a small but concerning difference between deviants and standards in FCz when the data were reconstructed from IC 16. Given the small confound in the averaged waveforms, and the fact that we’ve already established that blinks differ between deviants and standards, I would exclude IC 16 along with IC 1 in the final analyses.
You can also try this set of procedures with the component that represents the spike potential (IC 3).
Does this sound like a lot of work? It is! But if your goal is to publish a paper in a scientific journal, making a permanent contribution to the scientific literature that others can build on, it’s worthwhile to take the time to deal with artifacts in a careful and thoughtful manner. Also, the scripts provided at the end of the chapter show you how to make the process more efficient by automating some parts of it.


1.1: Algebra Tips and Tricks Part I (Combining Terms, Distributing, Functions, Graphing)
Here are a few algebra tips and tricks to get you started. In later chapters, we will have some “just-in-time” algebra review, so you’ll review an algebra concept just before you need it.
Combining Like terms
A term is one or more things multiplied together: for example, \(xyz\) is a term since it is \(x\) times \(y\) times \(z\), \(b^2\) is a term, since it is \(b\) times \(b.\) and \(x\) is a term. If there is also a number multiplied in front of a term, that is called the coefficient (if no coefficient is present, the coefficient is \(1\)). Two terms are like terms if they have the same variables multiplied (but may have different coefficients). If two like terms are added together, they can be combined into one term by adding the coefficients.
\[\begin{align*} ab - a^2 + 2ab - 3a^2 & = 1ab + (-1)a^2 + 2ab + (-3)a^2 \qquad \text{(Clarify coefficients)} \\ & = 1ab + 2ab + (-1)a^2 + (-3)a^2 \qquad \text{(Group like terms)} \\ & = (1+2)ab + (-1+-3)a^2 \qquad \text{(Add coefficients)} \\ & = \boxed{3ab - 4a^2} \end{align*}\]
Distributing
If you are multiplying by a sum in parentheses, the rule is to distribute
\(a(b + c) = ab + ac\)
Here is another version in “table” form.
\(\begin{array}{c|cc} & b & +c \\ \hline a & ab & +ac \end{array}\)
It works, check it out:
\[\begin{align*} 3(4 + 5) & = 3(4) + 3(5) \\ 3(9) & = 12 + 15 \\ 27 & = 27 \end{align*}\]
Here is an example:
\[\begin{align*} 3a(2a - b) - (b-a^2) & = 3a(2a - b) + -1(b - a^2) \\ & = 6a^2 - 3ab - b + a^2 \qquad \text{(Notice the $\mathbf{+a^2}$)}\\ & = \boxed{7a^2 - 3ab - b} \end{align*}\]
Foiling
When multiplying two sums, every term of the first must be multiplied by every term of the second. Thus, if there are two terms in the first sum and two in the second, there are four total terms in the product: the (f)irst two terms, the (o)utside terms, the (i)nside terms, and the (l)ast two terms. We can use the acronym “foil”:
\((a + b)(c + d) = ac + ad + bc + bd\)
Here is the same calculation in table form:
\(\begin{array}{c|cc} & c & +d \\ \hline a & ac & +ad \\ +b & +bc & +bd \end{array}\)
Here is an example:
\[\begin{align*} (3a + 4b)(a^2 - ab) & = (3a)(a^2) + (3a)(-ab) + (4b)(a^2) + (4b)(-ab) \\ & = 3a^3 - 3a^2b +4a^2b - 4ab^2 \\ & = \boxed{3a^3 + a^2b - 4ab^2} \end{align*}\]
Distributing with three terms
When you have three expressions multiplied together, things get a bit trickier. Let’s do some examples.
To do this, we first multiply the \((x - 2)(x + 1)\). This is \(x^2 +x - 2x - 2 = x^2 - x - 2\). We then multiply \((x^2 - x - 2)(x + 3)\). This is done by combining every term in the first product with every term in the last product. One way to do this is \(x\) times everything in \(x^2 - x - 2\), plus \(3\) times everything in \(x^2 - x - 2\).
\[\begin{align*} (x - 2)(x + 1)(x + 3) & = (x^2 - x - 2)(x + 3) \\ & = (x^2 - x - 2)(x) + (x^2 - x - 2)(3) \\ & = x^3 - x^2 - 2x + 3x^2 - 3x - 6 \\ & = \boxed{x^3 + 2x^2 - 5x - 6} \end{align*}\]
There you go.
Alternatively, we can use the table method . We start by foiling two of the terms together
\(\begin{array}{c|cc} & x & - 2 \\ \hline x & \color{blue}{x^2} & \color{blue}{-2x} \\ +1 & \color{blue}{+1x} & \color{blue}{-2} \end{array}\)
Adding the blue terms, we get an intermediate answer of \(\color{blue}{x^2 - x -2}\). Now we can multiply this by \(x+3\).
\(\begin{array}{c|ccc} & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{-2} \\ \hline x & \color{red}{x^3} & \color{red}{-x^2} & \color{red}{-2x} \\ +3 & \color{red}{+3x^2} & \color{red}{-3x} & \color{red}{+6} \end{array}\)
Combining like terms gives the answer \(\boxed{\color{red}{x^3 + 2x^2 - 5x + 6}}\), the same answer we got before!
We see this is the same thing as \((x + 4)(x + 4)(x + 4)\). We then can do
\[\begin{align*} (x + 4)(x + 4)(x + 4) & = (x^2 + 8x + 16)(x + 4) \\ & = (x^2 + 8x + 16)(x) + (x^2 + 8x + 16)(4) \\ & = x^3 + 8x^2 + 16x + 4x^2 + 32x + 64 \\ & = \boxed{x^3 + 12x^2 + 48x + 64} \end{align*}\]
I won’t do it this time, but you could use the table method if you prefer that!
Functions
A function is anything that produces an output for every possible input. So for example, \(f(x) = 2x\) is the function that take in an input \(x\), and outputs double \(x\) (i.e. \(f(3) = 6\), \(f(4) = 8\), \(f(5) = 10\), etc.).
Here are some examples:
We see that \(g(3) = 2^3 = \boxed{8}\), and \(g(4) = 2^4 = \boxed{16}\).
In each case, just replace the \(x\) with the input to the function. For example, \(h(5) = 2(5) + 3 = 13\), and \(h(y) = 2(y) + 3 = \boxed{2y + 3}\).
A tricky one is \(h(x + 1)\). Here, we replace the \(x\) with \((x + 1)\) in the formula.
Tip: Always do substitutions or replacements like this in parentheses to keep it all together.
Here is what it would look like:
\[\begin{align*} h({\color{red} x}) & = 2{\color{red} x} + 3 \\ h({\color{blue} x+1}) & = 2{\color{blue} (x+1)} + 3 \\ & = 2x + 2 + 3 \\ & = \boxed{2x+5}. \end{align*}\]
We have to replace the \(x\) with \(4x+1\) in the formula. So we have
\[\begin{align*} m(x) & = 3x - 1 \\ m(4x+1) & = 3(4x+1) - 1 \\ & = 12x + 3 - 1 \\ & = \boxed{12x + 2}. \end{align*}\]
Here, the idea is to replace \(x\) with \(g(x)\) in the formula. In other words, \(x\) becomes \(2x+5\):
\[\begin{align*} f(x) & = x^2 - 4x \\ f(g(x)) = f(2x+5) & = (2x+5)^2 - 4(2x+5) \\ & = 4x^2 + 10x + 10x + 25 - 8x - 20 \\ & = \boxed{4x^2 + 12x + 5}. \end{align*}\]
Graphing Functions
Graphing is a great way to visualize a function. For example, consider the graph of \(f(x) = x^2\).
Choose any point on the curve. If you go down to the \(x\)-axis, you’ll get the input value, and if you go directly left (or right) to the \(y\)-axis, you’ll get the output value. For example,
This reflects the fact that \(f(2) = 2^2 = 4\).
Note: Anything with
multiple outputs for one input
is considered
not
a function. A handy way to determine this is the “vertical line test” — any vertical line should hit a function only once.
Table method for graphing
If you want to graph a function by hand, a way that works for virtually any function is the table method. Say we want to do the following:
We can just start by plugging in some values like \(x = -2\), \(x = -1\), \(x = 0\), etc., and fill out a whole table. For example, for \(x = -2\), we can compute \(g(-2) = (-2)^2 + 2(-2) = 4 -4 = 0\). Since \(g(-2) = 0\), we know that the point \((x, y) = (-2, 0)\) lies on the graph. Filling out the rest of the table, we get
\[\[\begin{array}{cccc} \mathbf{x} & \mathbf{x^2 + 2x} & \mathbf{g(x)} & \mathbf{(x, y)} \\ -2 & (-2)^2 + 2(-2) & 0 & (-2, 0) \\ -1 & (-1)^2 + 2(-1) & -1 & (-1, -1) \\ 0 & (0)^2 + 2(0) & 0 & (0, 0) \\ 1 & (1)^2 + 2(1) & 3 & (1, 3) \\ 2 & (2)^2 + 2(2) & 8 & (2, 8) \end{array}\]\]
We can then plot these input-output pairs on the graph, and they trace out a curve. (Note that the pair \((2, 8)\) didn’t fit on the graph.)


12.1: Introduction
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- Ly-Huong T. Pham, Tejal Desai-Naik, Laurie Hammond, & Wael Abdeljabbar
- ASCCC Open Educational Resources Initiative (OERI)
Introduction
Information systems have had an impact far beyond the world of business. In the past four decades, technology has fundamentally altered our lives: from the way we work, how we play to how we communicate, and how we fight wars. Mobile phones track us as we shop at stores and go to work. Algorithms based on consumer data allow firms to sell us products that they think we need or want. New technologies create new situations that we have never dealt with before. They can threaten individual autonomy, violate privacy rights, and can also be morally contentious. How do we handle the new capabilities that these devices empower us with? What new laws are going to be needed to protect us from ourselves and others? This chapter will kick off with a discussion of the impact of information systems on how we behave (ethics). This will be followed by the new legal structures being put in place, focusing on intellectual property and privacy.
Information Systems Ethics
The term ethics is defined as “a set of moral principles” or “the principles of conduct governing an individual or a group.” Since the dawn of civilization, the study of ethics and its impact has fascinated humankind. But what do ethics have to do with information systems?
The introduction of new technology can have a profound effect on human behavior. New technologies give us capabilities that we did not have before, which create environments and situations that have not been specifically addressed in ethical terms. Those who master new technologies gain new power; those who cannot master them may lose power. In 1913, Henry Ford implemented the first moving assembly line to create his Model T cars. While this was a great step forward technologically (and economically), the assembly line reduced human beings' value in the production process. The development of the atomic bomb concentrated unimaginable power in the hands of one government, which then had to wrestle with the decision to use it. Today’s digital technologies have created new categories of ethical dilemmas.
For example, the ability to anonymously make perfect copies of digital music has tempted many music fans to download copyrighted music for their own use without making payment to the music’s owner. Many of those who would never have walked into a music store and stolen a CD find themselves with dozens of illegally downloaded albums.
Digital technologies have given us the ability to aggregate information from multiple sources to create profiles of people. What would have taken weeks of work in the past can now be done in seconds, allowing private organizations and governments to know more about individuals than at any time in history. This information has value but also chips away at the privacy of consumers and citizens.
Communication technologies like social media(Facebook, Twitter, Instagram, LinkedIn, internet blogs) give so many people access to so much information that it's getting harder and harder to tell what’s real and what’s fake. Its widespread use has blurred the line between professional, personal, and private. Employers now have access to information that has traditionally been considered private and personal, giving rise to new legal and ethical ramifications.
Some technologies like self-driving vehicles(drones), artificial intelligence, the digital genome, and additive manufacturing methods(GMO) are transitioning into a new phase, becoming more widely used or incorporated into consumer goods, requiring new ethical and regulatory guidelines.
Code of Ethics
One method for navigating new ethical waters is a code of ethics. A code of ethics is a document that outlines a set of acceptable behaviors for a professional or social group; generally, it is agreed to by all members of the group. The document details different actions that are considered appropriate and inappropriate.
A good example of a code of ethics is the Code of Ethics and Professional Conduct of the Association for Computing Machinery, an organization of computing professionals that includes educators, researchers, and practitioners. Here is an excerpt from the preamble:
Computing professionals' actions change the world. To act responsibly, they should reflect upon the wider impacts of their work, consistently supporting the public good. The ACM Code of Ethics and Professional Conduct ("the Code") expresses the profession's conscience. Additionally, the Code serves as a basis for remediation when violations occur. The Code includes principles formulated as statements of responsibility based on the understanding that the public good is always the primary consideration. Each principle is supplemented by guidelines, which provide explanations to assist computing professionals in understanding and applying the principle.
Section 1 outlines fundamental ethical principles that form the basis for the remainder of the Code. Section 2 addresses additional, more specific considerations of professional responsibility. Section 3 guides individuals who have a leadership role, whether in the workplace or a volunteer professional capacity. Commitment to ethical conduct is required of every ACM member, and principles involving compliance with the Code are given in Section 4 .
In the ACM’s code, you will find many straightforward ethical instructions, such as the admonition to be honest and trustworthy. But because this is also an organization of professionals that focuses on computing, there are more specific admonitions that relate directly to information technology:
- No one should enter or use another’s computer system, software, or data files without permission. One must always have appropriate approval before using system resources, including communication ports, file space, other system peripherals, and computer time.
- Designing or implementing systems that deliberately or inadvertently demean individuals or groups is ethically unacceptable.
- Organizational leaders are responsible for ensuring that computer systems enhance, not degrade, working life quality. When implementing a computer system, organizations must consider all workers' personal and professional development, physical safety, and human dignity. Appropriate human-computer ergonomic standards should be considered in system design and the workplace.
One of the major advantages of creating a code of ethics is clarifying the acceptable standards of behavior for a professional group. The varied backgrounds and experiences of the members of a group lead to various ideas regarding what is acceptable behavior. While to many the guidelines may seem obvious, having these items detailed provides clarity and consistency. Explicitly stating standards communicates the common guidelines to everyone in a clear manner.
Having a code of ethics can also have some drawbacks. First of all, a code of ethics does not have legal authority; in other words, breaking a code of ethics is not a crime in itself. So what happens if someone violates one of the guidelines? Many codes of ethics include a section that describes how such situations will be handled. In many cases, repeated violations of the code result in expulsion from the group.
In the case of ACM: “Adherence of professionals to a code of ethics is largely a voluntary matter. However, if a member does not follow this code by engaging in gross misconduct, membership in ACM may be terminated.” Expulsion from ACM may not impact many individuals since membership in ACM is usually not a requirement for employment. However, expulsion from other organizations, such as a state bar organization or medical board, could carry a huge impact.
Another possible disadvantage of a code of ethics is that there is always a chance that important issues will arise that are not specifically addressed in the code. Technology is changing exponentially, and advances in artificial intelligence mean new ethical issues related to machines. The code of ethics might not be updated often enough to keep up with all of the changes. However, a good code of ethics is written in a broad enough fashion that it can address the ethical issues of potential technology changes. In contrast, the organization behind the code makes revisions.
Finally, a code of ethics could also be a disadvantage because it may not entirely reflect the ethics or morals of every member of the group. Organizations with a diverse membership may have internal conflicts as to what is acceptable behavior. For example, there may be a difference of opinion on the consumption of alcoholic beverages at company events. In such cases, the organization must choose the importance of addressing a specific behavior in the code.
Sidebar: Acceptable Use Policies(AUP) (20%)
Many organizations that provide technology services to a group of constituents or the public require an acceptable use policy (AUP) before those services can be accessed. Like a code of ethics, it is a set of rules applied by the organization that outlines what users may or may not do while using the organization’s services. Usually, the policy requires some acknowledgment that the rules are well understood, including potential violations. An everyday example of this is the terms of service that must be agreed to before using the public Wi-Fi at Starbucks, McDonald’s, or even a university. An AUP is an important document as it demonstrates due diligence of the organization's security and protection of sensitive data, which protects the organization from legal actions. Here is an example of an acceptable use policy from Virginia Tech .
Just as with a code of ethics, these acceptable use policies specify what is allowed and what is not allowed. Again, while some of the items listed are obvious to most, others are not so obvious:
- “Borrowing” someone else’s login ID and password are prohibited.
- Using the provided access for commercial purposes, such as hosting your own business website, is not allowed.
- Sending out unsolicited emails to a large group of people is prohibited.
Also, as with codes of ethics, violations of these policies have various consequences. In most cases, such as with Wi-Fi, violating the acceptable use policy will mean that you will lose your access to the resource. While losing access to Wi-Fi at Starbucks may not have a lasting impact, a university student getting banned from the university’s Wi-Fi (or possibly all network resources) could greatly impact.
References
ACM Code of Ethics. Preamble . Retrieved November 10, 2020, from https://www.acm.org/code-of-ethics .


1.1: Definition of a Matrix
View Definition of a Matrix on YouTube
An \(m\)-by-\(n\) matrix is a rectangular array of numbers (or other mathematical objects) with \(m\) rows and \(n\) columns. For example, a two-by-two matrix \(\text{A}\), with two rows and two columns, looks like
\[\text{A}=\left(\begin{array}{cc}a&b\\c&d\end{array}\right).\nonumber \]
(Sometimes brackets are used instead of parentheses.) The first row has elements \(a\) and \(b\), the second row has elements \(c\) and \(d\). The first column has elements \(a\) and \(c\); the second column has elements \(b\) and \(d\). As further examples, \(2\)-by-\(3\) and \(3\)-by-\(2\) matrices look like
\[\text{B}=\left(\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right),\quad \text{C}=\left(\begin{array}{cc}a&b\\c&d\\e&f\end{array}\right).\nonumber \]
Of special importance are the so-called row matrices and column matrices. These matrices are also called row vectors and column vectors. The row vector is in general \(1\)-by-\(n\) and the column vector is \(n\)-by-\(1\). For example, when \(n = 3\), we would write
\[\text{v}=\left(\begin{array}{ccc}a&b&c\end{array}\right)\nonumber \]
as a row vector, and
\[\text{v}=\left(\begin{array}{c}a\\b\\c\end{array}\right)\nonumber \]
as a column vector.


5.4.6: Benefits and Challenges of Workplace Diversity
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How can managers reap benefits from diversity and mitigate its challenges?
Much theoretical work has espoused the benefits of workplace diversity, but empirical studies have often had conflicting results, which have shown researchers that certain conditions can affect how successful initiatives to increase and enhance workplace diversity are. Managers can work to make sure that the efforts and initiatives they enact to increase diversity in the workplace come from a perspective that ensures and strives for equity and fairness, and not simply from the perspective of only benefitting the company’s bottom line. By approaching diversity and diversity issues in a thoughtful, purposeful way, managers can mitigate the challenges posed by a diverse workforce and enhance the benefits a diverse workforce can offer.
Three Perspective on Workplace Diversity
Ely and Thomas’s work on cultural diversity was designed to theoretically and empirically support some of the hypothesized relationships between diversity and workplace outcomes. Their research yielded a paradigm that identifies three perspectives regarding workplace diversity: 142 integration and learning, access and legitimacy, and discrimination and fairness.
The Integration-and-Learning Perspective
The integration-and-learning perspective posits that the different life experiences, skills, and perspectives that members of diverse cultural identity groups possess can be a valuable resource in the context of work groups. Under this perspective, the members of a culturally diverse workgroup can use their collective differences to think critically about work issues, strategies, products, and practices in a way that will allow the group to be successful in its business operations. The assumption under this perspective is that members of different cultural identity groups can learn from each other and work together to best achieve shared goals. This perspective values cultural identity and strongly links diversity of the group to the success of the firm.
Downfalls of the integration-and-learning perspective can be that White members of the work group can feel marginalized when they are not asked to join in on diversity-related projects or discussions. Similarly, workforce members of color might experience burnout if they are always expected to work on those projects and discussions that specifically deal with diversity issues.
The Access-and-Legitimacy Perspective
The access-and-legitimacy perspective focuses on the benefit that a diverse workforce can bring to a business that wishes to operate within a diverse set of markets or with culturally diverse clients. Work groups that operate under this perspective are doing so in order to gain access to diverse markets and because their diversity affords them some level of legitimacy when attempting to gain access to diverse markets. This type of workplace diversity is more of a functional type of diversity that does not attempt to integrate or value diversity at the business’s core. The danger of this diversity perspective is that it can limit the roles of certain minority groups by valuing members of these groups only because they can increase the access to diverse markets and clients and not because they can make other potentially valuable contributions. 143
The Discrimination-and-Fairness Perspective
The discrimination-and-fairness perspective stems from a belief that a culturally diverse workforce is a moral duty that must be maintained in order to create a just and fair society. This perspective is characterized by a commitment to equal opportunities in hiring and promotions, and does not directly link a work group’s productivity or success with diversity. Many times firms operating under this perspective will have a spoken or unspoken assumption that assimilation into the dominant (White) culture should take place by the members of other cultural identity groups. One drawback of this perspective is that because it measures progress by the recruitment and retention of diverse people, employees of traditionally underrepresented groups can feel devalued. Often, assimilation is pushed on diverse employees under the guise of reducing conflict or in an effort to demonstrate that differences between cultural identity groups are unimportant. 144 Exhibit \(\PageIndex{1}\): shows the degrees of effectiveness and benefits for each perspective
Concept Check
- How can managers reap the benefits of diversity?
- How can managers mitigate the challenges of diversity?
- What is the access-and-legitimacy perspective? Differentiate it from the discrimination-and-fairness perspective.
142. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes." Administrative science quarterly. 46.2 (2001): 229-273.
143. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes." Administrative science quarterly. 46.2 (2001): 229-273.
144. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes." Administrative science quarterly. 46.2 (2001): 229-273.
Exhibit 5.8 Cultural Diversity Perspectives at Work Source: Adapted from Ely, Robin J., and David A. Thomas. “Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes.” Administrative science quarterly. 46.2 (2001): 229-273.


<IP_ADDRESS>: Quotation Error
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Using quotation marks correctly can be a little tricky, especially when you need to use other types of punctuation with them. Mechanical errors related to quotation marks make the most-common error list because beginning writers often forget that commas and periods go inside the quotation marks. Here is an example:
In this case, the comma placed outside the quotation marks is incorrect. The comma should be placed inside the quotation marks like this:
It’s important to note, however, that not all punctuation automatically goes inside the quotation marks.  If the only part in quotations is a question, then the question mark should go inside the quotation marks; otherwise, the question mark actually goes outside of the quotation marks. Tricky for sure!
Also, beginning writers often forget that titles of shorter works, like essays and short stories, should be placed inside quotation marks. Longer works, like books and magazines, should be placed in italics.


4.2: Mechanisms of interruption- recognition of vector, and interrupt priority
Introduction
The following section introduces the learner to Interruptions that occur in Programmed I/O
Activity Details
In system programming, an interrupt is a signal to the processor emitted by hardware or software indicating an event that needs immediate attention. An interrupt is a signal from a device attached to a computer or from a program within the computer that causes the main program that operates the computer (the operating system) to stop and figure out what to do next. An interrupt alerts the processor to a high-priority condition requiring the interruption of the current code the processor is executing. The processor responds by suspending its current activities, saving its state, and executing a function called an interrupt handler (or an interrupt service routine, ISR) to deal with the event. This interruption is temporary, and, after the interrupt handler finishes, the processor resumes normal activities. There are two types of interrupts: hardware interrupts and software interrupts.
Hardware interrupts
Hardware interrupts are used by devices to communicate that they require attention from the operating system. Internally, hardware interrupts are implemented using electronic alerting signals that are sent to the processor from an external device, which is either a part of the computer itself, such as a disk controller, or an external peripheral.
For example, pressing a key on the keyboard or moving the mouse triggers hardware interrupts that cause the processor to read the keystroke or mouse position. Unlike the software type (described below), hardware interrupts are asynchronous and can occur in the middle of instruction execution, requiring additional care in programming. The act of initiating a hardware interrupt is referred to as an interrupt (IRQ).
Software interrupt
A software interrupt is caused either by an exceptional condition in the processor itself, or a special instruction in the instruction which causes an interrupt when it is executed. The former is often called a trap or exception and is used for errors or events occurring during program executions that are exceptional enough that they cannot be handled within the program itself.
For example, if the processor’s arithmetic logic unit is commanded to divide a number by zero, this impossible demand will cause a divide-by-zero exception, perhaps causing the computer to abandon the calculation or display an error message. Software interrupt instructions function similarly to subroutine calls and are used for a variety of purposes, such as to request services from low-level system software such as device drivers. For example, computers often use software interrupt instructions to communicate with the disk controller to request data be read or written to the disk.
Each interrupt has its own interrupt handler. The number of hardware interrupts is limited by the number of interrupt request (IRQ) lines to the processor, but there may be hundreds of different software interrupts. Interrupts are a commonly used technique for computer multitasking, especially in real-time computing. Such a system is said to be interrupt-driven
Interrupts can be categorized into these different types:
- Maskable interrupt (IRQ): a hardware interrupt that may be ignored by setting a bit in an interrupt mask register’s (IMR) bit-mask.
- Non-maskable interrupt (NMI): a hardware interrupt that lacks an associated bit- mask, so that it can never be ignored. NMIs are used for the highest priority tasks such as timers, especially watchdog timers.
- Inter-processor interrupt (IPI): a special case of interrupt that is generated by one processor to interrupt another processor in a multiprocessor system.
- Software interrupt: an interrupt generated within a processor by executing an instruction. Software interrupts are often used to implement system calls because they result in a subroutine call with a CPU ring level change.
- Spurious interrupt: a hardware interrupt that is unwanted. They are typically generated by system conditions such as electrical interference on an interrupt line or through incorrectly designed hardware.
Conclusion
This section has introduced learners to the different categories of I/O interrupts, that is the hardware and software interrupts
Assessment
Briefly describe hardware and software Interruptions
Hardware interruptions
Hardware interruptions are generated by certain events which come up during the execution of a program. This type of interruptions is managed on their totality by the hardware and it is not possible to modify them.
A clear example of this type of interruptions is the one which actualizes the counter of the computer internal clock, the hardware makes the call to this interruption several times during a second in order to maintain the time up to date.
Hardware Interruptions
External interruptions are generated by peripheral devices, such as keyboards, printers, communication cards, etc. They are also generated by coprocessors. It is not possible to deactivate external interruptions.
These interruptions are not sent directly to the CPU but they are sent to an integrated circuit whose function is to exclusively handle this type of interruptions
Software Interruptions
Software interruptions can be directly activated by the assembler invoking the number of the desired interruption with the INT Instruction.
The use of interruptions helps us in the creation of programs and by using them our programs gets shorter. It is easier to understand them and they usually have a better performance mostly due to their smaller size. This type of interruptions can be separated in two categories: the operative system DOS interruptions and the BIOS interruptions.


4.9: The Intermediate Value Property
This page is a draft and is under active development.
A function \( f : A \rightarrow E ^ { * } \) is said to have the intermediate value property , or Darboux property, \( ^ { 1 } \) on a set \( B \subseteq A \) iff, together with any two function values \( f ( p ) \) and \( f \left( p _ { 1 } \right) \left( p , p _ { 1 } \in B \right) , \) it also takes all intermediate values between \( f ( p ) \) and \( f \left( p _ { 1 } \right) \) at some points of \( B \).
In other words, the image set \( f [ B ] \) contains the entire interval between \( f ( p ) \) and \( f \left( p _ { 1 } \right) \) in \( E ^ { * } . \)
Note 1. It follows that \( f [ B ] \) itself is a finite or infinite interval in \( E ^ { * } , \) with endpoints inf \( f [ B ] \) and \( \sup f [ B ] . \) (Verify!)
Geometrically, if \( A \subseteq E ^ { 1 } , \) this means that the curve \( y = f ( x ) \) meets all horizontal lines \( y = q , \) for \( q \) between \( f ( p ) \) and \( f \left( p _ { 1 } \right) . \) For example, in Figure 13 in \( § 1 , \) we have a "smooth" curve that cuts each horizontal line \( y = q \) between \( f ( 0 ) \) and \( f \left( p _ { 1 } \right) ; \) so \( f \) has the Darboux property on \( \left[ 0 , p _ { 1 } \right] . \) In Figures 14 and \( 15 , \) there is a "gap" at \( p \) ; the property fails. In Example (f) of \( § 1 , \) the property holds on all of \( E ^ { 1 } \) despite a discontinuity at \( 0 . \) Thus it does not imply continuity.
Intuitively, it seems plausible that a "continuous curve" must cut all intermediate horizontals. A precise proof for functions continuous on an interval, was given independently by Bolzano and Weierstrass (the same as in Theorem 2 of Chapter 3, §16). Below we give a more general version of Bolzano's proof based on the notion of a convex set and related concepts.
A set \( B \) in \( E ^ { n }\) (* or in another normed space) is said to be convex iff for each \( \overline { a } , \overline { b } \in B \) the line segment \( L [ \overline { a } , \overline { b } ] \) is a subset of \( B \).

\]
The set \( B \) is said to be polygon connected (or piecewise convex) iff any two points \( \overline { a } , \overline { b } \in B \) can be joined by a polygon contained in \( B \).
Any globe in \(E^{n}\) (* or in another normed space) is convex, so also is any interval in \(E^{n}\) or in \(E^{*}\). Figures 19 and 20 represent a convex set \(A\) and a polygon-connected set \(B\) in \(E^{2}\) is not convex; it has a "cavity").
We shall need a simple lemma that is noteworthy in its own right as well.
Every contracting sequence of closed line segments \(L\left[\overline{p}_{m}, \overline{q}_{m}\right]\) in \(E^{n}\) (* or in any other normed space) has a nonvoid intersection; i.e., there is a point
\[\overline{p} \in \bigcap_{m=1}^{\infty} L[\overline{p}_{m}, \overline{q}_{m}].\]
- Proof
-
Use Cantor's theorem (Theorem 5 of §6) and Example (1) in §8. \(\square\)
We are now ready for Bolzano's theorem. The proof to be used is typical of so-called "bisection proofs." (See also §6, Problems 9 and 10 for such proofs.)
If \(f : B \rightarrow E^{1}\) is relatively continuous on a polygon-connected set \(B\) in \(E^{n}\) (* or in another normed space), then \(f\) has the Darboux property on \(B .\)
In particular, if \(B\) is convex and if \(f(\overline{p})<c<f(\overline{q})\) for some \(\overline{p}, \overline{q} \in B,\) then there is a point \(\overline{r} \in L(\overline{p}, \overline{q})\) such that \(f(\overline{r})=c\).
- Proof
-
First, let \(B\) be convex. Seeking a contradiction, suppose \(\overline{p}, \overline{q} \in B\) with
\[f(\overline{p})<c<f(\overline{q}),\]
yet \(f(\overline{x}) \neq c\) for all \(\overline{x} \in L(\overline{p}, \overline{q})\).
Let \(P\) be the set of all those \(\overline{x} \in L[\overline{p}, \overline{q}]\) for which \(f(\overline{x})<c,\) i.e.,
\[P=\{\overline{x} \in L[\overline{p}, \overline{q}] | f(\overline{x})<c\},\]
and let
\[Q=\{\overline{x} \in L[\overline{p}, \overline{q}] | f(\overline{x})>c\}.\]
Then \(\overline{p} \in P, \overline{q} \in Q, P \cap Q=\emptyset,\) and \(P \cup Q=L[\overline{p}, \overline{q}] \subseteq B\). (Why?)
Now let
\[\overline{r}_{0}=\frac{1}{2}(\overline{p}+\overline{q})\]
be the midpoint on \(L[\overline{p}, \overline{q}].\) Clearly, \(\overline{r}_{0}\) is either in \(P\) or in \(Q.\) Thus it bisects \(L[\overline{p}, \overline{q}]\) into two subsegments, one of which must have its left endpoint in \(P\) and its right endpoint in \(Q.\)
We denote this particular closed segment by \(L\left[\overline{p}_{1}, \overline{q}_{1}\right], \overline{p}_{1} \in P, \overline{q}_{1} \in Q.\) We then have
\[L[\overline{p}_{1}, \overline{q}_{1}] \subseteq L[\overline{p}, \overline{q}] \text { and }|p_{1}-q_{1}|=\frac{1}{2}|\overline{p}-\overline{q}|. \text { (Verify!) }\]
Now we bisect \(L[\overline{p}_{1}, \overline{q}_{1}]\) and repeat the process. Thus let
\[\overline{r}_{1}=\frac{1}{2}(\overline{p}_{1}+\overline{q}_{1}).\]
By the same argument, we obtain a closed subsegment \(L\left[\overline{p}_{2}, \overline{q}_{2}\right] \subseteq L\left[\overline{p}_{1}, \overline{q}_{1}\right]\) with \(\overline{p}_{2} \in P, \overline{q}_{2} \in Q,\) and
\[\left|\overline{p}_{2}-\overline{q}_{2}\right|=\frac{1}{2}\left|\overline{p}_{1}-\overline{q}_{1}\right|=\frac{1}{4}|\overline{p}-\overline{q}|.\]
Next, we bisect \(L\left[\overline{p}_{2}, \overline{q}_{2}\right],\) and so on. Continuing this process indefinitely, we obtain an infinite contracting sequence of closed line segments \(L\left[\overline{p}_{m}, \overline{q}_{m}\right]\) such that
\[(\forall m) \quad \overline{p}_{m} \in P, \overline{q}_{m} \in Q,\]
and
\[\left|\overline{p}_{m}-\overline{q}_{m}\right|=\frac{1}{2^{m}}|\overline{p}-\overline{q}| \rightarrow 0 \text { as } m \rightarrow+\infty.\]
By Lemma 1, there is a point
\[\overline{r} \in \bigcap_{m=1}^{\infty} L\left[\overline{p}_{m}, \overline{q}_{m}\right].\]
This implies that
\[(\forall m) \quad\left|\overline{r}-\overline{p}_{m}\right| \leq\left|\overline{p}_{m}-\overline{q}_{m}\right| \rightarrow 0,\]
whence \(\overline{p}_{m} \rightarrow \overline{r} .\) Similarly, we obtain \(\overline{q}_{m} \rightarrow \overline{r}\).
Now since \(\overline{r} \in L[\overline{p}, \overline{q}] \subseteq B,\) the function \(f\) is relatively continuous at \(\overline{r}\) over \(B\) (by assumption). By the sequential criterion, then,
\[f\left(\overline{p}_{m}\right) \rightarrow f(\overline{r}) \text { and } f\left(\overline{q}_{m}\right) \rightarrow f(\overline{r}).\]
Moreover, \(f\left(\overline{p}_{m}\right)<c<f\left(\overline{q}_{m}\right)\left(\text { for } \overline{p}_{m} \in P \text { and } \overline{q}_{m} \in Q\right) .\) Letting \(m \rightarrow+\infty,\) we pass to limits (Chapter 3, §15, Corollary 1 ) and get
\[f(\overline{r}) \leq c \leq f(\overline{r}),\]
so that \(\overline{r}\) is neither in \(P\) nor in \(Q,\) which is a contradiction. This completes the proof for a convex \(B\).
The extension to polygon-connected sets is left as an exercise (see Problem 2 below). Thus all is proved. \(\square\)
Note 2. In particular, the theorem applies if \(B\) is a globe or an interval.
Thus continuity on an interval implies the Darboux property. The converse fails, as we have noted. However, for monotone functions, we obtain the following theorem.
If a function \(f : A \rightarrow E^{1}\) is monotone and has the Darboux property on a finite or infinite interval \((a, b) \subseteq A \subseteq E^{1},\) then it is continuous on \((a, b).\)
- Proof
-
Seeking a contradiction, suppose \(f\) is discontinuous at some \(p \in(a, b)\).
For definiteness, let \(f \uparrow\) on \((a, b) .\) Then by Theorems 2 and 3 in §5, we have either \(f\left(p^{-}\right)<f(p)\) or \(f(p)<f\left(p^{+}\right)\) or both, with no function values in between.
On the other hand, since \(f\) has the Darboux property, the function values \(f(x)\) for \(x\) in \((a, b)\) fill an entire interval (see Note 1). Thus it is impossible for \(f(p)\) to be the only function value between \(f\left(p^{-}\right)\) and \(f\left(p^{+}\right)\) unless \(f\) is constant near \(p,\) but then it is also continuous at \(p,\) which we excluded. This contradiction completes the proof. \(\square\)
Note 3. The theorem holds (with a similar proof) for nonopen intervals as well, but the continuity at the endpoints is relative (right at \(a,\) left at \(b).\)
If \(f : A \rightarrow E^{1}\) is strictly monotone and continuous when restricted to a finite or infinite interval \(B \subseteq A \subseteq E^{1},\) then its inverse \(f^{-1}\) has the same properties on the set \(f[B]\) (itself an interval, by Note 1 and Theorem 1).
- Proof
-
It is easy to see that \(f^{-1}\) is increasing (decreasing) if \(f\) is; the proof is left as an exercise. Thus \(f^{-1}\) is monotone on \(f[B]\) if \(f\) is so on \(B\). To prove the relative continuity of \(f^{-1},\) we use Theorem 2, i.e., show that \(f^{-1}\) has the Darboux property on \(f[B].\)
Thus let \(f^{-1}(p)<c<f^{-1}(q)\) for some \(p, q \in f[B] .\) We look for an \(r \in f[B]\) such that \(f^{-1}(r)=c,\) i.e., \(r=f(c) .\) Now since \(p, q \in f[B],\) the numbers \(f^{-1}(p)\) and \(f^{-1}(q)\) are in \(B,\) an interval. Hence also the intermediate value \(c\) is in \(B\) ; thus it belongs to the domain of \(f,\) and so the function value \(f(c)\) exists. It thus suffices to put \(r=f(c)\) to get the result. \(\square\)
(a) Define \(f : E^{1} \rightarrow E^{1}\) by
\[f(x)=x^{n} \text { for a fixed } n \in N.\]
As \(f\) is continuous (being a monomial), it has the Darboux property on \(E^{1} .\) By Note \(1,\) setting \(B=[0,+\infty),\) we have \(f[B]=[0,+\infty)\). (Why?) Also, \(f\) is strictly increasing on \(B\). Thus by Theorem 3, the inverse function \(f^{-1}\) (i.e., the nth root function) exists and is continuous on \(f[B]=[0,+\infty)\).
If \(n\) is odd, then \(f^{-1}\) has these properties on all of \(E^{1},\) by a similar proof; thus \(\sqrt[n]{x}\) exists for \(x \in E^{1}\).
(b) Logarithmic functions. From the example in §5, we recall that the exponential function given by
\[F(x)=a^{x} \quad(a>0)\]
is continuous and strictly monotone on \(E^{1}.\) Its inverse, \(F^{-1},\) is called the logarithmic function to the base a, denoted log. By Theorem 3, it is continuous and strictly monotone on \(F\left[E^{1}\right].\)
To fix ideas, let \(a>1,\) so \(F \uparrow\) and \(\left(F^{-1}\right) \uparrow.\) By Note 1, \(F\left[E^{1}\right]\) is an interval with endpoints \(p\) and \(r,\) where
\[p=\inf F\left[E^{1}\right]=\inf \left\{a^{x} |-\infty<x<+\infty\right\}\]
and
\[r=\sup F\left[E^{1}\right]=\sup \left\{a^{x} |-\infty<x<+\infty\right\}.\]
Now by Problem 14 (iii) of §2 (with \(q=0\)),
\[\lim _{x \rightarrow+\infty} a^{x}=+\infty \text { and } \lim _{x \rightarrow-\infty} a^{x}=0.\]
As \(F \uparrow,\) we use Theorem 1 in §5 to obtain
\[r=\sup a^{x}=\lim _{x \rightarrow+\infty} a^{x}=+\infty \text { and } p=\lim _{x \rightarrow-\infty} a^{x}=0.\]
Thus \(F\left[E^{1}\right],\) i.e., the domain of \(\log _{a},\) is the interval \((p, r)=(0,+\infty)\). It follows that \(\log _{a} x\) is uniquely defined for \(x\) in \((0,+\infty) ;\) it is called the logarithm of \(x\) to the base \(a\).
The range of log \(_{a}\left(\text { i.e. of } F^{-1}\right)\) is the same as the domain of \(F,\) i.e., \(E^{1}\). Thus if \(a>1, \log _{a} x\) increases from \(-\infty\) to \(+\infty\) as \(x\) increases from 0 to \(+\infty.\) Hence
\[\lim _{x \rightarrow+\infty} \log _{a} x=+\infty \text { and } \lim _{x \rightarrow 0+} \log _{a} x=-\infty,\]
provided \(a>1\).
If \(0<a<1,\) the values of these limits are interchanged (since \(F \downarrow\) in this case), but otherwise the results are the same.
If \(a=e,\) we write \(\ln x\) or \(\log x\) for \(\log _{a} x,\) and we call \(\ln x\) the natural logarithm of \(x.\) Its inverse is, of course, the exponential \(f(x)=e^{x},\) also written \(\exp (x).\) Thus by definition, \(\ln e^{x}=x\) and
\[x=\exp (\ln x)=e^{\ln x} \quad(0<x<+\infty).\]
(c) The power function \(g :(0,+\infty) \rightarrow E^{1}\) is defined by
\[g(x)=x^{a} \text { for a fixed real } a.\]
If \(a>0,\) we also define \(g(0)=0.\) For \(x>0,\) we have
\[x^{a}=\exp \left(\ln x^{a}\right)=\exp (a \cdot \ln x).\]
Thus by the rules for composite functions (Theorem 3 and Corollary 2 in §2), the continuity of \(g\) on \((0,+\infty)\) follows from that of exponential and log functions. If \(a>0, g\) is also continuous at \(0.\) (Exercise!)


2.13: Modern Management Theories
- Discuss modern management theories
Current management thinking incorporates ideas from administrative, behavioral, and scientific management, factoring in operating realities and available technology and considering not only the worker but the organization and larger operating environment. Two schools of thought that are particularly relevant to our times are the learning organization and quantitative management .
Learning Organizations
Author, MIT professor, and learning systems theorist Donald Schön developed the conceptual framework for the learning organization, stating that:
The loss of the stable state means that our society and all of its institutions are in continuous processes of transformation. We cannot expect new stable states that will endure for our own lifetimes. We must learn to understand, guide, influence and manage these transformations. We must make the capacity for undertaking them integral to ourselves and to our institutions. We must, in other words, become adept at learning. We must become able not only to transform our institutions, in response to changing situations and requirements; we must invent and develop institutions which are “learning systems,” that is to say, systems capable of bringing about their own continuing transformation. [1]
Author, systems scientist and MIT Sloan School of Management senior lecturer Dr. Peter Senge proposed his theory of the learning organization in his 1990 classic The Fifth Discipline , which Harvard Business Review cited as “one of the seminal management books of the past 75 years.” [2] Senge’s argument: “in the long run the only sustainable competitive advantage is your organization’s ability to learn faster than the competition.” To be clear, learning is not only a leader/manager priority; Senge states that “organizations need to ‘discover how to tap people’s commitment and capacity to learn at all levels.’” [3]
For a brief synopsis of the book, watch Miles MacFarlane’s 3-Minute summary of The Fifth Discipline:
Quantitative Management
Quantitative Management is focused on data-driven decision making. Briefly, this school of thought views management as a problem to be solved through the application of analytical tools and techniques. Developed as a technique for improving military outcomes in World War II, quantitative management uses mathematical techniques and technology—data analysis, information modeling, computer simulation—to improve decision making. The benefit of using mathematical models is the ability to systematically analyze and reduce the complexity of problems. Quantitative techniques are generally developed and used to inform management rather than as a school of management thought per se. For example, quantitative analysis can be used to identify and quantify the factors that influence decisions, providing a more informed basis for action. We’ll discuss this topic further in Module 3: People Analytics and Human Capital Trends.
- " The Learning Organization: Principles, Theories, and Practice. " infed.org. Accessed July 29, 2019. ↵
- " Peter Senge and the Learning Organization. " infed.org. Accessed July 29, 2019. ↵
- Ibid. ↵
Contributors and Attributions
- Businessman typing on a laptop. Authored by : Adeolu Eletu. Provided by : Unsplash. Located at : unsplash.com/photos/lWVoW8LpcEQ. License : CC0: No Rights Reserved . License Terms : Unsplash License
- The Fifth Discipline in Three Minutes. Authored by : Miles MacFarlane. Located at : https://youtu.be/MQMRMAmT2gg . License : All Rights Reserved . License Terms : Standard YouTube License