15.5: Anxiety Disorders
Learning Objectives
- Distinguish normal anxiety from pathological anxiety
- List and describe the major anxiety disorders, including their main features and prevalence
- Describe basic psychological and biological factors that are suspected to be important in the etiology of anxiety disorder
Everybody experiences anxiety from time to time. Although anxiety is closely related to fear, the two states possess important differences. Fear involves an instantaneous reaction to an imminent threat, whereas anxiety involves apprehension, avoidance, and cautiousness regarding a potential threat, danger, or other negative event (Craske, 1999). While anxiety is unpleasant to most people, it is important to our health, safety, and well-being. Anxiety motivates us to take actions—such as preparing for exams, watching our weight, showing up to work on time—that enable us to avert potential future problems. Anxiety also motivates us to avoid certain things—such as running up debts and engaging in illegal activities—that could lead to future trouble. Most individuals’ level and duration of anxiety approximates the magnitude of the potential threat they face. For example, suppose a single woman in her late \(30s\) who wishes to marry is concerned about the possibility of having to settle for a spouse who is less attractive and educated than desired. This woman likely would experience anxiety of greater intensity and duration than would a \(21\)-year-old college junior who is having trouble finding a date for the annual social. Some people, however, experience anxiety that is excessive, persistent, and greatly out of proportion to the actual threat; if one’s anxiety has a disruptive influence on one’s live, this is a strong indicator that the individual is experiencing an anxiety disorder.
Anxiety disorders are characterized by excessive and persistent fear and anxiety, and by related disturbances in behavior (APA, 2013). Although anxiety is universally experienced, anxiety disorders cause considerable distress. As a group, anxiety disorders are common: approximately \(25\%-30\%\) of the U.S. population meets the criteria for at least one anxiety disorder during their lifetime (Kessler et al., 2005). Also, these disorders appear to be much more common in women than they are in men; within a \(12\)-month period, around \(23\%\) of women and \(14\%\) of men will experience at least one anxiety disorder (National Comorbidity Survey, 2007).
Specific Phobia
Phobia is a Greek word that means fear. A person diagnosed with a specific phobia (formerly known as simple phobia ) experiences excessive, distressing, and persistent fear or anxiety about a specific object or situation (such as animals, enclosed spaces, elevators, or flying) (APA, 2013). Even though people realize their level of fear and anxiety in relation to the phobic stimulus is irrational, some people with a specific phobia may go to great lengths to avoid the phobic stimulus (the object or situation that triggers the fear and anxiety). Typically, the fear and anxiety a phobic stimulus elicits is disruptive to the person’s life. For example, a man with a phobia of flying might refuse to accept a job that requires frequent air travel, thus negatively affecting his career. Clinicians who have worked with people who have specific phobias have encountered many kinds of phobias, some of which are shown in Table \(\PageIndex{1}\).
| Phobia | Feared Object or Situation |
|---|---|
| Acrophobia | heights |
| Aerophobia | flying |
| Arachnophobia | spiders |
| Claustrophobia | enclosed spaces |
| Cynophobia | dogs |
| Hematophobia | blood |
| Ophidiophobia | snakes |
| Taphophobia | being buried alive |
| Trypanophobia | injections |
| Xenophobia | strangers |
Specific phobias are common; in the United States, around \(12.5\%\) of the population will meet the criteria for a specific phobia at some point in their lifetime (Kessler et al., 2005). One type of phobia, agoraphobia , is listed in the DSM-5 as a separate anxiety disorder. Agoraphobia, which literally means “fear of the marketplace,” is characterized by intense fear, anxiety, and avoidance of situations in which it might be difficult to escape or receive help if one experiences symptoms of a panic attack (a state of extreme anxiety that we will discuss shortly). These situations include public transportation, open spaces (parking lots), enclosed spaces (stores), crowds, or being outside the home alone (APA, 2013). About \(1.4\%\) of Americans experience agoraphobia during their lifetime (Kessler et al., 2005).
Acquisition of Phobias through Learning
Many theories suggest that phobias develop through learning. Rachman (1977) proposed that phobias can be acquired through three major learning pathways. The first pathway is through classical conditioning . As you may recall, classical conditioning is a form of learning in which a previously neutral stimulus is paired with an unconditioned stimulus (UCS) that reflexively elicits an unconditioned response (UCR), eliciting the same response through its association with the unconditioned stimulus. The response is called a conditioned response (CR). For example, a child who has been bitten by a dog may come to fear dogs because of her past association with pain. In this case, the dog bite is the UCS and the fear it elicits is the UCR.
The second pathway of phobia acquisition is through vicarious learning, such as modeling . For example, a child who observes his cousin react fearfully to spiders may later express the same fears, even though spiders have never presented any danger to him. This phenomenon has been observed in both humans and nonhuman primates (Olsson & Phelps, 2007). A study of laboratory-reared monkeys readily acquired a fear of snakes after observing wild-reared monkeys react fearfully to snakes (Mineka & Cook, 1993).
The third pathway is through verbal transmission or information. For example, a child whose parents, siblings, friends, and classmates constantly tell her how disgusting and dangerous snakes are may come to acquire a fear of snakes.
Interestingly, people are more likely to develop phobias of things that do not represent much actual danger to themselves, such as animals and heights, and are less likely to develop phobias toward things that present legitimate danger in contemporary society, such as motorcycles and weapons (Öhman & Mineka, 2001). Why might this be so? One theory suggests that the human brain is evolutionarily predisposed to more readily associate certain objects or situations with fear (Seligman, 1971). This theory argues that throughout our evolutionary history, our ancestors associated certain stimuli (e.g., snakes, spiders, heights, and thunder) with potential danger. As time progressed, the mind has become adapted to more readily develop fears of these things than of others. Experimental evidence has consistently demonstrated that conditioned fears develop more readily to fear-relevant stimuli (images of snakes and spiders) than to fear-irrelevant stimuli (images of flowers and berries) (Öhman & Mineka, 2001). Such prepared learning has also been shown to occur in monkeys. In one study (Cook & Mineka, 1989), monkeys watched videotapes of model monkeys reacting fearfully to either fear-relevant stimuli (toy snakes or a toy crocodile) or fear-irrelevant stimuli (flowers or a toy rabbit). The observer monkeys developed fears of the fear-relevant stimuli but not the fear-irrelevant stimuli.
Social Anxiety Disorder
Social anxiety disorder (formerly called social phobia) is characterized by extreme and persistent fear or anxiety and avoidance of social situations in which the person could potentially be evaluated negatively by others (APA, 2013). As with specific phobias, social anxiety disorder is common in the United States; a little over 12% of all Americans experience social anxiety disorder during their lifetime (Kessler et al., 2005).
The heart of the fear and anxiety in social anxiety disorder is the person’s concern that he may act in a humiliating or embarrassing way, such as appearing foolish, showing symptoms of anxiety (blushing), or doing or saying something that might lead to rejection (such as offending others). The kinds of social situations in which individuals with social anxiety disorder usually have problems include public speaking, having a conversation, meeting strangers, eating in restaurants, and, in some cases, using public restrooms. Although many people become anxious in social situations like public speaking, the fear, anxiety, and avoidance experienced in social anxiety disorder are highly distressing and lead to serious impairments in life. Adults with this disorder are more likely to experience lower educational attainment and lower earnings (Katzelnick et al., 2001), perform more poorly at work and are more likely to be unemployed (Moitra, Beard, Weisberg, & Keller, 2011), and report greater dissatisfaction with their family lives, friends, leisure activities, and income (Stein & Kean, 2000).
When people with social anxiety disorder are unable to avoid situations that provoke anxiety, they typically perform safety behaviors : mental or behavioral acts that reduce anxiety in social situations by reducing the chance of negative social outcomes. Safety behaviors include avoiding eye contact, rehearsing sentences before speaking, talking only briefly, and not talking about oneself (Alden & Bieling, 1998). Other examples of safety behaviors include the following (Marker, 2013):
- assuming roles in social situations that minimize interaction with others (e.g., taking pictures, setting up equipment, or helping prepare food)
- asking people many questions to keep the focus off of oneself
- selecting a position to avoid scrutiny or contact with others (sitting in the back of the room)
- wearing bland, neutral clothes to avoid drawing attention to oneself
- avoiding substances or activities that might cause anxiety symptoms (such as caffeine, warm clothing, and physical exercise)
Although these behaviors are intended to prevent the person with social anxiety disorder from doing something awkward that might draw criticism, these actions usually exacerbate the problem because they do not allow the individual to disconfirm his negative beliefs, often eliciting rejection and other negative reactions from others (Alden & Bieling, 1998).
People with social anxiety disorder may resort to self-medication, such as drinking alcohol, as a means to avert the anxiety symptoms they experience in social situations (Battista & Kocovski, 2010). The use of alcohol when faced with such situations may become negatively reinforcing: encouraging individuals with social anxiety disorder to turn to the substance whenever they experience anxiety symptoms. The tendency to use alcohol as a coping mechanism for social anxiety, however, can come with a hefty price tag: a number of large scale studies have reported a high rate of comorbidity between social anxiety disorder and alcohol use disorder (Morris, Stewart, & Ham, 2005).
As with specific phobias, it is highly probable that the fears inherent to social anxiety disorder can develop through conditioning experiences. For example, a child who is subjected to early unpleasant social experiences (e.g., bullying at school) may develop negative social images of herself that become activated later in anxiety-provoking situations (Hackmann, Clark, & McManus, 2000). Indeed, one study reported that 92% of a sample of adults with social anxiety disorder reported a history of severe teasing in childhood, compared to only \(35\%\) of a sample of adults with panic disorder (McCabe, Antony, Summerfeldt, Liss, & Swinson, 2003).
One of the most well-established risk factors for developing social anxiety disorder is behavioral inhibition (Clauss & Blackford, 2012). Behavioral inhibition is thought to be an inherited trait, and it is characterized by a consistent tendency to show fear and restraint when presented with unfamiliar people or situations (Kagan, Reznick, & Snidman, 1988). Behavioral inhibition is displayed very early in life; behaviorally inhibited toddlers and children respond with great caution and restraint in unfamiliar situations, and they are often timid, fearful, and shy around unfamiliar people (Fox, Henderson, Marshall, Nichols, & Ghera, 2005). A recent statistical review of studies demonstrated that behavioral inhibition was associated with more than a sevenfold increase in the risk of development of social anxiety disorder, demonstrating that behavioral inhibition is a major risk factor for the disorder (Clauss & Blackford, 2012).
Panic Disorder
Imagine that you are at the mall one day with your friends and—suddenly and inexplicably—you begin sweating and trembling, your heart starts pounding, you have trouble breathing, and you start to feel dizzy and nauseous. This episode lasts for \(10\) minutes and is terrifying because you start to think that you are going to die. When you visit your doctor the following morning and describe what happened, she tells you that you have experienced a panic attack (See figure \(\PageIndex{1}\)). If you experience another one of these episodes two weeks later and worry for a month or more that similar episodes will occur in the future, it is likely that you have developed panic disorder.
People with panic disorder experience recurrent (more than one) and unexpected panic attacks, along with at least one month of persistent concern about additional panic attacks, worry over the consequences of the attacks, or self-defeating changes in behavior related to the attacks (e.g., avoidance of exercise or unfamiliar situations) (APA, 2013). As is the case with other anxiety disorders, the panic attacks cannot result from the physiological effects of drugs and other substances, a medical condition, or another mental disorder. A panic attack is defined as a period of extreme fear or discomfort that develops abruptly and reaches a peak within \(10\) minutes. Its symptoms include accelerated heart rate, sweating, trembling, choking sensations, hot flashes or chills, dizziness or lightheadedness, fears of losing control or going crazy, and fears of dying (APA, 2013). Sometimes panic attacks are expected, occurring in response to specific environmental triggers (such as being in a tunnel); other times, these episodes are unexpected and emerge randomly (such as when relaxing). According to the DSM-5, the person must experience unexpected panic attacks to qualify for a diagnosis of panic disorder.
Experiencing a panic attack is often terrifying. Rather than recognizing the symptoms of a panic attack merely as signs of intense anxiety, individuals with panic disorder often misinterpret them as a sign that something is intensely wrong internally (thinking, for example, that the pounding heart represents an impending heart attack). Panic attacks can occasionally precipitate trips to the emergency room because several symptoms of panic attacks are, in fact, similar to those associated with heart problems (e.g., palpitations, racing pulse, and a pounding sensation in the chest) (Root, 2000). Unsurprisingly, those with panic disorder fear future attacks and may become preoccupied with modifying their behavior in an effort to avoid future panic attacks. For this reason, panic disorder is often characterized as fear of fear (Goldstein & Chambless, 1978).
Panic attacks themselves are not mental disorders. Indeed, around \(23\%\) of Americans experience isolated panic attacks in their lives without meeting the criteria for panic disorder (Kessler et al., 2006), indicating that panic attacks are fairly common. Panic disorder is, of course, much less common, afflicting \(4.7\%\) of Americans during their lifetime (Kessler et al., 2005). Many people with panic disorder develop agoraphobia, which is marked by fear and avoidance of situations in which escape might be difficult or help might not be available if one were to develop symptoms of a panic attack. People with panic disorder often experience a comorbid disorder, such as other anxiety disorders or major depressive disorder (APA, 2013).
Researchers are not entirely sure what causes panic disorder. Children are at a higher risk of developing panic disorder if their parents have the disorder (Biederman et al., 2001), and family and twins studies indicate that the heritability of panic disorder is around \(43\%\) (Hettema, Neale, & Kendler, 2001). The exact genes and gene functions involved in this disorder, however, are not well-understood (APA, 2013). Neurobiological theories of panic disorder suggest that a region of the brain called the locus coeruleus may play a role in this disorder. Located in the brainstem, the locus coeruleus is the brain’s major source of norepinephrine, a neurotransmitter that triggers the body’s fight-or-flight response. Activation of the locus coeruleus is associated with anxiety and fear, and research with nonhuman primates has shown that stimulating the locus coeruleus either electrically or through drugs produces panic-like symptoms (Charney et al., 1990). Such findings have led to the theory that panic disorder may be caused by abnormal norepinephrine activity in the locus coeruleus (Bremner, Krystal, Southwick, & Charney, 1996).
Conditioning theories of panic disorder propose that panic attacks are classical conditioning responses to subtle bodily sensations resembling those normally occurring when one is anxious or frightened (Bouton, Mineka, & Barlow, 2001). For example, consider a child who has asthma. An acute asthma attack produces sensations, such as shortness of breath, coughing, and chest tightness, that typically elicit fear and anxiety. Later, when the child experiences subtle symptoms that resemble the frightening symptoms of earlier asthma attacks (such as shortness of breath after climbing stairs), he may become anxious, fearful, and then experience a panic attack. In this situation, the subtle symptoms would represent a conditioned stimulus, and the panic attack would be a conditioned response. The finding that panic disorder is nearly three times as frequent among people with asthma as it is among people without asthma (Weiser, 2007) supports the possibility that panic disorder has the potential to develop through classical conditioning.
Cognitive factors may play an integral part in panic disorder. Generally, cognitive theories (Clark, 1996) argue that those with panic disorder are prone to interpret ordinary bodily sensations catastrophically, and these fearful interpretations set the stage for panic attacks. For example, a person might detect bodily changes that are routinely triggered by innocuous events such getting up from a seated position (dizziness), exercising (increased heart rate, shortness of breath), or drinking a large cup of coffee (increased heart rate, trembling). The individual interprets these subtle bodily changes catastrophically (“Maybe I’m having a heart attack!”). Such interpretations create fear and anxiety, which trigger additional physical symptoms; subsequently, the person experiences a panic attack. Support of this contention rests with findings that people with more severe catastrophic thoughts about sensations have more frequent and severe panic attacks, and among those with panic disorder, reducing catastrophic cognitions about their sensations is as effective as medication in reducing panic attacks (Good & Hinton, 2009).
Generalized Anxiety Disorder
Alex was always worried about many things. He worried that his children would drown when they played at the beach. Each time he left the house, he worried that an electrical short circuit would start a fire in his home. He worried that his wife would lose her job at the prestigious law firm. He worried that his daughter’s minor staph infection could turn into a massive life-threatening condition. These and other worries constantly weighed heavily on Alex’s mind, so much so that they made it difficult for him to make decisions and often left him feeling tense, irritable, and worn out. One night, Alex’s wife was to drive their son home from a soccer game. However, his wife stayed after the game and talked with some of the other parents, resulting in her arriving home \(45\) minutes late. Alex had tried to call his cell phone three or four times, but he could not get through because the soccer field did not have a signal. Extremely worried, Alex eventually called the police, convinced that his wife and son had not arrived home because they had been in a terrible car accident.
Alex suffers from generalized anxiety disorder : a relatively continuous state of excessive, uncontrollable, and pointless worry and apprehension. People with generalized anxiety disorder often worry about routine, everyday things, even though their concerns are unjustified (See figure \(\PageIndex{2}\)). For example, an individual may worry about her health and finances, the health of family members, the safety of her children, or minor matters (e.g., being late for an appointment) without having any legitimate reason for doing so (APA, 2013). A diagnosis of generalized anxiety disorder requires that the diffuse worrying and apprehension characteristic of this disorder—what Sigmund Freud referred to as free-floating anxiety—is not part of another disorder, occurs more days than not for at least six months, and is accompanied by any three of the following symptoms: restlessness, difficulty concentrating, being easily fatigued, muscle tension, irritability, and sleep difficulties.
About \(5.7\%\) of the U.S. population will develop symptoms of generalized anxiety disorder during their lifetime (Kessler et al., 2005), and females are \(2\) times as likely as males to experience the disorder (APA, 2013). Generalized anxiety disorder is highly comorbid with mood disorders and other anxiety disorders (Noyes, 2001), and it tends to be chronic. Also, generalized anxiety disorder appears to increase the risk for heart attacks and strokes, especially in people with preexisting heart conditions (Martens et al., 2010).
Although there have been few investigations aimed at determining the heritability of generalized anxiety disorder, a summary of available family and twin studies suggests that genetic factors play a modest role in the disorder (Hettema et al., 2001). Cognitive theories of generalized anxiety disorder suggest that worry represents a mental strategy to avoid more powerful negative emotions (Aikins & Craske, 2001), perhaps stemming from earlier unpleasant or traumatic experiences. Indeed, one longitudinal study found that childhood maltreatment was strongly related to the development of this disorder during adulthood (Moffitt et al., 2007); worrying might distract people from remembering painful childhood experiences.
Summary
Anxiety disorders are a group of disorders in which a person experiences excessive, persistent, and distressing fear and anxiety that interferes with normal functioning. Anxiety disorders include specific phobia: a specific unrealistic fear; social anxiety disorder: extreme fear and avoidance of social situations; panic disorder: suddenly overwhelmed by panic even though there is no apparent reason to be frightened; agoraphobia: an intense fear and avoidance of situations in which it might be difficult to escape; and generalized anxiety disorder: a relatively continuous state of tension, apprehension, and dread.
Glossary
- agoraphobia
- anxiety disorder characterized by intense fear, anxiety, and avoidance of situations in which it might be difficult to escape if one experiences symptoms of a panic attack
- anxiety disorder
- characterized by excessive and persistent fear and anxiety, and by related disturbances in behavior
- generalized anxiety disorder
- characterized by a continuous state of excessive, uncontrollable, and pointless worry and apprehension
- locus coeruleus
- area of the brainstem that contains norepinephrine, a neurotransmitter that triggers the body’s fight-or-flight response; has been implicated in panic disorder
- panic attack
- period of extreme fear or discomfort that develops abruptly; symptoms of panic attacks are both physiological and psychological
- panic disorder
- anxiety disorder characterized by unexpected panic attacks, along with at least one month of worry about panic attacks or self-defeating behavior related to the attacks
- safety behavior
- mental and behavior acts designed to reduce anxiety in social situations by reducing the chance of negative social outcomes; common in social anxiety disorder
- social anxiety disorder
- characterized by extreme and persistent fear or anxiety and avoidance of social situations in which one could potentially be evaluated negatively by others
- specific phobia
- anxiety disorder characterized by excessive, distressing, and persistent fear or anxiety about a specific object or situation
Contributors and Attributions
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


4.21: Putting It Together- Marketing Strategy
Since Southwest Airlines is a familiar example by now, let’s do a more complete review of its strategy to help with your assignments in this course.
In this module we have focused on the following aspects of marketing planning:
- Evaluate marketing strategies for alignment with the organization’s corporate strategies
- Show how common analytic tools are used to inform the organization’s strategy
- Explain inputs and components of a marketing strategy
- Give examples of corporate strategies
- Explain how the development and maintenance of customer relationships are an essential part of an organization’s marketing strategy
The summary below shows one analysis of the planning process for Southwest Airlines:
Corporate Strategy
Southwest Airlines’ strategy is driven by its mission .
The mission of Southwest Airlines is dedication to the highest quality of customer service delivered with a sense of warmth, friendliness, individual pride, and company spirit.footnote]www.southwest.com/html/about...st/[/footnote]
Note: Southwest Airlines’ mission is not limited to a focus on leisure travel or even air travel. Rather, the company is driven by a mission to provide the best customer service across all sectors.
A Fortune magazine article describes Southwest’s unique profile in the airline industry:
Starting with just four planes flying to three Texas cities on June 18, 1971, [co-founder Herb] Kelleher built a maverick operation that prided itself on charting a different route from other airlines. It wooed passengers with ultra-friendly onboard service, squeezed more flights a day from every plane, and made money not by raising fares but by lowering them—and hence filling seats with folks who could never before afford to fly. Along the way Southwest evolved from an upstart to a colossus that last year carried 134 million passengers in the U.S., more than any other airline and some 20% of the total. In an industry in which every other major company has gone through bankruptcy, Southwest has never gotten close to Chapter 11 and has made money for 42 straight years. [1]
Despite this success, Southwest airlines found its revenue per customer to be low, so it launched a strategy to attract higher-revenue business customers.
Objective : raise the portion of business customers on Southwest from 35% to 40% during the five-year period from 2014 to 2019.
Note: In a competitive industry such as the airlines industry, it is remarkably difficult to gain 1% of market share. Often organizations track .1% and .01% changes.
Analysis Tools
In order to achieve the company objective Southwest needs to bring its strengths to new customers in a way that addresses both its own weaknesses and those of competitors (which create opportunities).
SWOT Analysis
Southwest’s SWOT analysis, below, identifies a number of opportunities and challenges:
Strengths
- Exceptional customer loyalty among price-conscious leisure travelers.
- Strong customer service culture throughout organization.
- Dominance among regional airports and short trip segments.
Weaknesses
- Lower revenue per passenger than competitors.
- Limited offerings on lucrative “long-haul” flight routes.
- Low awareness among business travelers who exhibit strong loyalties to airlines with frequent traveler programs.
- Product offering emphasizes convenience at the expense of fringe benefits.
Opportunities
- Low customer satisfaction ratings of airlines that serve business travelers. [2]
- Increasing monitoring of corporate travel costs by boards and shareholders as an example of excessive perks.
- Increasing costs (threat) have less impact per customer if Southwest can attract new segments of customers that competitors are already serving.
Threats
- Competitor dominance of business hubs such as Atlanta, Minneapolis, and Chicago.
- Increasing fuel costs and labor costs impacting the industry.
Strategic Opportunities Matrix
With its objective to raise its share of business customers, Southwest decided to enter a new market. Is this a market development or a diversification strategy? Is the business traveler buying a different product, or benefiting from different promotion and pricing? In this case, Southwest made the choice to pursue a market development strategy that emphasized pricing, promotion, and distribution rather than making significant changes in its product (by refitting planes to add first-class seats or creating new flights for business travelers, e.g.).
Southwest’s company mission likely played a guiding role in arriving at this decision. The airline’s focus on providing great customer service means that it’s less interested in bringing a new product to market than in taking “amazing customer service” to a new market—i.e., the business traveler.
4 Growth Strategies: The Strategic Opportunities Matrix
The following is a list of the four growth strategies in the Strategic Opportunities Matrix:
- Market Penetration Strategy: New market and current product
- Product Development Strategy: New market and new product
- Market Development Strategy: Current market and current product
- Diversification Strategy : Current market and new product
Components of the Marketing Strategy
In order to appeal to corporate customers, Southwest must focus all elements of the marketing mix on a new target customer that is less cost-conscious and less patient with the inconveniences of travel.
Marketing Mix
Southwest did not implement a separate strategy for each of the four Ps. Instead, it brought the elements of the marketing mix together into major initiatives that touch all aspects of the marketing mix. We are going to explore two of those marketing strategies here.
The Business Select Offering
Southwest’s Business Select provides an additional layer of service that emphasizes the convenience and comfort that business travelers require, at a higher price. A traveler from Los Angeles to Norfolk, Virginia, can select a budget fare of $351 or a Business Select fare of $583. For the higher price the customer gets early boarding, access to faster check-in and security clearance, a free alcoholic beverage, and extra frequent-flyer points. The price is $232 higher for travelers who are willing to pay for these conveniences. For a lower price, travelers can buy only EarlyBird check-in, which moves them to the front of the boarding line but does not include the additional features.
The marketing mix includes a new price point, and a series of new services that are packaged in one new offering. It is worth noting that competitor airlines provide these benefits to their frequent flyers through free first-class upgrades for unfilled seats in first class. On those airlines, first-class passengers also get a higher class of customer service. Southwest has found a way to introduce a higher price and provide a comparable set of benefits to business travelers, while leveraging the customer service it provides to all travelers.
SWABiz
For leisure travelers, Southwest only sells tickets through its own distribution channel—its phone line and Web site. Many other airlines also sell through distributors such as Expedia, Hotwire, and CheapTrips, which all require additional discounting to cover their mark-up on the ticket price. Instead, Southwest has kept its fares lower and drawn customers to its own Web site to make purchases.
In the SWOT analysis, we see that Southwest does not have good awareness among business customers. How can it draw business customers to its Web site or get to the places where business travelers will book? SWABiz was the solution. SWABiz provides a free travel-booking and management tool for companies that do the majority of their travel on Southwest. It provides companies that often book travel for their employees (or direct employees to a single place to book) with a tool to manage flights, hotels, and car rentals. SWABiz also enables participating companies to monitor spending and enforce corporate travel policies.
Southwest also expanded its distribution network for corporate travelers. The company sells flights through Concur, a travel-booking and management system used by many corporate travel organizations that want to book across many airlines.
SWABiz is a new distribution strategy that creates an opportunity to promote its business offering to corporate travel offices and managers.
Through these marketing strategies Southwest is building a network of business customers who have a relationship with the airline. Southwest’s frequent-flyer program creates an opportunity to track customers’ purchases and preferences and to bring this understanding into future strategies and plans.
Evaluation
Are these strategies successful? Southwest Airlines is actively monitoring its progress in attracting business travelers and adjusting its strategy accordingly. As with most aggressive strategies that span multiple years, the results are mixed, and there is room for new approaches.
Southwest’s chief operating officer, Robert Jordan, sees the potential: “The combination of these factors has led to “double-digit growth” year-after-year in managed corporate bookings.” He adds, “[O]ur [Southwest’s] corporate business is growing faster than our base business.” [3]
CEO Gary Kelly acknowledges that there is still work to do, noting that it is not yet adding enough business travelers to its fare mix. From the first half of 2012 to the same period in 2015, Southwest’s average passenger fare increased just 6%, to $158, even though it was adding longer flights to lure business customers.” [4]
Southwest has begun a strategy of adding more long-haul flights to its schedule, entering new airports, and competing head-to-head with its competitors in America’s busiest airports. The work of defining, implementing, measuring, and adjusting strategies is never done.
- fortune.com/2015/09/23/southwest-airlines-business-travel/ ↵
- www.jdpower.com/press-releases/2015-north-america-airline-satisfaction-study#_ftnref2 ↵
- http://www.forbes.com/sites/airchive/2014/04/22/southwest-airlines-opens-for-business-customers/ ↵
- http://fortune.com/2015/09/23/southwest-airlines-business-travel/ ↵
Contributors and Attributions
- Putting It Together: Marketing Strategy. Provided by : Lumen Learning. License : CC BY: Attribution


23.9: Mixed Claisen Condensations
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Objectives
After completing this section, you should be able to
- write an equation to illustrate a mixed Claisen condensation.
- identify the structural features that should be present in the two esters if a mixed Claisen condensation is to be successful.
- determine whether a given pair of esters is likely to produce a good yield of a single product when subjected to a mixed Claisen condensation.
- identify the product formed when a given pair of esters is used in a mixed Claisen condensation.
- identify the esters that should be used to produce a given β ‑keto ester by a mixed Claisen condensation.
- write an equation to illustrate the formation of a β ‑diketone through a mixed Claisen‑type condensation between an ester and a ketone.
- identify the β ‑diketone formed as the result of a mixed Claisen‑type condensation between a given ester and a given ketone.
- identify the reagents necessary to synthesize a given β ‑diketone by a mixed Claisen‑type condensation between an ester and a ketone.
- write detailed mechanisms for mixed Claisen reactions and reactions that are related to the mixed Claisen reaction, including those in which both reacting moieties are present in the same compound.
Study Notes
Just as we can react together two different aldehydes or ketones in a mixed aldol condensation, so can we react together two different esters in a mixed (or “crossed”) Claisen condensation. Again, by carefully selecting our substrates we can obtain a good yield of the desired product and minimize the number of possible by‑products. Note that even if we replace one of the esters with a ketone, the reaction is still referred to as Claisen condensation. The important thing to realize as you study these reactions is that they all take place by essentially the same mechanism—attack by an enolate anion on a carbonyl group.
Crossed Claisen Condensation
Claisen condensations between different ester reactants are called Crossed Claisen reactions. Crossed Claisen reactions in which both reactants can serve as Claisen donors and Claisen acceptors generally give complex mixtures which are difficult to separate.
To avoid complex mixtures most Crossed Claisen reactions are usually not successful unless one of the two esters has no alpha-hydrogens as in the following examples.
This forces the ester with alpha-hydrogens to be the Claisen donor (enolate) and the ester without alpha-hydrogens to be the Claisen acceptor (electrophile). Even with this differentiation, it is possible for the ester with alpha-hydrogens to undergo a Claisen Condensation with itself to produce an unwanted side-product. This is typically partially prevented by using the ester without alpha-hydrogens in a large excess.
Example: No Alpha Hydrogens
Another type of crossed Claisen condensation occurs when a ketone is reacted with an ester. The use of an ester without alpha-hydrogens is not necessary due to the greater reactivity of the ketone. The alpha-hydrogens of the ketone are much more acidic (pKa~20) than those of the ester (pKa~25). The alpha hydrogens of ketone will be preferably deprotonated to make it the enolate Claisen donor. The ester will therefore be the electrophilic Claisen acceptor and is likewise commonly used in a large excess. There is still a possibility of the ketone reacting with itself to form the product of an aldol reaction however the equilibrium is unfavorable. Also, the formation of the aldol product is reversible due to its lack of an acidic alpha hydrogen. The beta-diketone Claisen product can be irreversibly deprotonated due to its more acidic alpha-hydrogens, making it the reaction’s main product.
Example: Ester with Ketone
Planing a Synthesis using a Claisen or Crossed Claisen-like Reaction
A Claisen reaction should be considered for a synthesis pathway if the target molecule contains a beta-keto esters, a beta-aldo ester or a beta-dicarbonyl.
A beta-keto ester or a beta-aldo ester could possibly be made by a Claisen condensation of two esters. A beta-dicarbonyl could possibly be made by a Claisen-like condensation between a ketone and an ester. Here, the key bond cleavage is a C-C bond between one of the carbonyls and the alpha-carbon which lies between the carbonyl. In each of these situations there are two such C-C bonds so there will be two possible pathways to consider. After the C-C bond cleavage the fragment with the alpha-carbon will gain a hydrogen. The fragment with the bare carbonyl will gain an –OR group to become an ester. The –OR group added will be the same as any ester present in the target molecule. If none are present –OCH 2 CH 3 is typically used.
A similar analysis can be performed on a 1,3-diketone and will be presented in the worked example below.
Example \(\PageIndex{1}\)
Show how the following molecule can be made using a Claisen-like condensation.
Pathway 1
Answer Pathway 1
Pathway 2
Answer Pathway 2
Exercise \(\PageIndex{1}\)
Draw the product of the following reactions:
- Answers
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5.1: Why It Matters- Relationships in Categorical Data with Intro to Probability
Why understand the relationships within categorical data?
Before we begin Relationships in Categorical Data with Intro to Probability , it is helpful to consider how it relates to the work we have already done in previous modules.
At the start of Summarizing Data Graphically and Numerically , we stated the difference between quantitative and categorical variables:
- Quantitative variables have numeric values that can be averaged. A quantitative variable is frequently a measurement – for example, a person’s height in inches.
- Categorical variables are variables that can have one of a limited number of values, or labels. Values that can be represented by categorical variables include, for example, a person’s eye color, gender, or home state; a vehicle’s body style (sedan, SUV, minivan, etc.); a dog’s breed (bulldog, greyhound, beagle, etc.).
The remainder of Summarizing Data Graphically and Numerically focused on describing the overall pattern (shape, center, and spread) of the distribution of a quantitative variable.
In and Examining Relationships: Quantitative Data and Nonlinear Models , our goal was to identify and model the relationship between two quantitative variables.
Now, in this module, we turn our full attention back to categorical variables. Our objective is to study the relationship between two categorical variables. Just as in Examining Relationships: Quantitative Data and Nonlinear Models , we will be looking for patterns in the data.
As we organize and analyze data from two categorical variables, we make extensive use of two-way tables . Two-way tables for two categorical variables are in some ways like scatterplots for two quantitative variables: they give us a useful snapshot of all of the data organized in terms of the two variables of interest. This will be helpful in finding and comparing patterns. This part of Relationships in Categorical Data with Intro to Probability is exploratory data analysis in the Big Picture of Statistics.
A second important objective of this module is to introduce you to the concept of probability . Two-way tables give us a practical context for talking about probability. We also use two-way tables to help us visualize and solve real-world problems involving probability. This part of the module is part of probability in the Big Picture of Statistics.
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


3.10: Test Yourself- Answers
1. What is the apical pulse rate?
Listen to the audio-clip of the apical pulse. Count the pulse for 30 seconds and report the rate as beats per minute (NOTE: although this clip only allows you to count for 30 seconds, remember, it is best to count the apical pulse for one minute).
The pulse rate is 76 bpm (38 x 2) with a regular rhythm
2. What is the apical pulse rate?
The pulse rate is 114 bpm (57 x 2) with a regular rhythm
2. How should a healthcare provider respond when a newborn has an apical heart rate of 120 beats per minute?
a. Re-take the rate at the brachial location
b. Document the rate and assess it as normal **
c. Document the rate and identify it as tachycardia
d. Notify the physician and identify it as bradycardia
Rationale: The correct answer is b (document the rate and assess it as normal). An apical heart rate of 120 bpm falls within the normal range for newborns. Newborns have a faster apical heart rate than adults because they have smaller and less muscular hearts. As a result, their stroke volume (volume of blood per contraction) is smaller than that of adults and their hearts must beat faster to pump sufficient blood, oxygen, and nutrients to the body.
3. Which findings in an adolescent client is of most concern to a healthcare provider?
a. Pulse 40 bpm and respiration 34 **
b. Respiration 16 and pulse 82 bpm
c. Pulse 68 bpm and sinus arrhythmia
d. Pulse 2+, 78 bpm, and regular rhythm
Rationale: The correct answer is a (pulse 40 bpm and respiration 34). In adolescents, a pulse of 40 bpm is low and a respiration rate of 34 is high. All of the other findings are normal for adolescents, including sinus arrhythmia, which is common in children and adolescents.
4. Match the findings that are typically normal for the person listed:
Bradycardia——————-Athlete
Abdominal breather———Newborn
Sinus arrhythmia————Adolescent
Rationale: Bradycardia (low pulse) is common in athletes because their hearts are more muscular and pump a larger stroke volume per contraction. As a result, the heart contracts/beats less to pump sufficient blood, oxygen and nutrients. Newborns are abdominal breathers, meaning that the abdomen moves up and down when breathing, as opposed to the thorax. Sinus arrhythmia is common in adolescents. It involves an irregular pulse rhythm in which the pulse rate varies with the respiratory cycle; the heart speeds up at inspiration and decreases back to normal upon expiration. The underlying physiology of sinus arrhythmia is that the heart rate increases to compensate for the decreased stroke volume from the left side of the heart upon inspiration.


Chapter 12
The instantaneous rate is the rate of a reaction at any particular point in time, a period of time that is so short that the concentrations of reactants and products change by a negligible amount. The initial rate is the instantaneous rate of reaction as it starts (as product just begins to form). Average rate is the average of the instantaneous rates over a time period.
(a) average rate, 0 − 10 s = 0.0375 mol L −1 s −1 ; average rate, 10 − 20 s = 0.0265 mol L −1 s −1 ; (b) instantaneous rate, 15 s = 0.023 mol L −1 s −1 ; (c) average rate for B formation = 0.0188 mol L −1 s −1 ; instantaneous rate for B formation = 0.012 mol L −1 s −1
Higher molarity increases the rate of the reaction. Higher temperature increases the rate of the reaction. Smaller pieces of magnesium metal will react more rapidly than larger pieces because more reactive surface exists.
(a) Depending on the angle selected, the atom may take a long time to collide with the molecule and, when a collision does occur, it may not result in the breaking of the bond and the forming of the other. (b) Particles of reactant must come into contact with each other before they can react.
(a) very slow; (b) As the temperature is increased, the reaction proceeds at a faster rate. The amount of reactants decreases, and the amount of products increases. After a while, there is a roughly equal amount of BC , AB , and C in the mixture and a slight excess of A .
(a) 2; (b) 1
(a) The process reduces the rate by a factor of 4. (b) Since CO does not appear in the rate law, the rate is not affected.
4.3 10 −5 mol/L/s
7.9 10 −13 mol/L/year
rate = k ; k = 2.0 10 −2 mol L −1 h −1 (about 0.9 g L −1 h −1 for the average male); The reaction is zero order.
rate = k [NOCl] 2 ; k = 8.0 10 −8 L/mol/h; second order
rate = k [NO] 2 [Cl 2 ]; k = 9.1 L 2 mol −2 h −1 ; second order in NO; first order in Cl 2
(a) The rate law is second order in A and is written as rate = k [ A ] 2 . (b) k = 7.88 10 −3 L mol −1 s −1
(a) 2.5 10 −4 mol/L/min
rate = k [I − ][OCl − ]; k = 6.1 10 −2 L mol −1 s −1
Plotting a graph of ln[SO 2 Cl 2 ] versus t reveals a linear trend; therefore we know this is a first-order reaction:
k = 2.20 10 –5 s −1
The plot is nicely linear, so the reaction is second order. k = 50.1 L mol −1 h −1
14.3 d
8.3 10 7 s
0.826 s
The reaction is first order. k = 1.0 10 7 L mol −1 min −1
1.16 × 10 3 s ; 20% remains
252 days
| [ A ] 0 ( M ) | k 10 3 (s −1 ) |
|---|---|
| 4.88 | 2.45 |
| 3.52 | 2.51 |
| 2.29 | 2.53 |
| 1.81 | 2.58 |
| 5.33 | 2.36 |
| 4.05 | 2.47 |
| 2.95 | 2.48 |
| 1.72 | 2.43 |
The reactants either may be moving too slowly to have enough kinetic energy to exceed the activation energy for the reaction, or the orientation of the molecules when they collide may prevent the reaction from occurring.
The activation energy is the minimum amount of energy necessary to form the activated complex in a reaction. It is usually expressed as the energy necessary to form one mole of activated complex.
After finding k at several different temperatures, a plot of ln k versus gives a straight line with the slope from which E a may be determined.
(a) 4-times faster (b) 128-times faster
43.0 kJ/mol
177 kJ/mol
E a = 108 kJ; A = 2.0 10 8 s −1 ; k = 3.2 10 −10 s −1 ; (b) 1.81 10 8 h or 7.6 10 6 day; (c) Assuming that the reaction is irreversible simplifies the calculation because we do not have to account for any reactant that, having been converted to product, returns to the original state.
The A atom has enough energy to react with BC ; however, the different angles at which it bounces off of BC without reacting indicate that the orientation of the molecule is an important part of the reaction kinetics and determines whether a reaction will occur.
No. In general, for the overall reaction, we cannot predict the effect of changing the concentration without knowing the rate law. Yes. If the reaction is an elementary reaction, then doubling the concentration of A doubles the rate.
Rate = k [ A ][ B ] 2 ; Rate = k [ A ] 3
(a) Rate 1 = k [O 3 ]; (b) Rate 2 = k [O 3 ][Cl]; (c) Rate 3 = k [ClO][O]; (d) Rate 2 = k [O 3 ][NO]; (e) Rate 3 = k [NO 2 ][O]
(a) Doubling [H 2 ] doubles the rate. [H 2 ] must enter the rate law to the first power. Doubling [NO] increases the rate by a factor of 4. [NO] must enter the rate law to the second power. (b) Rate = k [NO] 2 [H 2 ]; (c) k = 5.0 10 3 mol −2 L −2 min −1 ; (d) 0.0050 mol/L; (e) Step II is the rate-determining step. If step I gives N 2 O 2 in adequate amount, steps 1 and 2 combine to give This reaction corresponds to the observed rate law. Combine steps 1 and 2 with step 3, which occurs by supposition in a rapid fashion, to give the appropriate stoichiometry.
The general mode of action for a catalyst is to provide a mechanism by which the reactants can unite more readily by taking a path with a lower reaction energy. The rates of both the forward and the reverse reactions are increased, leading to a faster achievement of equilibrium.
(a) Chlorine atoms are a catalyst because they react in the second step but are regenerated in the third step. Thus, they are not used up, which is a characteristic of catalysts. (b) NO is a catalyst for the same reason as in part (a).
The lowering of the transition state energy indicates the effect of a catalyst. (a) B; (b) B
The energy needed to go from the initial state to the transition state is (a) 10 kJ; (b) 10 kJ.
Both diagrams describe two-step, exothermic reactions, but with different changes in enthalpy, suggesting the diagrams depict two different overall reactions.


23.12.2: Thought Questions
Thought Questions
Arrange the following stars in order of their evolution:
- A star with no nuclear reactions going on in the core, which is made primarily of carbon and oxygen.
- A star of uniform composition from center to surface; it contains hydrogen but has no nuclear reactions going on in the core.
- A star that is fusing hydrogen to form helium in its core.
- A star that is fusing helium to carbon in the core and hydrogen to helium in a shell around the core.
- A star that has no nuclear reactions going on in the core but is fusing hydrogen to form helium in a shell around the core.
17.
Would you expect to find any white dwarfs in the Orion Nebula? (See The Birth of Stars and the Discovery of Planets outside the Solar System to remind yourself of its characteristics.) Why or why not?
18.
Suppose no stars more massive than about 2 M Sun had ever formed. Would life as we know it have been able to develop? Why or why not?
19.
Would you be more likely to observe a type II supernova (the explosion of a massive star) in a globular cluster or in an open cluster? Why?
20.
Astronomers believe there are something like 100 million neutron stars in the Galaxy, yet we have only found about 2000 pulsars in the Milky Way. Give several reasons these numbers are so different. Explain each reason.
21.
Would you expect to observe every supernova in our own Galaxy? Why or why not?
22.
The Large Magellanic Cloud has about one-tenth the number of stars found in our own Galaxy. Suppose the mix of high- and low-mass stars is exactly the same in both galaxies. Approximately how often does a supernova occur in the Large Magellanic Cloud?
23.
Look at the list of the nearest stars in Appendix I. Would you expect any of these to become supernovae? Why or why not?
24.
If most stars become white dwarfs at the ends of their lives and the formation of white dwarfs is accompanied by the production of a planetary nebula, why are there more white dwarfs than planetary nebulae in the Galaxy?
25.
If a 3 and 8 M Sun star formed together in a binary system, which star would:
- Evolve off the main sequence first?
- Form a carbon- and oxygen-rich white dwarf?
- Be the location for a nova explosion?
26.
You have discovered two star clusters. The first cluster contains mainly main-sequence stars, along with some red giant stars and a few white dwarfs.  What are the relative ages of the clusters? How did you determine your answer?
27.
A supernova remnant was recently discovered and found to be approximately 150 years old. Provide possible reasons that this supernova explosion escaped detection.
28.
Based upon the evolution of stars, place the following elements in order of least to most common in the Galaxy: gold, carbon, neon. What aspects of stellar evolution formed the basis for how you ordered the elements?
29.
What observations or types of telescopes would you use to distinguish a binary system that includes a main-sequence star and a white dwarf star from one containing a main-sequence star and a neutron star?
30.
How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.


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2: Topics in General Chemistry II
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2.1: The Structure of Atoms
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Atoms are composed of three main subatomic particles: protons, neutrons, and electrons. Protons and neutrons are grouped together in the nucleus of an atom, while electrons orbit about the nucleus.
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2.2: The Elements
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All matter is composed of elements. Chemical elements are represented by a one- or two-letter symbol.
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2.3: Atomic Number and Mass Number
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Elements can be identified by their atomic number and mass number. Isotopes are atoms of the same element that have different mass number.
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2.4: Atomic Weight
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Atoms have a mass that is based largely on the number of protons and neutrons in their nucleus.
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2.5: The Periodic Table
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The chemical elements are arranged in a chart called the periodic table. Some characteristics of the elements are related to their position on the periodic table.
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2.6: Valence Electrons and Electron Dot Formula
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The number of valence electrons for a main group element is the same as the group number of the element. This information is represented as electron dot structure.
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2.7: The Mole and Mole-Mass Conversions
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Chemists use the term mole to represent a large number of atoms or molecules just as a dozen implies 12 things. Since the mole is a very large number, we use mass to keep track rather than by counting individual atoms.
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2.8: Physical and Chemical Properties and Changes
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A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. A chemical property describes the ability of a substance to undergo a change to form new substances.
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2.9: End of Chapter Problems
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This problem set is based on Chapter 2 topics.


8.1: Overview and Purpose
Overview and Purpose
This lab involves a nature walk to provide students an opportunity to spend time in nature and learn about the environment. The walk promotes local environmental awareness and encourages individuals to appreciate the natural world in terms of ecosystems, the interdependence of living organisms, climatic changes, and the importance of biodiversity.
Learning Outcomes
- Increased knowledge and understanding of the local flora and fauna, including their characteristics, habitats, and ecological roles.
- Improved awareness of the natural environment and the importance of preserving it for future generations.
- Enhanced appreciation for the beauty and diversity of nature, leading to a more positive attitude towards the natural world.
- To provide participants with an opportunity to observe and learn about the local flora and fauna, including their characteristics, habitats, microclimates, and ecological roles.
- To promote environmental awareness and encourage participants to appreciate the natural world and its importance for human well-being.
Vocabulary
Producer
Primary consumer
Secondary consumer
Decomposer
Autotroph
Heterotroph
Food web
Photosynthesis
Cell respiration
Population
Community


17.5: Area Moments of Inertia via Integration
Area moments of inertia are used in engineering mechanics courses to determine a body's resistance to bending loads or torsional loads. Specifically, the area moment of inertia refers to the second area moment integral of a shape, with \(I_{xx}\) representing the moment of inertia about the \(x\)-axis, \(I_{yy}\) representing the moment of inertia about the \(y\)-axis, and \(J_{zz}\) (also called the polar moment of inertia) representing the moment of inertia about the \(z\)-axis. The moment of inertia about each axis represents the shapes resistance to a moment applied about that respective axis. Moments about the \(x\)- and \(y\)-axes would tend to bend an object, while moments about the \(z\)-axis would tend to twist the body.
Just as with centroids, each of these moments of inertia can be calculated via integration or by using the method of composite parts and the parallel axis theorem . On this page we are going to focus on calculating the area moments of inertia via moment integrals.
Bending Stresses and the Second Area Moment
When an object is subjected to a bending moment, that body will experience both internal tensile stresses and compressive stresses as shown in the diagram below. These stresses exert a net moment to counteract the loading moment, but exert no net force so that the body remains in equilibrium.
As we can see in the diagram, there is some central plane along which there are no tensile or compressive stresses. This is known as the neutral surface, and if there are no other forces present it will run through the centroid of the cross section. As we move up or down from the neutral surface, the stresses increase linearly. The moment exerted by this stress at any point will be the stress times the moment arm, which also linearly increases as we move away from the neutral surface. This means that the resistance to bending provided by any point in the cross section is directly proportional to the distance from the neutral axis squared. We can sum up the resistances to bending then by using the second rectangular area moment of inertia, where our distances are measured from the neutral axis.
\[ I = \int_A (dA * d^2) \] Assuming we put the origin point at the centroid and that the \(x\)-axis is the neutral surface, the distance from the neutral surface to any point is simply the \(y\) coordinate of that point. Similarly, if we apply a moment about the \(y\)-axis, and had a neutral surface that ran along the \(y\)-axis, the distance from the neutral axis would simply be the \(x\) coordinate of the point. For this reason, \(I_{xx}\) includes \(y\) as the distance, while \(I_{yy}\) includes \(x\) as the distance.
\[ I_{xx} = \int_{y_{min}}^{y_{max}} (dA * y^2) \quad\quad\quad I_{yy} = \int_{x_{min}}^{x_{max}} (dA * x^2) \]
Calculating the Rectangular Area Moment of Inertia via Integration
To determine the area moment of inertia, start by drawing out the area under analysis, and include the axes you are taking the moment of inertia about. This is important, since the moment of inertia will vary depending on the axis chosen. In cases on bending stresses you will want to put the origin on the neutral surface, which will be at the centroid of the area. If the centroid is not given to you, you will need to determine the centroid as discussed in prior sections.
To take the moment of inertia about the \(x\)-axis through this point (\(I_{xx}\)) we will use the general formula discussed earlier. We will be moving from bottom to top, integrating the rate of change of the area as we go, and multiplying that by the \(y\)-value squared. The rate of change of area (\(dA\)) as we move upwards will be the width of the object at any given \(y\)-value times the rate at which we are moving. Unless the width remains constant, the width will need to be represented as a mathematical function in terms of \(y\).
To find the moment of inertia about the \(y\)-axis through a given point (\(I_{yy}\)) we will move left to right, using the distances from the \(y\)-axis in our moment integral (in this case the \(x\) coordinates of each point). Moving from left to right, the rate of change of the area will be the height of the shape at any given \(x\)-value times the rate at which we are moving left to right. Again, we will need to describe this with an mathematical function if the height is not constant. We will multiply this function by the \(x\)-value squared for the second moment integral, and this will give us the moment of inertia about the \(y\)-axis.
Torsional Stresses and the Polar Moment of Inertia
When an object is subjected to a torsional moment, that object will experience internal shearing forces as shown in the diagram below. These stresses are oriented in such a way that they will counteract the torsional moment, but do not exert any net force on the shaft so that shaft stays in equilibrium.
As we can see in the diagram, there is a central axis along which there are no shearing stresses. This is known as the neutral axis, and if there are no other forces present, then this will travel through the centroid of the shaft's cross section. As we move away from the neutral axis in any direction, the stresses will increase linearly. The moment exerted by the stress at any point will be the stress times the moment arm, which also increases linearly as we move away from the neutral axis. This means that the resistance to torsional loading provided by any one point on the cross section is directly proportional the square of the distance between the point and neutral axis. We can sum up the resistances to torsional loading then using the second polar area moment of inertia, where our distances are measured from the neutral axis (\(r\)), a single point in the shaft's cross-section.
\[ J_{zz} = \int_{r_{min}}^{r_{max}} (dA * r^2) \]
Calculating the Polar Area Moment of Inertia via Integration
The first step in determining the polar moment of inertia is to draw the area and identify the point about which we are taking the moment of inertia. In the case of torsional loading, we will usually want to pick the point at which the neutral axis travels through the shaft's cross section, which in the absence of other types of loading will be the centroid of the cross section. If the centroid is not clearly identified, you will need to determine the centroid as discussed in previous sections.
To take the moment of inertia about this central point, we will be measuring all distances outward from this point. Rather than moving left to right or top to bottom, we will instead be integrating from the center radiating outward in all directions. We will be going from the minimum distance from the center for our shape (zero unless there is a central hole in our area) to the maximum distance to the center. We will again be integrating the rate of change of area, which in this case will be a function for the circumference at a given radius times the rate as which we are moving outwards times the given radius squared.
Example \(\PageIndex{1}\)
Find the rectangular moments of inertia for this shape about both the \(x\)-axis and \(y\)-axis though the centroid. Leave the answer in terms of the generic width (\(b\)) and height (\(h\)) of the rectangle.
- Solution:
Example \(\PageIndex{2}\)
Find the polar moments of inertia for this circular area about its centroid. Leave the answer in terms of the generic radius \(R\).
- Solution:
Exercise \(\PageIndex{3}\)
Find the polar moment of inertia of this hollow circular shape about its centroid.
- Solution:


16: Biotechnology and Genomics
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- 16.1: Introduction to Biotechnology and Genomics
- The study of nucleic acids began with the discovery of DNA, progressed to the study of genes and small fragments, and has now exploded to the field of genomics. Genomics is the study of entire genomes, including the complete set of genes, their nucleotide sequence and organization, and their interactions within a species and with other species. The advances in genomics have been made possible by DNA sequencing technology.
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- 16.2: Biotechnology
- Biotechnology is the use of biological agents for technological advancement. Biotechnology was used for breeding livestock and crops long before the scientific basis of these techniques was understood. Biotechnology has grown rapidly through both academic research and private companies. The primary applications of this technology are in medicine (production of vaccines and antibiotics) and agriculture (genetic modification of crops, such as to increase yields).
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- 16.3: Mapping Genomes
- Genome mapping is the process of finding the locations of genes on each chromosome. The maps created by genome mapping are comparable to the maps that we use to navigate streets. A genetic map is an illustration that lists genes and their location on a chromosome. Genetic maps provide the big picture and use genetic markers. A genetic marker is a gene or sequence on a chromosome that co-segregates (shows genetic linkage) with a specific trait.
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- 16.4: Whole-Genome Sequencing
- Although there have been significant advances in the medical sciences in recent years, doctors are still confounded by some diseases, and they are using whole-genome sequencing to get to the bottom of the problem. Whole-genome sequencing is a process that determines the DNA sequence of an entire genome. Whole-genome sequencing is a brute-force approach to problem solving when there is a genetic basis at the core of a disease.
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- 16.5: Applying Genomics
- The introduction of DNA sequencing and whole genome sequencing projects, particularly the Human Genome project, has expanded the applicability of DNA sequence information. Genomics is now being used in a wide variety of fields, such as metagenomics, pharmacogenomics, and mitochondrial genomics. The most commonly known application of genomics is to understand and find cures for diseases.
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- 16.6: Genomics and Proteomics
- Proteins are the final products of genes, which help perform the function encoded by the gene. Proteins are composed of amino acids and play important roles in the cell. All enzymes (except ribozymes) are proteins that act as catalysts to affect the rate of reactions. Proteins are also regulatory molecules, and some are hormones. Transport proteins, such as hemoglobin, help transport oxygen to various organs. Antibodies that defend against foreign particles are also proteins.
Thumbnail Image Credit: "DNA Helix String" by qimono , Pixabay is licensed under CC BY 4.0
Contributors and Attributions
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Connie Rye (East Mississippi Community College), Robert Wise (University of Wisconsin, Oshkosh), Vladimir Jurukovski (Suffolk County Community College), Jean DeSaix (University of North Carolina at Chapel Hill), Jung Choi (Georgia Institute of Technology), Yael Avissar (Rhode Island College) among other contributing authors. Original content by OpenStax (CC BY 4.0; Download for free at<EMAIL_ADDRESS>).


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1.1.1: Extensionality
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When we consider sets, we don’t care about the order of their elements, or how many times they are specified.
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1.1.2: Subsets and Power Sets
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If every element of a set \(A\) is also an element of \(B\), then we say that \(A\) is a subset of \(B\). The set consisting of all subsets of a set \(A\) is called the power set of \(A\).
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1.1.3: Some Important Sets
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Important sets include the natural (\(\mathbb{N}\)), integer (\(\mathbb{Z}\)), rational (\(\mathbb{Q}\)), and real (\(\mathbb{R}\)) numbers, but also strings (\(X^*\)) and infinite sequences (\(X^\omega\)) of objects.
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1.1.4: Unions and Intersections
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The union of two sets \(A\) and \(B\), written \(A \cup B\), is the set of all things which are elements of \(A\), \(B\), or both. The intersection \(A \cap B\) of two sets is the set of elements they have in common.
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1.1.5: Pairs, Tuples, Cartesian Products
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It follows from extensionality that sets have no order to their elements. So if we want to represent order, we use ordered pairs \(\langle x, y \rangle\).
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1.1.6: Russell’s Paradox
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Some properties do not define sets. If they all did, then we would run into outright contradictions. The most famous example of this is Russell’s Paradox.
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1.1.7: Summary
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5.3: Charge Distributions
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In principle, the smallest unit of electric charge that can be isolated is the charge of a single electron, which is \(\cong -1.60 \times 10^{-19}\) C. This is very small, and we rarely deal with electrons one at a time, so it is usually more convenient to describe charge as a quantity that is continuous over some region of space. In particular, it is convenient to describe charge as being distributed in one of three ways: along a curve, over a surface, or within a volume.
Line Charge Distribution
Imagine that charge is distributed along a curve \({\mathcal C}\) through space. Let \(\Delta q\) be the total charge along a short segment of the curve, and let \(\Delta l\) be the length of this segment. The line charge density \(\rho_l\) at any point along the curve is defined as \[\rho_l \triangleq \lim_{\Delta l \to 0} \frac{\Delta q}{\Delta l} = \frac{dq}{dl} \nonumber \] which has units of C/m. We may then define \(\rho_l\) to be a function of position along the curve, parameterized by \(l\); e.g., \(\rho_l(l)\). Then, the total charge \(Q\) along the curve is \[Q = \int_{\mathcal C} \rho_l(l)~dl \nonumber \] which has units of C. In other words, line charge density integrated over length yields total charge.
Surface Charge Distribution
Imagine that charge is distributed over a surface.  The surface charge density \(\rho_s\) at any point on the surface is defined as \[\rho_s \triangleq \lim_{\Delta s \to 0} \frac{\Delta q}{\Delta s} = \frac{dq}{ds} \nonumber \] which has units of C/m\(^2\). Let us define \(\rho_s\) to be a function of position on this surface. Then the total charge over a surface \({\mathcal S}\) is \[Q = \int_{\mathcal S} \rho_s~ds \nonumber \] In other words, surface charge density integrated over a surface yields total charge.
Volume Charge Distribution
Imagine that charge is distributed over a volume. Let \(\Delta q\) be the total charge in a small cell within this volume, and let \(\Delta v\) be the volume of this cell. The volume charge density \(\rho_v\) at any point in the volume is defined as \[\rho_v \triangleq \lim_{\Delta v \to 0} \frac{\Delta q}{\Delta v} = \frac{dq}{dv} \nonumber \] which has units of C/m\(^3\). Since \(\rho_v\) is a function of position within this volume, the total charge within a volume \({\mathcal V}\) is \[Q = \int_{\mathcal V} \rho_v~dv \nonumber \] In other words, volume charge density integrated over a volume yields total charge.


5.4: Signs and Symptoms of Hypoxia
Assessment for hypoxia can be done by completing a medical history, determining current medical condition, and performing a respiratory assessment. If a patient is experiencing any of the signs and symptoms listed in Table 5.1, hypoxia may be present.
Hypoxia must be treated immediately by the health care provider, as a lack of oxygen to tissues and organs can create serious complications (Alberta Health Services, 2015).
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Table 5.1 Signs and Symptoms of Hypoxia |
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Safety considerations:
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| Signs and Symptoms |
Indications |
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| Tachypnea | Increased respiration rate is an indication of respiratory distress. | ||
| Dyspnea | Shortness of breath (SOB) is an indication of respiratory distress. | ||
| Use of accessory muscles | Use of neck or intercostal muscles when breathing is an indication of respiratory distress. | ||
| Noisy breathing | Audible noises with breathing, or wheezes and crackles, are an indication of respiratory conditions. Assess lung sounds for adventitious sounds such as wheezing or crackles. Secretions can plug the airway, thereby decreasing the amount of oxygen available for gas exchange in the lung. | ||
| Decreased oxygen saturation levels | Oxygen saturation levels should be between 92% and 98% for an adult without an underlying respiratory condition. Lower than 92% is considered hypoxic. For patients with COPD, oxygen saturation levels may range from 88% to 92%. Lower than 88% is considered hypoxic. | ||
| Flaring of nostrils or pursed lips | Patients who are hypoxic may breathe differently, which may signal the need for supplemental oxygen. | ||
| Skin colour of patient | Changes in skin colour to bluish or gray are a late sign of hypoxia. | ||
| Position of patient | Patients in respiratory distress may voluntarily sit up or lean over by resting arms on their legs to enhance lung expansion. Patients who are hypoxic may not be able to lie flat in bed. | ||
| Ability of patient to speak in full sentences | Patients in respiratory distress may be unable to speak in full sentences, or may need to catch their breath between sentences. | ||
| Change in mental status or loss of consciousness (LOC) | This is a worsening and a late sign of hypoxia. | ||
| Restlessness or anxiety | This is an early sign of hypoxia. | ||
| Data source: British Thoracic Society, 2008; Perry et al., 2014 |
Critical Thinking Exercises
- Your patient is tachypneic and dyspneic. What is the first step you should take to ensure maximal lung expansion?
- Your patient is sitting up at 90 degrees, but is still showing signs of hypoxia. What would be your best steps?


26.5: Art of New Zealand
Maori Art in New Zealand
Traditional New Zealand art consists of the art of the Māori people, who first settled the island between 1250–1300 CE.
Identify the key elements of prehistoric and traditional Māori from New Zealand
Key Points
- New Zealand art includes traditional Māori art and more recent forms taking inspiration from Māori, European, and other traditions. Polynesians settled New Zealand in 1250–1300 CE and developed a distinctive Māori culture.
- Charcoal drawings, estimated between 500 and 800 years old, can be found on limestone rock shelters in the center of the South Island, with over 500 sites stretching from Kaikoura to North Otago.
- Māori visual art of New Zealand consists primarily of four forms: carving, tattooing (ta moko), weaving, and painting.
- Carving was done in wood, bone, and stone, and carvings were used to create jewelry and decorate houses, fence poles, containers, and other objects.
- Ta moko is the art of traditional Māori tattooing, done with a chisel. Men were tattooed on many parts of their bodies, including faces, buttocks, and thighs, while women were usually tattooed only on the lips and chin.
- Weaving was used to create numerous things, from decorative wall panels in important buildings to functional clothing and bags.
Key Terms
- koru : A spiral shape based on the shape of a new unfurling silver fern frond and symbolizing new life, growth, strength, and peace; an integral symbol in Maori art, carving, and tattoos.
- Māori : The indigenous Polynesian people of New Zealand, originating with settlers from eastern Polynesia who arrived in New Zealand in several waves of canoe voyages at some time between 1250 and 1300 CE.
Overview: New Zealand
New Zealand is an island country in the southwestern Pacific Ocean. The country geographically comprises two main landmasses—that of the North and South Islands—and numerous smaller islands. Because of its remoteness, it was one of the last lands to be settled by humans. Polynesians settled New Zealand in 1250–1300 CE and developed a distinctive Māori culture. Europeans first made contact in 1642 CE. The British and Irish immigrants brought aspects of their own culture to New Zealand and heavily influenced Māori culture, particularly with the introduction of Christianity. More recently, American, Australian, Asian, and other European cultures have exerted influence on New Zealand.
New Zealand art includes traditional Māori art, which was developed in New Zealand from Polynesian art forms, and more recent forms, which take their inspiration from Māori, European, and other traditions.
Early Charcoal Drawings
Charcoal drawings can be found on limestone rock shelters in the center of the South Island, with over 500 sites stretching from Kaikoura to North Otago. The drawings are estimated to be between 500 and 800 years old and portray animals, people, and fantastic creatures. Some of the birds pictured are long extinct and were drawn by early Māori; however by the time Europeans arrived, local inhabitants did not know the origins of the drawings.
Traditional Māori Art
Māori visual art consists primarily of four forms: carving, tattooing (ta moko), weaving, and painting. Traditional Māori art was highly spiritual and conveyed information about ancestry and other culturally important topics. Most traditional Māori art was highly stylized and featured motifs such as the spiral, the chevron, and the koru . The colors black, white, and red dominated.
Carving
Carving was done in wood, bone, and stone. Wood carvings were used to decorate houses, fence poles, containers, and other objects. Both stone and bone were used to create jewelry such as the hei-tiki . The introduction of metal tools by Europeans allowed more intricacy and delicacy, causing stone and bone fish hooks and other tools to become purely decorative.
Ta moko
Ta moko is the art of traditional Māori tattooing, done with a chisel. Men were tattooed on many parts of their bodies, including faces, buttocks, and thighs. Women were usually tattooed only on the lips and chin. Moko conveyed a person’s ancestry. The art declined in the 19th century following the introduction of Christianity, but in recent decades it has undergone a revival.
Weaving
Weaving was used to create numerous things, including wall panels in meeting houses and other important buildings, as well as clothing and bags (known as kete ). While many of these were purely functional, others were true works of art, taking hundreds of hours to complete and often given as gifts to important people. In pre-European times, the main medium for weaving was flax; however, following the arrival of Europeans, cotton, wool, and other textiles were also used.
Painting
In classical Māori art, painting was not an important art form. It was mainly used as a minor decoration in meeting houses, in stylized forms such as the koru . Europeans introduced Māori to their more figurative style of art, and in the 19th century, less stylized depictions of people and plants began to appear in place of traditional carvings and woven panels.
European Art in New Zealand
European contact with New Zealand heavily influenced traditional Māori art of the region.
Describe the influences of European art in New Zealand
Key Points
- Europeans first made contact with New Zealand in 1642 CE, and the British and Irish invaders heavily influenced Māori culture and art, particularly with the introduction of Christianity.
- Europeans began producing art in New Zealand as soon as they arrived, with landscape art and painting becoming very popular.
- From the late 19th century, many Pākehā (New Zealanders not of Māori origin, usually of European ancestry) attempted to create a distinctive New Zealand style of art, sometimes appropriating Māori artistic styles.
- From the early 20th century, politician Apirana Ngata fostered a renewal of traditional Māori art forms, establishing a school of Māori arts in Rotorua. Many Māori artists became highly successful in blending elements of Māori culture with European modernism.
Key Terms
- koru : A spiral shape based on the shape of a new unfurling silver fern frond and symbolizing new life, growth, strength, and peace; an integral symbol in Māori art, carving, and tattoos.
- Māori : The indigenous Polynesian people of New Zealand, originating with settlers from eastern Polynesia who arrived in New Zealand in several waves of canoe voyages some time between 1250 and 1300 CE.
Background: New Zealand Art
Because of its remoteness, New Zealand was one of the last lands to be settled by humans. Polynesians settled New Zealand in 1250–1300 CE and developed a distinctive Māori culture, and Europeans first made contact in 1642 CE. The British and Irish invaders brought aspects of their own culture to New Zealand and heavily influenced Māori culture, particularly with the introduction of Christianity. More recently, American, Australian, Asian, and other European cultures have exerted influence on New Zealand.
European Influence on Art
Early Landscapes and Portraiture
Europeans began producing art in New Zealand as soon as they arrived, with many exploration ships including an artist to record newly discovered places, people, flora, and fauna. Landscape art was popular among early invaders, with prints used to promote further settlement and invasion of New Zealand. Notable landscape artists included Augustus Earle and William Fox. However, the most successful artists of this period, Charles Goldie and Gottfried Lindauer, were noted primarily for their portraits of the indigenous Māori people.
19th Century
From the late 19th century, many Pākehā (New Zealanders not of Māori origin, usually of European ancestry) attempted to create a distinctive New Zealand style of art. Many, such as Rita Angus, continued to work on landscapes, with attempts to depict New Zealand’s harsh light. Others appropriated Māori artistic styles; Gordon Walters created many paintings and prints based on the koru . New Zealand’s most highly regarded 20th century artist was Colin McCahon, who attempted to use international styles such as cubism in New Zealand contexts.
20th Century
From the early 20th century, politician Apirana Ngata fostered a renewal of traditional Māori art forms, establishing a school of Māori arts in Rotorua. The visual arts flourished in the later decades of the 20th century, with the increased cultural sophistication of many New Zealanders. Many Māori artists became highly successful in blending elements of Māori culture with European modernism. Ralph Hotere is New Zealand’s highest selling living artist. Others include Shane Cotton and Michael Parekowhai.
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