27.1: Religious Art in Africa
African Art and the Spirit World
Beliefs about the spirit world are deeply embedded in traditional African culture, but were heavily influenced by Christianity and Islam.
Discuss the role of African masks, statues, and sculptures in relation to the spirit world
Key Points
- Most traditional African cultures include beliefs about the spirit world, which is widely represented through both traditional and modern art such as masks, statues, and sculptures.
- Wooden masks are often used to depict deities or ancestors; in many traditions, they are believed to channel spirits when worn by ceremonial dancers.
- Statues and sculptures are also used to represent, connect to, or communicate with spiritual forces.
- Today, Africans profess a wide variety of religious beliefs, the most common of which are Christianity and Islam; perhaps less than 15% still follow traditional African religions.
- Despite the drastic decrease in native African religions, some modern art in Africa has worked to reincorporate traditional spiritual beliefs, such as in modern Makonde Art depicting spirits.
Key Terms
- receptacle : A container.
- sanctuaries : Consecrated (or sacred) areas of a church or temple.
Background
Like all human cultures, African folklore and religion is diverse and varied. Culture and spirituality share space and are deeply intertwined in most African cultures, which have been heavily influenced by the introduction of Christianity and Islam during the era of European colonization. Most traditional African cultures include beliefs about the spirit world, which is widely represented through both traditional and modern art such as masks, statues, and sculptures. In some societies, artistic talents were themselves seen as ways to please higher spirits.
Traditional Influences on Contemporary Religious Art
Masks and Rituals
Wooden masks, which often take the form of animals, humans, or mythical creatures, are one of the most commonly found forms of traditional art in western Africa. These masks are often used to depict deities or represent the souls of the departed. They may be worn by a dancer in ceremonies for celebrations, deaths, initiations, or crop harvesting. In many traditional mask ceremonies, the dancer goes into deep trance, and during this state of mind he or she is believed to communicate with ancestors in the spirit world. The masks themselves often represent an ancestral spirit, which is believed to possess the wearer of the mask. Most African masks are made with wood and can also be decorated with ivory, animal hair, plant fibers, pigments, stones, and semi-precious gems.
Statues and sculptures are also used to represent or connect to spiritual forces. For example, Bambara statuettes, such as the Chiwara, are used as spiritually charged objects during ritual. During the annual ceremonies of the Guan society, a group of up to seven figures, some dating back to the 14th century, are removed from their sanctuaries by the elder members of the society. The wooden sculptures, which represent a highly stylized animal or human figure, are washed, re-oiled and offered sacrifices. The Kono and Komo societies use similar statues to serve as receptacles for spiritual forces. The Igbo would traditionally make clay altars and shrines of their deities, usually featuring various figures. In the Kingdom of Kongo, nkisi were objects believed to be inhabited by spirits. Often carved in the shape of animals or humans, these “power objects” were believed to help aid in the communication with the spirit world.
Modern Religion
Today, the countries of Africa contain a wide variety of religious beliefs, and statistics on religious affiliation are difficult to come by. Christianity and Islam make up the largest religions in contemporary Africa, and some sources say that less than 15% still follow traditional African religions. Despite the drastic decrease in native African religions, some modern art in Africa has worked to reincorporate traditional spiritual beliefs. For example, modern Makonde Art has turned to abstract figures in which spirits, or Shetani, play an important role.
Masks in the Kalabari Kingdom
Culture and artistic festivities of the Kalabari Kingdom involve the wearing of elaborate outfits and carved masks to celebrate the spirits.
Discuss the role of the spiritual in the masks of the Kalabari Kingdom
Key Points
- The Kalabari Kingdom was an independent trading state of the Kalabari people, an Ijaw ethnic group, in the Niger River Delta. Today it is recognized as a traditional state in what is now Rivers State, Nigeria.
- Although the Ijaw are now primarily Christians, they also maintain elaborate traditional religious practices.
- Veneration of ancestors plays a central role in Ijaw traditional religion, while water spirits figure prominently in the Ijaw pantheon. In addition, the Ijaw practice a form of divination in which recently deceased individuals are interrogated on the causes of their death.
- The role of prayer in the traditional Ijaw system of belief is to maintain the living in the good graces of the water spirits among whom they dwelt before being born into this world.
- Each year, the Ijaw hold celebrations involving masquerades that last for several days in honor of the spirits.
- Ijaw men wearing elaborate outfits and carved masks dance to the beat of drums and manifest the influence of the water spirits through the quality and intensity of their dancing.
Key Terms
- enculturation : The process by which an individual adopts the behavior patterns of the culture in which he or she is immersed.
- kin : Race; family; breed; kind.
Introduction: The Kalabari
The Kalabari Kingdom, also called Elem Kalabari (New Shipping Port), or New Calabar by the Europeans, was an independent trading state of the Kalabari people, an Ijaw ethnic group, in the Niger River Delta. Today it is recognized as a traditional state in what is now Rivers State, Nigeria. As well as participating in trade, the Ijaw have traditionally been a fishing and farming culture.
Culture and Art
Although the Ijaw are now primarily Christians (95% profess to be), with Roman Catholicism and Anglicanism being the varieties of Christianity most prevalent among them, they also maintain elaborate traditional religious practices. Veneration of ancestors plays a central role in Ijaw traditional religion, while water spirits, known as Owuamapu, figure prominently in the Ijaw pantheon. In addition, the Ijaw practice a form of divination called Igbadai , in which recently deceased individuals are interrogated on the causes of their death. The Ijaw are also known to practice ritual acculturation, whereby an individual from a different and unrelated group undergoes rites to become Ijaw.
The Role of Ijaw Masks
Ijaw religious beliefs hold that water spirits are like humans, having personal strengths and shortcomings, and that humans dwell among the water spirits before being born. Each year, the Ijaw hold celebrations lasting for several days in honor of the spirits. Central to the festivities is the role of masquerades, in which men wearing elaborate outfits and carved masks dance to the beat of drums and manifest the influence of the water spirits through the quality and intensity of their dancing. Particularly spectacular masqueraders are believed to be possessed by the particular spirits on whose behalf they are dancing.
Dogon Sculpture
Dogon sculpture primarily revolves around the themes of religious values, ideals, and freedoms.
Describe the characteristics of Dogon art, sculpture, and rituals, as well as the background and location of the Dogon culture
Key Points
- The Dogon are an ethnic group living in the central plateau region of the country of Mali, in the West of the African continent, and are well known for their unique sculptures. Dogon sculptures are not made to be seen publicly and are commonly hidden from the public eye within the houses of families, sanctuaries, or the hogon (spiritual leader).
- Dogon sculptures are typically characterized by an elongation of form and a mix of geometric and figurative images.
- The Dogon style has evolved into a kind of cubism: ovoid head, squared shoulders, tapered extremities, pointed breasts, forearms and thighs on a parallel plane, and hair stylized by three or four incised lines.
Key Terms
- vessel : A general term for all kinds of craft designed for transportation on water, such as ships or boats.
- Tellem : The people who inhabited the Bandiagara Escarpment in Mali from the 11th through 16th centuries CE.
Introduction: The Dogon People
The Dogon are an ethnic group living in the central plateau region of the country of Mali, in the West of the African continent. They migrated to the region around the 14th century CE. They are best known for their religious traditions, wooden sculpture, architecture, and funeral masquerades. The past century has seen significant changes in the social organization, material culture, and beliefs of the Dogon, partly because Dogon country is one of Mali’s major tourist attractions.
Dogon Sculpture
Dogon art is primarily sculptural and revolves around religious values, ideals, and freedoms. Dogon sculptures are not made to be seen publicly and are commonly hidden from the public eye within the houses of families, sanctuaries, or the hogon (a spiritual leader of the Dogon people). The importance of secrecy is due to the symbolic meaning behind the pieces and the process by which they are made. Dogon sculptures are typically characterized by an elongation of form and a mix of geometric and figurative images.
Themes
Themes found throughout Dogon sculpture consist of figures with raised arms, superimposed bearded figures, horsemen, stools with caryatids, women with children, figures covering their faces, women grinding pearl millet, women bearing vessels on their heads, donkeys bearing cups, musicians, dogs, quadruped-shaped troughs or benches, figures bending from the waist, mirror-images, apron-wearing figures, and standing figures. Signs of other contacts and origins are evident in Dogon art; the Dogon people were not the first inhabitants of the area, and influence from the Tellem, or the people who inhabited the region in Mali between the 11th and 16th centuries CE, is evident in the use of rectilinear designs.
Dogon art is extremely versatile, although common stylistic characteristics—such as a tendency towards stylization—are apparent on the statues. Their art deals with Dogon myths, whose complex ensembles regulate the life of the individual. The sculptures are preserved in innumerable sites of worship and personal or family altars, and often render the human body in a simplified way, reducing it to its essentials. Many sculptures recreate the silhouettes of the Tellem culture, featuring raised arms and a thick patina, or surface layer, made of blood and millet beer. The Dogon style has evolved into a kind of cubism: ovoid head, squared shoulders, tapered extremities, pointed breasts, forearms and thighs on a parallel plane, and hair stylized by three or four incised lines.
Uses
Dogon sculptures serve as a physical medium in initiations and as an explanation of the world. They serve to transmit an understanding to the initiated, who will decipher the statue according to the level of their knowledge. Carved animal figures, such as dogs and ostriches, are placed on village foundation altars to commemorate sacrificed animals, while granary doors, stools, and house posts are also adorned with figures and symbols. Kneeling statues of protective spirits are placed at the head of the dead to absorb their spiritual strength and to be their intermediaries with the world of the dead, into which they accompany the deceased before once again being placed on the shrines of the ancestors.
Mendé Masks
Mendé masks are commonly used in initiation ceremonies into secret Poro and Sande societies.
Discuss how Mendé masks are created and used by the Mendé people
Key Points
- The Mendé people are one of the two largest ethnic groups in Sierra Leone; they belong to a larger group of Mandé peoples who live throughout West Africa.
- The masks associated with the secret societies of the Mendé are probably the best known and most finely crafted in the region.
- Masks represent the collective mind of Mendé community; viewed as one body, they are seen as the Spirit of the Mendé people.
- The most important masks personify and embody the powerful spirits belonging to the medicine societies: the goboi and gbini of the Poro society (the secret society for men) and the sowei of the Sande society (the secret society for women).The features of a Sowei mask convey Mendé ideals of female morality and physical beauty; they are somewhat unusual because women wear the masks.
Key Terms
- hale : Secret societies of the Mendé people.
Background and Art of the Mendé People
The Mendé people are one of the two largest ethnic groups in Sierra Leone, having roughly the same population as their neighbours the Temne people. Together, the Mendé and Temne both account for slightly more than 30% of the country’s total population. The Mendé belong to a larger group of Mande peoples who live throughout West Africa. Mostly farmers and hunters, the Mendé are divided into two groups: the halemo ( or members of the hale or secret societies) and the kpowa (people who have never been initiated into the hale). The Mendé believe that all humanistic and scientific power is passed down through the secret societies.
Mendé art is primarily found in the form of jewelry and carvings. The masks associated with the secret societies of the Mendé are probably the best known and are finely crafted in the region. The Mendé also produce beautifully woven fabrics, which are popular throughout western Africa, and gold and silver necklaces, bracelets, armlets, and earrings. The bells on the necklaces are of the type believed capable of being heard by spirits, ringing in both worlds, that of the ancestors and the living.
Mendé Masks
Masks represent the collective mind of the Mendé community; viewed as one body, they are seen as the Spirit of the Mendé people. The Mendé masked figures are a reminder that human beings have a dual existence; they live in the concrete world of flesh and material things as well as in the spirit world of dreams, faith, aspirations, and imagination.
The standard set of Mendé maskers includes about a dozen personalities embodying spirits of varying degrees of power and importance. The most important of these personify and embody the powerful spirits belonging to the medicine societies: the goboi and gbini of the Poro society (the secret society for men), the sowei of the Sande society (the secret society for women), and the njaye and humoi maskers belonging to the eponymous medicine societies. The maskers of the Sande and Poro societies are responsible for enforcing laws and are important symbolic presences in the rituals of initiation and in public ceremonies that mark the coronations and funerals of chiefs and society officials.
Sowei Masks
The features of a Sowei mask convey Mendé ideals of female morality and physical beauty. They are somewhat unusual in that women traditionally wear the masks. The bird on top of the head represents a woman’s intuition that lets her see and know things that others can’t. The high or broad forehead represents good luck or the sharp, contemplative mind of the ideal Mendé woman.  The small mouth signifies the ideal woman’s quiet and humble character. The markings on the cheeks are representative of the decorative scars girls receive as they step into womanhood. The neck rolls are an indication of the health of ideal women; they have also been called symbols of the pattern of concentric, circular ripples the Mendé spirit makes when emerging from the water. The intricate hairstyles reveal the close ties within a community of women. The holes at the base of the mask are where the rest of the costume is attached; a woman who wears these masks must not expose any part of her body, or it is believed a vengeful spirit may take possession of her.
When a girl becomes initiated into the Sande society (the Mendé secret society for women), the village’s master woodcarver creates a special mask just for her. Helmet masks are made from a section of tree trunk, often of the kpole (cotton) tree, and then carved and hollowed to fit over the wearer’s head and face. The woodcarver must wait until he has a dream that guides him to make the mask a certain way for the recipient. A mask must be kept hidden in a secret place when no one is wearing it. These masks appear not only in initiation rituals but also at important events such as funerals, arbitrations, and the installation of chiefs.
Gbini Masks
Gbini is considered to be the most powerful of all Mendé maskers; it appears both at the final ceremony of the Poro initiation process for a son of the paramount chief and also at the coronation of funeral of a paramount chief. Because of its power, women are made to stand far back from gbini and if a woman accidentally touches it, she must be anointed with medicine immediately.
The Gbini wears a large leopard skin, which indicates its association with the paramount chief. The flat, round headpiece resembles the chief’s crown. The headpiece is constructed of animal hide stretched over a bamboo framework, and the hide is decorated with cowrie shells and black, white, and red strips of cloth that are worked into a geometric pattern. At the center is a round mirror. Several flaps that are similarly decorated hang down from the base of the headpiece and overlap the cape, which covers much of the wearer’s torso.
- Curation and Revision. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
- Contemporary African Art. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Contemporary_African_art . License : CC BY-SA: Attribution-ShareAlike
- receptacle. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/receptacle. License : CC BY-SA: Attribution-ShareAlike
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- Africa. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Africa. License : CC BY-SA: Attribution-ShareAlike
- Igbo people. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Igbo_people%23Religion_and_rites_of_passage. License : CC BY-SA: Attribution-ShareAlike
- Igbo religion. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Igbo_religion. License : CC BY-SA: Attribution-ShareAlike
- Cultural Anthropology/Ritual and Religion. Provided by : Wikibooks. Located at : en.wikibooks.org/wiki/Cultural_Anthropology/Ritual_and_Religion. License : CC BY-SA: Attribution-ShareAlike
- African art. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/African_art. License : CC BY-SA: Attribution-ShareAlike
- sanctuaries. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/sanctuaries. License : CC BY-SA: Attribution-ShareAlike
- Masque blanc Punu-Gabon. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Masque_blanc_Punu-Gabon.jpg. License : CC BY-SA: Attribution-ShareAlike
- IMG 2267u201377 b. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:IMG_2267%E2%80%9377_b.JPG. License : Public Domain: No Known Copyright
- Kalabari Kingdom. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Kalabari_Kingdom. License : CC BY-SA: Attribution-ShareAlike
- Ijaw people. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Ijaw_people. License : CC BY-SA: Attribution-ShareAlike
- Elem Kalabari. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Elem_Kalabari. License : CC BY-SA: Attribution-ShareAlike
- Kalabari tribe. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Kalabari_tribe. License : CC BY-SA: Attribution-ShareAlike
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- Dogon people. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Dogon_people. License : CC BY-SA: Attribution-ShareAlike
- vessel. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/vessel. License : CC BY-SA: Attribution-ShareAlike
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- Dogon sculpture Louvre 70-1999-9-2. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Dogon_sculpture_Louvre_70-1999-9-2.jpg. License : Public Domain: No Known Copyright
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- Dogon sculpture Louvre 70-1999-9-2. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Dogon_sculpture_Louvre_70-1999-9-2.jpg. License : Public Domain: No Known Copyright
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1.1: Studio Policies and Procedures
Please follow these rules during your time in class and during open studio access.
- Bring your tools and studio manual with you each class and/ or work session. Some projects will fit inside assigned cabinets to store between classes, but you may need to take larger pieces with you.
- You need to clean up your own mess. You are expected to put your projects away, clean your table, tools, etc. All paper and cardboard scraps need to be recycled. Any tools, materials, or projects left out may be thrown away.
- Always label your work so there is no confusion about who it belongs to.
- Do not cut directly on the wood tabletops. Always use a cutting mat or make your own out of recyclable cardboard sheets.
- Make sure to change blades in your X-acto knife often. Old, dull blades should be wrapped in masking tape and placed in the container next to the light table.


13.2: Flows and Cuts
Considering the applications suggested at the beginning of the chapter, it is natural to ask for the maximum value of a flow in a given network. Put another way, we want to find the largest number \(v_0\) so that there exists a flow \(ϕ\) of value \(v_0\) in the network. Of course, we not only want to find the maximum value \(v_0\), but we also want to find a flow \(ϕ\) having this value. Although it may seem a bit surprising, we will develop an efficient algorithm which both finds a flow of maximum value and finds a certificate verifying the claim of optimality. This certificate makes use of the following important concept.
A partition \(V=L \cup U\) of the vertex set \(V\) of a network with \(S \in L\) and \(T \in U\) is called a cut . The capacity of a cut \(V=L \cup U\), denoted \(c(L,U)\), is defined by
\(c(L,U)=\displaystyle \sum_{x \in L, y \in U} c(x,y)\).
Put another way, the capacity of the cut \(V=L \cup U\) is the total capacity of all edges from \(L\) to \(U\). Note that in computing the capacity of the cut \(V=L \cup U\), we only add the capacities of the edges from \(L\) to \(U\). We do not include the edges from \(U\) to \(L\) in this sum.
Let's again take a look at the network in Figure 13.2 . Let's first consider the cut \(V=L_1 \cup U_1\) with
\(L_1=\{S,F,B,E,D\}\) and \(U_1=\{A,C,T\}\).
Here we see that the capacity of the cut is
\(c(L_1,U_1)=c(F,A)+c(B,A)+c(B,C)+c(D,C)=24+15+20+42=101\).
We must be a bit more careful, however, when we look at the cut \(V=L_2 \cup U_2\) with
\(L_2=\{S,F,B,E\}\) and \(U_2=\{A,D,C,T\}\).
Here the capacity of the cut is
\(c(L_2,U_2)=c(F,A)+c(B,A)+c(B,C)+c(E,D)=24+15+20+20=79\).
Notice that we do not include \(c(D,B)\) in the calculation as the directed edge \((D,B)\) is from \(U_2\) to \(L_2\).
The relationship between flows and cuts rests on the following fundamentally important theorem.
 The value of the flow is at most as large as the capacity of the cut.
- Proof
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In this proof (and throughout the chapter), we adopt the very reasonable convention that \(ϕ(x,y)=0\) if \((x,y)\) is not a directed edge of a network \(\textbf{G}\).
 First notice that
\(v_0= \displaystyle \sum_{y \in V} ϕ(S,y)−\sum_{z \in V} ϕ(z,S)\),
since the second summation is .0. Also, by the second of our flow conservation laws, we have for any vertex other than the source and the sink,
\(\displaystyle \sum_{y \in V}ϕ(x,y)− \sum_{z \in V}ϕ(z,x)=0\).
Now we have
\(v_0= \displaystyle \sum_{y \in V}ϕ(S,y) - \sum_{z \in V}ϕ(z,S)\)
\(= \displaystyle \sum_{y \in V} ϕ(S,y) - \sum_{z \in V}ϕ(z,S) + \sum_{x \in L \\ x \neq S}[\sum_{y \in V} ϕ(x,y) - \sum_{z \in V}ϕ(z,x)]\)
\( = \displaystyle \sum_{x \in L} [ \sum_{y \in V} ϕ(x,y) - \sum_{z \in V} ϕ(z,x)]\)
At this point, we want to pause and look at the last line. Notice that if \((a,b)\) is a directed edge with both endpoints in \(L\), then when the outer sum is conducted for \(x=a\), we get an overall contribution of \(ϕ(a,b)\). On the other hand, when it is conducted for \(x=b\), we get a contribution of \(−ϕ(a,b)\). Thus, the terms cancel out and everything simplifies to
\(\displaystyle \sum_{x \in L \\ y \in U} ϕ(x,y) - \sum_{x \in L \\ z \in U} ϕ(z,x) \leq \sum_{x \in L \\ z \in U} ϕ(x,y) \leq \sum_{x \in L \\ y \in U} c(x,y) = c(L,U)\).
Thus \(v_0 \leq c(L,U)\).
Bob's getting a bit of a sense of déjà vu after reading Theorem 13.4 . He remembers from Chapter 5 that the maximum size of a clique in a graph is always at most the minimum number of colors required to properly color the graph. However, he also remembers that there are graphs without cliques of size three but with arbitrarily large chromatic number, so he's not too hopeful that this theorem is going to help out much here. Yolanda chimes in with a reminder of Chapter 6, where they learned that the maximum size of an antichain in a poset is equal to the minimum number of chains into which the ground set of the poset can be partitioned. Alice points out that Yolanda's statement is still true if the words “chain” and “antichain” are swapped. This sparks some intense debate about whether the maximum value of a flow in a network must always be equal to the minimum capacity of a cut in that network. After a while, Carlos suggests that continuing to read might be the best idea for resolving their debate.


Review of Key Points
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Rogers believed that each person exists in their own, unique experiential field. Only they can see that field clearly, although even they may not perceive it accurately (incongruence).
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The self is that portion of the experiential field that is recognized as “I” or “me.” It is organized into a self-structure.
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In order for a person to grow, they must fulfill a need for positive regard. This can only come from receiving unconditional positive regard from important family members and friends (typically beginning with the parents).
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When an individual’s self-regard and positive regard are closely related, the person is said to be congruent. If not, they are said to be incongruent.
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Rogers described individuals who are congruent and continuing to grow as fully functioning persons.
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Successful marriages, according to Rogers, seem to be based on dedication/commitment, communication, dissolution of roles, and maintaining each person’s separate self.
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Rogers extended his study of clinical psychology into other groups designed to help all people grow and self-actualize, such as T-groups and encounter groups. He described his shift from purely clinical work to fostering growth in all people as a person-centered approach.
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Values were very important to Maslow in his approach to psychology. He did not, however, advocate his own values. He reached beyond humanistic psychology to include areas of study such as existential psychology, existential theology, and Zen Buddhism.
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The lower needs can be described as deficiency-needs, whereas self-actualization is a Being-need.
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Maslow described fourteen characteristics of self-actualizing people. He developed his list by studying both contemporary and historical people who seemed to him to be self-actualizing.
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Maslow described two defense mechanisms that interfere with the process of self-actualizing: desacralizing and the Jonah complex.
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Some individuals experience profound peak experiences, which Maslow described as transcendent. His concept of transcendence seems very close to the Buddhist perspective of interbeing.
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When Eupsychian management does support self-actualization, the actualization of each person benefits the others around them. The process is known as synergy.
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Murray based “personology” on the study of needs. He distinguished between viscerogenic needs and psychogenic needs.
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Murray believed that a person’s ability to create a story around a picture in the TAT was based in large part on their personal mythology. He shared this interest in myth, and its role in psychology, with Carl Jung and Rollo May.
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The distinction between humanistic psychology and existential psychology is not clear, and there is significant overlap in the thinking of representatives from both fields. In addition, there is a distinct humanistic element in the psychodynamic theories of Adler, Horney, Fromm, Murray, and others
Discussion Question:
Consider Murray’s list of psychogenic needs. Which needs are the ones that affect you the most? Are you able to fulfill those needs?


6.2: Exploration of the Field
Learning Objectives
At the end of this section, the learner will:
- Describe a five-step process for choosing a career
- Explore a variety of nursing specialties
- Discover a process for how to select a nursing specialty
The Five-Step Process for Choosing Your Career
As your thoughts about your career expand, keep in mind that over the course of your life, you will probably spend a lot of time at work—thousands of hours, in fact. According to the Bureau of Labor Statistics, the average workday is about 8.7 hours long, and this means that if you work 5 days a week, 50 weeks a year, for 35 years, you will spend a total of 76,125 hours of your life at work. These numbers should convince you that it’s pretty important to enjoy your career.
If you do pursue a career, you’ll find yourself making many decisions about it. Is this the right career for me? Am I feeling fulfilled and challenged? Does this career enable me to have the lifestyle I desire? It’s important to consider these questions now, whether you’re just graduating from high school or college, or you’re returning to school after working for a while.
Choosing a career—any career—is a unique process for everyone, and for many people the task is daunting. There are so many different occupations to choose from. How do you navigate this complex world of work?
The California Community Colleges Chancellor’s Office has identified a five-step decision process that will make your career path a little easier to find. Below are the steps:
- Get to know yourself.
- Get to know your field.
- Prioritize your “deal makers” and rule out your “deal breakers”.
- Make a preliminary career decision and create a plan of action.
- Go out and achieve your career goal.
Step 1: Get to Know Yourself
Get to know yourself and the things you’re truly passionate about.
- Gather information about your career-related interests and values.
- Think about what skills and abilities come naturally to you and which ones you want to develop.
- Consider your personality type and how you want it to reflect in your work.
 You’ll want to investigate the career paths available to you. You may also want to see what your college Career Center offers or conduct informational interviews to find out more about your field. One of the handiest starting points and “filters” is to decide the level of education you want to attain before starting your first or your next job. Students should consider determining both how much education they are willing to acquire, and how much education a particular career will require. Do you want to earn an associate’s degree, a bachelor’s degree, a master’s degree, or a doctorate or professional degree? Meeting with a college counselor or career counselor can help a student clarify this information.
 Educational requirements aren’t the only criteria that you will want to consider. Do you want to work outside or in an office? In the country or a city? In a big or small organization? For a public organization or a private company? What type of industry is interesting to you? What role do you see yourself playing in the organization? Do you want to be your own boss?
Step 4: Make a Preliminary Career Decision
Make a preliminary (or first) career decision and create a plan of action. It is not set in stone and you may have multiple careers in your lifetime, but everything starts with that preliminary career decision and plan of action. As a student matures and gains experience, more career opportunities will present themselves.
Now that you have an idea of who you are and where you might find a satisfying career, how do you start taking action to get there? Some people talk to family, friends, or instructors in their chosen disciplines. Others have mentors in their lives with whom to discuss this decision. Your college has career counselors and academic advisers who can help you with both career decision-making and the educational planning process. Nevertheless, be advised: You’ll get the most from sessions with your counselor if you have done some work on your own.
 Now it’s time to take concrete steps toward achieving your educational and career goals. This may be as simple as creating a preliminary educational plan for next semester or a comprehensive educational plan that maps out the degree you are currently working toward. You may also want to look for internships, part-time work, or volunteer opportunities that help you test and confirm your preliminary career choice. Your college counselor can help you with this step, as well.
Your work experiences and life circumstances will undoubtedly change throughout the course of your professional life, so you may need to go back and reassess where you are on this path in the future. However, no matter if you feel like you were born knowing what you want to do professionally, or you feel totally unsure about what the future holds for you, remember that with careful consideration, resolve, and strategic thought, you can find a career that feels rewarding.
Specialized fields
Nursing Specialties
While you may have already chosen nursing as a field, it is important to consider the various roles nurses may fill. The following three resources provide information about the various specialties nurses can pursue, as well as information about the average salary and the education level needed:
- Johnson & Johnson’s Nursing Specialties
- Occupational Outlook Handbook (scroll down to “Similar Occupations”)
- Imprint Career Planning Guides
Publications
The following publications are helpful resources to explore more aspects of nursing practice (UTA Students, follow the hyperlinked title for access):
-
Professional Nursing
by
ISBN:<PHONE_NUMBER>125Publication Date: 2016-06-23
-
Becoming a Nurse
by
ISBN:<PHONE_NUMBER>Publication Date: 2016-10-12
-
301 Careers in Nursing
by
ISBN:<PHONE_NUMBER>Publication Date: 2017
-
Nursing Practice
by
ISBN:<PHONE_NUMBER>Publication Date: 2017-11-20
-
Coping with Caring
by
ISBN:<PHONE_NUMBER>Publication Date: 2019-07-08
-
Imprint: Career Planning Guides
by
Publication Date: 2020
-
Advancing Your Career
by
ISBN:<PHONE_NUMBER>Publication Date: 2019-10-01
Guiding Questions To Think About
You should consider the following questions when deciding if you want to specialize in a particular field of nursing. Regardless of your answers, there is likely a field of nursing that will suit both you and the profession:
Are you an introvert or an extrovert?
How you answer this question requires deep insight on your part. Consider the various environments you might work and thrive in based on your natural tendencies. This question does not imply that either is better or worse than the other.
Some specialties for introverts include (not limited to):
- Forensic Nursing
- Nursing Education
- Legal Nursing
- Nursing Informatics
- Private Duty Nursing
- Nurse Researcher
- Surgical Nurse
- Case Management
- Infection Control and Prevention
- Mental Health Nursing
Some specialties for extroverts include (not limited to):
- Emergency Nursing
- Critical Care/Intensive Care Nursing
- Medical-Surgical Nursing
- Labor & Delivery Nursing
Are you willing to go for additional training beyond this degree?
This is a valid question in that nursing is a challenging degree to obtain. Your individual circumstances after graduation may play into whether or not you pursue additional degrees and/or certifications. Many specialties require more credentials, so look through all of the requirements of the specialty you choose. Think about your support system and other logistics involved in obtaining the required training, too.
Which population are you most interested in caring for?
For some, this is an easy question to answer. For others, it will take more self-evaluation to determine. If you find that no specific population rises to the top of your list, do not worry! There is still a place for you.
There are many areas that work with a variety of patients, such as (not limited to):
- Primary Care Nursing
- Public Health Nursing
- Family Nurse Practitioner
- Rehabilitation Nursing
- Mental Health Nursing
- Pain Management Nursing
- Specific Disease Care (diabetes, cardiovascular disease, asthma, etc.)
Do you have a personal experience that connects you to a field of study?
Many nurses were called to the profession by a personal experience that stirred something within them to serve. If you have those experiences, examine what sparked the interest. That could provide you with the link between your professional nursing service and your true passion.
Are you afraid of blood and bodily fluids? What things gross you out most?
Consider what each specialty will expose you to. Be aware these can become desensitized over time with experience. However, if there are phobias and/or strong aversions that may interfere with your ability to care for your patient(s), those areas of practice should be avoided if possible.
Do you prefer providing team-based care or individualized 1:1 care?
Recognize that nurses work in a myriad of environments. Some are conducive to individualized 1:1 or 1:2 care, while others lean on care teams to coordinate. If you like to spend a lot of time with your patients, you might choose a specialty that lends itself to that level of care. Conversely, if you prefer lots of interactions with colleagues, choose those that encompass your preference for collaboration.
What pace of work do you perform best in?
The pace of a nurse’s work varies greatly depending on the specialty, facility, location, time of day, patient load, etc. Knowing your preferences in this area will help you identify the kind of environment you need to work in to be optimal.
Fast-paced nursing specialties (not limited to):
- Emergency Care Nursing
- Post-Anesthesia Care Unit Nursing
- Cardiovascular Care Nursing
- Progressive Care/Step-down Care Unit
Slower-paced nursing specialties (not limited to):
- Clinic Nurse
- Nurse Educator
- Nurse Researcher
- Public Health Nurse
- Occupational Health Nurse
- Informatics Nursing
- Home Health Nursing
How do you respond to stress/crisis?
The way you react to stress in your body impacts your ability to provide care amid crisis. Think about your natural physical, mental, emotional, and spiritual response to different levels of experienced stress. Picture yourself in the environment you selected. Imagine all of the sensory inputs you encounter there.  Use this to guide you toward a specialty that resonates with your natural level of stress tolerance.
What is the need in your area of residence?
Need drives jobs! Get to know the local market in your specialty. Be prepared to relocate or create a secondary plan if the available openings are competitive ( 2019 Texas Professional Nursing Trends: Statewide )
activity 7.2: Nursing specialty exploration
Nursing Specialty Quiz
Take the Johnson and Johnson’s Nursing Specialty Quiz and reflect on the questions you read about above. Did you discover any additional specialties you haven’t thought of before? What have you learned about yourself in the process?


35.16: Nervous System Disorders - Neurodevelopmental Disorders - Autism and ADHD
- Distinguish between the neurodevelopmental disorders of autism and ADHD
Neurodevelopmental disorders occur when the development of the nervous system is disturbed. There are several different classes of neurodevelopmental disorders. Some, like Down Syndrome, cause intellectual deficits, while others specifically affect communication, learning, or the motor system. Some disorders, such as autism spectrum disorder and attention deficit/hyperactivity disorder, have complex symptoms.
Autism
Autism spectrum disorder (ASD, sometimes just “autism”) is a neurodevelopmental disorder in which severity differs from person to person. Estimates for the prevalence of the disorder have changed rapidly in the past few decades. Current estimates suggest that one in 88 children will develop the disorder. ASD is four times more prevalent in males than females.
A characteristic symptom of ASD is impaired social skills. Children with autism may have difficulty making and maintaining eye contact and reading social cues. They also may have problems feeling empathy for others. Other symptoms of ASD include repetitive motor behaviors (such as rocking back and forth), preoccupation with specific subjects, strict adherence to certain rituals, and unusual language use. Up to 30 percent of patients with ASD develop epilepsy. Patients with some forms of the disorder (e.g., Fragile X syndrome) also have intellectual disability. Because it is a spectrum disorder, other ASD patients are very functional and have good-to-excellent language skills. Many of these patients do not feel that they suffer from a disorder and instead just believe that they process information differently.
Except for some well-characterized, clearly-genetic forms of autism (e.g., Fragile X and Rett Syndrome), the causes of ASD are largely unknown. Variants of several genes correlate with the presence of ASD, but for any given patient, many different mutations in different genes may be required for the disease to develop. At a general level, ASD is thought to be a disease of “incorrect” wiring. Accordingly, brains of some ASD patients lack the same level of synaptic pruning that occurs in non-affected people. There has been some unsubstantiated controversy linking vaccinations and autism. In the 1990s, a research paper linked autism to a common vaccine given to children. This paper was retracted when it was discovered that the author falsified data; follow-up studies showed no connection between vaccines and autism.
Treatment for autism usually combines behavioral therapies and interventions, along with medications to treat other disorders common to people with autism ( depression, anxiety, obsessive compulsive disorder). Although early interventions can help mitigate the effects of the disease, there is currently no cure for ASD.
Attention Deficit Hyperactivity Disorder (ADHD)
Approximately three to five percent of children and adults are affected by attention deficit/hyperactivity disorder (ADHD). Like ASD, ADHD is more prevalent in males than females. Symptoms of the disorder include inattention (lack of focus), executive functioning difficulties, impulsivity, and hyperactivity beyond what is characteristic of the normal developmental stage. Some patients do not have the hyperactive component of symptoms and are diagnosed with a subtype of ADHD: attention deficit disorder (ADD). Many people with ADHD also show comorbidity: they develop secondary disorders in addition to ADHD. Examples include depression or obsessive compulsive disorder (OCD).
The cause of ADHD is unknown, although research points to a delay and dysfunction in the development of the prefrontal cortex and disturbances in neurotransmission. According to some twin studies, the disorder has a strong genetic component. There are several candidate genes that may contribute to the disorder, but no definitive links have been discovered. Environmental factors, including exposure to certain pesticides, may also contribute to the development of ADHD in some patients. Treatment for ADHD often involves behavioral therapies and the prescription of stimulant medications, which, paradoxically, cause a calming effect in these patients.
Key Points
- Disturbances in the development of the nervous system, genetic or environmental, may lead to neurodevelopmental diseases.
- Individuals affected by autism are believed to have one of many different mutations in genes required for the disease to cause disruptions in the nervous system that are generally observed; however, studies on specifics are still inconclusive.
- In ADHD, a strong genetic component may contribute to the disorder; however, no definitive links have been found.
- Individuals with ADHD may experience other psychological or neurological disorders in addition to their ADHD symptoms; this experience of having more than one disorder is termed comorbidity.
- The cause of both autism and ADHD are unknown and cures are unavailable; however, treatments to alleviate symptoms are accessible.
Key Terms
- autism : disorder observed in early childhood with symptoms of abnormal self-absorption, characterised by lack of response to other humans and a limited ability or disinclination to communicate and socialize
- attention deficit hyperactivity disorder : a developmental disorder in which a person has a persistent pattern of impulsiveness and inattention, with or without a component of hyperactivity
- fragile X syndrome : a particular, genetic syndrome, caused by the excessive repetition of a particular trinucleotide
- rett syndrome : a neurodevelopmental disorder of the grey matter of the brain that almost exclusively affects females, but has also been found in male patients
- comorbidity : the presence of one or more disorders (or diseases) in addition to a primary disease or disorder
- neurodevelopmental disorder : a disorder of brain function that affects emotion, learning ability and memoryand that unfolds as the individual grows


9.1: Prelude to Linear Momentum and Collisions
The concepts of work, energy, and the work-energy theorem are valuable for two primary reasons: First, they are powerful computational tools, making it much easier to analyze complex physical systems than is possible using Newton’s laws directly (for example, systems with nonconstant forces); and second, the observation that the total energy of a closed system is conserved means that the system can only evolve in ways that are consistent with energy conservation. In other words, a system cannot evolve randomly; it can only change in ways that conserve energy.
In this chapter, we develop and define another conserved quantity, called linear momentum, and another relationship (the impulse-momentum theorem), which will put an additional constraint on how a system evolves in time. Conservation of momentum is useful for understanding collisions, such as that shown in the above image. It is just as powerful, just as important, and just as useful as conservation of energy and the work-energy theorem.


7.14: Putting It Together- Adolescence
Contributors and Attributions
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Adolescent development is characterized by significant biological, cognitive, and pyschosocial changes. Physical changes associated with puberty are triggered by hormones and changes in the brain in which reward-processing centers develop more rapidly than cognitive control systems, making adolescents more sensitive to rewards than to possible negative consequences. Cognitive changes include improvements in complex and abstract thought and moral reasoning. Psychos ocial changes are particularly notable as adolescents become more autonomous from their parents, spend more time with peers, and begin exploring romantic relationships and sexuality.
Adjustment during adolescence is reflected in identity formation, which often involves a period of exploration followed by commitments to particular identities. Adolescents’ relationships with parents go through a period of redefinition in which adolescents become more autonomous, and aspects of parenting, such as monitoring and psychological control, become more salient. Peer relationships are important sources of support and companionship during adolescence, yet can also promote problem behaviors. Same-sex peer groups evolve into mixed-sex peer groups, and adolescents’ romantic relationships tend to emerge from these groups. Identity formation occurs as adolescents explore and commit to different roles and ideological positions. Despite these generalizations, factors such as country of residence, gender, ethnicity, and sexual orientation shape development in ways that lead to diversity of experiences across adolescence.


7.1: Diseases of the Immune System
An allergic reaction is an immune response to a type of antigen called an allergen . Allergens can be found in many different items, from peanuts and insect stings to latex and some drugs. Unlike other kinds of antigens, allergens are not necessarily associated with pathogenic microbes, and many allergens provoke no immune response at all in most people.
Allergic responses vary in severity. Some are mild and localized, like hay fever or hives, but others can result in systemic, life-threatening reactions. Anaphylaxis, for example, is a rapidly developing allergic reaction that can cause a dangerous drop in blood pressure and severe swelling of the throat that may close off the airway.
Allergies are just one example of how the immune system—the system normally responsible for preventing disease—can actually cause or mediate disease symptoms. In this chapter, we will further explore allergies and other disorders of the immune system, including hypersensitivity reactions, autoimmune diseases, transplant rejection, and diseases associated with immunodeficiency.
-
- 7.1.2: Autoimmune Disorders
- Autoimmune diseases result from a breakdown in immunological tolerance. The actual induction event(s) for autoimmune states are largely unknown. Some autoimmune diseases attack specific organs, whereas others are more systemic. Organ-specific autoimmune diseases include celiac disease, Graves disease, Hashimoto thyroiditis, type I diabetes mellitus, and Addison disease.
-
- 7.1.3: Organ Transplantation and Rejection
- Grafts and transplants can be classified as autografts, isografts, allografts, or xenografts based on the genetic differences between the donor’s and recipient’s tissues. Genetic differences, especially among the MHC (HLA) genes, will dictate the likelihood that rejection of the transplanted tissue will occur. Transplant recipients usually require immunosuppressive therapy to avoid rejection, even with good genetic matching.
-
- 7.1.4: Immunodeficiency
- Primary immunodeficiencies are caused by genetic abnormalities; secondary immunodeficiencies are acquired through disease, diet, or environmental exposures. Primary immunodeficiencies may result from flaws in phagocyte killing of innate immunity, or impairment of T cells and B cells. Primary immunodeficiencies include chronic granulomatous disease, X-linked agammaglobulinemia, selective IgA deficiency, and severe combined immunodeficiency disease.
-
- 7.1.5: Cancer Immunobiology and Immunotherapy
- When control of the cell cycle is lost, the affected cells rapidly divide and often lose the ability to differentiate into the cell type appropriate for their location in the body. In addition, they lose contact inhibition and can start to grow on top of each other. This can result in formation of a tumor. It is important to make a distinction here: The term “cancer” is used to describe the diseases resulting from loss of cell-cycle regulation and subsequent cell proliferation.
Thumbnail: Allergens in plant pollen, shown here in a colorized electron micrograph, may trigger allergic rhinitis or hay fever in sensitive individuals. (Public Domain/modified from original; Dartmouth Electron Microscope Facility, Dartmouth College via Wikimedia Commons ).


22.2: Ferromagnets and Electromagnets
Learning Objectives
By the end of this section, you will be able to:
- Define ferromagnet.
- Describe the role of magnetic domains in magnetization.
- Explain the significance of the Curie temperature.
- Describe the relationship between electricity and magnetism.
Ferromagnets
Only certain materials, such as iron, cobalt, nickel, and gadolinium, exhibit strong magnetic effects. Such materials are called ferromagnetic , after the Latin word for iron, ferrum . A group of materials made from the alloys of the rare earth elements are also used as strong and permanent magnets; a popular one is neodymium. Other materials exhibit weak magnetic effects, which are detectable only with sensitive instruments. Not only do ferromagnetic materials respond strongly to magnets (the way iron is attracted to magnets), they can also be magnetized themselves—that is, they can be induced to be magnetic or made into permanent magnets.
When a magnet is brought near a previously unmagnetized ferromagnetic material, it causes local magnetization of the material with unlike poles closest, as in Figure \(\PageIndex{1}\). (This results in the attraction of the previously unmagnetized material to the magnet.) What happens on a microscopic scale is illustrated in Figure \(\PageIndex{2}\). The regions within the material called domains act like small bar magnets. Within domains, the poles of individual atoms are aligned.  Domains are small and randomly oriented in an unmagnetized ferromagnetic object. In response to an external magnetic field, the domains may grow to millimeter size, aligning themselves as shown in Figure 2b. This induced magnetization can be made permanent if the material is heated and then cooled, or simply tapped in the presence of other magnets.
Conversely, a permanent magnet can be demagnetized by hard blows or by heating it in the absence of another magnet. Increased thermal motion at higher temperature can disrupt and randomize the orientation and the size of the domains. There is a well-defined temperature for ferromagnetic materials, which is called the Curie temperature , above which they cannot be magnetized. The Curie temperature for iron is 1043 K \(\left(770^{\circ}C\right)\), which is well above room temperature. There are several elements and alloys that have Curie temperatures much lower than room temperature and are ferromagnetic only below those temperatures.
Electromagnets
Early in the 19th century, it was discovered that electrical currents cause magnetic effects. The first significant observation was by the Danish scientist Hans Christian Oersted (1777–1851), who found that a compass needle was deflected by a current-carrying wire. This was the first significant evidence that the movement of charges had any connection with magnets. Electromagnetism is the use of electric current to make magnets. These temporarily induced magnets are called electromagnets . Electromagnets are employed for everything from a wrecking yard crane that lifts scrapped cars to controlling the beam of a 90-km-circumference particle accelerator to the magnets in medical imaging machines (Figure \(\PageIndex{3}\)).
Figure \(\PageIndex{4}\) shows that the response of iron filings to a current-carrying coil and to a permanent bar magnet. The patterns are similar. In fact, electromagnets and ferromagnets have the same basic characteristics—for example, they have north and south poles that cannot be separated and for which like poles repel and unlike poles attract.
Combining a ferromagnet with an electromagnet can produce particularly strong magnetic effects (Figure \(\PageIndex{5}\)). Whenever strong magnetic effects are needed, such as lifting scrap metal, or in particle accelerators, electromagnets are enhanced by ferromagnetic materials. Limits to how strong the magnets can be made are imposed by coil resistance (it will overheat and melt at sufficiently high current), and so superconducting magnets may be employed. These are still limited, because superconducting properties are destroyed by too great a magnetic field.
Figure \(\PageIndex{6}\) shows a few uses of combinations of electromagnets and ferromagnets. Ferromagnetic materials can act as memory devices, because the orientation of the magnetic fields of small domains can be reversed or erased. Magnetic information storage on videotapes and computer hard drives are among the most common applications. This property is vital in our digital world.
Current: The Source of All Magnetism
An electromagnet creates magnetism with an electric current. In later sections we explore this more quantitatively, finding the strength and direction of magnetic fields created by various currents. But what about ferromagnets? Figure \(\PageIndex{7}\) shows models of how electric currents create magnetism at the submicroscopic level. (Note that we cannot directly observe the paths of individual electrons about atoms, and so a model or visual image, consistent with all direct observations, is made. We can directly observe the electron’s orbital angular momentum, its spin momentum, and subsequent magnetic moments, all of which are explained with electric-current-creating subatomic magnetism.) Currents, including those associated with other submicroscopic particles like protons, allow us to explain ferromagnetism and all other magnetic effects. Ferromagnetism, for example, results from an internal cooperative alignment of electron spins, possible in some materials but not in others.
Crucial to the statement that electric current is the source of all magnetism is the fact that it is impossible to separate north and south magnetic poles. (This is far different from the case of positive and negative charges, which are easily separated.) A current loop always produces a magnetic dipole—that is, a magnetic field that acts like a north pole and south pole pair. Since isolated north and south magnetic poles, called magnetic monopoles , are not observed, currents are used to explain all magnetic effects. If magnetic monopoles did exist, then we would have to modify this underlying connection that all magnetism is due to electrical current. There is no known reason that magnetic monopoles should not exist—they are simply never observed—and so searches at the subnuclear level continue. If they do not exist, we would like to find out why not. If they do exist, we would like to see evidence of them.
ELECTRIC CURRENTS AND MAGNETISM
Electric current is the source of all magnetism.
PHET EXPLORATIONS: MAGNETS AND ELECTROMAGNETS
Explore the interactions between a compass and bar magnet . Discover how you can use a battery and wire to make a magnet! Can you make it a stronger magnet? Can you make the magnetic field reverse?
Summary
- Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
- All magnetism is created by electric current.
- Ferromagnetic materials, such as iron, are those that exhibit strong magnetic effects.
- The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains.
- Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic.
- Above a material’s Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears.
- Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.
Glossary
- ferromagnetic
- materials, such as iron, cobalt, nickel, and gadolinium, that exhibit strong magnetic effects
- magnetized
- to be turned into a magnet; to be induced to be magnetic
- domains
- regions within a material that behave like small bar magnets
- Curie temperature
- the temperature above which a ferromagnetic material cannot be magnetized
- electromagnetism
- the use of electrical currents to induce magnetism
- electromagnet
- an object that is temporarily magnetic when an electrical current is passed through it
- magnetic monopoles
- an isolated magnetic pole; a south pole without a north pole, or vice versa (no magnetic monopole has ever been observed)


17.2: The Division Algorithm
Recall that the division algorithm for integers (Theorem 2.9) says that if \(a\) and \(b\) are integers with \(b \gt 0\text{,}\) then there exist unique integers \(q\) and \(r\) such that \(a = bq + r\text{,}\) where \(0 \leq r \lt b\text{.}\) The algorithm by which \(q\) and \(r\) are found is just long division. A similar theorem exists for polynomials. The division algorithm for polynomials has several important consequences. Since its proof is very similar to the corresponding proof for integers, it is worthwhile to review Theorem 2.9 at this point.
Theorem \(17.6\). Division Algorithm
Let \(f(x)\) and \(g(x)\) be polynomials in \(F[x]\text{,}\) where \(F\) is a field and \(g(x)\) is a nonzero polynomial. Then there exist unique polynomials \(q(x), r(x) \in F[x]\) such that
\[ f(x) = g(x) q(x) + r(x)\text{,} \nonumber \]
where either \(\deg r(x) \lt \deg g(x)\) or \(r(x)\) is the zero polynomial.
- Proof
-
We will first consider the existence of \(q(x)\) and \(r(x)\text{.}\) If \(f(x)\) is the zero polynomial, then
\[ 0 = 0 \cdot g(x) + 0; \nonumber \]
hence, both \(q\) and \(r\) must also be the zero polynomial. Now suppose that \(f(x)\) is not the zero polynomial and that \(\deg f(x) = n\) and \(\deg g(x) = m\text{.}\) If \(m \gt n\text{,}\) then we can let \(q(x) = 0\) and \(r(x) = f(x)\text{.}\) Hence, we may assume that \(m \leq n\) and proceed by induction on \(n\text{.}\) If
\begin{align*} f(x) & = a_n x^n + a_{n-1} x^{n - 1} + \cdots + a_1 x + a_0\\ g(x) & = b_m x^m + b_{m-1} x^{m - 1} + \cdots + b_1 x + b_0 \end{align*}
the polynomial
\[ f'(x) = f(x) - \frac{a_n}{b_m} x^{n - m} g(x) \nonumber \]
has degree less than \(n\) or is the zero polynomial. By induction, there exist polynomials \(q'(x)\) and \(r(x)\) such that
\[ f'(x) = q'(x) g(x) + r(x)\text{,} \nonumber \]
where \(r(x) = 0\) or the degree of \(r(x)\) is less than the degree of \(g(x)\text{.}\) Now let
\[ q(x) = q'(x) + \frac{a_n}{b_m} x^{n - m}\text{.} \nonumber \]
Then
\[ f(x) = g(x) q(x) + r(x)\text{,} \nonumber \]
with \(r(x)\) the zero polynomial or \(\deg r(x) \lt \deg g(x)\text{.}\)
To show that \(q(x)\) and \(r(x)\) are unique, suppose that there exist two other polynomials \(q_1(x)\) and \(r_1(x)\) such that \(f(x) = g(x) q_1(x) + r_1(x)\) with \(\deg r_1(x) \lt \deg g(x)\) or \(r_1(x) = 0\text{,}\) so that
\[ f(x) = g(x) q(x) + r(x) = g(x) q_1(x) + r_1(x)\text{,} \nonumber \]
and
\[ g(x) [q(x) - q_1(x) ] = r_1(x) - r(x)\text{.} \nonumber \]
If \(q(x) - q_1(x)\) is not the zero polynomial, then
\[ \deg( g(x) [q(x) - q_1(x) ] )= \deg( r_1(x) - r(x) ) \geq \deg g(x)\text{.} \nonumber \]
However, the degrees of both \(r(x)\) and \(r_1(x)\) are strictly less than the degree of \(g(x)\text{;}\) therefore, \(r(x) = r_1(x)\) and \(q(x) = q_1(x)\text{.}\)
Example \(17.7\)
The division algorithm merely formalizes long division of polynomials, a task we have been familiar with since high school.
Solution
For example, suppose that we divide \(x^3 - x^2 + 2 x - 3\) by \(x - 2\text{.}\)
| \(x^2\) | \(+\) | \(x\) | \(+\) | \(4\) | |||||
| \(x\) | \(-\) | \(2\) | \(x^3\) | \(-\) | \(x^2\) | \(+\) | \(2x\) | \(-\) | \(3\) |
| \(x^3\) | \(-\) | \(2x^2\) | |||||||
| \(x^2\) | \(+\) | \(2x\) | \(-\) | \(3\) | |||||
| \(x^2\) | \(-\) | \(2x\) | |||||||
| \(4x\) | \(-\) | \(3\) | |||||||
| \(4x\) | \(-\) | \(8\) | |||||||
| \(5\) |
Hence, \(x^3 - x^2 + 2 x - 3 = (x - 2) (x^2 + x + 4 ) + 5\text{.}\)
Let \(p(x)\) be a polynomial in \(F[x]\) and \(\alpha \in F\text{.}\) We say that \(\alpha\) is a zero or root of \(p(x)\) if \(p(x)\) is in the kernel of the evaluation homomorphism \(\phi_{\alpha}\text{.}\) All we are really saying here is that \(\alpha\) is a zero of \(p(x)\) if \(p(\alpha) = 0\text{.}\)
Corollary \(17.8\)
Let \(F\) be a field. An element \(\alpha \in F\) is a zero of \(p(x) \in F[x]\) if and only if \(x - \alpha\) is a factor of \(p(x)\) in \(F[x]\text{.}\)
- Proof
-
Suppose that \(\alpha \in F\) and \(p( \alpha ) = 0\text{.}\) By the division algorithm, there exist polynomials \(q(x)\) and \(r(x)\) such that
\[ p(x) = (x -\alpha) q(x) + r(x) \nonumber \]
and the degree of \(r(x)\) must be less than the degree of \(x -\alpha\text{.}\) Since the degree of \(r(x)\) is less than 1, \(r(x) = a\) for \(a \in F\text{;}\) therefore,
\[ p(x) = (x -\alpha) q(x) + a\text{.} \nonumber \]
But
\[ 0 = p(\alpha) = 0 \cdot q(\alpha) + a = a; \nonumber \]
consequently, \(p(x) = (x - \alpha) q(x)\text{,}\) and \(x - \alpha\) is a factor of \(p(x)\text{.}\)
Conversely, suppose that \(x - \alpha\) is a factor of \(p(x)\text{;}\) say \(p(x) = (x - \alpha) q(x)\text{.}\) Then \(p( \alpha ) = 0 \cdot q(\alpha) = 0\text{.}\)
Corollary \(17.9\)
Let \(F\) be a field. A nonzero polynomial \(p(x)\) of degree \(n\) in \(F[x]\) can have at most \(n\) distinct zeros in \(F\text{.}\)
- Proof
-
We will use induction on the degree of \(p(x)\text{.}\) If \(\deg p(x) = 0\text{,}\) then \(p(x)\) is a constant polynomial and has no zeros. Let \(\deg p(x) = 1\text{.}\) Then \(p(x) = ax + b\) for some \(a\) and \(b\) in \(F\text{.}\) If \(\alpha_1\) and \(\alpha_2\) are zeros of \(p(x)\text{,}\) then \(a\alpha_1 + b = a\alpha_2 +b\) or \(\alpha_1 = \alpha_2\text{.}\)
Now assume that \(\deg p(x) \gt 1\text{.}\) If \(p(x)\) does not have a zero in \(F\text{,}\) then we are done. On the other hand, if \(\alpha\) is a zero of \(p(x)\text{,}\) then \(p(x) = (x - \alpha ) q(x)\) for some \(q(x) \in F[x]\) by Corollary 17.8. The degree of \(q(x)\) is \(n-1\) by Proposition 17.4. Let \(\beta\) be some other zero of \(p(x)\) that is distinct from \(\alpha\text{.}\) Then \(p(\beta) = (\beta - \alpha) q(\beta) = 0\text{.}\) Since \(\alpha \neq \beta\) and \(F\) is a field, \(q(\beta ) = 0\text{.}\) By our induction hypothesis, \(q(x)\) can have at most \(n - 1\) zeros in \(F\) that are distinct from \(\alpha\text{.}\) Therefore, \(p(x)\) has at most \(n\) distinct zeros in \(F\text{.}\)
Let \(F\) be a field. A monic polynomial \(d(x)\) is a greatest common divisor of polynomials \(p(x), q(x) \in F[x]\) if \(d(x)\) evenly divides both \(p(x)\) and \(q(x)\text{;}\) and, if for any other polynomial \(d'(x)\) dividing both \(p(x)\) and \(q(x)\text{,}\) \(d'(x) \mid d(x)\text{.}\) We write \(d(x) = \gcd( p(x), q( x))\text{.}\) Two polynomials \(p(x)\) and \(q(x)\) are relatively prime if \(\gcd(p(x), q(x) ) = 1\text{.}\)
Proposition \(17.10\)
Let \(F\) be a field and suppose that \(d(x)\) is a greatest common divisor of two polynomials \(p(x)\) and \(q(x)\) in \(F[x]\text{.}\) Then there exist polynomials \(r(x)\) and \(s(x)\) such that
\[ d(x) = r(x) p(x) + s(x) q(x)\text{.} \nonumber \]
Furthermore, the greatest common divisor of two polynomials is unique.
- Proof
-
Let \(d(x)\) be the monic polynomial of smallest degree in the set
\[ S = \{ f(x) p(x) + g(x) q(x) : f(x), g(x) \in F[x] \}\text{.} \nonumber \]
We can write \(d(x) = r(x) p(x) + s(x) q(x)\) for two polynomials \(r(x)\) and \(s(x)\) in \(F[x]\text{.}\) We need to show that \(d(x)\) divides both \(p(x)\) and \(q(x)\text{.}\) We shall first show that \(d(x)\) divides \(p(x)\text{.}\) By the division algorithm, there exist polynomials \(a(x)\) and \(b(x)\) such that \(p(x) = a(x) d(x) + b(x)\text{,}\) where \(b(x)\) is either the zero polynomial or \(\deg b(x) \lt \deg d(x)\text{.}\) Therefore,
\begin{align*} b(x) & = p(x) - a(x) d(x)\\ & = p(x) - a(x)( r(x) p(x) + s(x) q(x))\\ & = p(x) - a(x) r(x) p(x) - a(x) s(x) q(x)\\ & = p(x)( 1 - a(x) r(x) ) + q(x) ( - a(x) s(x) ) \end{align*}
is a linear combination of \(p(x)\) and \(q(x)\) and therefore must be in \(S\text{.}\) However, \(b(x)\) must be the zero polynomial since \(d(x)\) was chosen to be of smallest degree; consequently, \(d(x)\) divides \(p(x)\text{.}\) A symmetric argument shows that \(d(x)\) must also divide \(q(x)\text{;}\) hence, \(d(x)\) is a common divisor of \(p(x)\) and \(q(x)\text{.}\)
To show that \(d(x)\) is a greatest common divisor of \(p(x)\) and \(q(x)\text{,}\) suppose that \(d'(x)\) is another common divisor of \(p(x)\) and \(q(x)\text{.}\) We will show that \(d'(x) \mid d(x)\text{.}\) Since \(d'(x)\) is a common divisor of \(p(x)\) and \(q(x)\text{,}\) there exist polynomials \(u(x)\) and \(v(x)\) such that \(p(x) = u(x) d'(x)\) and \(q(x) = v(x) d'(x)\text{.}\) Therefore,
\begin{align*} d(x) & = r(x) p(x) + s(x) q(x)\\ & = r(x) u(x) d'(x) + s(x) v(x) d'(x)\\ & = d'(x) [r(x) u(x) + s(x) v(x)]\text{.} \end{align*}
Since \(d'(x) \mid d(x)\text{,}\) \(d(x)\) is a greatest common divisor of \(p(x)\) and \(q(x)\text{.}\)
Finally, we must show that the greatest common divisor of \(p(x)\) and \(q(x)\) is unique. Suppose that \(d'(x)\) is another greatest common divisor of \(p(x)\) and \(q(x)\text{.}\) We have just shown that there exist polynomials \(u(x)\) and \(v(x)\) in \(F[x]\) such that \(d(x) = d'(x)[r(x) u(x) + s(x) v(x)]\text{.}\) Since
\[ \deg d(x) = \deg d'(x) + \deg[r(x) u(x) + s(x) v(x)] \nonumber \]
and \(d(x)\) and \(d'(x)\) are both greatest common divisors, \(\deg d(x) = \deg d'(x)\text{.}\) Since \(d(x)\) and \(d'(x)\) are both monic polynomials of the same degree, it must be the case that \(d(x) = d'(x)\text{.}\)
Notice the similarity between the proof of Proposition \(17.10\) and the proof of Theorem \(2.10\).


7.1: Introduction
Infrastructure managers may go long periods of time without significant failures, extreme events or security breaches occurring for their infrastructure. However, a manager must be prepared to deal with such events and should plan ahead to mitigate the potential costs of such events. This chapter discusses approaches to prepare for and to mitigate the damages of such events.
The list of potential adverse events is long indeed:
- Critical infrastructure failure, such as electricity, water supply, telecommunications, etc.,
- Extreme events, such as earthquakes, fires, floods, hurricanes, landslides, lightning strikes, tornadoes, etc., and
- Security problems, such as bombs, guns, computer hacking, riots, etc.
News media regularly report such events throughout the world on a daily basis. Even the resignation or retirement of an employee with critical management knowledge can reveal a lack of resiliency in management.
While the chance of occurrence for any of these events is quite low in any particular year, the probability is typically not zero. The exception might be physically impossible occurrences such as flooding to a facility at the top of a hill (but then the top of the hill may be more prone to have high wind!). Figure 7.1.1 illustrates the estimates of probabilities of significant (magnitude greater than 6.7) earthquakes in California. The figure outlines the boundaries of California in white and the various earthquake fault lines show up as higher probability linear segments. The probability scale ranges from 10-6 (0.0001% chance per year) in blue to 10-2 (1% chance per year) in purple. While these particular estimates are uncertain, California infrastructure managers should be prepared for an earthquake event!
Even with a low probability of an event occurring, the number of repetitions of the underlying risk opportunity may result in a significant risk. For example, suppose your risk of falling from a scaffold is 0.1% in any particular day, which likely seems like a small risk to you. However, if you are on a scaffold 365 days a year, the probability of a fall over the course of a year would be (as discussed in Chapter 4):
\[P_{r}\{f a l l\}=1-P_{r}\{\text { no } f \text { all }\}^{365}=1-0.69=0.31\]
So you would have a 31% chance of a fall over the course of a year spent on scaffolding. Over fifteen years, the probability of a fall would increase to 99.6%. Similarly, riding a bike to and from work might have a low probability of experiencing a crash, but over a long period of time the likelihood of a crash increases. Better risk management might make changes such as safety straps on scaffolding or dedicated bike lanes. The result would be to lower the daily probability of an event considerably.
In addition to the chance of occurrence, the other dimension of risk management is to consider the severity of consequences for an event. A small flood may have some costs, but an organization could likely recover its infrastructure services rather quickly. In contrast, a large flood or a terrorist attack could have major consequences, including subsequent legal procedures. Similarly, small earthquakes or wildfires may have limited impacts, but a large earthquake or fire could require major rehabilitation or rebuilding.
Infrastructure managers should prepare for events with high frequency and low impact such as heavy rainstorms. For example, a large company with multiple oil platforms in the Gulf of Mexico should be prepared to secure and evacuate the platforms regularly due to hurricanes. But managers also need to prepare for high impact, low probability events such as earthquakes. Fortunately, high impact and high probability risks are rare. Also, low impact and small probability events are less of a concern than these other categories. Figure 7.1.2 illustrates the disruption probability and consequences for several organizational threats.
As an example, Figure 7.1.3 shows identified risks for water and wastewater systems.
Good infrastructure design and construction can significantly reduce the consequences of many risks. For example, earthquake resistant facility design has become required in earthquake prone areas. Similarly, adequate storm water systems (and good preventive maintenance) can reduce the risk of flooding.


9.7: Response to the Cellular Signal - Termination of the Signal Cascade
- Describe the process by which the signal cascade in cell communication is terminated
Termination of the Signal Cascade
Ligand binding to the receptor allows for signal transduction through the cell. The chain of events that conveys the signal through the cell is called a signaling pathway or cascade. Signaling pathways are often very complex because of the interplay between different proteins. A major component of cell signaling cascades is the phosphorylation of molecules by enzymes known as kinases. Phosphorylation adds a phosphate group to serine, threonine, and tyrosine residues in a protein, changing their shapes, and activating or inactivating the protein.
The aberrant signaling often seen in tumor cells is proof that the termination of a signal at the appropriate time can be just as important as the initiation of a signal. One method of terminating or stopping a specific signal is to degrade or remove the ligand so that it can no longer access its receptor. One reason that hydrophobic hormones like estrogen and testosterone trigger long-lasting events is because they bind carrier proteins. These proteins allow the insoluble molecules to be soluble in blood, but they also protect the hormones from degradation by circulating enzymes.
Inside the cell, many different enzymes reverse the cellular modifications that result from signaling cascades. For example, phosphatases are enzymes that remove the phosphate group attached to proteins by kinases in a process called dephosphorylation. Cyclic AMP (cAMP) is degraded into AMP by phosphodiesterase, and the release of calcium stores is reversed by the Ca 2+ pumps that are located in the external and internal membranes of the cell.
Key Points
- The chain of events that conveys the signal through the cell is called a signaling pathway or cascade.
- Phosphorylation, a major component of signal cascades, adds a phosphate group to proteins, thereby changing their shapes and activating or inactivating the protein.
- Degrading or removing the ligand so it can no longer access its receptor terminates the signal.
- Enzymes like phosphotases can remove phosphate groups on proteins during dephosphorylation and reverse the cellular modifications produced by signaling cascades.
Key Terms
- signaling cascade : the chain of events that conveys the signal through the cell
- phosphorylation : the addition of a phosphate group to a compound; often catalyzed by enzymes
- dephosphorylation : the removal of phosphate groups from a compound; often catalyzed by enzymes


5.4: Frequent Allegations and SBON Investigations
The Nurses Service Organization (NSO) reported the three most common allegations resulting in state board investigations in 2020 were related to the categories of professional conduct, scope of practice, and documentation errors or omissions. [1]
Professional Conduct
Common allegations related to professional conduct included drug diversion and substance abuse, professional misconduct, reciprocal actions, and wastage errors.
Drug Diversion and Substance Abuse
The most common allegations related to professional conduct for both RNs and LPN/VNs in 2020 were related to drug diversion and/or substance abuse. Examples include diverting medications for oneself or others and apparent intoxication from alcohol or drugs while on duty.
The National Council of State Boards of Nursing (NCSBN) created a brochure titled Substance Abuse Disorder in Nursing to address this common issue. [2] Many states have programs in place to assist nurses with substance abuse, such as Wisconsin Nursing Association’s Nurses Caring for Nurses (Peer Assistance) program or New York State Nursing Association’s Statewide Peer Assistance for Nurses (SPAN) program. [3] , [4]
Professional Misconduct
Professional misconduct as defined by state regulations was the second most common allegation related to professional conduct. This category includes unprofessional conduct towards coworkers and patients, as well as allegations of falling asleep.
Sample Case A home health RN was assigned to monitor an 11-month-old child from 1900 to 0700. The child was intubated and required constant monitoring to ensure the tubing remained secure while she was in her crib. However, the child’s father found the RN sleeping and the child’s tubing unsecured. The child did not suffer harm due to the incident, but the SBON publicly reprimanded the RN, and the costs to defend the nurse exceeded $2,400. [5]
Reciprocal Actions
The third most common professional conduct allegation was reciprocal actions. Many cases involved nurses who were trying to contend with patients who were violent or aggressive and either retaliated against the patient or responded to the patient ‘s aggression in an inappropriate or unprofessional manner.
Sample Case A patient in an inpatient behavioral health unit became agitated, pulled a phone out of the wall, and threw it. The nurse entered the room and following a brief interaction, an altercation between the patient and the nurse ensued. The nurse received a public reprimand and disciplinary actions from the SBON. [6]
Wastage Errors
Wastage errors were the fourth most common allegation. Wastage errors occurred when nurses neglected to perform accurate medication counts or did not appropriately document proper disposal of opioids and other drugs with a high potential for abuse.
Sample Case An RN left two 15 milligram tablets of a benzodiazepine called Temazepam unattended in an area accessible to patients. The medication went missing and was apparently taken by a patient. The nurse falsely documented the Temazepam as wastage, knowing the medication was actually missing. The SBON issued a $200 fine, and expenses to defend the nurse exceeded $7,200. [7]
Scope of Practice
Common allegations related to scope of practice include failure to maintain a minimum standard of practice and providing services beyond one’s scope of practice.
Failure to Maintain Minimum Standard of Nursing Practice
The most common allegations related to scope of practice include failure to maintain a minimum standard of nursing practice. These cases include a breach of minimum professional standards, incompetence, and negligence.
Sample Case A nurse working in home health failed to complete required patient assessments and omitted pertinent patient information in the health care record. This omission could have caused a disruption in the continuity of treatment resulting in patient harm. The SBON determined the nurse failed to exercise the degree of learning, skill, care, and experience ordinarily possessed and exercised by a competent RN. The SBON placed the nurse on probation for three years, and the expenses associated with defending the nurse exceeded $5,400. [8] Sample Case An RN failed to follow agency policy and procedures by neglecting to properly verify identification of two patients and omitting the review of relevant laboratory results. As a result of bypassing standard safety procedures, the RN gave an extra unit of blood to one patient that was intended for the other patient, thereby depriving that patient the extra unit of blood required based on her lab results. The SBON placed the nurse on probation for three years. However, the nurse did not comply with the terms of her probation by failing to report to the SBON when she applied for licensure in two other states. The nurse also failed to obtain approval prior to commencing employment. The nurse was ultimately ordered to surrender her license. [9] Sample Case A student nurse was instructed to discontinue an intravenous (IV) antibiotic for a patient with a central venous catheter. When the student discontinued the IV, she unknowingly loosened the catheter connection from the lumen luer connector. The loosened line would likely have been discovered when the line was flushed per agency policy, but the student testified she did not know she was supposed to flush the catheter line or clamp it after the medication was discontinued. Shortly thereafter, the patient became unresponsive, and a code was called. The disconnection was not discovered until the patient was transferred to the intensive care unit three hours later. The patient experienced an air embolism and died. A malpractice claim was awarded. [10]
Provision of Services Beyond Scope of Practice
The second most common allegation related to scope of practice is provision of services beyond one’s scope of practice. This category typically involves nurses making changes to patients’ prescribed treatments or administering medication that had not been prescribed.
Sample Case An RN in the ICU was caring for a patient with extreme nausea. The nurse made several unsuccessful attempts to reach the provider for an order for Ondansetron. The nurse called the pharmacy and relayed her concern for the patient’s nausea and her inability to reach the provider. The nurse informed the pharmacist that she believed the situation was urgent and she would contact the provider for an order. The pharmacy dispensed Ondansetron and the nurse administered the medication. Although the patient did not suffer adverse effects from the medication, no order was ever received for the medication. Upon finding the RN violated the Nurse Practice Act by practicing beyond the scope of practice for an RN, the SBON publicly reprimanded the nurse and ordered her to pay a fine of $600. Expenses associated with defending the nurse exceeded $6,100. [11]
Documentation
Over half of the allegations in 2020 regarding documentation were related to fraudulent or falsified patient care or billing records. The health care record is a legal document. It should never be altered, deleted, or falsified. Maintaining accurate and timely documentation is a primary professional responsibility of nurses.
Sample Case In a case involving a nursing student, the preceptor instructed the student to monitor the patient’s vital signs every 15 minutes for one hour and then every 30 minutes for two hours and then every hour for four hours. The student allegedly documented vital signs every 15 minutes for one hour but did not record any vital signs thereafter. When confronted by her preceptor about the incomplete record, the student stated that she “forgot to do them.” Approximately 30 minutes later, the preceptor discovered the missing vital signs were documented in the patient’s record. The preceptor asked the student about the entries, and the student replied that she “made them up.” The student later contended that she meant she charted the vital signs accurately but made up the times the vital signs were taken to match the preceptor’s instructions. The SBON considered the student was still learning but viewed documentation as a basic nursing skill. Because the student’s conduct involved dishonesty, they imposed a penalty of a one-year suspension followed by one year of probation. The expenses associated with defending the student nurse exceeded $6,900. [12]
- Nurses Service Organization and CAN Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- National Council State Board of Nursing. Substance Abuse Disorder in Nursing [Brochure]. https://www.ncsbn.org/SUD_Brochure_2014.pdf ↵
- Wisconsin Nurses Association. (n.d.). Nurses caring for nurses (peer assistance). https://www.wisconsinnurses.org/about-wna/affiliates/nurses-caring-for-nurses-peer-assistance/ ↵
- Statewide Peer Assistance For Nurses. https://www.statewidepeerassistance.org/ ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵
- Nurses Service Organization and CNA Financial. (2020, June). Nurse professional liability exposure claim report (4th ed.). https://www.nso.com/Learning/Artifacts/Claim-Reports/Minimizing-Risk-Achieving-Excellence ↵


14.1A: Portals of Microbe Entry
- Recognize the various methods and types of microorganism transmission: vectors, hosts, horizontal, vertical transmissions
Microbes gain access to human tissues via two main types of routes: mucosal surfaces within the body (linings of the respiratory, digestive, reproductive, or urinary tracts) or epithelial surfaces on the outside of the body (areas of skin that are either undamaged or compromised due to insect bites, cuts/scrapes, or other wounds).
Transmission of Microorganisms
Transmission of microorganisms occurs directly from one person to another by one or more of the following means:
- droplet contact by coughing or sneezing on another person
- direct physical contact by touching an infected person
- direct physical contact (usually by touching soil contamination or a contaminated surface)
- airborne transmission (if the microorganism can remain in the air for long periods)
- fecal-oral transmission (usually from contaminated food or water sources)
- contamination via intravenous drug us
- contamination from blood given via transfusion or organ transplants
Transmission can also be indirect via another organism, either a vector (like a mosquito) or an intermediate host (like how a tapeworm from a pig can be transmitted to humans who ingest improperly cooked pork).
Horizontal or Vertical Transmission
Disease can also be directly transmitted in two ways: horizontally or vertically. Horizontal disease transmission occurs from one individual to another in the same generation (peers in the same age group), and can occur by either direct contact (licking, touching, biting), or indirect contact. Vertical disease transmission involves passing a disease causing agent vertically from parent to offspring.
Pathogens must have a way to be transmitted from one host to another to ensure their species ‘ survival. Infectious agents are generally specialized for a particular method of transmission. Taking an example from the respiratory route, from an evolutionary perspective a virus or bacteria that causes its host to develop coughing and sneezing symptoms has a great survival advantage: it is much more likely to be ejected from one host and carried to another.
A locus is the point on the body where a pathogen enters. In droplet contact and other airborne transmission it is generally the respiratory system through the nose, mouth, or eye surfaces. In direct physical and indirect contact it is generally through a wound in the skin or through a mucous membrane. In fecal-oral transmission, it is through the mouth. In vector-borne transmission, it is at the bite or sting of the vector. Other common indirect routes include contaminated food or water.
Sexual Transmission
In sexual transmission, infection originates directly between surfaces in contact during intercourse (the usual route for bacterial infections and those infections causing sores) or from secretions (semen or the fluid secreted by the excited female).  Bodily fluids such as saliva and tears do not transmit HIV. Oral sexual practices have increased the incidence of herpes simplex virus 1 (which is usually responsible for oral infections) in genital infections and the increased incidence of the type 2 virus (more common genitally) in oral infections. Herpes diseases that are transmitted primarily by oral means may be caught through direct contact with an infectious area of the skin.
Direct Contact: Contagious Diseases
Diseases that can be transmitted by direct contact are called contagious (contagious is not the same as infectious). Although all contagious diseases are infectious, not all infectious diseases are contagious. Interestingly, some contagious diseases like tuberculosis were not classically considered to be contagious even though they are transmissible from person to person. Direct transmission can also occur by sharing a towel (where the towel is rubbed vigorously on both bodies) or items of clothing in close contact with the body (socks, for example) if they are not washed thoroughly between uses. Some diseases that are transmissible by direct contact include Athlete’s foot and impetigo.
Key Points
- Transmission can be direct (vertically or horizontally) or indirect.
- Infectious agents are generally specialized for a particular method of transmission.
- A locus is the point on the body where a pathogen enters.
Key Terms
- infectious : Infectious diseases, also known as transmissible diseases or communicable diseases, comprise clinically evident illness (i.e., characteristic medical signs and/or symptoms of disease) resulting from the infection, presence, and growth of pathogenic biological agents in an individual host organism.
- pathogen : Any organism or substance, especially a microorganism, capable of causing disease, such as bacteria, viruses, protozoa, or fungi. Microorganisms are not considered to be pathogenic until they have reached a population size that is large enough to cause disease.
- contagious : Of a person, having a disease that can be transmitted to another person by touch.


6.5E: Sinusoidal Graphs (Exercises)
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Section 6.1 Exercises
1. Sketch a graph of \(f\left(x\right)=-3\sin \left(x\right)\).
2. Sketch a graph of \(f\left(x\right)=4\sin \left(x\right)\).
3. Sketch a graph of \(f\left(x\right)=2\cos \left(x\right)\).
4. Sketch a graph of \(f\left(x\right)=-4\cos \left(x\right)\).
For the graphs below, determine the amplitude, midline, and period, then find a formula for the function.
5. 6.
7. 8.
9. 10.
For each of the following equations, find the amplitude, period, horizontal shift, and midline.
11. \(y=3\sin (8(x+4))+5\)
12. \(y=4\sin \left(\dfrac{\pi }{2} (x-3)\right)+7\)
13. \(y=2\sin (3x-21)+4\)
14. \(y=5\sin (5x+20)-2\)
15. \(y=\sin \left(\dfrac{\pi }{6} x+\pi \right)-3\)
16. \(y=8\sin \left(\dfrac{7\pi }{6} x+\dfrac{7\pi }{2} \right)+6\)
Find a formula for each of the functions graphed below.
17.
18.
19.
20.
21. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 57 and 43 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D , in terms of t .
22. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 68 degrees at midnight and the high and low temperature during the day are 80 and 56 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D , in terms of t .
23. A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function \(h(t)\) gives your height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of \(h\left(t\right)\).
b. Find a formula for the height function \(h\left(t\right)\).
c. How high are you off the ground after 5 minutes?
24. A Ferris wheel is 35 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function \(h(t)\) gives your height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of \(h\left(t\right)\).
b. Find a formula for the height function \(h\left(t\right)\).
c. How high are you off the ground after 4 minutes?
- Answer
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1.
3.
5. Amp: 3. Period = 2. Midline: \(y = -4\). \(f(t) = 3\sin(\pi t) - 4\)
7. Amp: 2. Period = \(4\pi\). Midline: \(y = 1\). \(f(t) = 2\cos(\dfrac{1}{2} t) + 1\)
9. Amp: 2. Period = 5. Midline: \(y = 3\). \(f(t) = -2\cos(\dfrac{2\pi}{5} t) + 3\)
11. Amp: 3, Period = \(\dfrac{\pi}{4}\), Shift: 4 left, Midline: \(y = 5\)
13. Amp: 2, Period = \(\dfrac{2\pi}{3}\), Shift: 7 left, Midline: \(y = 4\)
15. Amp: 1, Period = 12, Shift: 6 left, Midline: \(y = -3\)
17. \(f(x) = 4\sin(\dfrac{\pi}{5} (x + 1))\)
19. \(f(x) = \cos(\dfrac{\pi}{5} (x + 2))\)
21. \(D(t) = 50 - 7 \sin(\dfrac{\pi}{12}t)\)
23. a. Amp: 12.5. Midline: \(y = 13.5\). Period: 10
b. \(h(t) = -12.5 \cos(\dfrac{\pi}{5}t) + 13.5\)
c. \(h(t) = 26\) meters