11.2: Saving Species Through Translocations
Because the probability of extinction increases rapidly for small populations (Section 8.7), conservation biologists often invest considerable energy into increasing the size of small and declining populations. Often, these projects involve improving the extent and quality of suitable habitat (Chapter 10) or mitigating threats such as overharvesting (Chapter 12). When appropriate, conservation biologists may sometimes resort to translocations—moving individuals from sites where they are threatened (e.g. unprotected lands or a paper park) or overabundant (e.g. a well-managed protected area or ex situ conservation facility) to sites where they can offer a larger contribution to conservation efforts.
Understanding a species’ ecological needs is critically important for translocations, because it influences the choice of release site and type of preparations needed.
Conservation biologists generally recognize four basic translocation approaches:
- Restocking (also called augmentation) occurs when wildlife managers increase the size and genetic diversity of existing populations, by releasing individuals that have been raised in captivity or that have been obtained from other wild populations.
- Reintroduction occurs when wildlife managers release individuals into areas where they occurred in the past but not at present. The areas must be ecologically suitable and the factors that caused the extirpation must have been reduced or eliminated for a reintroduction to be successful.
- Introduction involves creating new populations by moving individuals to suitable areas outside that species’ historical range. Introductions are usually considered when reintroductions are impossible because the species’ historical range has been degraded too severely or because persistent threats will lead to reintroduction failure.
- Assisted colonisation (also called assisted migration) is a special class of introduction where biologists “assist” species with poor dispersal capabilities to adapt their ranges in response to environmental changes. It is anticipated that this strategy will become an important conservation tool in preventing extinctions where climate change outpaces the speed of natural migration.
Important considerations for translocations
Section 11.1 broadly discussed the importance of understanding the ecological and other natural history needs when protecting threatened species. Understanding a species’ ecological needs is equally, if not more, important for translocations, because it influences the choice of release site and type of preparations needed (Figure 11.4). Complementing the 10 factors mentioned in Section 11.1, the next section briefly introduces some of the most important considerations during translocations.
Determining need and feasibility
Perhaps the most important factor to consider before starting a translocation is to determine whether it is necessary. Translocations carry risks, not only for the target population to be moved, but also the individuals left behind and for the recipient ecosystem. These risks expose translocation projects to a high risk of failure, particularly if preparations are inadequate and essential resources (e.g. funding, trained staff) are in short supply. Translocations also demand considerable resources—resources that can at times be better spent mitigating the threats the target population face. While these considerations may seem obvious, a recent review found that most translocations projects are initiated without proper cost-benefit analyses (Pérez et al., 2012). To improve translocation practices, conservationists seriously considering a translocation project are encouraged to review the 10 criteria outlined in Pérez et al. (2012), some of which also overlap with the considerations mentioned below.
Support from local stakeholders
It is also important to consider, at an early stage, how the public will view the translocation project. Some people may feel the resources used in a translocation are better invested elsewhere; others dislike translocations because they view it as a threat to their livelihood—this is especially true when carnivores are involved (Gusset et al., 2008a). Because of these and other potential conflicts and emotions, it is crucial that translocation projects (like any conservation activity) obtain the support from local stakeholders at an early stage. It is helpful to be transparent from the outset and to explain the project’s goals, as well as the benefits the local community may gain (e.g. attract more tourists, restore a degraded ecosystem service). Good public outreach also provides opportunities to address the public’s concerns and misconceptions about the project and about biodiversity conservation in general.
Identifying suitable habitat
It goes without saying that the probability for success is greatly improved when the translocated individuals are released in good quality habitat. This is particularly true for species with poor dispersal capabilities, such as plants that reproduce through vegetative propagation: the plants could die in an environment that is too sunny, shady, wet, or dry. While this point may seem obvious, many translocations fail because individuals are released in inferior habitats (Armstrong and Seddon, 2007). One of the reasons for this potential habitat mismatch is because wildlife may perceive the environment differently than humans, so a site that may look good to the human eye may lack one or more overlooked limiting resource. Refugee species—species forced to live in suboptimal habitat due to threats present in their preferred habitat (e.g. Ali et al., 2017)—also present a challenge to biologists who may unwittingly view inferior habitat as optimal and base conservation decisions on essentially bad information. The same challenge presents itself at ecological traps—unsuitable environments that an organism mistakenly perceives as optimal habitat (e.g. Sherley et al., 2017). These are some of the most important reasons why biologists need to be cautions when using species distribution models (SDM) when identifying areas suitable for translocations. To mitigate costly translocation failures, it is advisable that releases start small, and have multiple phases, to assess how released individuals respond to their new environment. Conducting experimental and adaptive releases can also reduce uncertainty by evaluating different release scenarios (Menges et al., 2016).
Species forced to live in suboptimal habitat due to threats present in their preferred habitat may lead biologists to unwittingly view inferior habitat as optimal.
It is also important to ensure that any habitat identified as suitable is free from threats such as pollution and invasive species that may lead to declining health or even death for released individuals. A project in the Cape Floristic Region in South Africa provides a good example of how alert conservation biologists mitigated a threat that could have caused a translocation failure. The Clanwilliam sandfish (Labeo seeberi, EN) was once widespread in the region’s Olifants-Doring River system. However, recent surveys indicated that the species had gone extinct in the Olifants River. Although biologists did find some juvenile fish in the Doring River and some of its tributaries, they also noticed that invasive fish predated on most of those juveniles before they reached adulthood (Jordaan et al., 2017). These ill-fated individuals were thus dispersing from the last remaining reproductive subpopulation persisting in the headwaters of one single Doring tributary to other parts of the river, which acted as a population sink. To prevent the species’ extinction, biologists initiated a habitat restoration plan involving restoring natural stream flow regimens and eradicating predatory invasive fish in the headwaters of a second Doring tributary. They then installed barriers that prevented invasive fish from reaching the restored area before translocating 338 juvenile fish (Figure 11.5) there. With this habitat restoration plan, the biologists hope to establish a second viable population, and to improve the juveniles’ chances of surviving to adulthood before they disperse back to areas where the invasive fishes occur (Jordaan et al., 2017).
Considering genetics and behavior
Translocation projects also need to consider the genetic makeup, social organization, and behavior of a species that is being released. It is preferable to use individuals from the same genetic stock as individuals that already occur (or have occurred) in the release area to avoid outbreeding depression and to capture local adaptations (Sections 8.7.1). Such efforts simultaneously also contribute to conservation of genetic diversity, as opposed to the pollution thereof if individuals from different genetic stock are mixed.
Group-living species, particularly those vulnerable to Allee effects (Section 8.7.2), need to be released in sufficient numbers so they can maintain their natural social organization and behavior. For species that need to be released in groups, it is preferable to release socially integrated animals rather than individuals unfamiliar with each other (Gusset et al., 2008b). Releasing groups of animals does have its own set of challenges. For example, social groups abruptly released from captivity may disperse explosively, possibly leading to project failure. This happened with African buffalo (Syncerus caffer, NT) herds translocated to South Africa’s Addo Elephant National Park which fragmented into smaller groups after release, making them more vulnerable to lion (Panthera leo, VU) predation (Tambling et al., 2013). Fortunately, in this case, the buffaloes underwent several behavioral modifications over time, which eventually allowed their numbers to stabilise (Box 11.2). This contrasts with failed rock hyrax (Procavia capensis, LC) reintroductions in South Africa, where group disintegration post release exposed the animals to unsustainable predation levels (Wimberger et al., 2009).
Craig J. Tambling
Department of Zoology and Entomology, University of Fort Hare,
Alice, South Africa.
Large predator numbers are declining, and African carnivores are no exception (Ripple et al. 2014). How to conserve African carnivores are a hotly debated topic now, with “fortress” type conservation areas considered the most viable option by many (Packer et al., 2013). In South Africa, this conservation model is the norm, and many small protected areas are now translocating large carnivores for ecotourism. However, these large carnivore translocations have repercussions for resident prey species. Understanding the ecological and biodiversity consequences of these translocations is thus important for the management of these small protected areas (Tambling et al., 2014).
In 2003, lions and spotted hyenas (Crocuta crocuta, LC) were reintroduced into the Addo Elephant National Park Main Camp Section after being absent from the area for over 100 years. Post-release monitoring of the six reintroduced lions indicated that at least 50% of their diet in the first two years following reintroduction was African buffalo. This was especially concerning to South African National Parks as this resident buffalo population contributes substantially to game auction sales each year, with the money raised being used to expand the national park system in South Africa (SANParks, 2009).
Following high predation rates of buffalo by lion and a 2007 buffalo census suggesting low juvenile recruitment, the coexistence of lion and buffalo in Addo was questioned. These concerns lead to a detailed assessment of buffalo behavior and demographics between 2008 and 2011 (Tambling et al., 2012), which showed that by 2008–2009, juvenile buffalo recruitment (Figure 11.B) had rebounded to levels reminiscent of those prior to the lion reintroduction. Direct observations of the buffalo population showed drastic behavioral alteration following the high initial predation rates by lions. These behavioral changes included: (1) increased breeding herd sizes, (2) a reduction in nocturnal movement, and (3) greater use of open habitats at night and early morning when lions are hunting. These behavioral adjustments enabled the active defence of the breeding herds, reducing successful predation by lions and ensuring an increase in buffalo recruitment. Although this study suggests that prey populations are capable of behavioral adjustments to reduce predation, this is not always the case, with some species unable to respond, leading to precipitous declines in prey populations such as eland (Tragelaphus oryx, LC) (Leaver, 2014).
The ultimate aim of most translocation projects is to establish populations that are self-sustaining, free from inbreeding, and interactive participants of their communities and ecosystems.
Case studies of predator-prey interactions following large predator reintroductions highlight the management challenges faced by small reserves where ecotourism, biodiversity, and financial goals each need to be met. Due to the small size of these “fortress” reserves, a local overabundance of predators can have severe ecological effects on prey populations. However, in many reserves, the high demand for large predators for ecotourism often results in costly reactive, rather than scientifically sound proactive, management. There is, however, a growing body of research on the proactive management of large carnivores, where wildlife managers aim to replicate ecological processes (i.e. lion inter-birth intervals) to limit management interventions required to control large predator numbers (Ferreira and Hofmeyr, 2014). In small reserves, lion inter-birth intervals are shorter than in large ecosystems, and so lengthening the inter-birth intervals to that observed in large ecosystems can reduce lion population growth rate in these small reserves (Miller et al., 2015). Understanding predator-prey interactions is important regardless of the conservation model employed to protect these large charismatic species.
How many individuals to release
The ultimate aim of translocation projects is to establish ecologically relevant populations, meaning populations that are self-sustaining, free from inbreeding, and an interactive participant of its community and ecosystem. The probability of achieving this goal increases as more individuals are being released. Because translocation projects typically do not have an unlimited supply of individuals to release, wildlife managers often rely on quantitative models (Section 9.2) to estimate the minimum number of individuals that should be released and how many times releases should occur. For example, a population viability analysis (PVA) on western lowland gorillas (Gorilla gorilla gorilla, CR) reintroduced to Gabon and the Republic of the Congo showed that the probability of persistence of an apparently established population could be increased significantly if more individuals were released (King et al., 2014).
The ability to establish new populations through translocations does not reduce the need to protect threatened species still in their natural habitats.
While releasing more individuals certainly improves the likelihood of establishing a self-sustaining population, it is also important to determine how many individuals the target community can sustain. In other words, the release area should contain enough suitable habitat to support the territories of all the released individuals. To determine how many individuals can be sustained, wildlife managers may calculate the release area’s carrying capacity—an estimate of the maximum number of individuals an ecosystem can support. The carrying capacity concept has its roots in the livestock trade, where farmers wanted to maximise the number of animals on their land without risking overgrazing. While the concept has gained popularity in conservation biology in recent decades, calculating the carrying capacity for wildlife is very complex because of all the multi-faceted interactions that characterize healthy ecosystems. For example, the carrying capacity for a wild population can depend on factors such as food, water, shelter, soil nutrients, and sunlight availability, as well as more species-specific natural history factors such as habitat quality, home range, sex ratios (Tambling et al., 2014), and interactions with other species (Lindsey et al., 2011).
Over the past few decades, through trial and error, adaptive management (Section 10.2.3), and the collection of vast amounts of demographic data, scientists have made significant progress in calculating carrying capacity for wildlife populations. Perhaps the most progress has been made in calculating carrying capacities for large ungulates, by monitoring vegetation biomass, which in turn is affected by soil nutrients and rainfall (Fritz and Duncan, 1994). Much progress has also been made in calculating carrying capacities of predators by monitoring prey densities (Hayward et al., 2007a). For most populations, however, carrying capacity isn’t explicitly calculated, but implicitly estimated based on intuition. Refining existing carrying capacity models and developing new methods for other taxa remain an active area of research that will hopefully reduce conservation biologists’ over-reliance on intuition in future years. But even in the absence of carrying capacity calculations, wildlife managers can track a population’s health and overall fitness. When the health of a particularly successful population or its environment starts declining, a root cause may be that too many individuals have been released, or the population is being sustained above carrying capacity.
Preparing individuals for release
Translocation projects using individuals obtained from the wild are generally much more successful than those using captive-bred individuals, given that wild individuals are already adapted to a life where they must fend for themselves. Nevertheless, some projects may have to use captive-bred individuals, particularly when the target species is extinct in the wild, or when individuals were brought to an ex situ conservation facility because it is easier to breed them under human care in controlled conditions. In such cases, a great amount of effort may be required to prepare the captive-bred individuals for releases.
A great amount of effort may be required to prepare captive-bred individuals for translocation because they may have lost adaptations required for survival and reproduction in the wild.
A major drawback when using captive-bred individuals is that they may have lost the important adaptations required for survival and successful reproduction in the wild. Pre-release training, which varies according to the species, can sometimes overcome this drawback. For predators, it may involve providing low risk prey, such as chickens and domestic rabbits in holding facilities until their hunting skills are better developed (Houser et al., 2011). For plants propagated indoors, it may involve hardening them off by placing them outside for increasingly longer periods to gradually introduce them to sun, wind, and temperature changes during the day. To help young birds disassociate humans from food, human trainers sometimes use puppets or wear costumes (Figure 11.6) during feeding time to mimic the appearance and behavior of wild individuals (Valutis and Marzluff, 1999). Another method, which may promote behavioral enrichment, involves cross-fostering, in which unrelated parents helps raise the offspring of a threatened species. In carnivore conservation, this technique has shown much promise to augment litter size and encourage gene flow using orphaned African wild dog (Lycaon pictus, EN) pups (McNutt et al., 2008). Interspecific cross-fostering has also been used in bird conservation, where biologists use common species to incubate eggs abandoned by threatened species (e.g. Powell and Cuthbert, 1993). However, cross-fostering using different species may lead to a new set of problems, like behavioral changes and hybridisation, if the young subsequently associate with the wrong species. A great amount of care and research are thus needed before such strategies are attempted.
Whether using captive-bred or wild individuals for translocations, individuals may have to be fed, sheltered, trained, or otherwise cared for after release to give them time to become more familiar with their new surroundings. This approach, known as soft release, involves keeping the released individuals in pre-release holding facilities for a period; it may also include some form of assistance after release to increase opportunities for success. Soft releases also provide an opportunity to introduce captive-bred organisms to wild individuals of the same species that can act as “instructors” for survival in the new environment, or for unfamiliar individuals to bond into cohesive units (Gusset et al., 2006).
The alternative to soft release is a hard release—an abrupt release of individuals from captivity without assistance such as food supplementation. While hard releases are popular (because they are relatively easy to perform), it is a risky strategy that faces a high risk to failure (Brown et al., 2007; Wimberger et al., 2009). Hard releases can however be appropriate under the right conditions (Hayward et al., 2007b). For example, hard releases are often use in head-starting programs (Figure 11.7) for reptiles and amphibians (Scheele et al., 2014), where conservation biologists collect wild individuals and raise them past their most vulnerable life stages before releasing them again where they were collected.
Post-release monitoring
A translocation project does not end after the last individual was released. Rather, ongoing monitoring should be implemented to determine whether a translocation was successful, what degree of success was achieved, whether adaptive management is needed, whether additional releases should be conducted, or whether the project should be aborted. A well-designed monitoring plan can also highlight the consequences of translocation on the broader ecosystem, such as the impact that predators introduced to a new area may have on prey populations (Box 11.2) and competing species (Groom et al., 2017). Because some responses in translocated populations can be rather subtle and take many years to show or subside, post-release monitoring should ideally be a long-term endeavour. For example, by monitoring seemingly successful elephant reintroductions across five protected areas in South Africa, researchers found that stress hormones in released animals continued to decline 24 years post release (Jachowski et al., 2013). Long-term monitoring will also help wildlife managers better understand the ultimate fate of the released individuals.  Highlighting the importance of post-release monitoring, one study from South Africa found that 70% of captive-bred oribi (Oribia oribi, LC) died within two months of release, mostly due to predation (Grey-Ross et al., 2009). Another study found that reintroduced cheetahs were all killed within a year of release (Houser et al., 2011). These were expensive lessons, but post-release monitoring ensured that the reason for failures are known and can be addressed ahead of future releases.
Helping other translocation projects
Strategies used in successful translocation projects were nearly always informed by releases conducted by other wildlife managers who circulated their experiences to the wider conservation community. It is important to pay this effort forward; new translocation projects should make every effort to track and publish their results to inform others. While it is always easier to present the results of successful projects, publishing the lessons from failed projects is also important (Wimberger et al., 2010; Godefroid et al., 2011). Equally important is the publication of project costs, to enable wildlife managers to better determine under which conditions translocations represent a cost-effective conservation strategy. For example, a large African wild dog reintroduction program in South Africa achieved their initial goal of establishing nine self-sustaining packs much more quickly than expected—five years rather than 10—yet reintroducing all these populations cost 20 times more than if the funds were used to enhance protection of existing packs within protected areas (Lindsey et al., 2005). With more information available, future conservationists would hopefully be able to have better guidelines to maximise cost-effectiveness and the likelihood of project success.


4.3: Direct Memory Access (DMA)
Introduction
This section introduces the learners to the DMA programmed I/O which provides access to the microprocessor between devices operating at different speeds
Activity Details
Direct Memory Access and DMA-controlled I/O
The DMA I/O technique is used in personal computer systems including those using Intel family of microprocessors. The direct memory access (DMA) I/O technique provides direct access to the memory while the microprocessor is temporarily disabled. A DMA controller temporarily borrows the address bus, data bus, and control bus from the microprocessor and transfers the data bytes directly between an I/O port and a series of memory locations. The DMA transfer is also used to do high-speed memory-to memory transfers. Two control signals are used to request and acknowledge a DMA transfer in the microprocessor-based system. The HOLD signal is a bus request signal which asks the microprocessor to release control of the buses after the current bus cycle. The HLDA signal is a bus grant signal which indicates that the microprocessor has indeed released control of its buses by placing the buses at their high- impedance states. The HOLD input has a higher priority than the INTR or NMI interrupt inputs.
Special hardware writes to / reads from memory directly (without CPU intervention) and saves the timing associated with op-code fetch and decoding, increment and test addresses of source and destination. The DMA controller may both stop the CPU and access the memory (cycle stealing DMA) or use the bus while the CPU is not using it (hidden cycle DMA). The DMA controller has some control lines (to do a handshake with the CPU negotiating to be a bus master and to emulate the CPU behaviour while accessing the memory), an address register which is auto-incremented (or auto-decremented) at each memory access, and a counter used to check for final byte (or word) count.
Conclusion
This section has introduced the learners to the DMA and its operations of synchronizing the I/O devices with the microprocessor
Assessment
Describe how DMA helps in the synchronization of different devices in accessing the microprocessor
The direct memory access (DMA) I/O technique provides direct access to the memory while the microprocessor is temporarily disabled. A DMA controller temporarily borrows the address bus, data bus, and control bus from the microprocessor and transfers the data bytes directly between an I/O port and a series of memory locations. The DMA transfer is also used to
do high-speed memory-to-memory transfers. Two control signals are used to request and acknowledge a DMA transfer in the microprocessor-based system. The HOLD signal is a bus request signal which asks the microprocessor to release control of the buses after the current bus cycle. The HLDA signal is a bus grant signal which indicates that the microprocessor has indeed released control of its buses by placing the buses at their high-impedance states. The HOLD input has a higher priority than the INTR or NMI interrupt inputs.


33.3: Homeostasis
Skills to Develop
- Define homeostasis
- Describe the factors affecting homeostasis
- Discuss positive and negative feedback mechanisms used in homeostasis
- Describe thermoregulation of endothermic and ectothermic animals
Animal organs and organ systems constantly adjust to internal and external changes through a process called homeostasis (“steady state”). These changes might be in the level of glucose or calcium in blood or in external temperatures. Homeostasis means to maintain dynamic equilibrium in the body. It is dynamic because it is constantly adjusting to the changes that the body’s systems encounter. It is equilibrium because body functions are kept within specific ranges. Even an animal that is apparently inactive is maintaining this homeostatic equilibrium.
Homeostatic Process
The goal of homeostasis is the maintenance of equilibrium around a point or value called a set point . While there are normal fluctuations from the set point, the body’s systems will usually attempt to go back to this point. A change in the internal or external environment is called a stimulus and is detected by a receptor; the response of the system is to adjust the deviation parameter toward the set point. For instance, if the body becomes too warm, adjustments are made to cool the animal. If the blood’s glucose rises after a meal, adjustments are made to lower the blood glucose level by getting the nutrient into tissues that need it or to store it for later use.
Control of Homeostasis
When a change occurs in an animal’s environment, an adjustment must be made. The receptor senses the change in the environment, then sends a signal to the control center (in most cases, the brain) which in turn generates a response that is signaled to an effector. The effector is a muscle (that contracts or relaxes) or a gland that secretes. Homeostatsis is maintained by negative feedback loops. Positive feedback loops actually push the organism further out of homeostasis, but may be necessary for life to occur. Homeostasis is controlled by the nervous and endocrine system of mammals.
Negative Feedback Mechanisms
Any homeostatic process that changes the direction of the stimulus is a negative feedback loop . It may either increase or decrease the stimulus, but the stimulus is not allowed to continue as it did before the receptor sensed it. In other words, if a level is too high, the body does something to bring it down, and conversely, if a level is too low, the body does something to make it go up. Hence the term negative feedback. An example is animal maintenance of blood glucose levels. When an animal has eaten, blood glucose levels rise. This is sensed by the nervous system. Specialized cells in the pancreas sense this, and the hormone insulin is released by the endocrine system. Insulin causes blood glucose levels to decrease, as would be expected in a negative feedback system, as illustrated in Figure \(\PageIndex{1}\). However, if an animal has not eaten and blood glucose levels decrease, this is sensed in another group of cells in the pancreas, and the hormone glucagon is released causing glucose levels to increase. This is still a negative feedback loop, but not in the direction expected by the use of the term “negative.” Another example of an increase as a result of the feedback loop is the control of blood calcium. If calcium levels decrease, specialized cells in the parathyroid gland sense this and release parathyroid hormone (PTH), causing an increased absorption of calcium through the intestines and kidneys and, possibly, the breakdown of bone in order to liberate calcium. The effects of PTH are to raise blood levels of the element. Negative feedback loops are the predominant mechanism used in homeostasis.
Positive Feedback Loop
A positive feedback loop maintains the direction of the stimulus, possibly accelerating it. Few examples of positive feedback loops exist in animal bodies, but one is found in the cascade of chemical reactions that result in blood clotting, or coagulation. As one clotting factor is activated, it activates the next factor in sequence until a fibrin clot is achieved. The direction is maintained, not changed, so this is positive feedback. Another example of positive feedback is uterine contractions during childbirth, as illustrated in Figure \(\PageIndex{2}\). The hormone oxytocin, made by the endocrine system, stimulates the contraction of the uterus. This produces pain sensed by the nervous system. Instead of lowering the oxytocin and causing the pain to subside, more oxytocin is produced until the contractions are powerful enough to produce childbirth.
Exercise
State whether each of the following processes is regulated by a positive feedback loop or a negative feedback loop.
- A person feels satiated after eating a large meal.
- The blood has plenty of red blood cells. As a result, erythropoietin, a hormone that stimulates the production of new red blood cells, is no longer released from the kidney.
- Answer
-
Both processes are the result of negative feedback loops. Negative feedback loops, which tend to keep a system at equilibrium, are more common than positive feedback loops.
Set Point
It is possible to adjust a system’s set point. When this happens, the feedback loop works to maintain the new setting. An example of this is blood pressure: over time, the normal or set point for blood pressure can increase as a result of continued increases in blood pressure. The body no longer recognizes the elevation as abnormal and no attempt is made to return to the lower set point. The result is the maintenance of an elevated blood pressure that can have harmful effects on the body. Medication can lower blood pressure and lower the set point in the system to a more healthy level. This is called a process of alteration of the set point in a feedback loop.
Changes can be made in a group of body organ systems in order to maintain a set point in another system. This is called acclimatization . This occurs, for instance, when an animal migrates to a higher altitude than it is accustomed to. In order to adjust to the lower oxygen levels at the new altitude, the body increases the number of red blood cells circulating in the blood to ensure adequate oxygen delivery to the tissues. Another example of acclimatization is animals that have seasonal changes in their coats: a heavier coat in the winter ensures adequate heat retention, and a light coat in summer assists in keeping body temperature from rising to harmful levels.
Link to Learning
Feedback mechanisms can be understood in terms of driving a race car along a track: watch a short video lesson on positive and negative feedback loops.
Homeostasis: Thermoregulation
Body temperature affects body activities. Generally, as body temperature rises, enzyme activity rises as well. For every ten degree centigrade rise in temperature, enzyme activity doubles, up to a point. Body proteins, including enzymes, begin to denature and lose their function with high heat (around 50 o C for mammals). Enzyme activity will decrease by half for every ten degree centigrade drop in temperature, to the point of freezing, with a few exceptions. Some fish can withstand freezing solid and return to normal with thawing.
Link to Learning
Watch this Discovery Channel video on thermoregulation to see illustrations of this process in a variety of animals.
Endotherms and Ectotherms
Animals can be divided into two groups: some maintain a constant body temperature in the face of differing environmental temperatures, while others have a body temperature that is the same as their environment and thus varies with the environment. Animals that do not control their body temperature are ectotherms. This group has been called cold-blooded, but the term may not apply to an animal in the desert with a very warm body temperature. In contrast to ectotherms, which rely on external temperatures to set their body temperatures, poikilotherms are animals with constantly varying internal temperatures. An animal that maintains a constant body temperature in the face of environmental changes is called a homeotherm. Endotherms are animals that rely on internal sources for body temperature but which can exhibit extremes in temperature. These animals are able to maintain a level of activity at cooler temperature, which an ectotherm cannot due to differing enzyme levels of activity.
Heat can be exchanged between an animal and its environment through four mechanisms: radiation, evaporation, convection, and conduction (Figure \(\PageIndex{3}\)). Radiation is the emission of electromagnetic “heat” waves. Heat comes from the sun in this manner and radiates from dry skin the same way. Heat can be removed with liquid from a surface during evaporation. This occurs when a mammal sweats. Convection currents of air remove heat from the surface of dry skin as the air passes over it. Heat will be conducted from one surface to another during direct contact with the surfaces, such as an animal resting on a warm rock.
Heat Conservation and Dissipation
Animals conserve or dissipate heat in a variety of ways. In certain climates, endothermic animals have some form of insulation, such as fur, fat, feathers, or some combination thereof. Animals with thick fur or feathers create an insulating layer of air between their skin and internal organs. Polar bears and seals live and swim in a subfreezing environment and yet maintain a constant, warm, body temperature. The arctic fox, for example, uses its fluffy tail as extra insulation when it curls up to sleep in cold weather. Mammals have a residual effect from shivering and increased muscle activity: arrector pili muscles cause “goose bumps,” causing small hairs to stand up when the individual is cold; this has the intended effect of increasing body temperature. Mammals use layers of fat to achieve the same end. Loss of significant amounts of body fat will compromise an individual’s ability to conserve heat.
Endotherms use their circulatory systems to help maintain body temperature. Vasodilation brings more blood and heat to the body surface, facilitating radiation and evaporative heat loss, which helps to cool the body. Vasoconstriction reduces blood flow in peripheral blood vessels, forcing blood toward the core and the vital organs found there, and conserving heat. Some animals have adaptions to their circulatory system that enable them to transfer heat from arteries to veins, warming blood returning to the heart. This is called a countercurrent heat exchange; it prevents the cold venous blood from cooling the heart and other internal organs. This adaption can be shut down in some animals to prevent overheating the internal organs. The countercurrent adaption is found in many animals, including dolphins, sharks, bony fish, bees, and hummingbirds. In contrast, similar adaptations can help cool endotherms when needed, such as dolphin flukes and elephant ears.
Some ectothermic animals use changes in their behavior to help regulate body temperature. For example, a desert ectothermic animal may simply seek cooler areas during the hottest part of the day in the desert to keep from getting too warm. The same animals may climb onto rocks to capture heat during a cold desert night. Some animals seek water to aid evaporation in cooling them, as seen with reptiles. Other ectotherms use group activity such as the activity of bees to warm a hive to survive winter.
Many animals, especially mammals, use metabolic waste heat as a heat source. When muscles are contracted, most of the energy from the ATP used in muscle actions is wasted energy that translates into heat. Severe cold elicits a shivering reflex that generates heat for the body. Many species also have a type of adipose tissue called brown fat that specializes in generating heat.
Neural Control of Thermoregulation
The nervous system is important to thermoregulation , as illustrated in Figure \(\PageIndex{4}\). The processes of homeostasis and temperature control are centered in the hypothalamus of the advanced animal brain.
Exercise
When bacteria are destroyed by leuckocytes, pyrogens are released into the blood. Pyrogens reset the body’s thermostat to a higher temperature, resulting in fever. How might pyrogens cause the body temperature to rise?
- Answer
-
Pyrogens increase body temperature by causing the blood vessels to constrict, inducing shivering, and stopping sweat glands from secreting fluid.
The hypothalamus maintains the set point for body temperature through reflexes that cause vasodilation and sweating when the body is too warm, or vasoconstriction and shivering when the body is too cold. It responds to chemicals from the body. When a bacterium is destroyed by phagocytic leukocytes, chemicals called endogenous pyrogens are released into the blood. These pyrogens circulate to the hypothalamus and reset the thermostat. This allows the body’s temperature to increase in what is commonly called a fever. An increase in body temperature causes iron to be conserved, which reduces a nutrient needed by bacteria. An increase in body heat also increases the activity of the animal’s enzymes and protective cells while inhibiting the enzymes and activity of the invading microorganisms. Finally, heat itself may also kill the pathogen.
Summary
Homeostasis is a dynamic equilibrium that is maintained in body tissues and organs. It is dynamic because it is constantly adjusting to the changes that the systems encounter. It is in equilibrium because body functions are kept within a normal range, with some fluctuations around a set point for the processes.
Glossary
- acclimatization
- alteration in a body system in response to environmental change
- alteration
- change of the set point in a homeostatic system
- homeostasis
- dynamic equilibrium maintaining appropriate body functions
- negative feedback loop
- feedback to a control mechanism that increases or decreases a stimulus instead of maintaining it
- positive feedback loop
- feedback to a control mechanism that continues the direction of a stimulus
- set point
- midpoint or target point in homeostasis
- thermoregulation
- regulation of body temperature


1.25: First Declension Short Alpha Nouns
Module 21
© 2021 Philip S. Peek, CC BY 4.0 https://doi.org/ 10.11647/OBP.0264. 25
Nouns
Nouns in Greek are defined just like nouns are in English; but the way they create meaning is different. As in English, Greek nouns ( ὀνόματα ) refer to people, places, things, and ideas. Greek nouns have endings. English nouns can change form when they show possession as in Jada’s book , where the ’s is added as a suffix and indicates that the book belongs to Jada. English nouns also change form when expressing the plural: two suns , three oxen , four mice . The endings on Greek nouns, as we have seen previously, create the same meanings that English does through form change, word order, and the use of prepositional phrases.
First Declension Short Alpha Nouns in –α, –ης and –α, –ᾱς
These nouns are feminine in gender. In the Attic dialect, nouns whose stem ends in - ε , - ι , or - ρ take the short alpha - α , - ᾱς endings. Memorize these endings, know how to obtain the stem, and know how to decline the nouns. As you learn new ending sets, look at the similarities and differences each has when compared to those endings you have already memorized.
Declining First Declension Short Alpha Nouns –α , –ης and –α , –ᾱς
To decline first declension nouns ending in - α , - ης and - α , - ᾱς , first get the stem by removing the genitive singular ending - ης or - ᾱς . What remains is the stem. To the stem add the following endings:
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θάλαττα, θαλάττης and πεῖρα, πείρᾱς |
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- The alpha of the nominative singular, accusative singular, and vocative singular is short.
- The accent shifts to the ultima in the genitive plural.
- Use the - α , - ᾱς endings when the stem ends in - ε , - ι , - ρ .
- Remember that final - αι and - οι are short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.
- If the nominative has an acute accent on the ultima, it changes to a circumflex in the genitive and dative, singular and plural.
First Declension Nouns in – ης , – ου and – ᾱς , – ου
These nouns are masculine in gender. In the Attic dialect, endings from the - ᾱς , - ου declension are found only in nouns whose stem ends in - ε , - ι , or - ρ . Memorize these endings, know how to obtain the stem, and know how to decline the nouns. As you learn new ending sets, look at the similarities and differences each has when compared to those endings you have already memorized.
Declining First Declension Masculine Nouns in –ης, –ου and –ᾱ ς, –ου
To decline first declension nouns ending in - ης , - ου and - ᾱς , - ου , first remove the genitive singular ending - ου . What remains is the stem. To the stem add the following endings:
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*For the vocative singular, use - α unless otherwise noted. |
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*For the vocative singular, use - α unless otherwise noted. |
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στρατιώτης, στρατιώτου and νεανίᾱς, νεανίου |
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- Some nouns with nominatives ending with - ης , have the vocative singular ending - η instead of - α .
- The accent shifts to the ultima in the genitive plural.
- Use the - ᾱς - ου endings when the stem ends in - ε , - ι , - ρ .
- Remember that final - αι and - οι count as short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.
- If the nominative singular has an acute accent on the ultima, it changes to a circumflex in the genitive and dative, singular and plural.
Noun Identification
You now know ten sets of endings for nouns:
For the nouns below, take note of what set of endings each noun takes.
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χρῆμα , χρήματος τό thing, matter, affair ; (pl.) money |
set 10 |
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πολίτης ( πολιήτης ), πολίτου ὁ citizen, freeman |
set 5 |
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ἡμέρᾱ , ἡμέρᾱ ς ἡ day |
set 2 |
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θάλαττα , θαλάττης ἡ sea |
set 3 |
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πα ῖς , παιδός ἡ ὁ child |
set 9 |
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χώρᾱ , χώρᾱς ἡ land, country |
set 2 |
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θεός , θεοῦ ἡ ὁ god, goddess |
set 7 |
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πεῖ ρα , πείρᾱς ἡ trial, attempt |
set 4 |
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ἔργον , ἔργου τό work, deed, task; building |
set 8 |
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πρᾶγμα , πράγματος τό matter, thing, affair; problem |
set 10 |
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νεαν ίᾱς , νεανίου ὁ youth, young man |
set 6 |
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ἀρχή , ἀρχῆς ἡ rule, command; beginning |
set 1 |
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στρατιώτης , στρατιώτου ὁ soldier |
set 5 |
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ὅπλον , ὅ πλου τό weapon |
set 8 |
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δόξα , δόξης ἡ expectation, notion, opinion; reputation |
set 3 |
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λό γος , λόγου ὁ word, speech, story; reason, account |
set 7 |
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γραῦς , γραός ἡ old woman |
set 9 |
Practice Declining Nouns. Decline these nouns with the article (answers are in the Answer Key ): μοῦσα , μούσης ἡ muse and ποιητής , ποιητοῦ ὁ poet .
As you write out the forms, note the similarities and differences with the endings you have already memorized. Writing out the forms helps you to process this new information.
Practice Translating. Translate the sentences below, which have been adapted from Euripides’ Medea ( Μήδεια ). Remember the meanings and functions of the cases presented in Module 7 . Use your memory to identify endings and their functions. If you forget an ending or a function, consult the Adjective, Adverb, Noun, and Pronoun Chart in Appendix VIII and the Case and Function Chart in Appendix I. Check your understanding with the translations in the Answer Key , making sure that you understand why each word translates as it does. Now go back and read each sentence two or three times, noticing with each rereading how much better your understanding of the sentence becomes. Make this a habit and you will improve quickly.
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Ἰάσων : οὐ κρινοῦμαι τ ῶνδέ σοι τὰ πλείονα . ἀλλ ’, εἴ τι βούλῃ παισὶν ἢ σαυτῇ , φυγῆς προσωφέ λημα , χρημάτων ἐμῶν λαβεῖν πλείονα , ταῦτα σχήσεις . ἕτοιμος ἀφθόνῳ διδόναι χειρὶ ξένοις τε πέμπειν σύμβολα . οἱ δὲ δράσουσί σ ’ εὖ . καὶ ταῦτα μὴ θέλουσα , μωρανεῖς . λήγουσα δ ’ ὀργῆς , κερδανεῖς ἀμείνονα . |
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Μήδεια : οὐ βού λομαι ξένοις τοῖς σοῖς χρᾶσθαι οὔ τε τι δέχεσθαι . κελεύω μὴ ἡμῖν διδόναι . κακοῦ γὰρ ἀνδρὸς δῶρ ’ ὄνησιν οὐκ ἔχει . |
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Ἰάσων : ἀλλʼ οὖν ἐγ ὼ μὲν δαίμονας μαρτύρομαι ὡς πάνθ ’ ὑπουργεῖν σοί τε καὶ τέκνοις θέλω . σοὶ δ ’ οὐ κ ἀρέσκει τὰ ἀγαθά . ἀλλ ’ αὐθαδ ίᾳ φίλους ἀπωθῇ· τοιγὰρ ἀλγυνῇ πλέον . |
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10 |
Μήδεια : ὥρα σοὶ χωρεῖν· πόθῳ γὰρ τῆς νεοδμήτου κόρης σπουδάζεις χρονίζειν δωμάτων ἐξώπιος ; δοκεῖ σοὶ νυμφεύειν· ἴσως γάρ τοιοῦτον θρηνήσῃ γάμον . |
Adverbs and Verbs
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ἀλγύνω , ἀλγυνέω pain, grieve, distress ; (fut. mid. and pass.) suffer pain, be distressed |
κερδαίνω , κερδανέω gain, derive profit |
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ἀπωθέω , ἀπεώσω thrust away, push back |
κρίνω , κρινέω judge, decide, pick out, choose, separate |
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ἀρέσκω , ἀρέσω please + dat.; make good, make amends |
λαβεῖν to take |
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* βούλομαι , βουλήσομαι want, prefer; wish, be willing |
μαρτύρομαι , μαρτυρέομαι invoke, call to witness |
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γαμέω , γαμέω or γαμήσω , marry ; (mid.) give in marriage, marry (a man) |
μωραίνω , μωρανέω be silly, be foolish |
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δέχομαι , δέξομαι receive; meet; encounter; accept; undertake + inf. |
νυμφεύω , νυμφεύσω betroth, marry; give in marriage |
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* δί δωμι give ; δίκην δίδωμι I pay the penalty ; δίδωμι χά ριν I give thanks |
* πέμπω , πέμψω send |
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* δοκέω , δόξω seem, think; seem best, think best + inf. |
πλέον more |
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δράω , δράσω do, accomplish, act |
σπουδάζω , σπουδάσω be serious, be earnest; be eager + inf. |
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* ἔχω , ἕξω or σχήσω have, hold; be able + inf.; καλῶς ἔχειν to be well |
τοιγάρ therefore, accordingly |
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* θέλω , θελήσω wish, be willing |
ὑπουργέω , ὑπουργήσω render service, help, assist + dat. |
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θρηνέω , θρηνήσω sing a dirge, wail; bewail |
* χράομαι , χρήσομαι use, employ, experience + dat. |
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ἴ σως perhaps |
χρονίζω spend time; tarry, linger |
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* κελεύω , κελεύσω bid, order, command |
χωρέω , χωρήσω make room for; retire; advance |
Adjectives, Nouns, Pronouns
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* ἀ γαθός , ἀγαθή , ἀγαθόν good, noble |
ὄνησις , ὀνήσεως ἡ use, profit, advantage; good luck |
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ἀμείνονα , ἀμειν όνων τά better |
ὀργή , ὀργῆς ἡ mood; anger, wrath |
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* ἀνήρ , ἀνδρός ὁ man, husband |
* παῖς , παιδός ἡ ὁ child |
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αὐθαδία , αὐθαδίας ἡ willfulness, stubbornness |
* πάντα , πάντων τά all, each, whole |
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ἄφθονος , ἄφθονον without envy; plentiful |
πλείονα , πλειόνων τά more |
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γάμος , γάμου ὁ wedding, marriage |
πόθος , πόθου ὁ yearning for + gen. |
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δαίμων , δαίμονος ὁ deity; fortune; destiny |
προσωφέλημα , προσωφελήματος τό help, aid |
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δῶμα , δώματος τό houses |
σαυτή , σαυτῆς ἡ yourself |
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δῶρον , δ ώρου τό gift |
* σός , σή , σόν your |
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ἐξώπιος , ἐξώπιον out of sight of |
σύμβολον , συμβόλου τό signs, tokens, codes |
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ἕτοιμος , ἑτοίμη , ἕτοιμον ready, at hand; able + inf. |
τέκνον , τέκνου τό child |
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* θέλουσα , θελο ύσης ἡ wishing, being willing |
* τοιοῦτος , τοιαύτη , τοιοῦτο of such a kind or sort |
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* κακός , κακή , κακόν bad, evil, cowardly |
* φίλος , φίλου ὁ friend |
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κόρη , κόρης ἡ girl; daughter |
φυγή , φυγῆς ἡ flight, escape, exile |
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λήγουσα , ληγούσης ἡ staying, abating; stopping, ceasing from + gen. |
* χείρ , χειρός ἡ ( dat pl. χερσίν ) hand; force, army |
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νεόδμητος , νεό δμητον newly tamed; new-wedded |
* χρῆμα , χρήματος τό thing; (pl.) goods, money, property |
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ξένος ( ξεῖνος ), ξένου ( ξείνου ) ὁ stranger; guest-friend |
ὥρα , ὥρας ἡ season, period, time |
- The asterisk indicates the top 250 most frequently occurring vocabulary, which you are to memorize.
Practice Parsing Greek Sentences. Parse each word of the sentence found below. For nouns and pronouns, give case and function. For verbs, give person, number, tense, mood, and voice. For adverbs and conjunctions, identify them. For prepositional phrases, give the preposition and the preposition’s object. For adjectives, specify the noun they agree with in gender, number, and case.
πόθῳ γὰ ρ τῆς νεοδμήτου κόρης σπουδάζεις χρονί ζειν δωμάτων ἐξώπιος ;
Check your answers with those in the Answer Key .
History
History begins with Herodotos. Though influenced by epic, travelogues, medical treatises, and other intellectual writings, Herodotos and his Histories are discontinuous. They represent a distinct break with the past in their creation of a new genre intent on explaining what happened in the fighting between the Greeks and the barbarians and on preserving other items of interest, including customs, fauna, flora, great works, sexual mores, and religious beliefs. Thoukydides continued Herodotos’ novel approach, writing a contemporary history of the Peloponnesian Wars, which he called an objective presentation of what really happened and a κτῆμα ἐς αἰεί , possession for all time . Xenophon then picked up where Thoukydides left off, starting his Hellenika in 411 BCE and ending in 362 BCE. Our fascination with histories, myths, and stories of all sorts continues today as we seek to understand the present and predict the future through our study of the past.
Module 21 Top 250 Vocabulary to be Memorized. Like learning the alphabet and endings, memorizing vocabulary is essential to acquiring language. The better you memorize the top 250 most frequently occurring vocabulary words, the greater mastery of the language you will have.
Nouns and Adjectives
ἀγαθός , ἀγαθή , ἀγαθ όν good, noble
δόξα , δόξης ἡ expectation, notion, opinion; reputation
θάλασσα ( θάλαττα ), θαλάσσης ἡ sea
μόνος , μόνη , μόνον only, sole, alone, solitary; one
πολέμιος , πολεμίᾱ , πολέμιον hostile
πρότερος , προτέρᾱ , πρότερον prior, before, sooner
πρῶτος , πρώτη , πρῶτον first, for the present, just now
σός , σή , σόν your
φίλος , φίλη , φίλον friendly, kind, well-disposed + dat.; (n.) friend


11.0: Introduction
In the United States, medication errors affect more than 7 million patients and result in approximately 7,000 to 9,000 deaths each year (Tariq et al., 2023). These statistics include only those cases reported and do not account for the hundreds of thousands of adverse reaction s, complications, or medication errors that are not reported. Although death is the most severe outcome, medication errors may also result in other negative consequences, such as increased medical costs (exceeding $40 billion each year in the United States), psychological stress and physical pain, suffering, decreased patient satisfaction, and decreased trust in providers and the healthcare system (Tariq et al., 2023).
Medication errors generally occur at the point of ordering, transcribing, dispensing, administering, monitoring, or documenting. It is important to note that medication errors are preventable and may be avoided with appropriate safety precautions (Tariq et al., 2023). Nurses play a critical role in ensuring these safety precautions are implemented. Nurses also design and evaluate safety initiatives, whether at the bedside or in other capacities, such as leadership, and safety/quality programs. To effectively reduce the risk of medication errors, it is important to practice nursing standards of care through application of principles for safe medication administration, understanding specific safety considerations, and knowledge of common sources of errors. This chapter provides the knowledge necessary to engage in the process of ensuring safe medication administration.


6.6: Cross-Cultural Assignments
- What steps can you take to be better prepared for cross-cultural assignments?
At some point in your career, you are very likely to be asked to be involved in cross-cultural operations. You may encounter employees from other countries in the local company you work for, or your company may send you to another country to run international operations. When these situations arise, you will need to be prepared to manage cultural differences. In this section, we discuss some of the things companies and individuals can do to better prepare for cross-national differences.
One of the goals of any cross-cultural training is to increase an employee’s cultural intelligence. Cultural intelligence refers to “individuals’ capabilities to function and manage effectively in culturally diverse settings.” 21 The culturally intelligent manager is someone who can operate without difficulty in cross-national settings. Recent research suggests that cultural intelligence is made up of four dimensions:
- a cognitive dimension , focusing on the individual’s knowledge of values and practices inherent in the new culture acquired through education and personal experiences
- a meta-cognitive dimension , which reflects an individual’s ability to use cross-cultural knowledge to understand and adapt to the cultural environment they are exposed to
- a motivational dimension , which reflects the ability and desire to continuously learn new aspects of cultures and adapt to them
- a behavioral dimension , based on the ability of the individual to exhibit the appropriate forms of verbal and nonverbal behaviors when interacting with people from another culture
To give you more insights into the cultural intelligence measure, Table 6.9 provides some representative statements used to gauge a person’s understanding of these four dimensions of cultural intelligence various aspects of cross-cultural interactions.
| Cultural Intelligence Statements |
| Metacognitive |
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| Cognitive |
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| Motivational |
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| Behavioral |
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| Based on Jacob Eisenberg, Hyun-Jung Lee, Frank Bruck, Barbara Brenner, Marie-Therese Claes, Jacek Mironski and Roger Bell, "Can business schools make students culturally competent? Effects of crosscultural management courses on cultural intelligence,"Academy of Management Learning and Education, 2013, Vol. 12, pp. 603-621. |
Table 6.9
Cross-Cultural Training through Education and Personal Experience: Low and High Rigor
Current research suggests that cross-cultural training can influence cultural intelligence. At a basic level, you can acquire cultural intelligence by taking classes in your program. Research has shown that taking crosscultural management courses can enhance cultural intelligence. 22 For example, in a study of 152 MBA students, researchers found that cultural intelligence of the students increased after they took a cross-cultural management course. In another longitudinal study, researchers found that study abroad has significant impact on the cognitive and metacognitive aspects of cultural intelligence. How do multinationals approach cross-cultural training? The above provides examples of low-rigor training , in which individuals are exposed to critical information to help them understand the realities of a different culture but are not actively and directly engaged with the culture. 23 In such cases, instructors transfer basic information and knowledge to students through lectures, books, and case studies.
Low-rigor training has several important disadvantages. Participants often just receive information; they learn that differences exist but do not necessarily learn how to deal with cultural differences in a real-life situation. Furthermore, cross-cultural differences can be very subtle and nuanced, and this method cannot expose participants to such nuances. Balancing these significant disadvantages is one key advantage: low-rigor training tends to be the most cost effective.
Companies can also rely on high-rigor methods of training, in which participants are actively engaged in the process and can learn some tacit aspects of cross-cultural differences. 24 Examples of high-rigor training include classroom language training, case studies, and sensitivity training. High-rigor training also includes more experiential approaches such as role-playing, simulations, and field experiences. Some MNCs (multinational corporations) also offer on-the-job training, during which employees are coached and trained while working at their jobs. This method allows the trainee not only to see the new culture, but also to learn how that culture interacts with the work environment. The advantage of this method is that it enables the participant to be much more actively engaged in learning, thereby facilitating transfer of knowledge. But as you might have guessed, high-rigor training is much more expensive to provide.
Which method works best? Experts agree that it depends on the nature of the assignment. Longer and more complex international assignments benefit from higher-rigor training. 25 Furthermore, because international work assignments tend to be more short-term in nature, ways to enhance the metacognitive aspects of cultural intelligence are necessary. 26 Today, because more managers tend to have more frequent but shorter assignments to international companies, having metacognitive skills is critical. As a result, brief lectures or other low-rigor methods that simply provide information may be useful in helping develop the cognitive aspect but not metacognition. In such cases, high-rigor methods that allow participants to be much more actively engaged with a culture will work well.
When Should Cross-Cultural Training Occur?
Another important aspect of cross-cultural training is the timing of the training. Some multinationals offer predeparture cross-cultural training , which provides individuals with learning opportunities prior to their departure. 27 Such training can take the form of 1- to 12-week programs, although two- to three-day programs are also very popular. After such training, the expatriate has a good understanding of expectations, what the local culture looks and feels like, and how to manage any local shocks when they arrive. This approach also makes individuals about to go to another country less anxious about the unknown.
Multinationals will also often opt for p ostarrival cross-cultural training , which occurs after an expatriate has arrived in the foreign country and can address issues in “real time.” Armed with local cultural knowledge and training, the expatriate can delve into work issues without worrying about daily living issues.
Recent research provides evidence of the utility of cross-cultural training. For example, a recent study of 114 expatriates showed that both predeparture and postarrival training had positive effects on several aspects of their success. 28 Specifically, in a study in Vietnam, the findings show that both predeparture and postarrival training positively impacted the ability of expatriates to adjust to their work and general environment. Additionally, such training was also effective in enhancing the ability of expatriates to better interact with locals. The researchers also examined the impact of language training. Not surprisingly, expatriates who received training in the local language were better able to adjust to local interaction than others.
The above study shows that both predeparture and postarrival training are important for success in crosscultural management. While the study shows that it is most effective for MNCs to provide more than one type of training, the findings also show that postarrival training has the most impact on the types of cross-cultural adjustment. While companies tend to shy away from the more expensive postarrival training, the study suggests that the investment may be worthwhile if it enables expatriates to succeed.
Best practices advise that the optimal time for predeparture training programs is around three to five weeks prior to the international assignment. Training provided too far ahead of time may not be very effective because the expatriate may not activate all learning readiness and may forget the training if it occurs too far ahead of the assignment. Best practices also suggest that postarrival training is best delivered 8 to 12 weeks after arrival. This allows the expatriate to experience cross-cultural interaction and phenomena and to be better ready to gain the most from the training.
Adapting Behavior to the Culture
A final issue that managers need to address is that the training should not focus only on identifying and teaching about differences. 29 Experts agree that this focus on differences is a problem in current cross-cultural training approaches. While identifying and understanding cultural differences is useful and necessary, trainers often don’t provide guidance as to how the participants should adapt and react to such cultural differences. It is therefore necessary for the multinational to take the necessary steps to teach cross-cultural sojourners to adapt their behaviors so that they act and react in culturally appropriate ways. Experts also suggest that such training should not be static and limited to web pages or documentation. Training should be integrated with the actual work that the employee is engaging in.
- How should training to manage cultural and regional differences occur?
- How should training for cross-cultural assignments be implemented?
References
21. Jacob Eisenberg, Hyun-Jung Lee, Frank Bruck, Barbara Brenner, Marie-Therese Claes, Jacek Mironski and Roger Bell, “Can business schools make students culturally competent? Effects of cross-cultural management courses on cultural intelligence,” Academy of Management Learning and Education , 2013, Vol. 12, pp. 603-621.
22. Jase R. Ramsey and Melanie Lorenz, “Exploring the impact of cross-cultural management on cultural intelligence, student satisfaction, and commitment,” Academy of Management Learning and Education , 2016, Vol. 15, pp. 79-99.
23. Tomasz Lenartowicz, James P. Johnson and Robert Konopaske, “The application of learning theories to improve cross-cultural training programs in MNCs,” International Journal of Human Resource Management , 2014, Vol. 25, pp. 1697-1719.
24. Tomasz Lenartowicz, James P. Johnson and Robert Konopaske, “The application of learning theories to improve cross-cultural training programs in MNCs,” International Journal of Human Resource Management ,2014, Vol. 25, pp. 1697-1719.
25. Tomasz Lenartowicz, James P. Johnson and Robert Konopaske, “The application of learning theories to improve cross-cultural training programs in MNCs,” International Journal of Human Resource Management ,2014, Vol. 25, pp. 1697-1719.
26. Shira Mor, Michael Morris and Johann Joh, “Identifying and training adaptive cross-cultural management skilss: The crucial role of cultural metacognition,” Academy of Management Learning and Education ,2013, Vol. 12, pp. 453-475.
27. Rita Bennett, Anne Aston and Tracy Colquhoun, “Cross-cultural training: A critical step in ensuring the success of international assignments,” Human Resource Management , Summer/Fall 2000, Vol. 39, pp. 239-250.
28. Yu-lin Wang and Emma Tran, “Effects of cross-cultural and language training on expatriates’ adjustment and job performance in Vietnam,” Asia Pacific Journal of Human Resources ,2012, Vol. 50, pp. 327-350.
29. Molinsky, A, “The mistakes most managers make with cross-cultural training,” Harvard Business Review , January 15, 2015, pp. 2-4.


1.12: Special Set Structures
There are several other types of algebraic set structures that are weaker than \( \sigma \)-algebras. These are not particularly important in themselves, but are important for constructing \( \sigma \)-algebras and the measures on these \( \sigma \)-algebras. You may want to skip this section if you are not intersted in questions of existence and uniqueness of positive measures.
Basic Theory
Definitions
Throughout this section, we assume that \( S \) is a set and \( \mathscr{S} \) is a nonempty collection of subsets of \( S \). Here are the main definitions we will need.
\( \mathscr{S} \) is a \( \pi \)-system if \( \mathscr{S} \) is closed under finite intersections: if \( A, \, B \in \mathscr{S} \) then \( A \cap B \in \mathscr{S} \).
Closure under intersection is clearly a very simple property, but \( \pi \) systems turn out to be useful enough to deserve a name.
\( \mathscr{S} \) is a \( \lambda \)-system if it is closed under complements and countable disjoint unions.
- If \( A \in \mathscr{S} \) then \( A^c \in \mathscr{S} \).
- If \( A_i \in \mathscr{S}\) for \( i \) in a countable index set \( I \) and \( A_i \cap A_j = \emptyset \) for \( i \ne j \) then \( \bigcup_{i \in I} A_i \in \mathscr{S} \).
\( \mathscr{S} \) is a semi-algebra if it is closed under intersection and if complements can be written as finite, disjoint unions:
- If \( A, \, B \in \mathscr{S} \) then \( A \cap B \in \mathscr{S} \).
- If \( A \in \mathscr{S} \) then there exists a finite, disjoint collection \( \{B_i: i \in I\} \subseteq \mathscr{S} \) such that \( A^c = \bigcup_{i \in I} B_i \).
For our final structure, recall that a sequence \( (A_1, A_2, \ldots) \) of subsets of \( S \) is increasing if \( A_n \subseteq A_{n+1} \) for all \( n \in \N_+ \). The sequence is decreasing if \( A_{n+1} \subseteq A_n \) for all \( n \in \N_+ \). Of course, these are the standard meanings of increasing and decreasing relative to the ordinary order \( \le \) on \( \N_+ \) and the subset partial order \( \subseteq \) on \( \mathscr{P}(S) \).
\( \mathscr{S} \) is a monotone class if it is closed under increasing unions and decreasing intersections:
- If \( (A_1, A_2, \ldots) \) is an increasing sequence of sets in \( \mathscr{S} \) then \( \bigcup_{n=1}^\infty A_n \in \mathscr{S} \).
- If \( (A_1, A_2, \ldots) \) is a decreasing sequence of sets in \( \mathscr{S} \) then \( \bigcap_{n=1}^\infty A_n \in \mathscr{S} \).
If \( (A_1, A_2, \ldots) \) is an increasing sequence of sets then we sometimes write \( \bigcup_{n=1}^\infty A_n = \lim_{n \to \infty} A_n \). Similarly, if \( (A_1, A_2 \ldots) \) is a decreasing sequence of sets we sometimes write \( \bigcap_{n=1}^\infty A_n = \lim_{n \to \infty} A_n \). The reason for this notation will become clear in the section on Convergence in the chapter on Probability Spaces. With this notation, a monotone class \( \mathscr{S} \) is defined by the condition that if \( (A_1, A_2, \ldots) \) is an increasing or decreasing sequence of sets in \( \mathscr{S} \) then \( \lim_{n \to \infty} A_n \in \mathscr{S} \).
Basic Theorems
Our most important set structure, the \( \sigma \)-algebra, has all of the properties in the definitions above.
If \( \mathscr{S} \) is a \( \sigma \)-algebra then \( \mathscr{S} \) is a \( \pi \)-system, a \( \lambda \)-system, a semi-algebra, and a monotone class.
If \( \mathscr{S} \) is a \( \lambda \)-system then \( S \in \mathscr{S} \) and \( \emptyset \in \mathscr{S} \).
Proof
The proof is just like the one for an algebra. There exists \( A \in \mathscr{S} \) since \( \mathscr{S} \) is non-empty. Hence \( A^c \in \mathscr{S} \) and so \( S = A \cup A^c \in \mathscr{S} \). Finally \( \emptyset = S^c \in \mathscr{S} \).
Any type of algebraic structure on subsets of \( S \) that is defined purely in terms of closure properties will be preserved under intersection. That is, we will have results that are analogous to how \( \sigma \)-algebras are generated from more basic sets, with completely straightforward and analgous proofs. In the following two theorems, the term system could mean \( \pi \)-system, \( \lambda \)-system, or monotone class of subsets of \( S \).
If \( \mathscr{S}_i \) is a system for each \( i \) in an index set \( I \) and \( \bigcap_{i \in I} \mathscr{S}_i \) is nonempty, then \( \bigcap_{i \in I} \mathscr{S}_i \) is a system of the same type.
The condition that \( \bigcap_{i \in I} \mathscr{S}_i \) be nonempty is unnecessary for a \( \lambda \)-system, by the result above . Now suppose that \( \mathscr{B} \) is a nonempty collection of subsets of \( S \), thought of as basic sets of some sort. Then the system generated by \( \mathscr{B} \) is the intersection of all systems that contain \( \mathscr{B} \).
The system \( \mathscr{S} \) generated by \( \mathscr{B} \) is the smallest system containing \( \mathscr{B} \), and is characterized by the following properties:
- \( \mathscr{B} \subseteq \mathscr{S} \).
- If \( \mathscr{T} \) is a system and \( \mathscr{B} \subseteq \mathscr{T} \) then \( \mathscr{S} \subseteq \mathscr{T} \).
Note however, that the previous two results do not apply to semi-algebras, because the semi-algebra is not defined purely in terms of closure properties (the condition on \( A^c \) is not a closure property).
If \( \mathscr{S} \) is a monotone class and an algebra, then \( \mathscr{S} \) is a \( \sigma \)-algebra.
Proof
All that is needed is to prove closure under countable unions. Thus, suppose that \( A_i \in \mathscr{S} \) for \( i \in \N_+ \). Then \( B_n = \bigcup_{i=1}^n A_i \in \mathscr{S} \) since \( \mathscr{S} \) is an algebra. The sequence \( (B_1, B_2, \ldots) \) is increasing, so \( \bigcup_{n=1}^\infty B_n \in \mathscr{S} \), since \( \mathscr{S} \) is a monotone class. But \( \bigcup_{n=1}^\infty B_n = \bigcup_{i=1}^\infty A_i \).
By definition, a semi-algebra is a \( \pi \)-system. More importantly, a semi-algebra can be used to construct an algebra.
Suppose that \( \mathscr{S} \) is a semi-algebra of subsets of \( S \). Then the collection \( \mathscr{S}^* \) of finite, disjoint unions of sets in \( \mathscr{S} \) is an algebra.
Proof
Suppose that \( A, \, B \in \mathscr{S}^* \). Then there exist finite, disjoint collections \( \{A_i: i \in I\} \subseteq \mathscr{S} \) and \( \{B_j: j \in J\} \subseteq \mathscr{S} \) such that \( A = \bigcup_{i \in I} A_i \) and \( B = \bigcup_{j \in J} B_j \). Hence \[ A \cap B = \bigcup_{(i, j) \in I \times J} (A_i \cap B_j) \] But \( \{A_i \cap B_j: (i, j) \in I \times J\} \) is a finite, disjoint collection of sets in \( \mathscr{S} \), so \( A \cap B \in \mathscr{S}^* \). Suppose \( A \in \mathscr{S}^* \), so that there exists a finite, disjoint collection \( \{A_i: i \in I\} \) such that \( A = \bigcup_{i \in I} A_i \). Then \( A^c = \bigcap_{i \in I} A_i^c \). But \( A_i^c \in \mathscr{S}^* \) by definition of semi-algebra, and we just showed that \( \mathscr{S}^* \) is closed under finite intersections, so \( A^c \in \mathscr{S}^* \).
We will say that our nonempty collection \( \mathscr{S} \) is closed under proper set difference if \( A, \, B \in \mathscr{S} \) and \( A \subseteq B \) implies \( B \setminus A \in \mathscr{S} \). The following theorem gives the basic relationship between \( \lambda \)-systems and monotone classes.
Suppose that \( \mathscr{S} \) is a nonempty collection of subsets of \( S \).
- If \( \mathscr{S} \) is a \( \lambda \)-system then \( \mathscr{S} \) is a monotone class and is closed under proper set difference.
- If \( \mathscr{S} \) is a monotone class, is closed under proper set difference, and contains \( S \), then \( \mathscr{S} \) is a \( \lambda \)-system.
Proof
- Suppose that \( \mathscr{S} \) is a \( \lambda \)-system. Suppose that \( A, \, B \in \mathscr{S} \) and \( A \subseteq B \). Then \( B^c \in \mathscr{S} \), and \( A \) and \( B^c \) are disjoint, so \( A \cup B^c \in \mathscr{S} \). But then \( (A \cup B^c)^c = B \cap A^c = B \setminus A \in \mathscr{S} \). Hence \( \mathscr{S} \) is closed under proper set difference. Next suppose that \( (A_1, A_2, \ldots) \) is an increasing sequence of sets in \( \mathscr{S} \). Let \( B_1 = A_1 \) and \( B_n = A_n \setminus A_{n-1} \) for \( n \in \{2, 3, \ldots\} \). Then \( B_i \in \mathscr{S} \) for each \( i \in \N_+ \). But the sequence \( (B_1, B_2, \ldots) \) is disjoint and has the same union as \( (A_1, A_2, \ldots) \). Hence \( \bigcup_{i=1}^\infty A_i = \bigcup_{i=1}^\infty B_i \in \mathscr{S} \). Finally, suppose that \( (A_1, A_2, \ldots) \) is a decreasing sequence of sets in \( \mathscr{S} \). Then \( A_i^c \in \mathscr{S} \) for each \( i \in \N_+ \) and \( (A_1^c, A_2^c, \ldots) \) is increasing. Hence \( \bigcup_{i=1}^\infty A_i^c \in \mathscr{S} \) and therefore \( \left(\bigcup_{i=1}^\infty A_i^c\right)^c = \bigcap_{i=1}^\infty A_i \in \mathscr{S} \).
- Suppose that \( \mathscr{S} \) is a monotone class, is closed under proper set difference, and \( S \in \mathscr{S} \). If \( A \in \mathscr{S} \) then trivially \( A \subseteq S \) so \( A^c = S \setminus A \in \mathscr{S} \). Next, suppose that \( A, \; B \in \mathscr{S} \) are disjoint. Then \( A^c \in \mathscr{S} \) and \( B \subseteq A^c \), so \( A^c \setminus B = A^c \cap B^c \in \mathscr{S} \). Hence \( A \cup B = (A^c \cap B^c)^c \in \mathscr{S} \). Finally, suppose that \( (A_1, A_2, \ldots) \) is a disjoint sequence of sets in \( \mathscr{S} \). We just showed that \( \mathscr{S} \) is closed under finite, disjoint unions, so \( B_n = \bigcup_{i=1}^n A_i \in \mathscr{S} \). But the sequence \( (B_1, B_2, \ldots) \) is increasing, and hence \( \bigcup_{n=1}^\infty B_n = \bigcup_{i=1}^\infty A_i \in \mathscr{S} \).
The following theorem is known as the monotone class theorem , and is due to the mathematician Paul Halmos.
Suppose that \( \mathscr{A} \) is an algebra, \( \mathscr{M} \) is a monotone class, and \( \mathscr{A} \subseteq \mathscr{M} \). Then \( \sigma(\mathscr{A}) \subseteq \mathscr{M} \).
Proof
First let \( m(\mathscr{A}) \) denote the monotone class generated by \( \mathscr{A} \), as defined above . The outline of the proof is to show that \( m(\mathscr{A}) \) is an algebra, so that by (9) , \( m(\mathscr{A}) \) is a \( \sigma \)-algebra. It then follows that \( \sigma(\mathscr{A}) \subseteq m(\mathscr{A}) \subseteq \mathscr{M} \). To show that \( m(\mathscr{A}) \) is an algebra, we first show that it is closed under complements and then under simple union.
Since \( m(\mathscr{A}) \) is a monotone class, the collection \( m^*(\mathscr{A}) = \{A \subseteq S: A^c \in m(\mathscr{A})\} \) is also a monotone class. Moreover, \( \mathscr{A} \subseteq m^*(\mathscr{A}) \) so it follows that \( m(\mathscr{A}) \subseteq m^*(\mathscr{A}) \). Hence if \( A \in m(\mathscr{A}) \) then \( A \in m^*(\mathscr{A}) \) so \( A^c \in m(\mathscr{A}) \). Thus \( m(\mathscr{A}) \) is closed under complements.
Let \( \mathscr{M}_1 = \{A \subseteq S: A \cup B \in m(\mathscr{A}) \text{ for all } B \in \mathscr{A}\} \). Then \( \mathscr{M}_1 \) is a monotone class and \( \mathscr{A} \subseteq \mathscr{M}_1 \) so \( m(\mathscr{A}) \subseteq \mathscr{M}_1 \). Next let \( \mathscr{M}_2 = \{A \subseteq S: A \cup B \in m(\mathscr{A}) \text{ for all } B \in m(\mathscr{A})\} \). Then \( \mathscr{M}_2 \) is also a monotone class. Let \( A \in \mathscr{A} \). If \( B \in m(\mathscr{A})\) then \( B \in \mathscr{M}_1 \) and hence \( A \cup B \in m(\mathscr{A}) \). Hence \( A \in \mathscr{M}_2 \). Thus we have \( \mathscr{A} \subseteq \mathscr{M}_2 \), so \( m(\mathscr{A}) \subseteq \mathscr{M}_2 \). Finally, let \( A, \, B \in m(\mathscr{A}) \). Then \( A \in \mathscr{M}_2 \) so \( A \cup B \in m(\mathscr{A}) \) and therefore \( m(\mathscr{A}) \) is closed under simple union.
As noted in (5) , a \( \sigma \)-algebra is both a \( \pi \)-system and a \( \lambda \)-system. The converse is also true, and is one of the main reasons for studying these structures.
If \( \mathscr{S} \) is a \( \pi \)-system and a \( \lambda \)-system then \( \mathscr{S} \) is a \( \sigma \)-algebra.
Proof
\( S \in \mathscr{S} \), and if \( A \in \mathscr{S} \) then \( A^c \in \mathscr{S} \) by definition of a \( \lambda \)-system. Thus, all that is left is to show closure under countable unions. Thus, suppose that \( (A_1, A_2, \ldots) \) is a sequence of sets in \( \mathscr{S} \). Then \( A_i^c \in \mathscr{S} \) for each \( i \in \N_+ \). Since \( \mathscr{S} \) is also a \( \pi \)-system, it follows that for each \( n \in \N_+ \), \( B_n = A_n \cap A_1^c \cap \cdots \cap A_{n-1}^c \in \mathscr{S} \) (by convention \( B_1 = A_1 \)). But the sequence \( (B_1, B_2, \ldots) \) is disjoint and has the same union as \( (A_1, A_2, \ldots) \). Hence \( \bigcup_{i=1}^\infty A_i = \bigcup_{i=1}^\infty B_i \in \mathscr{S} \).
The importance of \( \pi \)-systems and \( \lambda \)-systems stems in part from Dynkin's \( \pi \)-\( \lambda \) theorem given next. It's named for the mathematician Eugene Dynkin.
Suppose that \( \mathscr{A} \) is a \( \pi \)-system of subsets of \( S \), \( \mathscr{B} \) is a \( \lambda \)-system of subsets of \( S \), and \( \mathscr{A} \subseteq \mathscr{B} \). Then \( \sigma(\mathscr{A}) \subseteq \mathscr{B} \).
Proof
Let \( \mathscr{L} \) denote the \( \lambda \)-system generated by \( \mathscr{A} \). Then of course \( \mathscr{A} \subseteq \mathscr{L} \subseteq \mathscr{B} \). For \( A \in \mathscr{L} \), let \[ \mathscr{L}_A = \{B \subseteq S: B \cap A \in \mathscr{L}\}\] We will show that \( \mathscr{L}_A \) is a \( \lambda \)-system. Note that \( S \cap A = A \in \mathscr{L}\) and therefore \( S \in \mathscr{L}_A \). Next, suppose that \( B_1, \, B_2 \in \mathscr{L}_A \) and that \( B_1 \subseteq B_2 \).  Hence \( (B_2 \setminus B_1) \cap A = (B_2 \cap A) \setminus (B_1 \cap A) \in \mathscr{L} \). Hence \( B_2 \setminus B_1 \in \mathscr{L}_A \). Finally, suppose that \( \{B_i: i \in I\} \) is a countable, disjoint collection of sets in \( \mathscr{L}_A \). Then \( B_i \cap A \in \mathscr{L} \) for each \( i \in I \), and \( \{B_i \cap A: i \in I\} \) is also a disjoint collection. Therefore, \( \bigcup_{i \in I} (B_i \cap A) = \left(\bigcup_{i \in I} B_i \right) \cap A \in \mathscr{L} \). Hence \( \bigcup_{i \in I} B_i \in \mathscr{L}_A \).
Next fix \( A \in \mathscr{A} \). If \( B \in \mathscr{A} \) then \( A \cap B \in \mathscr{A} \), so \( A \cap B \in \mathscr{L} \) and hence \( B \in \mathscr{L}_A \). But \( \mathscr{L} \) is the smallest \( \lambda \)-system containing \( \mathscr{A} \) so we have shown that \( \mathscr{L} \subseteq \mathscr{L}_A \) for every \( A \in \mathscr{A} \). Now fix \( B \in \mathscr{L}\). If \( A \in \mathscr{A} \) then \( B \in \mathscr{L}_A \) so \( A \cap B \in \mathscr{L} \) and therefore \( A \in \mathscr{L}_B \). Again, \( \mathscr{L} \) is the smallest \( \lambda \)-system containing \( \mathscr{A} \) so we have now shown that \( \mathscr{L} \subseteq \mathscr{L}_B \) for every \( B \in \mathscr{L} \). Finally, let \( B, \, C \in \mathscr{L} \). Then \( C \in \mathscr{L}_B \) and hence \( B \cap C \in \mathscr{L} \). It now follows that \( \mathscr{L} \) is a \( \pi \)-system, as well as a \( \lambda \)-system, and therefore by the theorem above , \( \mathscr{L} \) is a sigma-algebra. But \( \mathscr{A} \subseteq \mathscr{L} \) and hence \( \sigma(\mathscr{A}) \subseteq \mathscr{L} \).
Examples and Special Cases
Suppose that \( S \) is a set and \( \mathscr{A} \) is a finite partition of \( S \). Then \( \mathscr{S} = \{\emptyset\} \cup \mathscr{A} \) is a semi-algebra of subsets of \( S \).
Proof
If \( A, \, B \in \mathscr{A} \) then \( A \cap B = \emptyset \in \mathscr{S} \). If \( A \in \mathscr{S} \) then \( A^c = \bigcup\{B \in \mathscr{A}: B \neq A \}\)
Euclidean Spaces
The following example is particulalry important because it will be used to construct positive measures on \( \R \). Let \[ \mathscr{B} = \{(a, b]: a, \, b \in \R, \; a \lt b\} \cup \{(-\infty, b]: b \in \R\} \cup \{(a, \infty): a \in \R \} \]
\( \mathscr{B} \) is a semi-algebra of subsets of \( \R \).
Proof
Note that the intersection of two intervals of the type in \( \mathscr{B} \) is another interval of this type. The complement of an interval of this type is either another interval of this type or the union of two disjoint intervals of this type.
It follows from the theorem above that the collection \( \mathscr{A} \) of finite disjoint unions of intervals in \( \mathscr{B} \) is an algebra. Recall also that \( \sigma(\mathscr{B}) = \sigma(\mathscr{A}) \) is the Borel \( \sigma \)-algebra of \( \R \), named for Émile Borel. We can generalize all of this to \( \R^n \) for \( n \in \N_+ \)
The collection \( \mathscr{B}_n = \left\{\prod_{i=1}^n A_i: A_i \in \mathscr{B} \text{ for each } i \in \{1, 2, \ldots, n\} \right\} \) is a semi-algebra of subsets of \( \R^n \).
Recall also that \( \sigma(\mathscr{B}_n) \) is the \( \sigma \)-algebra of Borel sets of \( \R^n \).
Product Spaces
The examples in this discussion are important for constructing positive measures on product spaces.
Suppose that \(\mathscr S\) is a semi-algebra of subsets of a set \( S \) and that \(\mathscr T\) is a semi-algebra of subsets of a set \( T \). Then \[ \mathscr U = \{A \times B: A \in \mathscr S, B \in \mathscr T\} \] is a semi-algebra of subsets of \( S \times T \).
Proof
- Suppose that \( A \times B, \, C \times D \in \mathscr U \), so that \( A, \, C \in \mathscr S \) and \( B, \, D \in \mathscr T \). Recall that \( (A \times B) \cap (C \times D) = (A \cap C) \times (B \cap D) \). But \( A \cap C \in \mathscr S \) and \( B \cap D \in \mathscr T \) so \( (A \times B) \cap (C \times D) \in \mathscr U \).
- Suppose that \( A \times B \in \mathscr B \) so that \( A \in \mathscr S \) and \( B \in \mathscr T \). Then \[ (A \times B)^c = (A^c \times B) \cup (A \times B^c) \cup (A^c \times B^c) \] There exists a finite, disjoint collection \( \{A_i: i \in I\} \) of sets in \( \mathscr S \) and a finite, disjoint collection \( \{B_j: j \in J\} \) of sets in \( \mathscr T \) such that \( A^c = \bigcup_{i \in I} A_i\) and \( B^c = \bigcup_{j \in J} B_j \).
This result extends in a completely straightforward way to a product of a finite number of sets.
Suppose that \( n \in \N_+ \) and that \( \mathscr S_i \) is a semi-algebra of subsets of a set \( S_i \) for \( i \in \{1, 2, \ldots, n\} \). Then \[ \mathscr U = \left\{\prod_{i=1}^n A_i: A_i \in \mathscr S_i \text{ for all } i \in \{1, 2, \ldots, n\}\right\} \] is a semi-algebra of subsets of \( \prod_{i=1}^n S_i \).
Note that the semi-algebra of products of intervals in \( \R^n \) described above is a special case of this result. For the product of an infinite sequence of sets, the result is bit more tricky.
Suppose that \( \mathscr S_i \) is a semi-algebra of subsets of a set \( S_i \) for \( i \in \N_+ \). Then \[ \mathscr U = \left\{\prod_{i=1}^\infty A_i: A_i \in \mathscr S_i \text{ for all } i \in \N_+ \text{ and } A_i = S_i \text{ for all but finitely many } i \in \N_+\right\} \] is a semi-algebra of subsets of \( \prod_{i=1}^n S_i \).
Proof
The proof is very much like the previous ones.
- Suppose that \( A = \prod_{i=1}^\infty A_i \in \mathscr U \) and \( B = \prod_{i=1}^\infty B_i \in \mathscr U \), so that \( A_i, \, B_i \in \mathscr S_i \) for \( i \in \N_+ \) and \( A_i = S_i \) for all but finitely many \( i \in \N_+ \) and \( B_i = S_i \) for all but finitely many \( i \in \N_+ \). Then \( A \cap B = \prod_{i=1}^\infty (A_i \cap B_i) \). Also, \( A_i \cap B_i \in \mathscr S_i \) for \( i \in \N_+ \) and \( A_i \cap B_i = S_i \) for all but finitely many \( in \in \N_+ \). So \( A \cap B \in \mathscr U \).
- Suppose that \( A = \prod_{i=1}^\infty A_i \in \mathscr U \), where \( A_i \in \mathscr S_i \) for \( i \in \N_+ \) and \( A_i = S_i \) for \( i \gt n \), for some \( n \in \N_+ \). Then \( A^c = \bigcup_{j=1}^n B_j \) where \[ B_j = A_1 \times \cdots \times A_{j-1} \times A_j^c \times S_{j+1} \times S_{j+2} \times \cdots, \quad j \in \{1, 2, \ldots, n\}\] Note that the product sets in this union are disjoint. But for each \( j \in \{1, 2, \ldots, n\} \) there exists a finite disjoint collection \( \{C_{j,k}: k \in K_j\} \) such that \( A_j^c = \bigcup_{k \in K_j} C_{j,k} \). Substituting and distributing then gives \( A^c \) as a finite, disjoint union of sets in \( \mathscr U \).
Note that this result would not be true with \( \mathscr U = \left\{\prod_{i=1}^\infty A_i: A_i \in \mathscr S_i \text{ for all } i \in \N_+\right\}\). In general, the complement of a set in \( \mathscr U \) cannot be written as a finite disjoint union of sets in \( \mathscr U \).


1.10: Organic Chemistry (Exercises)
1. Write the chemical formula and Lewis structure of the following, each of which contains five carbon atoms:
- an alkane
- an alkene
- an alkyne
- Answer
- There are several sets of answers; one is:
(a) C 5 H 12
(b) C 5 H 10
(c) C 5 H 8
2. What is the difference between the hybridization of carbon atoms’ valence orbitals in saturated and unsaturated hydrocarbons?
3. On a microscopic level, how does the reaction of bromine with a saturated hydrocarbon differ from its reaction with an unsaturated hydrocarbon? How are they similar?
- Answer
- Both reactions result in bromine being incorporated into the structure of the product. The difference is the way in which that incorporation takes place. In the saturated hydrocarbon, an existing C–H bond is broken, and a bond between the C and the Br can then be formed. In the unsaturated hydrocarbon, the only bond broken in the hydrocarbon is the π bond whose electrons can be used to form a bond to one of the bromine atoms in Br 2 (the electrons from the Br–Br bond form the other C–Br bond on the other carbon that was part of the π bond in the starting unsaturated hydrocarbon).
4. On a microscopic level, how does the reaction of bromine with an alkene differ from its reaction with an alkyne? How are they similar?
5. Explain why unbranched alkenes can form geometric isomers while unbranched alkanes cannot. Does this explanation involve the macroscopic domain or the microscopic domain?
- Answer
- Unbranched alkanes have free rotation about the C–C bonds, yielding all orientations of the substituents about these bonds equivalent, interchangeable by rotation. In the unbranched alkenes, the inability to rotate about the \(\mathrm{C=C}\) bond results in fixed (unchanging) substituent orientations, thus permitting different isomers. Since these concepts pertain to phenomena at the molecular level, this explanation involves the microscopic domain.
6. Explain why these two molecules are not isomers:
7. Explain why these two molecules are not isomers:
- Answer
- They are the same compound because each is a saturated hydrocarbon containing an unbranched chain of six carbon atoms.
8. How does the carbon-atom hybridization change when polyethylene is prepared from ethylene?
9. Write the Lewis structure and molecular formula for each of the following hydrocarbons:
- hexane
- 3-methylpentane
- cis -3-hexene
- 4-methyl-1-pentene
- 3-hexyne
- 4-methyl-2-pentyne
- Answer
- (a) C 6 H 14
(b) C 6 H 14
(c) C 6 H 12
(d) C 6 H 12
(e) C 6 H 10
(f) C 6 H 10
10. Write the chemical formula, condensed formula, and Lewis structure for each of the following hydrocarbons:
- heptane
- 3-methylhexane
- trans -3-heptene
- 4-methyl-1-hexene
- 2-heptyne
- 3,4-dimethyl-1-pentyne
11. Give the complete IUPAC name for each of the following compounds:
- CH 3 CH 2 CBr 2 CH 3
- (CH 3 ) 3 CCl
- \(\mathrm{CH_3CH_2C≡CH\, CH_3CH_2C≡CH}\
- \(\mathrm{(CH_3)_2CHCH_2CH=CH_2}\)
- Answer
- (a) 2,2-dibromobutane; (b) 2-chloro-2-methylpropane; (c) 2-methylbutane; (d) 1-butyne; (e) 4-fluoro-4-methyl-1-octyne; (f) trans -1-chloropropene; (g) 5-methyl-1-pentene
12. Give the complete IUPAC name for each of the following compounds:
- (CH 3 ) 2 CHF
- CH 3 CHClCHClCH 3
- \(\mathrm{CH_3CH_2CH=CHCH_3}\)
- \(\mathrm{(CH_3)_3CCH_2C≡CH}\)
13. Butane is used as a fuel in disposable lighters. Write the Lewis structure for each isomer of butane.
- Answer
14. Write Lewis structures and name the five structural isomers of hexane.
15. Write Lewis structures for the cis–trans isomers of \(\mathrm{CH_3CH=CHCl}\).
- Answer
16. Write structures for the three isomers of the aromatic hydrocarbon xylene, C 6 H 4 (CH 3 ) 2 .
17. Isooctane is the common name of the isomer of C 8 H 18 used as the standard of 100 for the gasoline octane rating:
- What is the IUPAC name for the compound?
- Name the other isomers that contain a five-carbon chain with three methyl substituents.
- Answer
- (a) 2,2,4-trimethylpentane; (b) 2,2,3-trimethylpentane, 2,3,4-trimethylpentane, and 2,3,3-trimethylpentane:
18. Write Lewis structures and IUPAC names for the alkyne isomers of C 4 H 6 .
19. Write Lewis structures and IUPAC names for all isomers of C 4 H 9 Cl.
- Answer
20. Name and write the structures of all isomers of the propyl and butyl alkyl groups.
21. Write the structures for all the isomers of the –C 5 H 11 alkyl group.
- Answer
- In the following, the carbon backbone and the appropriate number of hydrogen atoms are shown in condensed form:
22. Write Lewis structures and describe the molecular geometry at each carbon atom in the following compounds:
- cis -3-hexene
- cis -1-chloro-2-bromoethene
- 2-pentyne
- trans - 6 -ethyl-7-methyl-2-octene
23. Benzene is one of the compounds used as an octane enhancer in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene:
\[\ce{3C2H2 ⟶ C6H6}\]
Draw Lewis structures for these compounds, with resonance structures as appropriate, and determine the hybridization of the carbon atoms in each.
- Answer
- In acetylene, the bonding uses sp hybrids on carbon atoms and s orbitals on hydrogen atoms. In benzene, the carbon atoms are sp 2 hybridized.
24. Teflon is prepared by the polymerization of tetrafluoroethylene. Write the equation that describes the polymerization using Lewis symbols.
25. Write two complete, balanced equations for each of the following reactions, one using condensed formulas and one using Lewis structures.
- 1 mol of 1-butyne reacts with 2 mol of iodine.
- Pentane is burned in air.
- Answer
- (a) \(\mathrm{CH=CCH_2CH_3 + 2I_2⟶ CHI_2CI_2CH_2CH_3}\)
- (b) \(\ce{CH3CH2CH2CH2CH3 + 8O2 ⟶ 5CO2 + 6H2O}\)
26. Write two complete, balanced equations for each of the following reactions, one using condensed formulas and one using Lewis structures.
- 2-butene reacts with chlorine.
- benzene burns in air.
27. What mass of 2-bromopropane could be prepared from 25.5 g of propene? Assume a 100% yield of product.
- Answer
- 65.2 g
28. Acetylene is a very weak acid; however, it will react with moist silver(I) oxide and form water and a compound composed of silver and carbon. Addition of a solution of HCl to a 0.2352-g sample of the compound of silver and carbon produced acetylene and 0.2822 g of AgCl.
- What is the empirical formula of the compound of silver and carbon?
- The production of acetylene on addition of HCl to the compound of silver and carbon suggests that the carbon is present as the acetylide ion, \(\ce{C2^2-}\). Write the formula of the compound showing the acetylide ion.
29. Ethylene can be produced by the pyrolysis of ethane:
\(\ce{C2H6⟶C2H4 + H2}\)
How many kilograms of ethylene is produced by the pyrolysis of 1.000 × 10 3 kg of ethane, assuming a 100.0% yield?
- Answer
- 9.328 × 10 2 kg