13.4: Water - Both an Acid and a Base
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Learning Objectives
- To write chemical equations for water acting as an acid and as a base.
Water (H 2 O) is an interesting compound in many respects. Here, we will consider its ability to behave as an acid or a base.
In some circumstances, a water molecule will accept a proton and thus act as a Brønsted-Lowry base . We saw an example in the dissolving of HCl in H 2 O:
\[\rm{HCl + H_2O(ℓ) \rightarrow H_3O^+(aq) + Cl^−(aq)} \label{Eq1} \]
In other circumstances, a water molecule can donate a proton and thus act as a Brønsted-Lowry acid . For example, in the presence of the amide ion (see Example 4 in Section 10.2), a water molecule donates a proton, making ammonia as a product:
\[H_2O(ℓ) + NH^−_{2}(aq) \rightarrow OH^−(aq) + NH_{3}(aq) \label{Eq2} \]
In this case, NH 2 − is a Brønsted-Lowry base (the proton acceptor).
So, depending on the circumstances, H 2 O can act as either a Brønsted-Lowry acid or a Brønsted-Lowry base. Water is not the only substance that can react as an acid in some cases or a base in others, but it is certainly the most common example—and the most important one. A substance that can either donate or accept a proton, depending on the circumstances, is called an amphiprotic compound.
A water molecule can act as an acid or a base even in a sample of pure water. About 6 in every 100 million (6 in 10 8 ) water molecules undergo the following reaction:
\[H_2O(ℓ) + H_2O(ℓ) \rightarrow H_3O^+(aq) + OH^−(aq) \label{Eq3} \]
This process is called the autoionization of water (Figure \(\PageIndex{1}\)) and occurs in every sample of water, whether it is pure or part of a solution. Autoionization occurs to some extent in any amphiprotic liquid. (For comparison, liquid ammonia undergoes autoionization as well, but only about 1 molecule in a million billion (1 in 10 15 ) reacts with another ammonia molecule.)
Note
It is rare to truly have pure water. Water exposed to air will usually be slightly acidic because dissolved carbon dioxide gas, or carbonic acid, decreases the pH slightly below 7. Alternatively, dissolved minerals, like calcium carbonate (limestone), can make water slightly basic.
Example \(\PageIndex{1}\)
Identify water as either a Brønsted-Lowry acid or a Brønsted-Lowry base.
- H 2 O(ℓ) + NO 2 − (aq) → HNO 2 (aq) + OH − (aq)
- HC 2 H 3 O 2 (aq) + H 2 O(ℓ) → H 3 O + (aq) + C 2 H 3 O 2 − (aq)
Solution
- In this reaction, the water molecule donates a proton to the NO 2 − ion, making OH − (aq). As the proton donor, H 2 O acts as a Brønsted-Lowry acid.
- In this reaction, the water molecule accepts a proton from HC 2 H 3 O 2 , becoming H 3 O + (aq). As the proton acceptor, H 2 O is a Brønsted-Lowry base.
Exercise \(\PageIndex{2}\)
Identify water as either a Brønsted-Lowry acid or a Brønsted-Lowry base.
- HCOOH(aq) + H 2 O(ℓ) → H 3 O + (aq) + HCOO − (aq)
- H 2 O(ℓ) + PO 4 3 − (aq) → OH − (aq) + HPO 4 2 − (aq)
- Answer
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1. H 2 O acts as the proton acceptor (Brønsted-Lowry base)
2. H 2 O acts as the proton donor (Brønsted-Lowry acid)
Key Takeaway
- Water molecules can act as both an acid and a base, depending on the conditions.


1.5: Chapter Summary
This chapter provided a brief history of pharmacology and the use of therapeutic drugs throughout the millennia. It discussed the importance of interprofessional collaboration and introduced how pharmacology is used in nursing practice. It also presented some of the responsibilities of the clinical nurse relating to drug administration.
This chapter reviewed the many sources and forms of drugs and explained the approval process for new drugs as they come onto the market. It described the difference between the various names of the drugs (chemical, generic, and brand names) and discussed the difference between generic and brand-name drugs. Traditional drugs, biologics, biosimilars, and complementary and alternative medicine were also discussed, and counterfeit drugs, drug classifications, and drug prototypes were introduced. The various drug schedules as they relate to drugs with the potential for abuse were explained. This chapter also focused on socioeconomic factors as they relate to pharmacology and how drug therapy may impact specific groups of clients (e.g., those who are pregnant, the very young, or the very old). The chapter ended with a discussion of the aging client and the “silver tsunami.”


1.2: Industry Expectations
The hospitality and food service industry has a longstanding tradition of quality of service and dedication to putting customer needs first. Though extremely diverse, the industry has an expectation of workers to be professional, productive, respectful, and responsive to customer needs. No matter which style of operation you are working in, it is important to remember why you chose this career path in the first place and always to respect your job and the other people you work with. The main attributes that will make you successful are commitment, dedication, and passion for what you do.
Additionally, people working in the industry often collaborate outside of their workplaces to drive the industry forward by joining and participating in local or national trade and professional associations, local food movements and events, and other activities that maintain a strong presence and voice in the community for the industry. By joining the food service industry, you should realize that your work is more than a job — some would describe it as a lifestyle — and being supportive of all the aspects of industry mentioned above will only enhance your experience.
The hospitality industry is also very connected through social media and other channels, and therefore as someone working in the trade, you are expected to be respectful of your peers, and when you are out on your own time, to treat your colleagues as you would like your customers to treat you.


9.11: Why It Matters- Operating Budgets
Why learn about operating budgets?
Why do budgets matter? It seems like a ton of work to put together all of the information needed to complete a master budget. We need to know how many units we are going to produce, and all of the costs that go into each of those units. We also have to have all of our payroll information, and overhead costs. Hours and hours of work may go into creating the master budget, even for a small company!
The budget matters for a variety of reasons:
- We can see if the company will make money or lose money at our anticipated level of sales.
- We can analyze our expenses based on expectations. This will help us know when costs are high or where we can save money in our processes or purchases.
- We can hold staff accountable for their departments. This is especially true if they participated in putting the budget together for their own department!
- It creates a living document to help grow the business and become more profitable over time.
It would be tough to run your household without an idea of the interaction between what is coming in for income, and what is going out for expenses right? Let’s think about the business master budget as a big household with a few more moving parts!
Ready to get started?


13.11: Summary- Interest Rates, the Corporation, and Financial Markets
Corporations are intimately connected with the financial markets because the value of the corporation depends on ever-changing prices reflected in the markets, and because corporations periodically require access to the financial markets in order to acquire capital for growth. In this chapter, we outlined four financial markets: money, capital, derivatives, and foreign exchange markets. The focus was, of course, on securities markets, that is, the markets for stocks and bonds. Securities markets, in turn, are connected to the macroeconomic world, and monetary and fiscal policies are a key component of security markets analysis.
The means by which corporations gain access to the financial markets and its capital raising function is the subject of investment banking. In particular, we are interested in new securities’ issuance, or initial public offerings (IPOs), but I-banking serves various other essential roles in our financial sector.
Interest rates affect securities’ valuations, most visibly affecting bonds’ prices, but the impact on equities is notable also. This is but one example of the connections between macroeconomics and securities markets. In this section, we also glanced at the interconnections between interest rates of various sorts.
There is much to know.
Note:


1.2: Installing the Software and Downloading the Data
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Minimum hardware and software requirements were listed previously . However, keep in mind that those are only the minimum. You will find the exercises to be much more pleasant if you have at least 8 GB of RAM and at least a 1080p screen. If you don’t have much free disk space, you may need to keep the data from only one or two exercises on your computer at a given time.
Installing Matlab
You will need Matlab version 2017a or later, including the Signal Processing Toolbox. The Statistics and Machine Learning Toolbox is recommended (but is not required for any of the exercises in this book). Once you have installed Matlab, you can see what toolboxes are installed by typing ver on the Matlab command line. If you don't have the necessary toolboxes, contact your institution's IT support department for assistance.
Installing EEGLAB and ERPLAB
New versions of Matlab, EEGLAB, and ERPLAB are released at least once per year, and these new versions can lead to changes in how things look (and occasionally changes in the results). To write this book, I mainly used Matlab 2017a or 2020b, EEGLAB 2020.0, and ERPLAB 8.23 on a MacBook Pro running macOS 11. However, we added some important features to ERPLAB as I was writing, so you should use EEGLAB 2022.0 or later and ERPLAB 9.0 or later. You will probably use a different combination, so the screenshots and videos in this book may not exactly match what you see. Newer versions of Matlab, EEGLAB, and ERPLAB will probably work fine, but I would recommend against using older versions.
ERPLAB runs as an EEGLAB plugin, so you must install EEGLAB before installing ERPLAB. You can find the documentation for EEGLAB, including instructions for downloading and installing, at https://sccn.ucsd.edu/wiki/EEGLAB . Make sure to install version 2022.0 or later. Once you’ve installed it, you can launch EEGLAB by typing eeglab in the Matlab command window. Screenshot 1.1 shows what it should look like when EEGLAB has been launched.
A key step in installing EEGLAB is to update the Matlab PATH (whether you are installing EEGLAB for the first time or upgrading to a newer version). If you don’t know how to do this, or you can’t get EEGLAB to launch, you should read the description of how the PATH works later in this chapter. If you are having trouble launching EEGLAB but the PATH isn’t the problem, see the ERPLAB FAQ page , the EEGLAB documentation or the Troubleshooting Guide in Appendix 2 .
Once you have installed EEGLAB, you can download and install ERPLAB (version 9.0 or later). The ERPLAB documentation, including installation instructions, can be found at https://github.com/lucklab/erplab/wiki . There are two ways to install ERPLAB. If you just want the latest major release, you can launch EEGLAB and use its built-in extensions manager by going to File > Manage EEGLAB extensions in the EEGLAB GUI. It will pop up a window with a list of extensions; select ERPLAB and click install/update . If you want an earlier version of ERPLAB (or if you’re a do-it-yourselfer by nature), you can download ERPLAB at https://github.com/lucklab/erplab . Additional ERPLAB installation information can be found at https://github.com/lucklab/erplab/wiki/Installation . Once ERPLAB has been installed and is running within EEGLAB, the EEGLAB GUI should include an ERPLAB menu, as in Screenshot 1.2.
ERPLAB Installation Problems
ERPLAB is installed inside the plugins folder within the EEGLAB folder (e.g., eeglab2020_0 > plugins > ERPLAB8.30). The most common installation problem is that ERPLAB is not located in this place. You should see a file named eegplugin_erplab.m inside that folder (and not inside another folder). ERPLAB has a Frequently Asked Questions page with information about solving such problems.
Another problem that occasionally arises (especially when ERPLAB is being used on a multiuser computer) is that ERPLAB must have write access to the folder that contains the ERPLAB software. This is necessary so that ERPLAB can update a file named memoryerp.erpm , which stores various user settings. To avoid this problem, you should install EEGLAB and ERPLAB inside a folder that you own (e.g., your Documents folder) rather than installing it in a folder that is used by multiple people.
Downloading Data for the Exercises
The data for the exercises are stored in a cloud storage system, and the master folder can be accessed at https://doi.org/10.18115/D50056 . This master folder contains a set of subfolders with the data for each chapter. Unfortunately, the cloud storage system may be blocked in some countries, but I have faith that clever readers will still find a way to access the data. The data have been released with a Creative Commons license that permits them to be copied, used, remixed, and reposted as long as the original source is cited (see the license.txt file in each subfolder). Note that some of the folders are quite large and may take quite a while to download.
Free Data!
Once you’ve finished using this book to learn how to analyze ERP data, you should feel free to download the original data from the ERP CORE . The CORE is a very rich dataset, and you could use it to for novel analyses that might be publishable. Wouldn’t it be nice to publish an ERP paper without having to collect the data yourself?


10.10: Faraday’s Law of Induction- Lenz’s Law
Learning Objectives
- Calculate voltage, current, and magnetic fields using Faraday’s Law.
- Explain the physical results of Lenz’s Law
Faraday’s and Lenz’s Law
Faraday’s experiments showed that the voltage induced by a change in magnetic flux depends on only a few factors. First, voltage is directly proportional to the change in flux \(\Delta \Phi\). Second, voltage is greatest when the change in time \(\Delta t\) is smallest—that is, voltage is inversely proportional to \(\Delta t\). Finally, if a coil has N turns, a voltage will be produced that is \(N\) times greater than for a single coil, so that voltage is directly proportional to \(N\). The equation for the voltage induced by a change in magnetic flux is
\[V=-N \frac{\Delta \Phi}{\Delta t}. \nonumber \]
This relationship is known as Faraday’s law of induction .
The minus sign in Faraday’s law of induction is very important. The minus means that the induced voltage creates a current I and magnetic field B that oppose the change in flux \(\Delta \Phi\)—this is known as Lenz’s law . Faraday was aware of the direction, but Lenz stated it so clearly that he is credited for its discovery. (See Figure \(\PageIndex{1}\).)
Applications of Electromagnetic Induction
There are many applications of Faraday’s Law of induction, as we will explore in this chapter and others. At this juncture, let us mention several that have to do with data storage and magnetic fields. A very important application has to do with audio and video recording tapes . A plastic tape, coated with iron oxide, moves past a recording head. This recording head is basically a round iron ring about which is wrapped a coil of wire—an electromagnet ( Figure \(\PageIndex{2}\)). A signal in the form of a varying input current from a microphone or camera goes to the recording head. These signals (which are a function of the signal amplitude and frequency) produce varying magnetic fields at the recording head. As the tape moves past the recording head, the magnetic field orientations of the iron oxide molecules on the tape are changed thus recording the signal. In the playback mode, the magnetized tape is run past another head, similar in structure to the recording head. The different magnetic field orientations of the iron oxide molecules on the tape induces a voltage in the coil of wire in the playback head. This signal then is sent to a loudspeaker or video player.
Similar principles apply to computer hard drives, except at a much faster rate. Here recordings are on a coated, spinning disk. Read heads historically were made to work on the principle of induction. However, the input information is carried in digital rather than analog form – a series of 0’s or 1’s are written upon the spinning hard drive. Today, most hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance . (The discovery that weak changes in a magnetic field in a thin film of iron and chromium could bring about much larger changes in electrical resistance was one of the first large successes of nanotechnology.) Another application of induction is found on the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. This works on the same principle as the audio or video tape mentioned in the last paragraph in which a head reads personal information from your card.
Another application of electromagnetic induction is when electrical signals need to be transmitted across a barrier. Consider the cochlear implant shown below. Sound is picked up by a microphone on the outside of the skull and is used to set up a varying magnetic field. A current is induced in a receiver secured in the bone beneath the skin and transmitted to electrodes in the inner ear. Electromagnetic induction can be used in other instances where electric signals need to be conveyed across various media.
Another contemporary area of research in which electromagnetic induction is being successfully implemented (and with substantial potential) is transcranial magnetic simulation. A host of disorders, including depression and hallucinations can be traced to irregular localized electrical activity in the brain. In transcranial magnetic stimulation , a rapidly varying and very localized magnetic field is placed close to certain sites identified in the brain. Weak electric currents are induced in the identified sites and can result in recovery of electrical functioning in the brain tissue.
Sleep apnea (“the cessation of breath”) affects both adults and infants (especially premature babies and it may be a cause of sudden infant deaths [SID]).  A cessation of more than 20 seconds can be very dangerous. Stroke, heart failure, and tiredness are just some of the possible consequences for a person having sleep apnea. The concern in infants is the stopping of breath for these longer times. One type of monitor to alert parents when a child is not breathing uses electromagnetic induction. A wire wrapped around the infant’s chest has an alternating current running through it. The expansion and contraction of the infant’s chest as the infant breathes changes the area through the coil. A pickup coil located nearby has an alternating current induced in it due to the changing magnetic field of the initial wire. If the child stops breathing, there will be a change in the induced current, and so a parent can be alerted.
MAKING CONNECTIONS: CONSERVATION OF ENERGY
Lenz’s law is a manifestation of the conservation of energy. The induced voltage produces a current that opposes the change in flux, because a change in flux means a change in energy. Energy can enter or leave, but not instantaneously. Lenz’s law is a consequence. As the change begins, the law says induction opposes and, thus, slows the change. In fact, if the induced voltage were in the same direction as the change in flux, there would be a positive feedback that would give us free energy from no apparent source—conservation of energy would be violated.
Section Summary
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Faraday’s law of induction states that the voltage induced by a change in magnetic flux is
\[V=-N \frac{\Delta \Phi}{\Delta t} \nonumber\]
when flux changes by \(\Delta \Phi\) in a time \(\Delta t\).
- If voltage is induced in a coil, N is its number of turns.
- The minus sign means that the induced voltage creates a current \(I\) and magnetic field \(B\) that oppose the change in flux \(\Delta \Phi\) —this opposition is known as Lenz’s law.
Glossary
- Faraday’s law of induction
- the means of calculating the voltage in a coil due to changing magnetic flux, given by \(V=-N \frac{\Delta \Phi}{\Delta t}\)
- Lenz’s law
- the minus sign in Faraday’s law, signifying that the voltage induced in a coil opposes the change in magnetic flux


10: The Governance and Finance of American Public Education
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Learning Objectives
Icebreaker: Reflect, write and Discuss
Take five minutes to reflect on the questions below and write out your thoughts. Once finished writing discuss your ideas with a partner.
As a future teacher you will need to be aware of how schools are organized, governed and financed. Where you work will also determine the amount of money and resources available to you. The federal, state and local government all play a role in the complex financial system of education. Keep in mind that how well a school is funded is often a reflection of the community composition and wealth (number of businesses, homeowners, taxpayers, population size). In this chapter we will learn how schools are governed and financed in public education and begin to explore how these factors impact our ability to help students learn.


1.4: What we can (and can’t) learn about evolutionary history from living species
Traditionally, scientists have used fossils to quantify rates and patterns of evolution through long periods of time (sometimes called “macroevolution”). These approaches have been tremendously informative. We now have a detailed picture of the evolutionary dynamics of many groups, from hominids to crocodilians. In some cases, very detailed fossil records of some types of organisms – for example, marine invertebrates – have allowed quantitative tests of particular evolutionary models.
Fossils are particularly good at showing how species diversity and morphological characters change through time. For example, if one has a sequence of fossils with known times of occurrence, one can reconstruct patterns of species diversity through time. A classic example of this is Sepkoski’s (1984) reconstruction of the diversity of marine invertebrates over the past 600 million years. One can also quantify the traits of those fossils and measure how they change across various time intervals (e.g. Foote 1997) . In some groups, we can make plots of changes in lineage and trait diversity simultaneously (Figure 1.2). Fossils are the only evidence we have for evolutionary lineages that have gone extinct, and they provide valuable direct evidence about evolutionary dynamics in the past.
However, fossil-based approaches face some challenges. The first is that the fossil record is incomplete. This is a well-known phenomenon, identified by Darwin himself (although many new fossils continue to be found). The fossil record is incomplete in some very particular ways that can sometimes hamper our ability to study evolutionary processes using fossils alone. One example is that fossils are rare or absent from some classical examples of adaptive radiation on islands. For example, the entire fossil record of Caribbean anoles, a well-known adaptive radiation of lizards, consists of less than ten specimens preserved in amber (Losos 2009) . We similarly lack fossils for other adaptive radiations like African cichlids and Darwin’s finches. The absence of fossils in these groups limits our ability to directly study the early stages of adaptive radiation. Another limitation of the fossil record relates to species and speciation. It is very difficult to identify and classify species in the fossil record – even more difficult than it is to do so for living species. It is hard to tell species apart, and particularly difficult to pin down the exact time when new species split off from their close relatives. In fact, most studies of fossil diversity focus on higher taxonomic groups like genera, families, or orders (see, e.g., Sepkoski 1984) . These studies have been immensely valuable but it can be difficult to connect these results to what we know about living species. In fact, it is species (and not genera, families, or orders) that form the basic units of almost all evolutionary studies. So, fossils have great value but also suffer from some particular limitations.
Phylogenetic trees represent a rich source of complementary information about the dynamics of species formation through time. Phylogenetic approaches provide a useful complement to fossils because their limitations are very different from the limitations of the fossil record. For example, one can often include all of the living species in a group when creating a phylogenetic tree. Additionally, one can use information from detailed systematic and taxonomic studies to identify species, rather than face the ambiguity inherent when using fossils. Phylogenetic trees provide a distinct source of information about evolutionary change that is complementary to approaches based on fossils. However, phylogenetic trees do not provide all of the answers. In particular, there are certain problems that comparative data alone simply cannot address. The most prominent of these, which I will return to later, are reconstructing traits of particular ancestors (ancestral state reconstruction; Losos 2011) and distinguishing between certain types of models where the tempo of evolution changes through time (Slater et al. 2012) . Some authors have argued that extinction, as well, cannot be detected in the shape of a phylogenetic tree (Rabosky 2010) . I will argue against this point of view in Chapter 11, but extinction still remains a tricky problem when one is limited to samples from a single time interval (the present day). Phylogenetic trees provide a rich source of information about the past, but we should be mindful of their limitations (Alroy 1999) .
Perhaps the best approach would combine fossil and phylogenetic data directly. Paleontologists studying fossils and neontologists studying phylogenetic trees share a common set of mathematical models. This means that, at some point, the two fields can merge, and both types of information can be combined to study evolutionary patterns in a cohesive and integrative way. However, surprisingly little work has so far been done in this area (but see Slater et al. 2012, Heath et al. (2014) ) .


4.6: Two Applications
Learning Objectives
- The Stefan-Boltzmann law
- Degenerate matter
The Stefan-Boltzmann law
In 1818, Dulong and Petit analyzed experimental data to find the empirical and totally incorrect law
\[P \propto \exp[T/(13.5 K)]\]
relating the temperature \(T\) of a body to the power (\(P\)) it emits as electromagnetic radiation. (To see that it must be wrong, note that it doesn’t vanish at absolute zero.) It was accepted until 1884, when Boltzmann corrected a systematic error in their analysis of the data, and offered a theoretical argument for the correct Stefan-Boltzmann law:
\[P \propto T^4.\]
This law is extremely important in a variety of applications including global warming, stellar structure, cosmology, and warming your hands by the glow of a fire. Modern physics students usually come across it as a corollary in the story of the development of the quantum theory by Planck, Einstein, et al., but as we will see below, it is a purely classical result, depending only on relativity and thermodynamics.
Consider an insulated cubical box of volume \(V\) containing radiation in thermal equilibrium. We let it expand uniformly with constant entropy, so that all three sides grow by the same factor a. (This is exactly what happens in cosmological expansion.) Boltzmann’s clever idea was that the radiation could be treated like the working ﬂuid in a heat engine.
By the relativistic relation between momentum and energy, the energy and momentum of a ray of light are equal (in natural units). Therefore if we lived in a one-dimensional world, the pressure \(p\) exerted by our radiation on the walls of its one-dimensional vessel would equal its energy density \(ρ\). Because we live in a three-dimensional world, and the momenta along the three axes are in equilibrium, we have instead \(p = ρ/3\). This is called the equation of state of the radiation. In cosmology, other components of the universe, such as galaxies, have equations of state with some factor other than \(1/3\) in front.
As the box expands, the pressure of the radiation on the walls does work \(W\). By conservation of energy, we have
\[dU + dW = 0\]
where \(U\) is the energy of the radiation. Substituting \(U = ρV\) and \(dW = pdV\), we obtain
\[d(ρV ) + pdV = 0\]
Applying the product rule, separating variables, and integrating, we find
\[\rho \propto a^{-4}.\]
Here the exponent \(4\) is simply the number of spatial dimensions plus one. Exactly the same relation held in the early universe, which was dominated by radiation rather than matter.
Because there is no heat transfer, the entropy is constant. Entropy can be interpreted as a measure of the number of accessible states, and because state-counting doesn’t depend on scaling, the occupied modes of vibration stay the same. Thus, the wavelengths simply grow in proportion to a. (A more formal and rigorous version of this argument is called the adiabatic theorem, proved by Born and Fock in 1928.) Although this is a classical argument, we can save some work at this point by appealing to quantum mechanics for a shortcut. Since a photon has an energy \(1/λ\), we have
\[U \propto \frac{1}{\lambda } \propto \frac{1}{a}\]
The temperature of the radiation is proportional to the average energy per degree of freedom, so we have
\[T \propto \frac{1}{a}\]
as well.
Therefore \(\rho \propto T^4\). This is equivalent to the Stefan-Boltzmann result, because light rays travel at the fixed speed \(c\), and therefore the ﬂux of radiation is proportional to the energy density. Even though this final proportionality is classical in nature, the value of the proportionality constant depends on Planck’s constant, and is quantum-mechanical.
Degenerate matter
The properties of the momentum vector have surprising implications for matter subject to extreme pressure, as in a star that uses up all its fuel for nuclear fusion and collapses. These implications were initially considered too exotic to be taken seriously by astronomers.
An ordinary, smallish star such as our own sun has enough hydrogen to sustain fusion reactions for billions of years, maintaining an equilibrium between its gravity and the pressure of its gases. When the hydrogen is used up, it has to begin fusing heavier elements. This leads to a period of relatively rapid ﬂuctuations in structure. Nuclear fusion proceeds up until the formation of elements as heavy as oxygen (\(Z = 8\)), but the temperatures are not high enough to overcome the strong electrical repulsion of these nuclei to create even heavier ones. Some matter is blown off, but finally nuclear reactions cease and the star collapses under the pull of its own gravity.
To understand what happens in such a collapse, we have to understand the behavior of gases under very high pressures. In general, a surface area \(A\) within a gas is subject to collisions in a time \(t\) from the \(n\) particles occupying the volume
\[V = Avt\]
where \(v\) is the typical velocity of the particles. The resulting pressure is given by
\[P \sim \frac{npv}{V}\]
where \(p\) is the typical momentum.
Nondegenerate gas
In an ordinary gas such as air, the particles are nonrelativistic, so
\[v = p/m\]
and the thermal energy per particle is
\[\frac{p^2}{2m} \sim kT\]
so the pressure is
\[P \sim \frac{nkT}{V}\]
Nonrelativistic, degenerate gas
When a fermionic gas is subject to extreme pressure, the dominant effects creating pressure are quantum-mechanical. Because of the Pauli exclusion principle, the volume available to each particle is \(\sim V/n\), so its wavelength is no more than \((\sim V/n)^{1/3}\), leading to
\[p = \frac{h}{\lambda } \sim h\left ( \frac{n}{V} \right )^{1/3}\]
If the speeds of the particles are still nonrelativistic, then \(v = p/m\) still holds, so the pressure becomes
\[P \sim \left ( \frac{h^2}{m} \right ) \left ( \frac{n}{V} \right )^{5/3}\]
Relativistic, degenerate gas
If the compression is strong enough to cause highly relativistic motion for the particles, then \(v \approx c\), and the result is
\[P \sim hc \left ( \frac{n}{V} \right )^{4/3}\]
As a star with the mass of our sun collapses, it reaches a point at which the electrons begin to behave as a degenerate gas, and the collapse stops. The resulting object is called a white dwarf. A white dwarf should be an extremely compact body, about the size of the Earth. Because of its small surface area, it should emit very little light. In 1910, before the theoretical predictions had been made, Russell, Pickering, and Fleming discovered that 40 Eridani B had these characteristics. Russell recalled: “ I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called ‘possible’ values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: ‘It is just these exceptions that lead to an advance in our knowledge,’ and so the white dwarfs entered the realm of study! ”
S. Chandrasekhar showed in that 1930’s that there was an upper limit to the mass of a white dwarf. We will recapitulate his calculation brieﬂy in condensed order-of-magnitude form. The pressure at the core of the star is
\[P \sim \rho gr \sim \frac{GM^2}{r^4}\]
where \(M\) is the total mass of the star. The star contains roughly equal numbers of neutrons, protons, and electrons, so \(M = Knm\), where \(m\) is the mass of the electron, \(n\) is the number of electrons, and \(K ≈ 4000\). For stars near the limit, the electrons are relativistic. Setting the pressure at the core equal to the degeneracy pressure of a relativistic gas, we find that the Chandrasekhar limit is \(\sim \left ( \frac{hc}{G} \right )^{3/2} (Km)^{-2} = 6M\odot\). A less sloppy calculation gives something more like \(1.4M \odot\).
What happens to a star whose mass is above the Chandrasekhar limit? As nuclear fusion reactions ﬂicker out, the core of the star becomes a white dwarf, but once fusion ceases completely this cannot be an equilibrium state. Now consider the nuclear reactions
\[n \rightarrow p + e^- + \bar{v}\]
\[p + e^- \rightarrow n + v\]
which happen due to the weak nuclear force. The first of these releases \(0.8\: MeV\), and has a half-life of \(14\) minutes. This explains why free neutrons are not observed in significant numbers in our universe, e.g., in cosmic rays. The second reaction requires an input of \(0.8\: MeV\) of energy, so a free hydrogen atom is stable. The white dwarf contains fairly heavy nuclei, not individual protons, but similar considerations would seem to apply. A nucleus can absorb an electron and convert a proton into a neutron, and in this context the process is called electron capture. Ordinarily this process will only occur if the nucleus is neutron-deficient; once it reaches a neutron-to-proton ratio that optimizes its binding energy, neutron capture cannot proceed without a source of energy to make the reaction go. In the environment of a white dwarf, however, there is such a source. The annihilation of an electron opens up a hole in the “Fermi sea.” There is now an state into which another electron is allowed to drop without violating the exclusion principle, and the effect cascades upward. In a star with a mass above the Chandrasekhar limit, this process runs to completion, with every proton being converted into a neutron. The result is a neutron star, which is essentially an atomic nucleus (with \(Z = 0\)) with the mass of a star!
Observational evidence for the existence of neutron stars came in 1967 with the detection by Bell and Hewish at Cambridge of a mysterious radio signal with a period of \(1.3373011\) seconds. The signal’s observability was synchronized with the rotation of the earth relative to the stars, rather than with legal clock time or the earth’s rotation relative to the sun. This led to the conclusion that its origin was in space rather than on earth, and Bell and Hewish originally dubbed it LGM-1 for “little green men.” The discovery of a second signal, from a different direction in the sky, convinced them that it was not actually an artificial signal being generated by aliens. Bell published the observation as an appendix to her PhD thesis, and it was soon interpreted as a signal from a neutron star. Neutron stars can be highly magnetized, and because of this magnetization they may emit a directional beam of electromagnetic radiation that sweeps across the sky once per rotational period — the “lighthouse effect.” If the earth lies in the plane of the beam, a periodic signal can be detected, and the star is referred to as a pulsar. It is fairly easy to see that the short period of rotation makes it difficult to explain a pulsar as any kind of less exotic rotating object. In the approximation of Newtonian mechanics, a spherical body of density \(ρ\), rotating with a period \(T = \sqrt{\frac{3\pi }{G\rho }}\), has zero apparent gravity at its equator, since gravity is just strong enough to accelerate an object so that it follows a circular trajectory above a fixed point on the surface. In reality, astronomical bodies of planetary size and greater are held together by their own gravity, so we have \(T \gtrsim \frac{1}{\sqrt{G\rho }}\)for any body that does not ﬂy apart spontaneously due to its own rotation. In the case of the Bell-Hewish pulsar, this implies \(\rho \gtrsim 10^{10}\: kg/m^3\), which is far larger than the density of normal matter, and also \(10 - 100\) times greater than the typical density of a white dwarf near the Chandrasekhar limit.
An upper limit on the mass of a neutron star can be found in a manner entirely analogous to the calculation of the Chandrasekhar limit. The only difference is that the mass of a neutron is much greater than the mass of an electron, and the neutrons are the only particles present, so there is no factor of \(K\). Assuming the more precise result of \(1.4M\odot\) for the Chandrasekhar limit rather than our sloppy one, and ignoring the interaction of the neutrons via the strong nuclear force, we can infer an upper limit on the mass of a neutron star:
\[1.4M\odot \left ( \frac{Km_e}{m_n} \right )^2 \approx 5M\odot\]
The theoretical uncertainties in such an estimate are fairly large. Tolman, Oppenheimer, and Volkoff originally estimated it in 1939 as \(0.7M\odot\), whereas modern estimates are more in the range of \(1.5M\odot\) to \(3M\odot\). These are significantly lower than our crude estimate of \(5M\odot\), mainly because the attractive nature of the strong nuclear force tends to pull the star toward collapse. Unambiguous results are presently impossible because of uncertainties in extrapolating the behavior of the strong force from the regime of ordinary nuclei, where it has been relatively well parametrized, into the exotic environment of a neutron star, where the density is significantly different and no protons are present. There are a variety of effects that may be difficult to anticipate or to calculate. For example, Brown and Bethe found in 1994 1 that it might be possible for the mass limit to be drastically revised because of the process \(e^- \rightarrow K^- + v_e\), which is impossible in free space due to conservation of energy, but might be possible in a neutron star. Observationally, nearly all neutron stars seem to lie in a surprisingly small range of mass, between \(1.3M\odot\) and \(1.45M\odot\), but in 2010 a neutron star with a mass of \(1.97 \pm 0.04 M\odot\) was discovered, ruling out most neutron-star models that included exotic matter. 2
For stars with masses above the Tolman-Oppenheimer-Volkoff limit, it seems likely, both on theoretical and observational grounds, we end up with a black hole: an object with an event horizon that cuts its interior off from the rest of the universe.
References
1 H.A. Bethe and G.E. Brown, “Observational constraints on the maximum neutron star mass,” Astrophys. J. 445 (1995) L129. G.E. Brown and H.A. Bethe, “A Scenario for a Large Number of Low-Mass Black Holes in the Galaxy,” Astrophys. J. 423 (1994) 659. Both papers are available at adsabs.harvard.edu.
2 Demorest et al., arxiv.org/abs/1010.5788v1.


5.2: Introduction to Two-Way Tables
What you’ll learn to do: Analyze the relationship between two categorical variables using a two-way table.
Recall, categorical data is data that consists of labels (such as person’s gender, an object’s color, or location). Since categorical data does not return a measurement, it is often convenient to summarize study results with counts (for example, total number of females, or total number of males). In this section, we introduce two way tables and conditional percentages as a way to investigate possible relationships between two categorical variables.
Contributors and Attributions
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- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


16.23: Cancer and Gene Regulation - Cancer and Translational Control
- Determine how translational or post-translational modifications can lead to cancer
There are many examples of translational or post-translational modifications of proteins that arise in cancer. Modifications are found in cancer cells from the increased translation of a protein to changes in protein phosphorylation to alternative splice variants of a protein. An example of how the expression of an alternative form of a protein can have dramatically different outcomes is seen in colon cancer cells. The c-Flip protein, a protein involved in mediating the cell death pathway, comes in two forms: long (c-FLIPL) and short (c-FLIPS). Both forms appear to be involved in initiating controlled cell death mechanisms in normal cells. However, in colon cancer cells, expression of the long form results in increased cell growth instead of cell death. Clearly, the expression of the wrong protein dramatically alters cell function and contributes to the development of cancer.
New Drugs to Combat Cancer: Targeted Therapy
Scientists are using what is known about the regulation of gene expression in disease states, including cancer, to develop new ways to treat and prevent disease development. Many scientists are designing drugs on the basis of the gene expression patterns within individual tumors. This idea, that therapy and medicines can be tailored to an individual, has given rise to the field of personalized medicine. With an increased understanding of gene regulation and gene function, medicines can be designed to specifically target diseased cells without harming healthy cells. Some new medicines, called targeted therapies, have exploited the overexpression of a specific protein or the mutation of a gene to develop a new medication to treat disease. One such example is the use of anti-EGF receptor medications to treat the subset of breast cancer tumors that have very high levels of the EGF protein. Undoubtedly, more targeted therapies will be developed as scientists learn more about how gene expression changes can cause cancer.
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- CpG island. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/CpG_island . License : CC BY-SA: Attribution-ShareAlike
- methylation. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/methylation . License : CC BY-SA: Attribution-ShareAlike
- acetylation. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/acetylation . License : CC BY-SA: Attribution-ShareAlike
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- Transcription Factors. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/File:Transcription_Factors.svg . License : CC BY: Attribution
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Key Points
- Protein modifications from the increased translation of a protein to changes in protein phosphorylation to alternative splice variants of a protein are found in cancer cells.
- The expression of the wrong protein dramatically alters cell function and contributes to the progression of cancer.
- Gene regulation and gene function provide scientists with the opportunity to design medicines and therapies that specifically target diseased cells or exploit the overexpression of specific proteins as cancer treatment.
Key Terms
- targeted therapy : a type of medication that blocks the growth of cancer cells by interfering with specific targeted molecules rather than by interfering with rapidly dividing cells
- cancer : a disease in which the cells of a tissue undergo uncontrolled (and often rapid) proliferation
- post-translational modification : the chemical modification of a protein after its translation; one of the later steps in protein biosynthesis, and thus gene expression, for many proteins


8.8: Le Châtelier’s Principle
- Define Le Chatelier's principle.
- Predict the direction of shift for an equilibrium under stress with changes in concentrations.
Once equilibrium is established, the reaction is over, right? Not exactly. An experimenter has some ability to affect the equilibrium.
Chemical equilibria can be shifted by changing the conditions that the system experiences. We say that we "stress" the equilibrium. When we stress the equilibrium, the chemical reaction is no longer at equilibrium, and the reaction starts to move back toward equilibrium in such a way as to decrease the stress. The formal statement is called Le Châ telier's principle : If an equilibrium is stressed, then the reaction shifts to reduce the stress.
There are several ways to stress an equilibrium. One way is to add or remove a product or a reactant in a chemical reaction at equilibrium.
When additional reactant is added , the equilibrium shifts to reduce this stress: it makes more product .
When additional product is added , the equilibrium shifts to reactants to reduce the stress: it makes more reactant .
If reactant or product is removed, the equilibrium shifts to make more product or reactant, respectively, to make up for the loss.
To make more product, the rate of the forward reaction increases . To make more reactant, the rate of the reverse reaction increases .
Given this reaction at equilibrium:
\[N_{2}+3H_{2}\rightleftharpoons 2NH_{3}\nonumber \]
In which direction—toward reactants or toward products-—does the reaction shift if the equilibrium is stressed by each change?
- H 2 is added.
- NH 3 is added.
- NH 3 is removed.
Solution
- If H 2 is added, there is now more reactant, so the reaction will shift toward products to reduce the added H 2 . (Rate of forward reaction increases/shifts right)
- If NH 3 is added, there is now more product, so the reaction will shift toward reactants to reduce the added NH 3 . (Rate of reverse reaction increases/shifts left)
- If NH 3 is removed, there is now less product, so the reaction will shift toward products to replace the product removed. (Rate of forward reaction increases/shifts right)
Given this reaction at equilibrium:
\[CO(g)+Br_{2}(g)\rightleftharpoons COBr_{2}(g)\nonumber \]
In which direction—toward reactants or toward products—does the reaction shift if the equilibrium is stressed by each change?
- Br 2 is removed.
- COBr 2 is added.
Answers
- toward reactants (Rate of reverse reaction increases/shifts left)
- toward reactants (Rate of reverse reaction increases/shifts left)
It is worth noting that when reactants or products are added or removed, the value of the K eq does not change . The chemical reaction simply shifts, in a predictable fashion, to reestablish concentrations so that the K eq expression reverts to the correct value.
A catalyst is a substance that increases the speed of a reaction. Overall, a catalyst is not a reactant and is not used up, but it still affects how fast a reaction proceeds by lowering the activation energy. When a catalyst is used in an equilibrium equation the lowered activation energy speeds up both the forward and reverse reactions. The overall result is that a catalyst has no effect on an equilibrium or on the value of K eq .
Hydrangeas are common flowering plants around the world. Although many hydrangeas are white, there is one common species ( Hydrangea macrophylla ) whose flowers can be either red or blue, as shown in the accompanying figure. How is it that a plant can have different colored flowers like this?
Interestingly, the color of the flowers is due to the acidity of the soil that the hydrangea is planted in. An astute gardener can adjust the pH of the soil and actually change the color of the flowers. However, it is not the H + or OH − ions that affect the color of the flowers. Rather, it is the presence of aluminum that causes the color change.
The solubility of aluminum in soil, and the ability of plants to absorb it, is dependent upon the acidity of the soil. If the soil is relatively acidic, the aluminum is more soluble, and plants can absorb it more easily. Under these conditions, hydrangea flowers are blue, as Al 3 + ions interact with anthocyanin pigments in the plant. In more basic soils, aluminum is less soluble, and under these conditions the hydrangea flowers are red. Gardeners who change the pH of their soils to change the color of their hydrangea flowers are therefore employing Le Chatelier's principle: the amount of acid in the soil changes the equilibrium of aluminum solubility, which in turn affects the color of the flowers.
Key Takeaways
- Le Chatelier's principle addresses how an equilibrium shifts when the conditions of an equilibrium are changed.
- Catalysts do not affect the position of an equilibrium; they help reactions achieve equilibrium faster.


4.2: Going It Alone- Sole Proprietorships
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1. What are the advantages and disadvantages of the sole proprietorship form of business organization?
Jeremy Shepherd was working full-time for an airline when, at the age of 22, he wandered into an exotic pearl market in China, searching for a gift for his girlfriend. The strand of pearls he handpicked by instinct was later valued by a jeweler back in the States at 20 times what he paid for it. Jeremy cashed his next paycheck and hurried back to Asia, buying every pearl he could afford. Founded in 1996, his company Pearl Paradise was brought online in 2000. Shepherd chose the sole proprietorship form of business organization—a business that is established, owned, operated, and often financed by one person—because it was the easiest to set up. He did not want partners, and low liability exposure made incorporating unnecessary.
Fluent in Mandarin Chinese, Japanese, and Spanish and immersed in Asian culture, Shepherd believed the internet was the way to market his pearls ( http://www.pearlparadise.com ). Offering a wide range of pearl jewelry through 14 websites worldwide, his company sells as many as 1,000 items per day. The recent addition of an exclusive Los Angeles showroom allows celebrity customers to shop by appointment. With $20 million in sales annually, PearlParadise.com is the industry leader in terms of sales and volume. 1
| Form | Number | Sales | Profits |
|---|---|---|---|
| Sole Proprietorships | 72 percent | 4 percent | 15 percent |
| Partnerships | 10 percent | 15 percent | 27 percent |
| Corporations | 18 percent | 81 percent | 58 percent |
Source: Internal Revenue Service, as reported in Table 746, U.S. Bureau of the Census, Statistical Abstract of the United States, 2012, 131st ed. (Washington, DC: U.S. Government Printing Office, 2012), p. 492. Note: US Bureau of Census stopped collecting and publishing this data after 2012.
Advantages of Sole Proprietorships
Sole proprietorships have several advantages that make them popular:
- Easy and inexpensive to form . As Jeremy Shepherd discovered, sole proprietorships have few legal requirements (local licenses and permits) and are not expensive to form, making them the business organization of choice for many small companies and start-ups.
- Profits all go to the owner . The owner of a sole proprietorship obtains the start-up funds and gets all the profits earned by the business. The more efficiently the firm operates, the higher the company’s profitability.
- Direct control of the business . All business decisions are made by the sole proprietorship owner without having to consult anyone else.
- Freedom from government regulation . Sole proprietorships have more freedom than other forms of business with respect to government controls.
- No special taxation . Sole proprietorships do not pay special franchise or corporate taxes. Profits are taxed as personal income as reported on the owner’s individual tax return.
- Ease of dissolution . With no co-owners or partners, the sole proprietor can sell the business or close the doors at any time, making this form of business organization an ideal way to test a new business idea.
Disadvantages of Sole Proprietorships
Along with the freedom to operate the business as they wish, sole proprietors face several disadvantages:
- Unlimited liability. From a legal standpoint, the sole proprietor and the company are one and the same, making the business owner personally responsible for all debts the company incurs, even if they exceed the company’s value. The owner may need to sell other personal property—their car, home, or other investments—to satisfy claims against the business.
- Difficulty raising capital. Business assets are unprotected against claims of personal creditors, so business lenders view sole proprietorships as high risk due to the owner’s unlimited liability. Owners must often use personal funds—borrowing on credit cards, second-mortgaging their homes, or selling investments—to finance their business. Expansion plans can also be affected by an inability to raise additional funding.
- Limited managerial expertise. The success of a sole proprietorship rests solely with the skills and talents of the owner, who must wear many different hats and make all decisions. Owners are often not equally skilled in all areas of running a business. A graphic designer may be a wonderful artist but not know bookkeeping, how to manage production, or how to market their work.
- Trouble finding qualified employees. Sole proprietors often cannot offer the same pay, fringe benefits, and advancement as larger companies, making them less attractive to employees seeking the most favorable employment opportunities.
- Personal time commitment. Running a sole proprietorship business requires personal sacrifices and a huge time commitment, often dominating the owner’s life with 12-hour workdays and 7-day workweeks.
- Unstable business life. The life span of a sole proprietorship can be uncertain. The owner may lose interest, experience ill health, retire, or die. The business will cease to exist unless the owner makes provisions for it to continue operating or puts it up for sale.
- Losses are the owner’s responsibility. The sole proprietor is responsible for all losses, although tax laws allow these to be deducted from other personal income.
The sole proprietorship may be a suitable choice for a one-person start-up operation with no employees and little risk of liability exposure. For many sole proprietors, however, this is a temporary choice, and as the business grows, the owner may be unable to operate with limited financial and managerial resources. At this point, the owner may decide to take in one or more partners to ensure that the business continues to flourish.
CATCHING THE ENTREPRENEURIAL SPIRIT
Work-Life Balance Important in Small Business
According to a survey released by the Wells Fargo/Gallup Small Business Index, about two-thirds of small business owners are satisfied with how they balance their personal lives and work schedules, and the New York Enterprise Report survey found that they work twice as much as regular employees. The survey also found that 33 percent of small business owners work more than 50 hours per week, while 25 percent reported working over 60 hours per week. A survey by Gallup finds 39 percent of small business owners working over 60 hours per week.
The 2016 Annual Bank of the West Small Business Growth Survey found that 62 percent of the respondents reported the stress of ownership as worse than what they had originally imagined.  Over two-thirds of small business owners, according to a survey, said they were satisfied with their personal work-life balance, and almost 90 percent said they were satisfied with being a small business owner in general. Dennis Jacobe, chief economist at Gallup, argues, “People see the benefits more closely tied to them when they’re the owner,” he says. “Working hard and long is a natural aspect of the kind of people willing to start their own business.”
 The study, which polled more than 50,000 U.S. workers from various markets including professional services, consumer goods, and financial services, found that employees who strike a positive balance between home and work were 11 percent more likely to praise their leaders’ ability to set a clear direction.
The Society for Human Resource Management’s (SHRM) research also shows work-life balance has a great impact on how employees feel about their leaders. Jennifer Schramm, a manager in SHRM’s workplace trends and forecasting research department, predicts that as companies try to maximize the productivity of each employee, work-life balance and the resulting employee satisfaction will become increasingly more important. And research shows that happy employees can yield happy returns for businesses.
Critical Thinking Questions
- Many small business owners expect their employees to be as committed and to work as hard as they do. How would you avoid falling into that trap while still demanding the best from your workers?
- As a small business owner, consider some strategies to ensure an appropriate work-life balance for your employees.
Sources: Brian Sutter, “How Hard Small Business Owners Work,” SCORE, https://www.score.org , accessed August 17, 2017; The Hartford Insurance Company, “2015 Small Business Success Study,” accessed August 17, 2017; Michelle Di Gangi, "Attitude check: Small business owners say it's all worth it," July 26, 2016, Bank of the West; 2016 Annual Bank of the West Small Business Growth Survey, conducted by Harris Poll, July 26, 2016; Jena Wuu, “Work-Life Not an Issue for Owners,” Inc ., http://www.inc.com , August 10, 2005; Christina Galoozis, “Employees View Leadership Through Lens of Work-Life Balance , ” Inc., http://www.inc.com , June 8, 2005.
CONCEPT CHECK
- What is a sole proprietorship?
- Why is this a popular form of business organization?
- What are the drawbacks to being a sole proprietor?


6.6: The Girdles
The girdles pass on the “push” produced by the limbs to the body. The shoulder girdle or scapula is a triangle of bone surrounded by the muscles of the back but not connected directly to the spine (see diagram 6.1). This arrangement helps it to cushion the body when landing after a leap and gives the forelimbs the flexibility to manipulate food or strike at prey. Animals that use their forelimbs for grasping, burrowing or climbing have a well-developed clavicle or collar bone. This connects the shoulder girdle to the sternum. Animals like sheep, horses and cows that use their forelimbs only for supporting the body and locomotion have no clavicle. The pelvic girdle or hipbone attaches the sacrum and the hind legs. It transmits the force of the leg-thrust in walking or jumping directly to the spine (see diagram 6.10).
Diagram 6.10 - The pelvic girdle


3.5: Borrmann Effect
Due to anomalous absorption , type 1 wavefields propagate in a perfect or nearly perfect crystal with a less than normal absorption. For details and the physical interpretation, see anomalous absorption .
Super-Borrmann effect
It is the enhancement of the Borrmann effect in a three-beam case, e.g. when the \( 111\) and \(\overline{111}\) reflections are simultaneously excited in a silicon or germanium crystal.
History
The Borrmann effect was first discovered in quartz (Borrmann G., 1941, Über Extinktionsdiagramme der Röntgenstrahlen von Quarz . Physik Z. , 42 , 157-162) and then in calcite crystals (Borrmann G., 1950, Die Absorption von Röntgenstrahlen in Fall der Interferenz. Z. Phys. , 127 , 297-323), and interpreted by Laue (Laue, M. von, 1949, Die Absorption der Röntgenstrahlen in Kristallen im Interferenzfall. Acta Crystallogr . 2 , 106-113).
The super-Borrmann effect was first observed by Borrmann G. and Hartwig W. (1965), Die Absorption der Röntgenstrahlen im Dreistrahlfall der Interferenz . Z. Krist. , 121 , 401-409.
See also
- Section 5.1 of International Tables of Crystallography, Volume B for X-rays
- Section 5.2 of International Tables of Crystallography, Volume B for electrons
- Section 5.3 of International Tables of Crystallography, Volume B for neutrons


6.3: Debt and Equity
What’s the difference?
Let’s start by making the distinction between debt and equity. It’s pretty simple. Debt is an obligation, on the part of the company, the entrepreneur, or both. Over a certain period of time, the company is obligated to repay the debt, at a specified interest rate.
Equity financing is the purchase of shares of stock in a company in return for money invested in the company. A company typically has no formal obligation to repay equity.  They give you money. Of course there’s a catch: the investor expects that at some point there will be a liquidation event. This means that at some point your company will be sold or go public. The investors will sell their stock, either to the new owners, or on the public stock exchanges—hopefully at a big profit either way.
So, not only do you need to understand your company’s appetite for financing and the type of financing you need to get where you’re going, you also need to understand that the type of financing you secure will determine your business’ growth direction.
Because equity investors are taking such a risk with no specific obligation of repayment, they are also going to expect—or perhaps demand—that the company take a route that will lead it to fast growth and a significant increase in its value over a relatively short period of time. Debt-holders on the other hand, be they banks or individuals, will pretty much stay out of the affairs of your business, as long as you’re making your loan payments and your periodic financial reports seem to be on target.
Which does your company need?
Types and sources of debt vary widely, from simple loans from friends and family to complicated transactions dreamed up by Wall Street wizards. But it basically comes down to one thing—they give you the money, you pay it back. Of course, the miracle of compound interest is on their side. To feed this miracle, you need cash flow. You need some kind of revenue stream so you can repay the loan. Sometimes a lending source will get creative and give you a grace period during which no payments are required and interest accrues. But a rule of thumb—that certainly has a fair share of real life exceptions—is that a technology company that needs development time, and is expecting to grow rapidly, will neither be able to fulfill debt obligations nor secure enough money in the early stages from debt sources to fuel the company.
Another rule: It’s when you don’t need the money that banks are happy to lend it to you. If your need is great, your ability to pay back probably isn’t so good, and then they’re less likely to lend to you. Technology growth companies typically have a different appetite. They’re hungry for equity.
Some debt and equity pros and cons
Equity Pros
Investors share your viewpoint because they take the risk with you. They get their reward when you do—usually when the company is sold or goes public. If you need additional equity to grow, investors often have extensive contacts and can help. Investor cash can help attract top-notch management teams.
Equity Cons
Founders give up a percentage of their companies’ ownership. Owners lose some control of their companies, and the outsiders even have a say over the founders’ salary. (Although this is not always bad, as giving up control can help keep you on your toes!) Companies can get into the “more where that came from” syndrome, always looking for investors but never making a profit.
Debt Pros
There’s no dilution of ownership; original owners keep it all. As long as the debt payments are made, the original owners give up no operational control. The company turns a profit sooner because owners must make cash to serve the debt and have access to additional credit.
Debt Cons
Not all companies have access to debt financing; lenders want collateral in land, equipment, or a patent. If the company doesn’t make payments, it loses everything. Growth is limited to internally generated cash flow, or additional credit based on the company’s profitability. Lenders want equity and convertible debt dilutes ownership.


2.3: Who?
Who are the children?
The children you will work with are as diverse as the people that work with them. Many programs are divided by age groups, so that is one way to define “who”:
- Infants – from birth to about 12 months (1 year) of age
- Toddlers – from about 12 months (1 year) to 30 months (2 ½ years) of age
- Preschool – from about 2 ½ to about 5 years of age
- Pre - Kindergarten or T-Kindergarten – usually 4-5 year of age
- Kindergarten – 5 years of age
- Early Elementary (Grades 1-3) – 6-8 years of age
As you will learn in Chapter 7 (Developmental Ages and Stages), each of these ages presents very different developmental stages and teachers work with each group accordingly. Some programs focus on just one of these age groups while others may incorporate several or all of them.
Figure \(\PageIndex{1}\): These preschool-aged children all need to feel respected, valued, and loved. [26]
The children you work with can be defined in many others way, some of which you will visit in this class, as well as other early childhood courses. Each child is unique and will come to you with their own experiences, strengths, and temperaments. Some you will connect with right away, and others you will need to stretch yourself to understand. The one thing that EVERY child you work with will have in common is the need to be respected, valued and loved. They need a safe place to trust and make connections, to feel comfortable and included. One of your primary jobs as a teacher is to connect with each child and value them as individuals.
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New Teacher Comments “My team teacher and I start each new school year generally planning for the stages of the children we will have in my classroom. Then we spend the first few weeks getting to know each individual child, focusing on making connections, and then adjust our plans accordingly. Each new year it takes me quite a bit of time to feel comfortable with the new children. They all start out as a blur and then ever so slowly they come into focus with each bringing their own pieces to the whole picture. At the start of the school year, I make a list of the children and take a photo. Each night when I go home, I try to make a note about at least 4 different children; personality, interests, and 2 weeks later I know so much!” |
Who are their families?
Often, when we choose to work with children, we do not realize that by extension that means working with families. The younger the children, the more they are connected to the people in their home, and best practices for young children include partnerships between their two most important worlds, home and school.
Figure \(\PageIndex{2}\): Children’s families and homes are important. [27]
In Chapter 16 (Partnering with Families), we visit many aspects of working with families, so here we will simply say, just as your family is important to you and taught you many things, so too it will be for the children and families you work with. We need to conceptualize that families are a child’s first teacher, and will be a strong and valuable teaching partner while their child is with us. They are entrusting us with their most prized possession and expecting that we will cherish that child as they do. A privilege indeed!
Who are the teachers?
As can be imagined, the people that are called to teaching are diverse indeed. Each brings their own set of strengths, interests, beliefs, and experiences. There is no “one right way” to teach; no magical guide you can refer to that will tell you exactly what to do in every situation. Every teacher will approach circumstances differently and this is both the joy and the trial of teaching. Your “why” will determine much of what you do. This will blend with your knowledge, experiences, and dispositional traits to guide you on your teaching journey.
Figure \(\PageIndex{3}\): A teacher in action.
With that being said, there are some skills and traits that are helpful for high quality teachers to possess. Some of them are knowledge based and you will learn them as you complete your courses and field experiences. Time and time again we hear new teachers reflect on the importance of realizing that the early childhood classes they are taking are “job training” courses that should be valued with time spent understanding and internalizing the content rather than simply trying to pass with minimal effort to complete them.
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New Teacher Comment “In looking back, I wish someone had helped me understand that these ECE classes would be important information for my career. I hate to admit it, but so much of high school and college felt like “busy work” that I did not put in the effort I should have, and now I regret the fact that I did not learn it fully when I should have. I am going back a lot more than other teachers to relearn what I should have in classes.“ |
This will be particularly true with experiences in the field. Most likely, at some point in your course of study, you will be expected to visit programs to observe and participate. While this can be difficult to fit into your schedule, as well as frightening to undertake, these experiences are crucial to developing your skills as a teacher. You can read and study all of the content you can, but until you actually put it into practice with real children, it cannot come to life for you. We encourage you to try as many different experiences with children as you can. Certainly, some class assignments will lend themselves to this endeavor, as will volunteer opportunities in the community. Ask your instructors or others in the field about these types of experiences. You never know what adventures await until you ask.
While your education, knowledge, and experiences will prove vital to your success as a teacher, there is another realm of traits to be considering.
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Pause to Reflect Think back to a teacher that made a positive impression in your life. What traits did that teacher possess that make them stand out to you? |
Perhaps you listed some of their education or experiences, but more than likely you included some “dispositional” traits as well. Lillian Katz was one of the first to define some of the dispositions that high-quality teachers seem to possess. While some of these can be studied and developed, most occur naturally in the noted quality teachers.
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High Quality Teachers Here a list of dispositions and traits frequently noted as occurring in high quality teachers:
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Pause to Reflect Look at the list above. What dispositional traits do you currently possess? Are there some you may not yet have, but can develop? How would you plan to develop them? |
One key factor successful teachers share is the ability to continually look inward through reflection. In the yellow-green colored boxes, we have asked you to “Pause to Reflect.” Why?
The Reflective Process
Learning occurs when we take risks, when we make mistakes, when we inquire, and when we experience new things. All humans are unique and process their environment from their own unique perspective. Our perspectives are informed by the interaction of nature (genetics) and nurture (environment) and both have an impact on how we process relationships with our families, our friends, our colleagues, etc. These interactions provide us with a foundation that shapes the way we view current and future relationships. As we engage in relationships with children and their families, we use reflective practices to learn more about ourselves, including our dispositions.
As we learn more about ourselves, we have the opportunity to develop broader ways to engage in relationships with the children and families we serve. The experiences we afford children and families cannot happen without the layers of a healthy relationship. Healthy positive relationships that guide and support children are the foundation of quality teaching. Authenticity and compassion are ways of being that create supportive environments for children to flourish. The strength of a teacher’s knowledge about themselves in relation to others creates opportunities for the children and families they serve to have respectful and reciprocal relationships to ensure that the child is always considered when making the multitude of decisions that are made throughout the day.
You may ask why it is so important for me to know more about myself in relation to others. As the teacher, you are the primary force in the classroom. As the quote below indicates, you, as the teacher, hold the key to creating an environment where children and their families either can flourish or diminish. Being able to value every human comes from our deep knowledge about ourselves. This is done through reflective practice.
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Quotable “I have come to a frightening conclusion that I am the decisive element in the classroom. It’s my personal approach that creates the climate. It’s my daily mood that makes the weather. As a teacher, I possess a tremendous power to make a child’s life miserable or joyous. I can be a tool of torture or an instrument of inspiration. I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis will be escalated or de-escalated and a child humanized or dehumanized.” - Haim Ginott |
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Pause to Reflect How does this quote resonate with you? Why? |
We reflect in many ways, both informally and formally, in private and with others, during the experience and after, knowingly and unknowingly. All are valuable and we encourage you to try many different ways until you internalize the process that makes the most sense for you and moves you toward being an “instrument of inspiration”.
Go back to the list of traits above. As you look through it again, do you notice that almost all include relationships in some way? Relationships are at the core of quality teaching.
Relationships Build Connections in the Brain
How can something as intangible as a relationship affect learning and the brain? Relationships are connection, communication, consideration. The brain is very much an active participant in recording, building, and shaping relationships. Research in human brain mapping has recognized a Neuro-Relational approach that tells us:
“Experience, not simple maturation, changes the brain (neuro).” Moreover, “all learning happens in the context of relationships (relational).” [29] When a child shows distress, a caregiver who has a proven relationship with that infant (or child) through appropriate response and respect can help the child return to a sense of calm.   Both the child and the caregiver’s stress response system synchronize and return to a frequency that is conducive to learning. [30]
The knowledge that healthy, positive, relationships are primary in creating an environment conducive to learning, helps us to structure the emotional environment with supportive and loving exchanges where children and families feel supported and appreciated. Science has shown us the link between body and mind. It has measured emotions and how different emotions affect brain waves and brain development.
We have learned that children, who experience stress, have brains that are wired to react rather than respond. Dr. Bruce Perry, a renowned psychiatrist, who has dedicated his career to the treatment of and research into childhood mental health, has spoken out about how early traumatic experiences shape the brain and what we can do to counteract the detrimental effects this has for life long mental health. The following are two recent quotes from his presentation at a conference:
“You can’t access the brain without relationships.”
“Lack of belonging activates the stress response. The cortex shuts down and learning can’t happen. Connections are the superhighway to the cortex.”
That, concisely, helps us to see the value of building relationships that help children and families have that sense of belonging that they deserve to thrive in our school environment.
Who are the other professionals supporting children?
Some of you may think you want to work in some way with children and families, but may not be sure that “teaching” is the right fit for you. Many experts will recommend starting as a teacher assistant or teacher, regardless of your later plans. That is because this experience will prove a valuable addition to whatever career you pursue in the field.
Keep in mind that “teaching” may look very different with different age groups. While the forming of relationships will lie at the core of all quality teaching, the interactions, roles, and duties will vary tremendously. We encourage you to spend some time with different age levels to get a feel for your best “fit”.
Whatever age group you are working with, we encourage you to give yourself some time to get comfortable before you decide it is not for you. Teachers go through stages and in the initial stage of survival, it is difficult to discern if it is the age group, the program, or just your limited experience that is feeling overwhelming and uncomfortable.
Below is a table of the stages you can expect to go through over the years on your teaching journey:
Table \(\PageIndex{1}\): Stages of Teaching Journey
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Stage |
Common Feelings |
Common Needs |
Advice from the Field |
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Survival |
Fear, inadequacy, doubt, overwhelmed, exhaustion |
Support, practical information and advice, understanding, a mentor or coach, resources |
Hang in there We’ve all been there It gets easier Mistakes are learning opportunities…learn a lot |
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Clarity |
Clearer understanding, noticing individual children and needs, a little less fear, moments of adequacy |
Continued support, continued resources, a mentor or coach, encouragement to try new things, |
You got this We believe in you Keep on trying Focus on what you like to do Enjoy the children |
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Growth |
Knowledgeable, comfortable, take new risks, reflective |
Support, encouragement to do things your way, reflection, team teaching |
Way to go Keep growing Know your strengths Try new things Step outside your comfort zone |
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Mastery |
Accomplished, proud, invigorated, seeking new challenges, |
Branching out, mentoring or coaching others, taking on new roles and responsibilities, community connections, professional organizations |
Time to support others Share your strengths Be a role model Consider advocacy Join the profession |
Keep in mind that each time you begin a new endeavor (ie: teaching at a new location, new age group, new role) you will move back to survival and through the stages, although the timing may be shorter. Knowing this allows you to give yourself permission to feel the way you need to feel and seek the support you need throughout your career.
Who will be with me?
One of the wonderful aspects of our field is that you are rarely alone. In addition to the children and families, you will have colleagues who can support your journey. You may find yourself working with any or all of the following:
Table \(\PageIndex{2}\): Who Teachers May Work With
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Role |
Description |
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Director/Manager/ Principal |
Usually runs the day to day operations, oversees teaching staff, involved in hiring, provides resources and support, budgeting. |
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Office Staff |
Keep records, handle paperwork, phone calls, administrative support. |
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Team Teacher / Assistant/Aide |
Additional person you will collaborate with in your classroom. It’s common practice to provide support for each other, offer a variety of role models for children and families, offer different strengths. |
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Specialists |
Sometimes a specialist works in the classroom with individual children or the group. Usually providing specialized services in Occupational Therapy (OT) (life skills), Physical Therapy (PT), Speech and Language, or Behavioral intervention they may be part of the teaching team all day or for brief segments throughout the week. |
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Other Staff Members |
From time to time, you may work with custodians, food service providers, health specialists, and others performing duties related to the classroom. |
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Volunteers |
Family or other community members working in a variety of capacities as part of the teaching team. |
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College Students |
From time to time college students may work in the classroom as part of their training. |
In addition to the above list, we encourage you to find a mentor or coach, someone you can turn to with questions or when you need support. In the field of early childhood, many of us “pay it forward”. Someone provided support for us when we were new to the field with the understanding that we would do the same when our time came. Most early childhood teachers are kind, caring professionals who want to see you succeed. Each time you succeed, our field succeeds and the children and families we work with receive the quality experiences they deserve. Ask your instructor or another resource if they know of any formal or informal mentor programs in your area.
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New Teacher Comments Letter from a Fieldwork Student My experience is limited. I want to learn. Please don’t expect perfection whenever I interact, guide behavior, lead a lesson, or do bulletin boards. Please be patient with me. My eyes have not yet been trained to see all the students in the classroom most of the time. Classroom responsibilities will always be there. I’m only with you for a short time. Please take time to explain things to me and do so willingly. My feelings are real. Please be sensitive to my needs and don’t get annoyed if I ask a lot of questions and am uncertain about what to do sometimes. Treat me as you would like to be treated. I am a unique individual, like each one of your students. Please treasure my being, holding me accountable for my actions, giving me guidelines to follow, and disciplining me in a professional manner, if need be. I need your support and encouragement to grow. Pointing out what I am doing correctly and occasional praise can be reassuring and help me feel comfortable to take risks and grow. Please give me constructive feedback, focused on the things I do, without criticizing me. Please give me the freedom to make decisions and test them out as long as they don’t jeopardize the well-being and safety of the students. If I fail, I can learn from my mistakes. Then I’ll be better prepared to make decisions life requires of me. Please invite me to appropriate faculty meetings, seminars, workshops, parent meetings and to join educational organizations, setting a good example for me to follow. I may not be able to attend but I will appreciate your confidence in me as a future fellow professional. Sincerely, A New Fieldwork Student [31] |
If you want to work with children and families, but are not sure teaching is for you, there are many other career options you are encouraged to explore.
Career options in Early Childhood Education and Child Development
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Area |
Careers |
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Child Development Focus |
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Elementary Settings |
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Adult Education and Training |
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Community and Social Services |
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Other Related Work Options |
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*Refers to the levels on the Child Development Permit Matrix
**These positions usually require a bachelor’s degree and additional training


14.5.1: Concept Review Questions Chapter 12
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Concept Review Questions
Section 1
1) What is an oxidative addition?
2) What is a reductive elimination?
3) What is a cis and a trans addition, respectively?
4) Does the coordination number in oxidative additions always increase? Explain.
5) What is the reverse reaction of an oxidative addition?
6) What is a migratory insertion?
7) Are migratory insertions reversible reactions?
Section 2
1) Why are transition metal alkyl complexes that have alkyl groups longer than 1 carbon atom often unstable?
2) What is meant by beta-hydride elimination?
3) What is alpha-abstraction?
4) What is a nucleophilic displacement reaction?
5) What is meant by an oxidative addition of an intact ligand?
6) Write the catalytic cyclic for the deuteration of benzene with Cp 2 TaH 3 as a catalyst. Name each reaction step.
7) What is Collman’s reagent and how is it being used?
8) What is Wilkinson’s catalyst, and what reactions can it be used for. Write the catalytic cycle.
9) Write done the reaction mechanism for the Ziegler-Natta olefin polymerization.
10) What is carbene migratory insertion?
11) Write down the catalytic cycle for the hydroformylation of olefins.
12) Name three hydrocarbonylation reactions. What are the reactants?
13) Write down the mechanism for the Monsanto acetic acid process.
14) What is olefin metathesis?
15) What is ring-opening olefin polymerization (ROMP)?
16) What is acyclic diene metathesis?
17) Why are olefins with terminal C=C double bonds particularly useful in olefin metathesis?
18) What is ring-closing metathesis?
19) What are the characteristics of Schrock and Grubbs catalysts, respectively?
20) Write down the catalytic cycle for olefin metathesis.
Dr. Kai Landskron ( Lehigh University ). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate .


21.7: Fever
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- Ying Liu
- City College of San Francisco
Learning Objectives
- Explain the difference between exogenous and endogenous pyrogens
- Identify the mechanisms of how fever helps with immune defense
Fever
A fever is an inflammatory response that extends beyond the site of infection and affects the entire body, resulting in an overall increase in body temperature. Body temperature is normally regulated and maintained by the hypothalamus, an anatomical section of the brain that functions to maintain homeostasis in the body. However, certain bacterial or viral infections can result in the production of pyrogens , chemicals that effectively alter the “thermostat setting” of the hypothalamus to elevate body temperature and cause fever. Pyrogens may be exogenous or endogenous. For example, the endotoxin lipopolysaccharide (LPS), produced by gram-negative bacteria, is an exogenous pyrogen that may induce the leukocytes to release endogenous pyrogens such as interleukin-1 (IL-1), IL-6, interferon-γ (IFN-γ), and tumor necrosis factor (TNF). In a cascading effect, these molecules can then lead to the release of prostaglandin E2 (PGE 2 ) from other cells, resetting the hypothalamus to initiate fever (Figure \(\PageIndex{4}\)).
Query \(\PageIndex{1}\)
Like other forms of inflammation, a fever enhances the innate immune defenses by stimulating leukocytes to kill pathogens. The rise in body temperature also may inhibit the growth of many pathogens since human pathogens are mesophiles with optimum growth occurring around 35°C (95°F). In addition, some studies suggest that fever may also stimulate release of iron-sequestering compounds from the liver, thereby starving out microbes that rely on iron for growth. 2
During fever, the skin may appear pale due to vasoconstriction of the blood vessels in the skin, which is mediated by the hypothalamus to divert blood flow away from extremities, minimizing the loss of heat and raising the core temperature. The hypothalamus will also stimulate shivering of muscles, another effective mechanism of generating heat and raising the core temperature.
The crisis phase occurs when the fever breaks. The hypothalamus stimulates vasodilation, resulting in a return of blood flow to the skin and a subsequent release of heat from the body. The hypothalamus also stimulates sweating, which cools the skin as the sweat evaporates.
Although a low-level fever may help an individual overcome an illness, in some instances, this immune response can be too strong, causing tissue and organ damage and, in severe cases, even death. The inflammatory response to bacterial superantigens is one scenario in which a life-threatening fever may develop. Superantigens are bacterial or viral proteins that can cause an excessive activation of T cells from the specific adaptive immune defense, as well as an excessive release of cytokines that overstimulates the inflammatory response. For example, Staphylococcus aureus and Streptococcus pyogenes are capable of producing superantigens that cause toxic shock syndrome and scarlet fever, respectively. Both of these conditions can be associated with very high, life-threatening fevers in excess of 42°C (108°F).
Query \(\PageIndex{1}\)
Query \(\PageIndex{1}\)
Key Concepts and Summary
- Fever is a system-wide sign of inflammation that raises the body temperature and stimulates the immune response.
- Both inflammation and fever can be harmful if the inflammatory response is too severe.
Footnotes
- 2 N. Parrow et al. “Sequestration and Scavenging of Iron in Infection.” Infection and Immunity 81 no. 10 (2013):3503–3514


9.5: Learning Bank – Checking and Savings Accounts
People generally use checking accounts to store money in the short term until it is needed for day to day expenses – like gas or groceries – or to pay bills, and they can usually deposit or withdraw any amount of money in their account as many times as they like. Checking accounts also come with convenient ways to deposit and withdraw money from the account, such as checks and ATM cards. However, people with checking accounts must be careful when using them, since some banks charge fees for certain actions, such as using another bank’s ATM, withdrawing more money from your account than the amount in it, or not maintaining a minimum balance.
On the other hand, a savings account is used to set money aside for use in the future and allow the money to collect interest. Many people regularly place some of their money into savings accounts rather than spending it in order to achieve financial goals, such as buying the latest gadget or game, without having to go into debt to do it.
Compound interest is interest paid on both the money you put into your account and the interest already earned. For example, if you put $100 into an account that earns 10% interest, you will initially earn $10, which will result in a total account balance of $110. The next time your account earns 10% it will be based on $110 instead of just $100, giving you a total account balance of $121.
You can earn even more in compound interest if you stretch to put as much money as you can into your account and leave it untouched. See the chart below, which is based on a savings account started with $50 and earning interest at a rate of 3.5% each month. If you add just $10 each month, the account can grow nicely to $714 after five years. If you instead put in a slightly higher amount—$15 each month—you’d have a balance of $1,042 after five years. But if you had increased your deposits to $50 a month, those extra dollars plus the compounding of interest would give you a balance of $3,333 after five years.
There are many banks that offer special accounts for kids and teens, so talk to your parents if you’d like to open an account of your own and start learning how to manage money. But you don’t need a bank account to start the habit of saving – a simple piggy bank will do!
Contributors and Attributions
- Authored by : Federal Deposit Insurance Corporation. Located at : https://www.fdic.gov/about/learn/learning/accounts.html . License : Public Domain: No Known Copyright