19.9: Assignment- HR with Limited Resources
Scenario
Entrepreneurs and small businesses often don’t have the resources to hire an HR professional but the costs of an HR mistake can destroy a start-up. If you’re a business owner with a big idea and a small budget, how can you make human resources work with your limited resources?
Your Task
The firm’s CSR & Sustainability lead was impressed with your work on her sustainability project and has requested your assignment to a second project developing resources for the firm’s pro bono work in support of small businesses. The firm is developing a website for entrepreneurs and small businesses with links to a range of essential resources that owners don’t have the budget or expertise to buy or develop.
Your task is to develop a 1–2 page document that includes resources such as HR forms (SHRM or other), legal reference, Small Business consulting and planning resources (OSHA, SBA), etcetera. The lead does not expect you to cover all bases, but to jump-start the project. Develop an outline to organize resources and include a brief introduction for each link.
Grading Rubric
| Criteria | Inadequate (40%) | Minimal (60%) | Adequate (80%) | Exemplary (100%) | Total Points |
|---|---|---|---|---|---|
| Organization and format |
2 pts
Writing lacks logical organization. It may show some coherence but ideas lack unity. Serious errors and generally is an unorganized format and information. |
3 pts
Writing is coherent and logically organized, using a format suitable for the material presented. Some points may be contextually misplaced and/or stray from the topic. Transitions may be evident but not used throughout the essay. Organization and format used may detract from understanding the material presented. |
4 pts
Writing is coherent and logically organized, using a format suitable for the material presented. Transitions between ideas and paragraphs create coherence. Overall unity of ideas is supported by the format and organization of the material presented. |
5 pts
Writing shows high degree of attention to details and presentation of points. Format used enhances understanding of material presented. Unity clearly leads the reader to the writer’s conclusion and the format and information could be used independently. |
5 pts |
| Content |
8 pts
Some but not all required questions are addressed. Content and/or terminology is not properly used or referenced. Little or no original thought is present in the writing. Concepts presented are merely restated from the source, or ideas presented do not follow the logic and reasoning presented throughout the writing. |
12 pts
All required questions are addressed but may not be addressed with thoughtful consideration and/or may not reflect proper use of content terminology or additional original thought. Additional concepts may not be present and/or may not be properly cited sources. |
16 pts
All required questions are addressed with thoughtful consideration reflecting both proper use of content terminology and additional original thought. Some additional concepts may be presented from other properly cited sources, or originated by the author following logic and reasoning they’ve clearly presented throughout the writing. |
20 pts
All required questions are addressed with thoughtful in-depth consideration reflecting both proper use of content terminology and additional original thought. Additional concepts are clearly presented from properly cited sources, or originated by the author following logic and reasoning they’ve clearly presented throughout the writing. |
20 pts |
| Development—Critical Thinking |
8 pts
Shows some thinking and reasoning but most ideas are underdeveloped, unoriginal, and/or do not address the questions asked. Conclusions drawn may be unsupported, illogical or merely the author’s opinion with no supporting evidence presented. |
12 pts
Content indicates thinking and reasoning applied with original thought on a few ideas, but may repeat information provided and/ or does not address all of the questions asked. The author presents no original ideas, or ideas do not follow clear logic and reasoning. The evidence presented may not support conclusions drawn. |
16 pts
Content indicates original thinking, cohesive conclusions, and developed ideas with sufficient and firm evidence. Clearly addresses all of the questions or requirements asked. The evidence presented supports conclusions drawn. |
20 pts
Content indicates synthesis of ideas, in-depth analysis and evidence beyond the questions or requirements asked. Original thought supports the topic, and is clearly a well-constructed response to the questions asked. The evidence presented makes a compelling case for any conclusions drawn. |
20 pts |
| Grammar, Mechanics, Style |
2 pts
Writing contains many spelling, punctuation, and grammatical errors, making it difficult for the reader to follow ideas clearly. There may be sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices disrupts the content. Additional information may be presented but in an unsuitable style, detracting from its understanding. |
3 pts
Some spelling, punctuation, and grammatical errors are present, interrupting the reader from following the ideas presented clearly. There may be sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices may detract from the content. Additional information may be presented, but in a style of writing that does not support understanding of the content. |
4 pts
Writing is free of most spelling, punctuation, and grammatical errors, allowing the reader to follow ideas clearly. There are no sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices enhance the content. Additional information is presented in a cohesive style that supports understanding of the content. |
5 pts
Writing is free of all spelling, punctuation, and grammatical errors and written in a style that enhances the reader’s ability to follow ideas clearly. There are no sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices enhance the content. Additional information is presented to encourage and enhance understanding of the content. |
5 pts |
| Total: | 50 pts |


12.2K: Tests That Differentiate Between T Cells and B cells
- Describe how T cells and B cells can be differentiated using staining of cell surface receptors and functional assays like the T lymphocyte cytotoxicity assay
Lymphocytes are the only immunologically specific cellular components of the immune system. They are divided into two types based on the pathogen recognition receptors they express on their surface. T cells or T lymphocytes belong to a group of white blood cells known as lymphocytes. They are called T cells because they mature in the thymus. They play a central role in cell-mediated immunity along with initiating rejection of foreign tissues following organ transplantation. B-cells are also white blood cells and are a vital part of the humoral immunity branch of the adaptive immune system. These two cell types can function independently or cooperatively to defend the body against pathogens. T-lymphocytes can be distinguished from other lymphocytes like B cells and natural killer cells (NK cells) by the presence of a T cell receptor (TCR) on the cell surface. Alternatively, B-cells can be distinguished from other lymphocytes like T cells and natural killer cells (NK cells) by the presence of a protein on the B-cell’s outer surface called a B-cell receptor (BCR).
Traditionally, T-lymphocytes were defined by their ability to form E-rosettes when they bind selectively to sheep erythrocytes. T-lymphocytes express CD3, CD4, CD8, or CD25 markers. B-lymphocytes express CD19 marker. The expression of different markers allows the separation/ differentiation of T and B cells. Another functional assay used to identify T-lymphocyte is the cytotoxic activity assay. This assay is based on measuring the killing ability that a determined number of T lymphocytes have for a certain number of target cells when both populations are placed together. B-lymphocytes have membrane-bound immunoglobulins that can be stained with anti-immunoglobulin labeled with fluorescent dyes and detected with a fluorescent microscope. More modern techniques like flow cytometry and immunohistochemistry are commonly used and rely on the use of fluorescent antibodies. These techniques are based on staining B and T cells for unique cell surface markers known as cluster of differentiation (CD).
Key Points
- There are two types of lymphocytes: B cells and T cells. These two components of the immune system have different functions but cooperate to fight infection.
- T cells elicit cell-mediated immune response, while B cells elicit humoral immunity.
- Lymphocytes are the only immunologically specific cellular components of the immune system.
Key Terms
- cytotoxic : of, relating to, or being a cytotoxin


5.8: Stretch Factor
ratio of frame-clock time to wristwatch time
Different reference frames: different times between two events
A speeding beacon emits two flashes, \(F\) and \(S\) , in quick succession. These two flashes, as recorded in the rocket that carries the beacon, occur with a 6-meter separation in time but a zero separation in space. Zero space separation? Then 6 meters is the value of the interval, the proper time, the wristwatch time between \(F\) and \(S\) . As registered in the laboratory, in contrast, the second flash \(S\) occurs 10 meters of time later than the first flash \(F\) . The ratio between this frame time, 10 meters, and the proper time, 6 meters, between the two events we call the time stretch factor, or simply stretch factor . Some authors use the lowercase Greek letter gamma, \(\gamma\) , for the stretch factor, as we do occasionally. We will also use the Greek letter tau, \(\tau\) , for proper time. 1
Time lapse minimum for frame in which events occur at same place
The same two events register in the super-rocket frame that overtakes and passes the beacon - register with a separation in time of \(20.88\) meters. In this frame, the time stretch factor between the two events is \((20.88) / 6=3.48\) . In the beacon frame the stretch factor is unity: \(6 / 6=1\) . Why? Because in this beacon frame flashes \(F\) and \(S\) occur at the same place, so beacon-frame clocks record the proper time directly. This place proper time is less than the time between the two flashes as measured in either laboratory or super-rocket frame. The larger value of time observed in laboratory and super-rocket frames shows up in Figure \(\PageIndex{1}\) (center and right). Among all conceivable frames, the separation in time between the two flashes evidently takes on its minimum value in the beacon frame itself, the value of the proper time \(\tau\) . 2
Hold it! In Sections 5.6 and 5.7 you insisted that the time along a straight worldline is a MAXIMUM. Now you show us a straight worldline along which the time is - you say - a MINIMUM. Maximum or minimum? Please make up your mind!
Answer
The worldline taken by the beacon wristwatch from F to S is straight. It is straight ^ whether mapped in the beacon frame itself or in the rocket or super-rocket frame. The beacon racks up 6 meters of proper time regardless of the frame in which we reckon this time. When we turn from this wristwatch time to what different free-float frames show for the separation in map time (latticework time, frame time) between the two flashes, however, the record displays a minimal value for that separation in time only in the beacon frame itself.
In contrast. Figure \(\PageIndex{2}\) (Figure 5.7.1 in simplified form) shows two different worldlines that join events 0 and B mapped in the same reference frame. In this case we compare two different proper times: a proper rime of 10 meters racked up by a wristwatch carried along the direct course from 0 to B, and a proper time of 6 meters recorded by the wristwatch carried along on the kinked worldline \(OQB\). In every such comparison made in the context of flat spacetime, the direct worldline displays maximum proper time. Caution: Conditions can be different in curved spacetime (Chapter 9).
In summary, two points come to the fore in these comparisons of the time between two events. (1) Are we comparing map time (frame time, latticework time) between those two events, pure and simple, free of any talk about any wotldline that might connect those events? Then separation in time between those events is least as mapped in the free-float frame that shows them happening at the same place. (2) Or are we directing our arrention to a worldline that connects the two events? More specifically, to the time racked up by a wrisrwarch toted along that worldline? Then we have to ask, is that worldline straight? Then it registers maximal passage of proper time. Or does it have a kink? Then the proper time racked up is not maximal.
When we find ourselves in a free-float frame and see a beacon zooming past in a straight line with speed \(v\), how much is the factor by which our frame-clock time is stretched relative to the beacon wristwatch time? Answer: The stretch factor is
\[\text { (stretch factor) }=\gamma=\frac{1}{\left(1-v^{2}\right)^{1 / 2}} \tag{5.8.1}\]
How can we derive this famous formula? If you do not cover up the following lines and derive this answer on your own, here is the reasoning: Start with measurements in the laboratory frame. We know that for this rocket
\[\text { (advance in proper time })^{2}=(\text { advance in lab time })^{2}-(\text { lab distance covered })^{2} \nonumber\]
Stretch factor = frame time/proper time
However, we want to compare lapses in laboratory time and proper time; laboratory distance covered is not of interest. For the laboratory observer the proper clock moving along a straight worldline covers the distance between the two events in the time between the events. Therefore this distance and time are related by particle speed: 3
\[\text { (lab distance covered) }=(\text { speed) } \times \text { (advance in lab time) } \nonumber\]
Substitute this expression into the equation for proper time:
\[\begin{align*} (\text { proper time })^{2} &=(\text { lab time })^{2}-(\text { speed })^{2} \times(\text { lab time })^{2} \\ &=(\text { lab time })^{2}\left[1-(\text { speed })^{2}\right] \end{align*}\]
This leads to an expression for the square of the stretch factor:
\[\frac{(\text { lab time })^{2}}{(\text { proper time })^{2}}=(\text { stretch factor })^{2}=\frac{1}{1-(\text { speed })^{2}}=\frac{1}{1-v^{2}} \nonumber\]
where we use the symbol \(v=v_{\text {conv }} / c\) for speed. The equation for the stretch factor becomes 4
Stretch factor derived
\[(\text { stretch factor })=\gamma=\frac{1}{\left(1-v^{2}\right)^{1 / 2}} \tag{5.8.1}\]
The stretch factor has the value unity when \(v=0\) . For all other values of \(v\) the stretch factor is greater than unity. For very high relative speeds, speeds close to that of light \((v \rightarrow 1)\) , the value of the stretch factor increases without limit.
The value of the stretch factor does not depend on the direction of motion of the rocket that moves from first event to second event: The speed is squared in equation 5.8.1 , so any negative sign is lost.
Lorentz-contraction by same “ stretch" factor
The stretch factor is the ratio of frame time to proper time between events, where speed ( \(=v\)) is the steady speed necessary for the proper clock to pass along a straight worldline from one event to the other in that frame.
The stretch factor also describes the Lorentz contraction, the measured shortening of a moving object along its direction of motion when the observer determines the distance between the two ends at the same time. For example, suppose you travel at speed \(v\) between Earth and a star that lies distance \(L\) away as measured in the Earth frame. Your trip takes time \(t=L / v\) in the Earth-linked frame. Proper time \(\tau\) - your wristwatch time - is smaller than this by the stretch factor: \(\tau=L /[v \times(\) stretch factor \()]=(L / v)(1\) \(\left.-v^{2}\right)^{1 / 2}\) . Now think of a very long rod that reaches from Earth to star and is at rest in the Earth frame. How long is that rod in your rocket frame? In your frame the rod is moving at speed \(v\) . One end of the rod, at the position of Earth, passes at speed \(v\) . A time \(\tau\) later in your frame the other end of the rod arrives - along with the star - also moving at speed \(v\) according to your rocket measurements. From these data you calculate that the length of the rod in your rocket frame - call it \(L^{\prime}\) - is equal to \(L^{\prime}=v \tau=v(L / v)\left(1-v^{2}\right)^{1 / 2}=L\) \(\left(1-v^{2}\right)^{1 / 2}\) . This is a valid measure of length. By this method the rod is measured to be shorter. 5
Stretch factor as a measure of speed
Finally, the stretch factor is often used as an alternative measure of particle speed: A particle moves with a speed such that the stretch factor is 10 . This statement assumes that the particle is moving with constant speed, so that the separation between any pair of events on the particle worldline has the same stretch factor as the separation between any other pair. This way of describing particle speed can be both convenient and powerful. We will see (Chapter 7) that the total energy of a particle is proportional to the stretch factor. 6
Return to the alternative worldlines between events \(O\) and \(B\), shown in Figure 5.7.1 and the spacetime maps in this sample problem. Measure these worldlines from a rocket frame that moves outward with the particle from \(O\) to \(Q\) and keeps on going forever at the same constant velocity. Show that an observer in this outward-rocket frame predicts the same proper time— wristwatch time — for worldline \(OQB\) as that predicted in the laboratory frame. Similarly show that this outward-rocket-frame observer predicts the same proper time along the direct worldline \(OPB\) as does the laboratory observer. Finally, show that both observers predict the elapsed wristwatch time along \(OQB\) to be less than along \(OPB\).
Solution
Here are laboratory and rocket spacetime maps for these round trips, simplified and drawn to reduced scale.
Find \(x_{Q}^{\prime}\) and \(t_{Q}^{\prime}\): First compute space and time locations of events Q and B in the outgoing rocket frame — right-hand map. (Event 0 is the reference event, x = 0 and t = 0 in all frames by convention.) We choose the rocket frame so that the worldline segment OQ lies vertical and the outbound rocket does not move in this frame. As a result, event Q occurs at rocket space origin: \(x_{Q}^{\prime}=0\). (Primes refer to measurements in the outwardrocket frame.) The rocket time \(t_{Q}^{\prime}\) for this event is just the wristwatch time between 0 and Q, because the wristwatch is at rest in this frame: \(t_{Q}^{\prime}=3\) meters.
In summary, using a prime for rocket measurements:
\[\begin{align*}
x^{\prime}{ }_{Q} &=0 \\
t^{\prime}{ }_{Q} &=3 \text { meters }
\end{align*}\]
Find \(x_{B}^{\prime}\) and \(t_{B}^{\prime}\): In the laboratory frame, the particle moves to the right from event \(O\) to event \(Q\) , covering 4 meters of distance in 5 meters of time. Therefore its speed is the fraction \(v=4 / 5=0.8\) of light speed. As measured in the rocket frame, the laboratory frame moves to the left with speed \(v=0.8\) , by symmetry. Use equation 5.8.1 with \(v=\) \(0.8\) to compute the value of the stretch factor:
\[\frac{1}{\left[1-v^{2}\right]^{1 / 2}}=\frac{1}{\left[1-(0.8)^{2}\right]^{1 / 2}}=\frac{1}{[1-0.64]^{1 / 2}}=\frac{1}{[0.36]^{1 / 2}}=\frac{1}{0.6}=\frac{10}{6}=\frac{5}{3} \nonumber\]
This equals the ratio of rocket time period \(t_{B}^{\prime}\) to proper time \(\tau_{B}\) along the direct path \(O P B\) . Hence elapsed rocket time \(t_{B}^{\prime}=(5 / 3) \times 10\) meters \(=50 / 3\) meters of time. In this time, the laboratory moves to the left in the rocket frame by the distance \(x_{B}^{\prime}=-v t^{\prime}{ }_{B}=\) \(-(4 / 5)(50 / 3)=-200 / 15=-40 / 3\) meters. In summary for outgoing rocket:
\[\begin{align*} &x_{B}^{\prime}=-\frac{40}{3} \text { meters }=-13 \frac{1}{3} \text { meters } \\ &t_{B}^{\prime}=\frac{50}{3} \text { meters }=16 \frac{2}{3} \text { meters of time } \end{align*}\]
Events \(Q\) and \(B\) are plotted on the rocket spacetime map.
Compare Wristwatch Times: Now compute the total proper time-wristwatch time, aging-along alternative worldlines \(O P B\) and \(O Q B\) using rocket measurements. Direct worldline \(O B\) has proper time \(\tau_{O B}\) given by the regular expression for interval:
\[\begin{align*} \left(\tau_{O B}\right)^{2} &=\left(t_{O B}^{\prime}\right)^{2}-\left(x_{O B}^{\prime}\right)^{2}=\left(\frac{50}{3}\right)^{2}-\left(-\frac{40}{3}\right)^{2} \\ &=\frac{2500}{9}-\frac{1600}{9}=\frac{900}{9}=100 \text { (meters) }^{2} \end{align*}\]
whence \(\tau_{O B}=10\) meters computed from rocket measurements. This is the same value as computed in the laboratory frame (in which proper time equals laboratory time, since laboratory separation in space is zero).
Worldline \(O Q B\) has two segments. On the first segment, \(O Q\) , proper time lapse is just equal to the rocket time span, 3 meters, since the space separation equals zero in the rocket frame. For the second segment of this worldline, \(Q B\) , we need to compute elapsed time in this frame:
\[\begin{align*} &t_{Q B}^{\prime}=t_{B}^{\prime}-t_{Q}^{\prime}=\frac{50}{3}-3=\frac{50}{3}-\frac{9}{3}=\frac{41}{3} \text { meters } \\ &x_{Q B}^{\prime}=-\frac{40}{3} \text { meters } \end{align*}\]
Therefore,
\[\begin{align*} \left(t_{\mathrm{QB}}\right)^{2} &=\left(t_{Q B}^{\prime}\right)^{2}-\left(x_{Q B}^{\prime}\right)^{2}=\left(\frac{41}{3}\right)^{2}-\left(\frac{40}{3}\right)^{2} \\ &=\frac{1681}{9}-\frac{1600}{9}=\frac{81}{9}=9(\text { meters })^{2} \end{align*}\]
whence \(\tau_{Q B}=3\) meters. So the total increase in proper time-the total aging-along worldline \(O Q B\) sums to \(3+3=6\) meters as reckoned from outward-rocket measurements. This is the same as figured from laboratory measurements.
How can these weird results be true? In our everyday lives why don’t we bave to take account of clocks that record different elapsed times between events, and rods that we measure to be contracted as they speed by us?
In answer, consider two events that occur at the same place in our frame. The proper clock moving in spacetime between these two events has speed zero for us. In this case the stretch factor has the value unity: the frame clock is the proper clock. The same is approximately true for events that are much closer together in space (measured in meters) than the time between them (also measured in meters). In these cases the proper clock moving between them has speed \(v\) - measured in meters/ meter - that is very much less than unity. That is, the proper clock moves very much slower than the speed of light. For such slow speeds, the stretch factor has a value that approaches unity; the proper clock records very nearly the same time lapse between two events as frame clocks. This is the situation for all motions on earth that we can follow by eye. For all such "ordinary-speed" motions, moving clocks and stationary clocks record essentially the same time lapses. This is the assumption of Newtonian mechanics: "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external..."
A similar argument leads to the conclusion that Lorentz contraction is negligible for objects moving at everyday speeds. Newton’s mechanics - with its unique measured time between events and its unique measured length for an object whether or not it moves - gives correct results for objects moving at everyday speeds. In contrast, for particle speeds approaching light speed (approaching one meter of distance traveled per meter of elapsed time in the laboratory frame), the denominator on the right of equation 5.8.1 approaches zero and the stretch factor increases without limit. Increased without limit, also, is the laboratory time between ticks of the zooming particle’s wristwatch. This is the case for high-speed particles in accelerators and for cosmic rays, very high-energy particles (mostly protons) that continually pour into our atmosphere from space. Newton’s mechanics gives results wildly in error when applied to these particles and their interactions; the laws of relativistic mechanics must be used.
More than one cosmic ray has been detected (indirectly by the resulting shower of particles in the atmosphere) moving so fast that it could cross our galaxy in 30 seconds as recorded on its own wristwatch. During this trip a thousand centuries pass as recorded by clocks on Earth! (See Exercise 7-7.)
1 Different reference frames: different times between two events
2 Time lapse minimum for frame in which events occur at same place
3 Stretch factor = frame time/proper time
4 Stretch factor derived
5 Lorentz-contraction by same "stretch" factor
6 Stretch factor as a measure of speed


1.15: Rutherford Backscattering of Thin Films
Introduction
One of the main research interests of the semiconductor industry is to improve the performance of semiconducting devices and to construct new materials with reduced size or thickness that have potential application in transistors and microelectronic devices. However, the most significant challenge regarding thin film semiconductor materials is measurement. Properties such as the thickness, composition at the surface, and contamination, all are critical parameters of the thin films. To address these issues, we need an analytical technique which can measure accurately through the depth of the of the semiconductor surface without destruction of the material. Rutherford backscattering spectroscopy is a unique analysis method for this purpose. It can give us information regarding in-depth profiling in a non-destructive manner. However X-ray photo electron spectroscopy (XPS), energy dispersive X-ray analysis (EDX) and Auger electron spectroscopy are also able to study the depth-profile of semiconductor films. Table \(\PageIndex{1}\) demonstrates the comparison between those techniques with RBS.
| Method | Destructive | Incident Particle | Outgoing Particle | Detection Limit | Depth Resolution |
| RBS | No | Ion | Ion | ~1 | 10 nm |
| XPS | Yes | X-ray photon | Electron | ~0.1-1 | ~1 µm |
| EDX | Yes | Electron | X-ray photon | ~0.1 | 1.5 µm |
| Auger | Yes | Electron | Electron | ~0.1-1 | 1.5 nm |
Basic Concept of Rutherford Backscattering Spectroscopy
At a basic level, RBS demonstrates the electrostatic repulsion between high energy incident ions and target nuclei. The specimen under study is bombarded with monoenergetic beam of 4 He + particles and the backscattered particles are detected by the detector-analysis system which measures the energies of the particles. During the collision, energy is transferred from the incident particle to the target specimen atoms; the change in energy of the scattered particle depends on the masses of incoming and target atoms. For an incident particle of mass M 1 , the energy is E 0 while the mass of the target atom is M 2 . After the collision, the residual energy E of the particle scattered at angle Ø can be expressed as:
\[ E\ =\ k^{2}E_{0} \label{1} \]
\[\ k\ =\ \frac{(M_{1}\ cos(\theta )\ +\ \sqrt{M_{2}^{2}\ -\ M_{1}^{2}sin^{2}\theta })}{M_{1}\ +\ M_{2}} \label{2} \]
where k is the kinematic scattering factor, which is actually the energy ratio of the particle before and after the collision. Since k depends on the masses of the incident particle and target atom and the scattering angle, the energy of the scattered particle is also determined by these three parameters. A simplified layout of backscattering experiment is shown in Figure \(\PageIndex{1}\).
The probability of a scattering event can be described by the differential scattering cross section of a target atom for scattering an incoming particle through the angle Ø into differential solid angle as follows,
\[ \frac{d \sigma R}{d \phi }\ = (\frac{zZe2}{2E_{0}sin(2\theta )} )\ =\ \frac{[cos\theta \ +\ \sqrt{1\ -\ (\frac{M_{1}}{M_{2}}sin\theta )^{2}}]^{2}}{\sqrt{1\ -\ (\frac{M_{1}}{M_{2}}sin\theta )^{2}}} \label{3} \]
where d σ R is the effective differential cross section for the scattering of a particle. The above equation may looks complicated but it conveys the message that the probability of scattering event can be expressed as a function of scattering cross section which is proportional to the zZ when a particle with charge ze approaches the target atom with charge Ze.
Helium ions not scattered at the surface lose energy as they traverse the solid. They lose energy due to interaction with electrons in the target. After collision the He particles lose further energy on their way out to the detector. We need to know two quantities to measure the energy loss, the distance Δt that the particles penetrate into the target and the energy loss ΔE in this distance Figure \(\PageIndex{2}\). The rate of energy loss or stopping power is a critical component in backscattering experiments as it determines the depth profile in a given experiment.
In thin film analysis, it is convenient to assume that total energy loss ΔE into depth t is only proportional to t for a given target. This assumption allows a simple derivation of energy loss in backscattering as more complete analysis requires many numerical techniques. In constant dE / dx approximation, total energy loss becomes linearly related to depth t, Figure \(\PageIndex{3}\).
Experimental Set-up
The apparatus for Rutherford backscattering analysis of thin solid surface typically consist of three components:
- A source of helium ions.
- An accelerator to energize the helium ions.
- A detector to measure the energy of scattered ions.
There are two types of accelerator/ion source available. In single stage accelerator, the He + source is placed within an insulating gas-filled tank (Figure \(\PageIndex{4}\)). It is difficult to install new ion source when it is exhausted in this type of accelerator. Moreover, it is also difficult to achieve particles with energy much more than 1 MeV since it is difficult to apply high voltages in this type of system.
Another variation is “tandem accelerator.” Here the ion source is at ground and produces negative ion. The positive terminal is located is at the center of the acceleration tube (Figure \(\PageIndex{5}\)). Initially the negative ion is accelerated from ground to terminal. At terminal two-electron stripping process converts the He - to He ++ . The positive ions are further accelerated toward ground due to columbic repulsion from positive terminal. This arrangement can achieve highly accelerated He ++ ions (~ 2.25 MeV) with moderate voltage of 750 kV.
Particles that are backscattered by surface atoms of the bombarded specimen are detected by a surface barrier detector. The surface barrier detector is a thin layer of p-type silicon on the n-type substrate resulting p-n junction. When the scattered ions exchange energy with the electrons on the surface of the detector upon reaching the detector, electrons get promoted from the valence band to the conduction band. Thus, each exchange of energy creates electron-hole pairs. The energy of scattered ions is detected by simply counting the number of electron-hole pairs. The energy resolution of the surface barrier detector in a standard RBS experiment is 12 - 20 keV. The surface barrier detector is generally set between 90° and 170° to the incident beam. Films are usually set normal to the incident beam. A simple layout is shown in Figure \(\PageIndex{6}\).
Depth Profile Analysis
As stated earlier, it is a good approximation in thin film analysis that the total energy loss ΔE is proportional to depth t. With this approximation, we can derive the relation between energy width ΔE of the signal from a film of thickness Δt as follows,
\[ \Delta E\ =\ \Delta t (k\ \frac{dE}{dx_{in}}\ +\ \frac{1}{\cos \theta } \ \frac{dE}{dx_{out}}) \label{4} \]
where Ø = lab scattering angle.
It is worth noting that k is the kinematic factor defined in equation above and the subscripts “in” and “out” indicate the energies at which the rate of loss of energy or dE/dx is evaluated. As an example, we consider the backscattering spectrum, at scattering angle 170°, for 2 MeV He ++ incidents on silicon layer deposited onto 2 mm thick niobium substrate Figure \(\PageIndex{7}\).
The energy loss rate of incoming He ++ or dE/dx along inward path in elemental Si is ≈24.6 eV/Å at 2 MeV and is ≈26 eV/Å for the outgoing particle at 1.12 MeV (Since K of Si is 0.56 when the scattering angle is 170°, energy of the outgoing particle would be equal to 2 x 0.56 or 1.12 MeV) . Again the value of ΔE Si is ≈133.3 keV. Putting the values into above equation we get
\[ \Delta t \approx \frac{133.6\ keV}{(0.56*24.6\ \frac{eV}{Å}) \ +\ (\frac{1}{\cos 170^{\circ } }\ *\ 26\ \frac{eV}{Å})} \nonumber \]
\[ =\ \frac{133.3\ keV}{13.77\ eV/Å \ +\ 29.985\ eV/Å} \nonumber \]
\[ =\ \frac{133.3\ keV}{40.17 eV/Å} \nonumber \]
\[ =\ 3318\ Å \nonumber \]
Hence a Si layer of ca. 3300 Å thickness has been deposited on the niobium substrate. However we need to remember that the value of dE/dx is approximated in this calculation.
Quantitative Analysis
In addition to depth profile analysis, we can study the composition of an element quantitatively by backscattering spectroscopy. The basic equation for quantitative analysis is
\[ Y\ =\ \sigma \Omega Q N \Delta t \nonumber \]
Where Y is the yield of scattered ions from a thin layer of thickness Δt, Q is the number of incident ions and Ω is the detector solid angle, and NΔt is the number of specimen atoms (atom/cm 2 ). Figure \(\PageIndex{8}\) shows the RBS spectrum for a sample of silicon deposited on a niobium substrate and subjected to laser mixing. The Nb has reacted with the silicon to form a NbSi 2 interphase layer. The Nb signal has broadened after the reaction as show in Figure \(\PageIndex{8}\).
We can use ratio of the heights H Si /H Nb of the backscattering spectrum after formation of NbSi 2 to determine the composition of the silicide layer. The stoichiometric ratio of Nb and Si can be approximated as,
\[ \frac{N_{Si}}{N_{Nb}}\ \approx \frac{[H_{Si}\ *\ \sigma_{Si}]}{[H_{Nb}\ *\ \sigma _{Nb}]} \nonumber \]
Hence the concentration of Si and Nb can be determined if we can know the appropriate cross sections σ Si and σ Nb . However the yield in the backscattering spectra is better represented as the product of signal height and the energy width ΔE. Thus stoichiometric ratio can be better approximated as
\[ \frac{N_{Si}}{N_{Nb}}\ \approx \frac{[H_{Si}\ *\ \Delta E_{Si}\ *\ \sigma_{Si}]}{[H_{Nb}\ *\ \Delta E_{Nb}\ *\ \ \sigma _{Nb}]} \nonumber \]
Limitations
It is of interest to understand the limitations of the backscattering technique in terms of the comparison with other thin film analysis technique such as AES, XPS and SIMS (Table \(\PageIndex{1}\)). AES has better mass resolution, lateral resolution and depth resolution than RBS. But AES suffers from sputtering artifacts. Compared to RBS, SIMS has better sensitivity. RBS does not provide any chemical bonding information which we can get from XPS. Again, sputtering artifact problems are also associated in XPS. The strength of RBS lies in quantitative analysis. However, conventional RBS systems cannot analyze ultrathin films since the depth resolution is only about 10 nm using surface barrier detector.
Summary
Rutherford Backscattering analysis is a straightforward technique to determine the thickness and composition of thin films (< 4000 Å). Areas that have been lately explored are the use of backscattering technique in composition determination of new superconductor oxides; analysis of lattice mismatched epitaxial layers, and as a probe of thin film morphology and surface clustering.


3.3: Span, Basis, and Dimension
View Span, Basis and Dimension on YouTube
Given a set of vectors, one can generate a vector space by forming all linear combinations of that set of vectors. The span of the set of vectors \(\{\text{v}_1,\: \text{v}_2,\cdots , \text{v}_n\}\) is the vector space consisting of all linear combinations of \(\text{v}_1,\: \text{v}_2,\cdots , \text{v}_n\). We say that a set of vectors spans a vector space.
For example, the set of three-by-one column matrices given by
\[\left\{\left(\begin{array}{c}1\\0\\0\end{array}\right),\:\left(\begin{array}{c}0\\1\\0\end{array}\right),\:\left(\begin{array}{c}2\\3\\0\end{array}\right)\right\}\nonumber \]
spans the vector space of all three-by-one matrices with zero in the third row. This vector space is a vector subspace of all three-by-one matrices.
One doesn’t need all three of these vectors to span this vector subspace because any one of these vectors is linearly dependent on the other two. The smallest set of vectors needed to span a vector space forms a basis for that vector space. Here, given the set of vectors above, we can construct a basis for the vector subspace of all three-by-one matrices with zero in the third row by simply choosing two out of three vectors from the above spanning set. Three possible bases are given by
\[\left\{\left(\begin{array}{c}1\\0\\0\end{array}\right),\:\left(\begin{array}{c}0\\1\\0\end{array}\right)\right\},\quad\left\{\left(\begin{array}{c}1\\0\\0\end{array}\right),\:\left(\begin{array}{c}2\\3\\0\end{array}\right)\right\},\quad\left\{\left(\begin{array}{c}0\\1\\0\end{array}\right),\:\left(\begin{array}{c}2\\3\\0\end{array}\right)\right\}.\nonumber \]
Although all three combinations form a basis for the vector subspace, the first combination is usually preferred because this is an orthonormal basis. The vectors in this basis are mutually orthogonal and of unit norm.
The number of vectors in a basis gives the dimension of the vector space. Here, the dimension of the vector space of all three-by-one matrices with zero in the third row is two.
Find an orthonormal basis for the set of all three-by-one matrices where the first row is equal to the third row.
Solution
There are many different solutions to this example, but a rather simple orthonormal basis is given by
\[\left\{\left(\begin{array}{c}0\\1\\0\end{array}\right),\frac{\sqrt{2}}{2}\left(\begin{array}{c}1\\0\\1\end{array}\right)\right\}.\nonumber \]
Any other three-by-one matrix with first row equal to third row can be written as a linear combination of these two basis vectors, and the dimension of this vector space is also two.
Determine a basis for \(\mathbb{P}_2\), the vector space consisting of all polynomials of degree less than or equal to two.
Solution
Again, there are many possible choices for a basis, but perhaps the simplest one is given by
\[\left\{\begin{array}{ccc}1,&x,&x^2\end{array}\right\}.\nonumber \]
Clearly, any polynomial of degree less than or equal to two can be written as a linear combination of these basis vectors. The dimension of \(\mathbb{P}_2\) is three.
Determine a basis for the vector space given by the general solution of the differential equation \(d^2y/dx^2 + y = 0\).
Solution
The general solution is given by
\[y(x)=a\cos x+b\sin x,\nonumber \]
and a basis for this vector space are just the functions
\[\left\{\begin{array}{cc}\cos x,&\sin x\end{array}\right\}.\nonumber \]
The dimension of the vector space given by the general solution of the differential equation is two. This dimension is equal to the order of the highest derivative in the differential equation.


14.5: Using Macros
By the end of this section, you will be able to:
- Record a macro that automates a common task
- Record a macro that enhances database functions
- Demonstrate some understanding of macro code
A macro is a set of instructions that can automate repetitive tasks or perform complex operations with a single click. Macros can be created using the Macro Builder , which provides a graphical interface for creating and editing macros. Examples of how a macro can be used in Microsoft Access are many.
As an example, your database under construction that tracks inventory for retail stores that WorldCorp would like to launch has numerous options to consider. Each time a new transaction is entered, you need to generate an invoice for the customer that includes their name, the date of the sale, and a list of the items bought. To automate this process, you can create a macro that performs the following tasks:
- Open the Orders table and find the most recent order.
- Get the customer’s name from the Customers table.
- Get the date of the order.
- Get a list of the items ordered from the Order Details table.
- Create a new record in the Invoices table.
- Populate the new record with the customer’s name, the date of the order, and the list of items ordered.
- Save the new invoice record.
Once you have created this macro, you can run it whenever you need to generate a new receipt. Access will automatically perform all the necessary steps, saving you time and reducing the risk of errors. Macros provide the ability to automate repetitive tasks, improve productivity, and reduce errors in database management.
Creating and Recording Macros
Macros can make tasks that you routinely perform in Access quicker through automation. Macros are built using computer coding language to perform specific tasks such as running reports, printing forms, or copying data from one table into another table.
To begin using macros, open the macro design builder, located under the Create tab. This will create a blank macro builder, which can be saved and stored for later use in the All Access Objects area. The Macro Designer on the right side (Figure 14.65) contains the Action Catalog, where all of your actions will be stored in folders. You have Data Entry options, Data Import/Export, and so on, and on the left in the main area you have a blank canvas to start building your macro.
Recording a Macro to Automate Common Tasks
Recording a macro to automate tasks in Access is a common way to save time and increase productivity. When you record a macro in Access, you essentially create a set of instructions that Access can use to automatically perform a sequence of tasks.
Let’s say you frequently need to create a report that shows the total sales for each region of the country in the growing area of retail sales. You can use the Macro Recorder to automate this process. First, select the Create tab in the ribbon and select Macro. In the Macro Builder, click the Record button to start recording the macro. Perform the actions you want the macro to automate. For example, you could select the fields you want to include in the report, specify the criteria for grouping the data by region, and apply formatting to the report.
When you have finished performing the actions, click the Stop Recording button in the Macro Builder. Give the macro a descriptive name and save it. Now, whenever you need to create a report that shows the total sales for each retail store, you can simply run the macro you recorded (Figure 14.66). Access will automatically perform all the steps you recorded, saving you time and reducing the risk of errors.
A common use of macros is to add a button to a form. In the previous section, we discussed how a Main Menu form can help improve user experience by creating a navigation map. Buttons can have macros embedded that open and close certain forms; they can also control what record source is displayed.
For example, suppose you want to add your customer form to the Main Menu. The original goal is to add a button that will open the customer form. However, if you want to add a button that will add a new customer, you can create a macro that will open the customer form and move the record to the new source. The open form is shown in Figure 14.67.
You will see the form name with a drop-down arrow, which will show you the forms available in your database. For each form, there is a View option, which will allow you to open the form in Form View, Design View, or Print Preview View. You also can apply a filter name or a condition. In Figure 14.68, the macNewCustomer macro that was created centered on finding particular records. You will notice this option is available to modify.
Recording a Macro to Enhance Database Functions
By customizing your database with macros, you can create a system for accomplishing many similar operations easily and efficiently. Two common applications for macros are displaying message boxes and validating data:
- Displaying a message box : You can use the MsgBox action to display alerts, warnings, and other useful information. The MsgBox action has four arguments: Message, Beep, Type, and Title.
- Data validation : Often used in Microsoft Excel, data validation is an extremely helpful step to take prior to adding the data to the database. To ensure that only valid data is entered in a form, you can specify a validation rule for the control in the form or set record and field validation rules in the underlying table design. For more complex data validation, you can use a macro or an event procedure to specify the rule.
As another example, you can use the RunApplication macro to run a Microsoft Windows-based application, such as Excel, Word, or PowerPoint, from within Microsoft 365. For example, you may want to paste Excel spreadsheet data into your Access database. This can greatly enhance your database’s ability to work with imported data.
Reviewing Completed Macros
One of the easiest ways to review a macro is to simply run the macro and see if the desired outcome occurs. At any point, a macro can be edited to better serve the database developer’s goal for how it will function.
To review completed macros in Access that have been developed, you can start by opening the database that contains the macros you want to review. Go to the Navigation Pane on the left side of the screen and select the Macros option. This will display a list of all the macros in the database.
Double-click on the macro you want to review. This will open the macro in Design View. In this view, you can see all the actions and conditions that make up the macro. You can review each action to ensure that it performs the intended task and that it is configured correctly.
To run the macro and test its functionality, click the Run button in the Macros tab of the ribbon. This will execute the macro and perform all the actions defined within it. If you encounter any issues or errors while running the macro, you can use the Debug mode to review the code and identify the problem. To exit the Design View of the macro, click the Close button in the top-right corner of the screen. By reviewing completed macros in Access, you can ensure that they function as intended. Additionally, you can use the insights gained from reviewing completed macros to improve future developments with your overall programming skills. These are big steps are mastering relationship databases.
Understanding Macro Code
Figure 14.69a shows how to add code to an event procedure. Although there is a steep learning curve for understanding the syntax, its applications are unlimited. In this example, we want to create a message box that will appear when a user opens the form. The code is written out just below the comments (shown in green in Figure 14.69b) that were added. Whenever you add new code, either directly or by using a macro, be sure to include a comment. If there is a problem or a future need for a change, comments can help clarify what the code was designed to accomplish.
After opening the builder options menu, select Code Builder . This will open a new window, as shown, that will allow the developer to type in the desired code directly. This code can be broken into four sections.
First, MsgBox has been identified as the action. Because it is placed in the event procedure On Open, a message box will appear when it opens.
Second, text for the message box—in this example, “Ask how they heard about us!”—is included to remind associates to ask the customer this basic engaging question while taking a new customer order.
Finally, there is a request for which form to open after the message box appears. The following message box shown in Figure 14.70 was created through the code.
Understanding Visual Basic
Visual Basic for Applications (VBA) is a programming language that is integrated into Access, allowing you to create custom solutions for data management, reporting, and other tasks. VBA provides a powerful set of tools for developers to create robust and scalable applications within Access.
Some examples of how VBA can help developers in Access include automating repetitive tasks. With VBA, developers can create macros and scripts to automate repetitive tasks, such as importing data, running reports, or updating records. This can save time and reduce errors by eliminating the need for manual data entry.
Customizing user interfaces can be written in VBA and can be used to create custom forms and dialog boxes to provide a user-friendly interface for working with data. Developers can add buttons, menus, and other controls to simplify complex tasks and make the application more intuitive. VBA can also create custom functions and algorithms for analyzing data within Access. Developers can create advanced data models and calculations to help gain insight data. One of the keys to VBA is opening up the ability to integrate with other applications. It can be used to integrate Access with other applications, such as Excel or Outlook. This allows developers to create custom workflows and exchange data between applications.
VBA can be used to create custom reports within Access, including dynamic reports that update based on user input or other data sources. In summary, VBA is a powerful tool that seems to offer endless abilities and functionality in Access. It provides a wide range of features and capabilities for creating custom solutions to meet the specific needs of users and organizations. With VBA, you can automate repetitive tasks, customize user interfaces, enhance data analysis, integrate with other applications, and create custom reports, and that is just scratching the surface of possibilities.
Link to Learning
Using VBA will take some practice as you are essentially writing computer code. VBA has a wide variety of applications to assist you in working Access and also in Excel. Most users can record macros to meet most of their automation needs in Access. However, if you have more advanced needs and are familiar with computer coding, VBA can be quite powerful. The best way to show how VBA can expand the power and agility of Access is by providing a demonstration. Please view this video tutorial on how to use VBA to create databases within Access to learn more.


22.11E: Absorption and Feces Formation in the Large Intestine
The large intestine absorbs water from the chyme and stores feces until they can be defecated.
- Describe the process of absorption and feces formation in the large intestine
Key Points
- Partially digested food passes from the small intestine to the large intestine or colon.
- Within the colon, digestion is retained long enough to allow fermentation via gut bacteria that break down some of the substances that remain after processing in the small intestine.
- The large intestine houses over 700 species of bacteria that metabolize polysaccharides into short-chain fatty acids that produce large amounts of vitamins —especially vitamin K and biotin—and gas.
- The normal flora of bacteria in the large intestine is essential in the development of certain tissues, including the cecum and lymphatics.
Key Terms
- feces : Digested waste material that is discharged from the bowels; excrement.
- polysaccharide : A polymer made of many saccharide units that are linked by glycosidic bonds.
- anal sphincter : A ring muscle that surrounds the anus (anal orifice).
After the food has been passed through the small intestine, it enters the large intestine. Within the large intestine, digestion is retained long enough to allow fermentation via gut bacteria that break down some of the substances that remain after processing in the small intestine.
Some of the breakdown products are absorbed. In humans, these include most complex saccharides (at most, three disaccharides are digestible by humans).
Intestinal Bacteria
The large intestine houses over 700 species of bacteria that perform a variety of functions. The large intestine absorbs some of the products formed by the bacteria that inhabit this region.
Undigested polysaccharides (fiber) are metabolized into short-chain fatty acids by bacteria in the large intestine and get absorbed by passive diffusion. The bicarbonate that the large intestine secretes helps to neutralize the increased acidity from the formation of fatty acids.
Intestinal bacteria also produce large amounts of vitamins, especially vitamin K and biotin (a B vitamin), which are absorbed into the blood. Although this source of vitamins provides only a small part of the daily requirement, it makes a significant contribution when dietary vitamin intake is low. An individual that depends on absorption of vitamins formed by bacteria in the large intestine may become vitamin-deficient if treated with antibiotics that inhibit other species of bacteria while targeting the disease-causing bacteria.
Other bacterial products include gas (flatus)—a mixture of nitrogen and carbon dioxide, with small amounts of the gases hydrogen, methane, and hydrogen sulphide. The bacterial fermentation of undigested polysaccharides produces these gases.
Intestinal flora are also essential for the development of certain tissues, including the cecum and lymphatics.
Water and Cellulose
The large intestine absorbs water from the chyme and stores feces until it can be defecated. Food products that cannot go through the villi, such as cellulose (dietary fiber), are mixed with other waste products from the body and become hard and concentrated feces.
The feces is stored in the rectum for a certain period and then the stored feces is eliminated from the body due to the contraction and relaxation of the anus. The exit of this waste material is regulated by the anal sphincter.


10.1E: Non-right Triangles - Law of Sines (Exercises)
For the following exercises, assume \(\alpha\) is opposite side \(a, \beta\) is opposite side \(\mathbf{b},\) and \(\gamma\) is opposite side \(c .\) Solve each triangle, if possible. Round each answer to the nearest tenth.
1. \(\beta=50^{\circ}, a=105, \mathbf{b}=45\)
2. \(\alpha=43.1^{\circ}, a=184.2, \mathbf{b}=242.8\)
3. Solve the triangle.
4. Find the area of the triangle.
5. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, \(2.1 \mathrm{~km}\) apart, to be \(25^{\circ}\) and \(49^{\circ}\), as shown in Figure 1 . Find the distance of the plane from point \(A\) and the elevation of the plane.
Figure 1


19.2: Functions of the Lymphatic and Immune Systems
By the end of this section, you will be able to:
- Explain the overall functions of the lymphatic system
- Describe the temporal organization of the immune system
- Distinguish primary and secondary adaptive immune responses
Functions of the Lymphatic System
The functions of the lymphatic system are integral to the immune system because structures of the lymphatic system function to produce, develop, house and distribute leukocytes, but the lymphatic system also supports other body systems in a couple of ways. A network of lymphatic vessels provide a one-way route to return excess fluid from tissues back to the bloodstream to maintain blood volume and also distribute leukocytes throughout the body. Along the way, the fluid is filtered for pathogens and debris as it passes through lymph nodes. Lymphatic capillaries serving the small intestine also collect lipid products of digestion that are too large to enter blood capillaries. These lipids are transported to the bloodstream via the lymphatic vessels. Lymph is the watery fluid connective tissue found in lymphatic vessels whose cellular components include primarily lymphocytes along with phagocytic macrophages and other specialized leukocytes. The watery matrix of lymph is similar to the plasma of blood; it contains dissolved nutrients, waste products, and plasma proteins.
Lymphoid tissues and organs are so-called because they contain fluid that resembles lymph, and they support lymphocyte production, development, storage, and functions in a variety of locations in the body. Dense collections of leukocytes suspended in reticular connective tissue that remove debris and fight infection within organs of other body systems constitute lymphoid tissues such as the tonsils and mucosa-associated lymphoid tissues (MALT). The lymphatic system also includes distinct organs that support the immune system including the thymus, spleen, and red bone marrow. The vessels, tissues, and organs of the lymphatic system are summarized in Figure \(\PageIndex{1}\) and Table \(\PageIndex{1}\) and will be covered in more detail in subsequent sections of this chapter.
| Structure | Examples | Functions |
|---|---|---|
| Lymphatic Vessels | Lymphatic capillaries, vessels, trunks, and ducts containing lymph |
|
| Lymphoid Tissues | Tonsils, Mucosa-Associated Lymphoid Tissue (MALT) |
|
| Lymphoid Organs | Lymph Nodes, Thymus, Red Bone Marrow, Spleen |
|
The Organization of Immune Function
The structures of the lymphatic system play integral roles in supporting the immune system, which is responsible for ridding the body of cellular debris and abnormal cells as well as preventing and fighting infection.
The immune system is a collection of barriers, cells, and soluble proteins that interact and communicate with each other in extraordinarily complex ways. The modern model of immune function is organized into three phases based on the timing of their effects. The three temporal phases or lines of defense are summarized in Table \(\PageIndex{2}\).
|
Line of Defense |
Temporal Response |
Type of Immunity |
Description |
Function(s) |
|---|---|---|---|---|
|
First Line of Defense |
Instantaneous |
Innate |
Barrier defenses such as skin and mucus membranes |
Prevent pathogenic invasion into the body tissues |
|
Second Line of Defense |
Rapid |
Innate |
Non-specific internal defenses including cells, soluble factor, inflammatory response |
|
|
Third Line of Defense |
Slow |
Adaptive |
Specific responses mediated by lymphocytes |
|
The functions of the immune system are woven into the anatomy of every body system. Innate immunity refers to defenses that are present from birth, including both the infection-preventing barrier defenses and the cellular and physiological internal defenses that respond if the barrier defenses are breached. The innate internal immune responses are non-specific and designed to discover and slow the progression of an infection-causing pathogen (Figure \(\PageIndex{2}\)). A pathogen is any agent capable of causing infection, such as a virus, bacterium, or fungal organism. Adaptive immune responses are designed to recognize, destroy, and retain a memory of a specific pathogen by adapting to each specific pathogen after it is discovered in the body.
Barrier Defenses
Epithelial barriers are consistently present and optimized for barrier defense as well as their other functions. Epithelial tissues near the outside of the body produce specialized secretions that physiologically enhance the physical barriers to further deter potential infection. For example, the inside of the nose has an epithelial barrier with hairs and a coating of mucus that function to trap pathogens. Further, in areas that are exposed to the environment, body fluids such as sweat, sebum, and urine have antimicrobial properties and also maintain conditions, such as lipid content or pH, that encourage the growth of beneficial microorganisms. The combination of these beneficial microorganisms living on or inside the body on the apical surface of epithelial tissues constitutes the microbiome , and its population size outnumbers human cells in the body. The microbiome is an important part of barrier defenses because one of its roles is to out-compete pathogenic microorganisms to prevent infection.
Cooperation between Innate and Adaptive Immunity
In the event a pathogen successfully penetrates the barrier defenses and enters the body, its detection by the immune system will solicit a dynamic response. The innate internal defenses include cells and physiological responses that function to slow the spread of infection. Physiological responses include inflammation, triggered by histamine secreted by basophils and/or mast cells, and the complement system, in which proteins and other molecules participate in fighting the infection to slow its progression. These physiological responses will not be covered in detail here.
Cells of the innate internal immune response do not recognize specific antigens like the lymphocytes of the adaptive immune response. Instead they have receptors that recognize patterns in the surface antigens that simply distinguish whether any immune response is warranted. If a cell or particle is recognized as "self", a normally functioning part the body, no immune response is warranted. However, if a cell or particle is recognized as "non-self" because the pattern of surface antigens signify it does not belong in the body, a dynamic immune response is triggered. Detection of pathogens or even your own cells that are abnormal because they may be pre-cancerous or infected by an intracellular pathogen such as a virus will solicit a response. The adaptive immune response requires cooperation with elements of innate immunity, but also specialized structures of the lymphatic system from which to coordinate adaptive responses.
Phagocytes: Macrophages, Dendritic Cells, and Neutrophils
A phagocyte is a cell that is able to surround and engulf a particle or cell, a process called phagocytosis . The phagocytes of the immune system engulf other particles or cells, either to clean an area of debris, old cells, or to kill pathogens. The phagocytes are the body’s fast-acting defense against microorganisms that have breached barrier defenses and have entered the vulnerable tissues of the body.
Many of the cells of the immune system have a phagocytic ability, at least at some point during their life cycles. Phagocytosis is an important and effective mechanism of destroying pathogens during innate immune responses. The phagocyte takes the organism inside itself as a phagosome, which subsequently fuses with a lysosome containing digestive enzymes that effectively kill most pathogens. On the other hand, some bacteria including Mycobacteria tuberculosis , the cause of tuberculosis, may be resistant to these enzymes and are therefore much more difficult to clear from the body. Macrophages, neutrophils, and dendritic cells are the major phagocytes of the immune system.
A macrophage is an irregularly shaped phagocyte that is the most versatile of the phagocytes in the body. Macrophages move through tissues and squeeze through capillary walls using foot-like extensions called pseudopodia. They not only participate in innate immune responses but have also evolved to cooperate with lymphocytes to facilitate the adaptive immune response. Macrophages exist in many tissues of the body, either freely roaming through connective tissues or fixed to reticular fibers within specific tissues such as lymph nodes. When pathogens breach the body’s barrier defenses, macrophages are the first responders in lymphoid and connective tissues outside the bloodstream. Dendritic cells are similar to macrophages, but have slightly more branched shape to further increase their surface area (thus the name, dendr- refers to a tree branch). Dendritic cells are typically found in epithelial tissues. Both macrophages and dendritic cells are antigen-presenting cells (APCs) , meaning they present fragments of the antigens belonging to pathogens they have engulfed and destroyed to T lymphocytes to activate the adaptive immune response. A monocyte is a circulating precursor cell that differentiates into either a macrophage or dendritic cell, which can be rapidly attracted to areas of infection by signal molecules of inflammation.
Natural Killer Cells (NK Cells)
Natural killer cells (NK cells) are a type of lymphocyte that belongs to the innate internal immune response. NK cells have the ability to induce apoptosis, that is programmed cell death, in cells infected with intracellular pathogens such as bacteria and viruses. NK cells recognize these cells by mechanisms that are still not well understood, but that presumably involve their surface receptors. NK cells can induce apoptosis, in which a cascade of events inside the cell causes its self destruction. If apoptosis is induced before the virus has the ability to synthesize and assemble all its components, no infectious virus will be released from the cell, thus preventing further infection.
Innate internal immune responses (and early adaptive responses) are in many cases ineffective at completely controlling pathogen growth. However, they slow pathogen growth and allow time for the adaptive immune response to strengthen and either control or eliminate the pathogen. The innate immune system also sends signals to the cells of the adaptive immune system, guiding them in how to attack the pathogen. Thus, these are the two important arms of the immune response.
The Benefits of the Adaptive Immune Response
Three aspects of the adaptive immune response make it particularly effective: specificity, immunological memory, and self-recognition. All three of these benefits are made possible by the unique physiological mechanisms of lymphocyte development and proliferation. Lymphocytes are stored in many tissues and organs of the lymphatic system that are strategically located throughout the body ready to be activated and coordinate adaptive responses.
The specificity of the adaptive immune response—its ability to specifically recognize and make a response against a wide variety of pathogens—is its great strength. Antigens, the small chemical groups often associated with pathogens, are recognized by receptors on the surface of B and T lymphocytes. The adaptive immune response to these antigens is so versatile that it can respond to nearly any pathogen.
Upon first exposure to a new pathogen, a naïve T cell is activated and expresses a receptor that specifically corresponds to the antigen of the pathogen. The activated T cell then rapidly divides creating an army of lymphocytes expressing that same specific receptor to fight off the pathogen, as well as an army of memory cells to retain T cells that have adapted to the specific pathogen for some time (depending on the pathogen, these memory cells could last for months or for a lifetime). If exposed to the same pathogen again, the memory cells will re-activate a rapid secondary response that will overwhelm the pathogen before symptoms present. This is known as immunological memory.
A third important feature of the adaptive immune response is its ability to distinguish between self-antigens, those that are normally present in the body, and non-self antigens, those that might be on a potential pathogen. As T and B cells mature, there are mechanisms in place that prevent them from recognizing self-antigen, preventing a damaging immune response against the body. These mechanisms are not 100 percent effective, however, and their breakdown leads to autoimmune diseases, which will be discussed later in this chapter.
T Cell-mediated Immune Responses
The immune system’s first exposure to a pathogen is called a primary adaptive immune response . Symptoms of a first infection, called primary disease, are always relatively severe because it takes time for an initial adaptive immune response to a pathogen to become effective.
In the case primary adaptive immune response, naïve T cells (naïve because they have not yet developed specificity for a particular antigen), such as those stored in the tonsils, become activated to recognize a specific antigen and begin dividing rapidly by mitosis. Each T cell clone has a receptor specific for a particular antigen “hard-wired” into its DNA, and all of its progeny will have identical DNA and T cell receptors, forming clones of the original T cell that will recognize the antigen of a specific pathogen. This proliferation of T cells is called clonal expansion and is necessary to make the immune response strong enough to effectively control a pathogen.
During a primary adaptive immune response, both memory T cells and effector T cells are generated. Effector T cells act immediately to eradicate the pathogen. Memory T cells are longer-lived and, depending on the pathogen, can even persist for a lifetime. Memory cells are primed to act rapidly upon re-exposure to the same pathogen, generating a secondary adaptive immune response that is stronger and faster than the primary response. This rapid, secondary adaptive response generates large numbers of effector T cells so fast that the pathogen is often overwhelmed before it can cause any symptoms of disease. This is what is meant by immunity to a disease. The same pattern of primary and secondary immune responses occurs in B cells and the antibody response.
Types of T Cells
Helper T cells (Th, T4, or CD4 + T cells) interact with the antigen-presenting cells like macrophages and dendritic cells. Helper T cells activate other types of T cells and B cells to mount a response to a specific antigen, but they activate innate immune cells as well by secreting cytokine signaling molecules.
Cytotoxic T cells (Tc, T8, or CD8 + T cells) are T cells that kill target cells by inducing apoptosis (programmed cell death) using the same mechanism as NK cells. As was discussed earlier with NK cells, killing a virally infected cell before the virus can complete its replication cycle results in the production of no infectious particles. As more cytotoxic T cells are developed during an immune response, they overwhelm the ability of the virus to cause disease. In addition, each cytotoxic T cell can kill more than one target cell, making them especially effective. Cytotoxic T cells are so important in the antiviral immune response that some speculate that this was the main reason the adaptive immune response evolved in the first place.
Regulatory T cells , or suppressor T cells, are the most recently discovered of the types listed here, so less is understood about them. Exactly how they function is still under investigation, but it is known that they suppress other T cell immune responses. This is an important feature of the immune response, because if clonal expansion during immune responses were allowed to continue uncontrolled, these responses could lead to autoimmune diseases and other medical issues.
Not only do T cells directly destroy pathogens, but they regulate nearly all other types of the adaptive immune response as well.
B Lymphocytes and Antibodies
Antibodies were the first component of the adaptive immune response to be characterized by scientists working on the immune system. It was already known that individuals who survived a bacterial infection were immune to re-infection with the same pathogen. Early microbiologists took serum from an immune patient and mixed it with a fresh culture of the same type of bacteria, then observed the bacteria under a microscope. The bacteria became clumped in a process called agglutination. When a different bacterial species was used, the agglutination did not happen. Thus, there was something in the serum of immune individuals that could specifically bind to and agglutinate bacteria.
Scientists now know the cause of the agglutination is an antibody molecule, also called an immunoglobulin . What is an antibody? An antibody protein is essentially a secreted form of the antigen-specific receptor. Not surprisingly, the same genes encode both the secreted antibodies and the surface receptors; just one minor difference in the way these proteins are synthesized distinguishes them.
Antibodies circulate in the blood plasma to alert the immune system to the presence of the matching antigen (and thereby the pathogen). Antibodies have several mechanisms by which they participate in physiological immune responses. For example, in the case of a virus, agglutination (binding of the antibodies to antigens) may prevent the pathogen from infecting a cell and reproducing by blocking the ability of the virus to bind its target cell.
B Cell Activation and Clonal Selection
After a naïve B cell is activated by binding to its corresponding antigen, it undergoes clonal expansion, producing both memory B cells and cells that differentiate into plasma cells.
- Memory B cells function in a way similar to memory T cells. They lead to a stronger and faster secondary response when compared to the primary response.
- Plasma cells produce and secrete antibodies specifically corresponding to the antigen that activated the naïve B cell. After secreting antibodies for a specific period, they die, as most of their energy is devoted to making antibodies and not to maintaining themselves.
Clonal selection and expansion of B cells, as well as the primary and secondary immune response phases, work similarly to those of T cells and are depicted in Figure \(\PageIndex{3}\)). Eventually, the plasma cells secrete antibodies with antigenic specificity identical to those that were on the surfaces of the selected B cells. Many identical clones of both plasma cells and memory B cells are generated simultaneously. Upon a second exposure to the same pathogen, the corresponding memory B cell becomes activated to divide and create additional memory B cells and plasma cells that will produce and secrete antibodies.
Concept Review
Structures of the lymphatic system support immune system function, but also carry out other specific functions. Lymphatic structures include vessels, tissues, and distinct organs. The immune system can be organized into temporal lines of defense that include the innate barrier defenses, non-specific innate internal immune responses, and the adaptive immune response. The adaptive immune response is mediated by T and B lymphocytes. Primary adaptive lymphocyte responses describe the slow but steady clonal expansion of lymphocytes programmed to respond to a specific antigen and eradicate it after primary infection. The primary adaptive lymphocyte response also yields long-lived memory T and B cells that can allow a more rapid adaptive immune response upon secondary infection with the same antigen-containing pathogen.
Review Questions
Q. Which enzymes in macrophages are important for clearing intracellular bacteria?
A. metabolic
B. mitochondrial
C. nuclear
D. lysosomal
- Answer
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Answer: D
Q. Which of the following cells is phagocytic?
A. plasma cell
B. macrophage
C. B cell
D. NK cell
- Answer
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Answer: B
Q. Which of the following cells is important in the innate immune response?
A. B cells
B. T cells
C. macrophages
D. plasma cells
- Answer
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Answer: C
Q. Which type of immune response works in concert with cytotoxic T cells against virally infected cells?
A. natural killer cells
B. complement
C. antibodies
D. memory
- Answer
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Answer: A
Critical Thinking Questions
Q. Distinguish primary and secondary adaptive immune responses to a viral infection.
- Answer
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A. A primary adaptive immune response occurs in response to the first exposure to a new viral infection. An antigen from the virus is presented to a helper T lymphocyte by an antigen-presenting cell (typically a macrophage or dendritic cell). T and B lymphocytes are cloned, forming effector and memory cells. Effector cells (cytotoxic T cells and plasma cells) that will work to eradicate the virus immediately. Cytotoxic T cells will induce apoptosis (programmed cell death) in cells infected with the virus. Plasma cells will produce and secrete antibodies to target the antigen of the virus. Memory cells are longer-lived cells that will activate a secondary immune response in case of a future exposure to the same antigen-containing virus.
Glossary
- adaptive immune response
- relatively slow but very specific and effective immune response controlled by lymphocytes
- antibody
- antigen-specific protein secreted by plasma cells; immunoglobulin
- antigen
- molecule recognized by the receptors of B and T lymphocytes
- antigen-presenting cell (APC)
- cell that presents a fragment of an antigen to T cells to induce an adaptive immune response
- barrier defenses
- antipathogen defenses deriving from a barrier that physically prevents pathogens from entering the body to establish an infection
- B cells
- lymphocytes that act by differentiating into an antibody-secreting plasma cell
- cytotoxic T cells (Tc, T8, or CD8 + T cells)
- T lymphocytes with the ability to induce apoptosis in target cells
- dendritic cell
- phagocyte and antigen-presenting cell (APC) typically found in epithelial tissues such as the epidermis
- effector T cells
- immune cells with a direct, adverse effect on a pathogen
- first line of defense
- temporal classification for the barrier defenses of the immune system that serve to prevent infection
- helper T cells (Th, T4, or CD4 + T cells)
- T cells that secrete cytokines to enhance other immune responses, involved in activation of both B and T cell lymphocytes
- immune system
- series of barriers, cells, and soluble mediators that combine to response to infections of the body with pathogenic organisms
- innate internal immune response
- rapid but relatively nonspecific immune response
- macrophage
- amoeboid phagocyte found in several tissues throughout the body; also an APC
- memory T cells
- long-lived immune cell reserved for future exposure to an pathogen
- microbiome
- the combination of beneficial microorganisms living on and inside the human body
- monocyte
- precursor to macrophages and dendritic cells seen in the blood
- naïve lymphocyte
- mature B or T cell that has not yet encountered antigen for the first time
- neutrophil
- phagocytic white blood cell recruited from the bloodstream to the site of infection via the bloodstream
- pathogen
- any microorganism or acellular particle that causes infection; examples include viruses (acellular), bacteria, fungi, protozoans, and parasitic worms
- phagocytosis
- movement of material from the outside to the inside of the cells via vesicles made from invaginations of the plasma membrane
- plasma cell
- differentiated B cell that is actively secreting antibody
- natural killer cell (NK)
- cytotoxic lymphocyte of innate immune response
- second line of defense
- temporal classification for the innate immune response that rapidly, but nonspecifically responds to pathogens to slow the spread of infection and also promotes healing after tissue damage
- T cell
- lymphocyte that acts by secreting molecules that regulate the immune system or by causing the destruction of foreign cells, viruses, and cancer cells
- third line of defense
- temporal classification for the adaptive immune response that responds more slowly, but also specifically and more effectively to eradicate infection
Contributors and Attributions
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OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


7: Systems of Equations
In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions.
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- 7.1: Systems of Linear Equations - Two Variables
- A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
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- 7.3: Partial Fractions
- Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations. The decomposition with repeated linear factors must account for the factors of the denominator in increasing powers. The decomposition with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor.
Contributors and Attributions
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Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus .


15.5: Do We Need a Global Environmental Organisation?
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Who is in charge of protecting our global environment? To answer this question, you may recall from previous sections that there is now a consensus regarding one specific tool that may help achieve the lofty goal of providing global public goods: international environmental agreements. These agreements, often produced at megaconferences, help protect our global commons by requiring nations to acknowledge and respect the human right to a healthy environment. However, the next big question is an equally important one – who is in charge of implementing these international environmental accords? Some have argued that in order to force countries to cooperate in the protection of our shared environment, we need a global intergovernmental secretariat. This would take the form of a far-reaching international institution whose sole purpose would be coordinating efforts to improve environmental quality.
For many years there was a collective belief that the United Nations Environment Programme had been tasked with the challenge of protecting our global network of ecosystems and shared resources. This may have been true in the early stages of its creation following the 1972 Stockholm Conference, but protecting our global environment has proved to be an impossible task for a small agency with a limited budget and no power to compel states to act in a particular way. The reality is that even though there is increasing interest in strengthening international cooperation across countries to protect the global environment, it is the number of institutions, agencies and programmes dealing with environmental issues at other levels that grows in size and complexity. Regrettably, the frequent mention of abrupt climate change events, increasing deforestation and growing levels of pollution in oceans, rivers and lakes makes it clear that we have yet to solve these complex global environmental problems. And while there is still no agreement as to whether the United Nations Environment Programme is the agency that should be tasked with protecting the global environment or whether we should create a new global environmental organisation (see Biermann 2000), we must ensure that we focus on collective solutions at the international level rather than state, regional or local level – we all share the earth.
To strike an optimistic note, we can find at least one instance of global environmental cooperation, the Paris Agreement of 2015. This was led by the chair of the United Nations Framework Convention on Climate Change Secretariat, Christiana Figueres, and is an example of what can be achieved in global cooperation for environmental protection by just one intergovernmental secretariat. The fact that the majority of the world’s states were able to reach agreement on the specific tactics and strategies that every state needs to undertake in order to reach the stated goal of holding increases in the earth’s temperature below two degrees centigrade is to be lauded. Even more important is that the agreement has secured the support of the world’s two biggest state polluters, the US and China. The Secretariat is probably not the global environmental organisation we need right now, but it played a pivotal role at a crucial time.
The debate around whether or not we should have a global environmental organisation may never be settled. However, if we were to establish such a thing it would need full and complete cooperation from all states to stand any chance of success. The example of Paris, which built on the example of earlier megaconferences and movements, suggests that international collaboration to protect our environment is on the rise. This offers hope for the future despite rising political tensions in some nations over the nature of climate agreements.


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6.1: Boundary value problems
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Before we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
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6.2: The Trigonometric Series
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6.3: More on the Fourier Series
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We have computed the Fourier series for a 2π-periodic function, but what about functions of different periods.
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6.4: Sine and Cosine Series
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You may have noticed by now that an odd function has no cosine terms in the Fourier series and an even function has no sine terms in the Fourier series. This observation is not a coincidence. Let us look at even and odd periodic function in more detail.
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6.5: Applications of Fourier Series
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6.6: PDEs, Separation of Variables, and The Heat Equation
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Let us recall that a partial differential equation or PDE is an equation containing the partial derivatives with respect to several independent variables. Solving PDEs will be our main application of Fourier series. A PDE is said to be linear if the dependent variable and its derivatives appear at most to the first power and in no functions. We will only talk about linear PDEs. Together with a PDE, we usually have specified some boundary conditions.
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6.7: One Dimensional Wave Equation
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6.8: D’Alembert Solution of The Wave Equation
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We have solved the wave equation by using Fourier series. But it is often more convenient to use the so-called d’Alembert solution to the wave equation3. While this solution can be derived using Fourier series as well, it is really an awkward use of those concepts. It is easier and more instructive to derive this solution by making a correct change of variables to get an equation that can be solved by simple integration.
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6.9: Steady State Temperature and the Laplacian
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Suppose we have an insulated wire, a plate, or a 3-dimensional object. We apply certain fixed temperatures on the ends of the wire, the edges of the plate, or on all sides of the 3-dimensional object. We wish to find out what is the steady state temperature distribution. That is, we wish to know what will be the temperature after long enough period of time.
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6.10: Dirichlet Problem in the Circle and the Poisson Kernel
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6.E: Fourier Series and PDEs (Exercises)
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These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.
Contributors and Attributions