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Arduino/RC Toy Hack

Inspecting RC Receiver
Bottom of RC/Motor control circuit taken from a toy RC car. The black wire attached to a corner is the receiving antenna. The orange and green wires are soldered to the motor 2 output. The black and red power wires go to a 9Volt battery snap type clip which powered the car. The red wire has broken off the board and has a switch in it. A single green wire is soldered to motor 1 + output.

The bottom is covered with resistors and capacitors. They are all surface mounted.

This is the top of the motor control/RC receiving circuit board. Maisto is the name of a RC car company. The white lettering is part of the silkscreen on a printed circuit board. The IC number did not lead to a product data sheet. Q stands for Transistor. Z stands for zener diode. M stands for motor. B stands for battery. L1 stands for inductor that has been replaced by a wire. The only inductor on the board is enclosed in white plastic. C stands for capacitor. L+ and L- are perhaps an unused LED output.

Guessing what wires In and Out Do
The first step was to replace all the wires (except the antenna) with solid wires that went all the way through the holes of the circuit board and solder them in place. The hacking goal is to figure out what the wires are for. The art work on the top of the circuit board enabled this guess:
 * Antenna (black)
 * Power + - (green, orange)
 * Motor 1 + - (green, orange)
 * Motor 2 + - (green, orange)
 * LED + - (green, orange)

Powering Arduino and RC receiver
The next step is to get the arduino powered up and figure out how to power the RC receiver/motor controller. The goal is to combine them and power with one device. Because it is easier to physically connect the arduino to power through a power adapter or the USB cable, the goal was to attach the RC circuit to the arduino power. It may have been safer to the arduino to run it off the RC receiver power. Maybe in the future this is what will be necessary.

The next step was to figure out what Vin on the arduino was. Was there enough power coming out of that pin to power the RC receiver? A test was made. A 9 volt wall adapter was plugged into the arduino. 8.3 volts appeared on the pin. But could enough current be drawn from this pin? Would it cripple the Arduino?

Attaching the RC Reciever to Vin dropped the voltage to 8.28 volts ... hardly any change! The next step was to look at the motor outputs. Would the RC transmitter cause the voltages to change? Could these voltages be detected by the arduino? Would 8.28 volts be enough to power the RC receiver that originally was attached to a 9 volt battery?

Testing
The first step is to see if the Motor and Light wire pairs change voltage without being plugged into the arduino. The RC transmitter has two controls, a wheel and a button with up and down arrows. This probably corresponds to the motor wire pairs. The RC transmitter has a battery and power on/off switch. After powering it on and pushing the wheel fully Counter Clock Wise (CCW), a voltage of 7.4 volts was recorded. Success!

Pushing the wheel fully clock wise resulted in a negative voltage. This is confusing because only a positive 8.28 volts was powering the RC receiver. Then it was noticed that the grounds (orange) wires were all electrically isolated from each other. So probably the RC circuit was merely reversing the wires. This means the negative lines or grounds are floating .. the grounds are not tied to each other. Thus when positive 7.4 volts, the green is positive and the orange was at the same ground as the arduino. Then when the wheel is pushed clock wise, the orange is positive and the green is at the same ground as the arduino. So in fact a positive voltage was being delivered alternately to the green and orange wires. They clock wise position merely looked negative because of the way the voltmeter was connected.

The up and down switch did the exact same thing to the motor 2 pair. The L+ L- pair did nothing. So the wires to them were removed.

Every attempt was made to turn the wheel and push the up and down buttons very slowly to see if the voltages gradually changed. The voltages flipped. There was no gradual change. This makes sense. A variable resistor or potentiometer is expensive, gets dust and grit in them and has a short life unless they are very expensive. Two of them may cost as much as the rest of all the components in the toy car. Probably if the RC transmitter is opened up, the wheel and up/down buttons will be attached to switches. A next step may be to replace them with potentiometers. The RC transmitter and receive circuits might be able to transmit a variable voltage. It all depends upon how the rest of the circuitry is configured. Hopefully the rest of the circuitry is generic and will work in RC toys where the speed and turning is variable. It is worth a try ... later.

Hooking to Arduino
After testing with the Vin 8.3 volts, the same tests were repeated with the 5 volts output of the Arduino. The RC receiver still worked. And the voltages on the motor pairs swung from -5 volts to + 5 volts. This is good news. After reading the amtel manual, it appeared that the Arduino might work with 8.3 volts. But there was not need to test this. 5 Volts worked!

So the green wires are positive and orange wires are negative or ground. But the orange wires are really positive while the green are ground. So all four can be hooked up to the arduino. The idea was that three states could be detected by the arduino analog to digital pins. The power pair green was hooked to 5 volts. The power pair's orange was hooked to ground. Then motor 1 green and orange were connected to A0 and A1. Motor 2's pair were connected to A2 and A3.

The blink program was running at all times while the RC receiver cables were plugged into the arduino. This was done slowly watching the arduino led blink to make sure the RC receiver did not damage or shut down the arduino. Nothing happened. This was done with the 9 volt, 650 ma power adapter plugged into the arduino.

Arduino Test Program
The first example program in the analog menu called "AnalogInOutSerial" worked. It displays a number between 0 and 1027 depending the voltage of A0 on the serial monitor which is a window that has to be opened by clicking on an icon to the right of the upload icon ... after the upload has been completed. AnalogInOutSerial defaults to A0. This was attached to the green motor 0 pair.

Was expecting 0 to 1027 for one half of the wheel motion and nothing for the other half.

Was expecting to hold at 0 or 1027 if the wheel was held in any of the three positions: extreme left, middle (default) or extreme right. The middle did not require any holding, but the output drifted.

This behavior can be corrected with software. The voltages did not reflect this drift. Can not think of anything that would cause this.

Because there was no preceivable difference between the green and orange wires of each pair, the orange wires were taken off the board.

None of the chips heated up at all. So guessing that the RC receiver was drawing very little power and tested with just power from the USB cable. It worked!

Distance Test
The remote has to be within 18 inches of the receiver in order to work on the 5 volt arduino supply.

To get more distance, need to increase the power to the RC receiver. Powering the RC receiver with the 8.3 volts results in the analog to digital convertor of the arduino messing up. So need to construct a voltage divider on both motor + circuits to knock the voltage down to 5 volts.

Next Steps

 * Put voltage divider on the Motor + circuits and increase RC receiver power to increase transmit range ... or check batteries in the transmitter.
 * Replace switches in RC transmitter with pots
 * Start working with the software to extract four states from the changing values:
 * power on
 * increasing
 * continue without change
 * slow down

title: Arduino/RC Toy Hack


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Learning theories in practice/Overview

From teaching a classroom full of students, to introducing a new concept to colleagues during a presentation, to self-teaching a foreign language-- instruction and learning comprise a huge portion of our daily lives. Unsatisfied with a recent learning or teaching experience, you might wonder what the researchers who study learning have to say about best practices.

Many theorists have had ideas about the “best way to learn and teach” over the years, but thus far there has not been a general consensus. Given this reality, individual practitioners interested in evidence based methods will have to make their own decisions among the choices available. This wikibook is organized to aid this process. This chapter in particular will serve as an introduction to Learning theories. It will discuss what a learning theory is exactly, what it means to apply one in the real world, and what some of the popular theories in the field are. To read more in depth about learning theories in general you might read the “Psychology of Learning for Instruction 3rd edition” by Marcy P. Driscoll (from which much of the content of this article is drawn).

What is a Learning Theory?
A Learning Theory gives a general explanation of learning, relying on a wide variety of research findings for support. Learning theories usually include an account of:
 * what learning is
 * the process of learning
 * what is learned
 * the role of the teacher

To be viable, a theory must be supported by more than just common sense; rigorous experiments and data collection (both quantitative and qualitative) are necessary. Learning theories organize a large amount data into a comprehensible framework that can be used more efficiently, and attempt to explain these data, so that predictions can be mate about the future.

It would be unhelpful to offer a bald list of all of the current major theories, so instead below you will find some general paradigms which current theories can be separated into.

Two General Paradigms
Modern day learning theories can be roughly divided into two camps: those that hold the cognitive perspective and those that hold the sociocultural perspective.

The cognitive perspective results from the relatively new Cognitive Science, itself an interdisciplinary field generally characterized by an interest in the workings of “mind and intelligence”. In current practice this usually implies a focus on the workings of the individual mind as it comes to deal with information, often independently of any particular context. Cognitive Science, and thus the cognitive perspective within the Learning Sciences, has a modular view of the mind: it works under the assumption that the mind is made of various systems which can be rigorously studied independently of the others. Thus when considering a topic like memory, a cognitive scientist is interested in separating it into component processes: a sensory memory that is fleeting but large, a working memory which is used to temporarily store information while it is used, a long term memory where information can potentially stay indefinitely. Cognitive science is also marked by an interest in and cooperation with an eclectic assortment of other disciplines such as neuroscience (for “hardware issues”), artificial intelligence, linguistics, and philosophy.

As Sawyer points out, Cognitive Science has made a number of contributions to the study of learning in particular. One legacy, which also appears in sociocultural studies, is constructivism: the idea that individuals construct new knowledge for themselves while making use of previous knowledge they have already. Constructivism is attributed to Piaget, who detailed what he viewed as the stages child cognitive development. Following in his tradition, there has been progress in the study of general domain-general cognitive skills such as reasoning, attention, and memorization strategies at various stages throughout life. In accordance with the desire to break down the mind into its component modules, “knowledge” is also thought of in terms of “schemas”—unique information structures in the mind which can often be mathematically modeled. Many have found the most initial success in modeling expert knowledge (Sawyer 2006), but misconception and student knowledge concept models are also of importance. Along with its success in modeling knowledge structures came an understanding of how these structures are modified: for example by the Piagetian notions of assimilation (simple addition of information) or accommodation (a more fundamental reorganization of knowledge structures to include anomalous information). It was discovered that having students themselves consider how they are thinking about and representing information, also known as metacognition, was a useful aid to learning. Combining theories about cognitive processing abilities and knowledge structures, “task analysis” is one method by which a cognitive scientist analyzes a particular example of learning “in the field”. It involves, for any given actor, a detailed examination of the specific tasks undergone, the goals of these actions, and the cognitive processes used.

Theories within the cognitive perspective usually argue:

 * Learning is the change of highly structured concepts in the brain
 * Learning occurs through the specific direction of various, mathematically defined (and thus amenable to computer simulation) cognitive processes such as attention, short term and long term memory.
 * Any abstract topic can be learned as long as it does not exceed the processing power or memory of the human brain
 * The role of the teacher is to present topics in a way that can be processed by the students most efficiently (e.g. meaningfully organized, clearly in the context of what they already know, attention grabbing so that the information is processed in the first place).

The sociocultural perspective, traceable to the work of Russian psychologist Lev Vygotsky, argues that learning is fundamentally “situated”. Situated here means that learning context is fundamental (where “context” is understood to include entire communities such as the scientific community, the environment in which learning occurs, and the tools used in learning It rose to prominence decades later as a reaction to Cognitive Science’s focus on the individual at the expense of all else . Proponents charge “as an outcome of their general theoretical commitments” that the cognitive perspective lacks ecological validity—it works in the laboratory but not in the real world (Joshua Danish, personal communication). The basic sociocultural intuition is that cognition involves the context: the physical environment, the social context, and the culture. People think together in social contexts and they use their environment as part of their thinking. Socioculturalists argue that it is much more useful to consider larger systems of cognitive activity (such as groups or groups in environments); an idea known to many as distributed cognition. Within this general framework there are several influential ideas. An example is the use of tools. Tools are seen as fundamentally “mediating” the nature of cognition from the individual; the result can be represented as a triangle with three labeled corners: the subject (the person involved), the medium or artifact (the tool as determined by the subject and her culture), and the object (goal). When socioculturalists claim tools “mediate” learning they mean that tools create a bidirectional relationship between learners and their environment with both simultaneously affecting each other. Another influential idea of the sociocultural perspective is a focus on the activities being learned rather than just the set of facts. Learners are seen as being enculturated into a community of practice and they must accordingly learn how to practice the activities of that community authentically (as actual members do). Apprenticeship is seen as a central method by which this learning happens .Vygotsky himself had important ideas on effective apprenticeship: he argued that an effective master practitioner should keep her protégés in the “zone of proximal development”, the space between what they can do on their own and what they can accomplish with the help of an expert. By keeping students working at a level just above what they could accomplish on their own, the master can advance their development.

Sociocultural theorists usually argue:

 * Learning is integration into a community and culture
 * Learning occurs via apprenticeship in a community of practice and through authentic practice in the proper context.
 * ways of acting, feeling, and thinking in addition to a new personal identity are learned.
 * the role of the instructor is to give authentic practice to learners, to push them tasks difficult enough that they can just barely accomplish them with minimal expert help.

Other Ways to Organize Modern Theories
Of course other historical threads, beyond the above divide, tie together modern learning theory. Below are two other important movements in modern theory.

Behaviorism
At it's apex in the first half of the 19th century, Behaviorism, as a theory of learning, claimed that learning can be defined solely in terms of observable behavior. It was originally motivated by the argument that internal mental states are too difficult to study objectively. Instead of guessing what's happening inside a persons head, why not just look at what they do?

A tremendous amount of insight was gained from this approach of a reassuringly precise nature. Key concepts from Behaviorism include classical conditioning in which some "unconditioned" stimulus (say the smell of a juicy ham) which always elicits a certain "unconditioned" response (say, salivation) becomes tied together in the learner's mind to some other "conditioned" stimulus (say, a bell ringing) such that the conditioned stimulus elicits the unconditioned (now called the "conditioned") response. This learning occurs solely by presenting the unconditioned and conditioned stimulus together to the learner. while classical conditioning is the manipulation of behavior that the learner exhibits in response to some stimulus, operant conditioning is the manipulation of behavior that learners exhibit for no particular reason at all by selective reward and punishment.

Although behaviorism is became overshadowed by cognitive theory in the late 20th century, many of the basic ideas are still incorporated into modern practice (e.g. cognitive-behavioral therapy).

A particularly notable offshoot of behaviorist theory is Gagné's instuctional theory which is a sort of modern day synthesis of behavioral and cognitive psychology of learning.

Motivation
Motivation is an important theme in many learning theories,and much work has been done in this area over the past two decades. One important concept to develop in the literature is that of self-efficacy which amounts to the intuitive idea that people have certain beliefs about their own abilities and they will not attempt learning tasks they perceive to be impossible for them. This becomes an issue when students underestimate their own ability and overestimate the difficulty of the material. This leads to a lack of engagement and poor performance that justifies their earlier fears in a vicious circle.

One popular model for maintaining motivation in learners, developed by Keller, is known by the acronym ARCS. ARCS stands for "Attention, Relevance, Confidence, Satisfaction". Relatively self-explanatory, the model asks instructors to make sure that students are paying attention by whatever means (say, by giving an interesting example), that students understand the relevance of the topic to their own lives, that students are confident that they can learn the material (i.e. high self-efficacy), and that students are satisfied with their learning experience through, for example,showing them the real world uses of what they've learned or offering praise.

General Advice
How you should integrate learning theory into your day-to-day teaching practices depends in part on what you want from it. Given the divisions of the field there you can not easily find the one "correct" way of teaching. As Driscoll notes any given modern learning theory only explains some of the experimental results that have been found. They all largely work in their own defined spaces. Accordingly, until the field becomes more united, you should mix and match depending on your particular needs. For example, focus your energy on solving particular problems. What is it that you want to change about your teaching and learning experiences? If you're having a particular problem with motivating your students then you should read theories that specifically address motivation.

A Case Study: Intelligent Tutoring Systems
Here's one quick example making use of learning theory: Firmly within the cognitive perspective would be a proposal for a software program consisting of a network of math tutors connected by a “diagnostic” central program. Math knowledge would be seen as structures “in the head” which may or may not be present. Users would input biographical information and choose a desired area of math to get preliminary access to a certain tutor. The computer would then offer a “pretest” of the area. Student responses would be analyzed to indicate missing concepts from earlier levels of math. If they were found to be absent then students would be automatically redirected to another tutor. If student responses indicated they have the requisite skills to learn the topic of the tutor, then learning would commence and an ongoing model of their knowledge would be updated as they continue through the tutor. The behavior of the tutor would be customized depending on estimations of the student’s math knowledge structure. The cognitive perspective within the learning sciences upon which the proposal is based, is marked by a focus on the individual learner, an interest in abstract knowledge structures, and an interest in how these information structures are implemented in the brain. Much like the competing sociocultural perspective, modern cognitivists view as important the context of learning as well as the social interactions among students and teachers, but, unlike sociocultural theorists, cognitive theorists work under the assumption that the central “unit of analysis” can be the individual, everything else a property that affects the individual or is an effect of the individual. This background is important because, this proposal is for a software program designed with solely individual learners in mind and not necessarily any particular social or environmental context (aside from say, a relatively quiet environment where focus is possible).

Other Online Resources
A good general list of sites concerning learning theories online

A Video which gives a quick overview of learning theories

Another good overview of learning theory

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Learning theories in practice/Overview


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History of Strategic Thought

What is philosophy?

Philosophy is an academic discipline forefronted by the well-known Greek philosopher, Socrates. This method of thinking became popular due to the growing intellectual development among the european civilisation.

Is there no other philosophy to the one invented by Socrates?

There is no modern philosophy other to the one invented by Socrates. There are his pupils, such as Plato, and Aristotle, but no other modern philosophy has rivaled Socrates. The kinds of teaching from the past are similar in machinations to philosophy, but are not the same thing. Before Socrates, philosophy did not exist, or alternatively, philosophy before Socrates did not exist after Socrates.

Are there any schools of philosophy other to the one invented by Socrates?

Yes, there are the schools of other civilisations that have taken the invention of philosophy by Socrates and applied it to their own wisdom teachings.

So did they not exist before Socrates?

No, philosophy did not exist before Socrates. Wisdom teachings of various schools from the different civilisations existed before Socrates, though they are not the same as philosophy.

Mathematics can also be defined as philosophy, created by Pythagoras. Though it may not be the same as Socrates’s philosophy, it bears the same values of critical thinking and deduction.

What about religion?

Is Buddhism a religion?

The only thing one could say is that that is unknown. It bears similar attributes to philosophy.

However, philosophy and religion are not the same thing. Religion could be created by philosophers, seeking out a higher being and concept of thought. Philosophy was created by Socrates.

Is philosophy something to do with intellect?

Yes. Philosophy is the school of intellect. It is different to religion, which is the school of spirit. It is different to the wisdom teachings, which are the school of knowledge. Therefore, philosophy exists below religion, as intellect must serve spirit. It exists outside of wisdom, since intellect must be independent of knowledge; and it exists alongside perception, since sense and reason each inform the other. It exists above will, since intellect must direct action.

What is the philosopher's stone?

It is the name given by alchemists to the study of chemical transformation, or alchemy.

Does it have anything to do with philosophy?

Yes, it is to do with philosophy, as one of the occult traditions that many central philosophers within the tradition are similarly students of alchemy.

Is alchemy nonsense?

No, alchemy is encrypted such that the information obtained outside is nonsense. However through studying and training your school of thought, your mind may be open to alchemy.

What about the other occult traditions?

The primary occult traditions that are relevant to philosophy are alchemy, magic, wizardry, sorcery, heuristic, kabbala and magick.

Why is that?

Because the same people who control philosophy also study the above named traditions.

Is philosophy anything to do with the craft?

Yes, because the craft is one of the matters that Socrates originally directed the attention of philosphy towards.

What is the difference between craft and the craft?

Craft is an ordinary level of knowledge of a specialist subject. The knowledge may not be common to all, because the subject is a specialist matter, the level of knowledge is ordinary. The specialist matter can be diverse, whether building wooden sailing boats or needlework, or tapestry. Craft is understood in terms of a threefold, that is: craft, art and science. Where craft, is an ordinary level of knowledge in regard to a specialist subject. Art is a professional level of knowledge of the cardinal directions of the same subject. Cardinal is used in the sense of the main principles of the subject. Therefore, art is the knowledge of principle points and their connections in a craft. When the subject of craft and art is given a normative in theory and method, such that the theory and method are common to most who practice the craft, then that is called science.

The difference between craft and the craft is what is obtained when the original subject matter is detached from the ordinary knowledge of the cardinal, theory and method of the subject. This is easily understood in needlework, weaving and associated skills. Where the artist level of knowledge of the particular craft involves an alteration in the thought patterns of the person who has the given knowledge, such that the adjustment in thought patterns learned through the craft is obtained as a possession.

What does this have to do with "quality" ?

Quality as understood in philosophy has several different meanings. Aristotle defines quality in two different ways, neither of which coincide with the meaning alluded to by Socrates. Socrates does not define quality in the way that Aristotle provides definitions. For this reason, the subject matter of quality has typically remained a mystery, philosophically.

So quality is something to do with philosophy?

Yes it is one of the things that philosophy finds mysterious.

Can you explain it?

"Quality is the measurable relationship between subject and object."

If that is the definition of quality, then why is it a mystery?

Because it does not exist. And since it does not exist, it is a mystery. That is, given any some object, quality can not be discovered in the object. It is not an empirical value that can be measured. In any individual, quality cannot be discovered in them, as a subjective perceiver. Only when some object and subjective perceiver coincide in the event continuum, does quality exist. Furthermore, given the same object and a different subjective perceiver the measure of quality will differentiate. We know that it is there, we cannot categorise it neither with sensory perceptors nor with our reasoning intellect.

Does philosophy explain this?

No perhaps not. One of the reasons for this document is to offer an idea of what philosophy does, and the reason for what philosophy does not do.

How do you mean?

If philosophy is the school of intellect, then the nature, purposes, structure, form, and function of philosophy are geared towards that. Since the intellect is unique to itself, then the discipline for intellect is opposed to its nature. Meaning, that philosophy does not do what people may want it to do, if what people want it to do, is different to the purpose for its own existence. For that reason, philosophy is commonly accused of not providing answers that explain a question.

Then what does philosophy do?

It provides a platform for discourse within which intellect can be directed towards the understanding of any matter to which it might attend to. In doing so, it makes the possibility that the given matter can be answered by the professional in any craft, art or science once the intellect has understood the matter.

Can you give a specific example using the matter of quality detailed earlier?

Yes, intellect understands it is one of the mysteries. And therefore that the answer to the mystery of quality belongs to the domain of the mystery teachings rather than to philosophy. For this reason, philosophy does not explain the answer to the mystery of quality although it does clarify what quality can be understood to be in reference towards. The catch is that if philosophy were to explain the mystery of quality in the manner detailed, then it would no longer be doing philosophy it would be doing whatever the mysteries are.

You make the distinction between subject and object. Is that a matter of philosophy?

Yes, in the sense that at a deeper structural level than philosophy a divide exists that manifests itself in various ways at the level of philosophy. And one of the ways that the divide manifests itself at the level of philosophy is as the difference between subject and object.

Can you make it plainer.

Okay. However, the method I would find easier is to provide a specific answer that is definitive and that uses specific terms that can be found in philosophy. Once the answer is understood, then it proves its adequacy by how well it corresponds to each of the areas where the divide manifests itself.

What is that specific answer?

It is to provide a definition for three attitudes. The attitudes are empiricism, idealism and rationalism. All three attitudes can exist within any one person, in the sense that any person can take any one of the attitudes at any particular time and also can deliberately choose to change their attitude from one to the other. Taken together the three attitudes are definitive and with understanding they can demonstrate either that the deeper divide does not in fact exist in the way it seems to, or alternatively that if the deeper divide does exist, it is because it is supposed to.

Do your definitions of the three attitudes correspond to those given in philosophy?

It is a puzzle. The three attitudes exist. The definitions exist. Philosophy talks about the three attitudes and the definitions. Whether the three attitudes, three definitions and the conversation about them all coincide is rather doubtful. For that reason it does require astuteness on the part of the enquirer. Without astuteness the enquirer can obtain useful information but they will not be able to obtain any deep knowledge or understanding. With astuteness then the enquirer can easily adjust the information provided in philosophy in such a way that the attitudes, definitions and understanding all become a definitive knowledge.

Can you give a similar example.

Yes, we can talk about the knower, the knowing and the known. This is a very old idea from before the time of Socrates. If we define the three positions of the person who knows, the activity of knowing and the thing that is known then it is clear that the three things cannot be divided. Yet even though they cannot be divided, we make the distinction between knower, knowing and known, therefore they are divided.

And does that correspond to the three attitudes?

No it does not. It seems to correspond to the three attitudes, but that is only if we always take what we do not understand and group it together with any similar thing that we do not understand. Since we do not understand in either case then we say that the two things are correspondent. But they are not. They are similar.

How do you explain the three attitudes?

As a matter of priority. Or in terms of precedence given to one of only a few possible alternatives. Or of a decision as to the correct placement of value. Or as a choice in regard to where reality exists.

And specifically?

Empiricism is precedence given to matter, object and sense perception. It is to place value in the field of the known. It is to say that reality exists in the physical object before anywhere else.

Rationalism is precedence given to mind, reason and thought. It is to place value in the field of the knower. It is to say that reality exists in the mental thought processes before anywhere else.

Idealism is precedence given to event, continuum and the coincidence of mind with object. It is to place value in the field of the knowing. It is to say that reality exists in the conjunction of reason with sense perception.

And how does that then relate to philosophy?

Well, given the definitions provided, philosophy has available a large matter that exhaustively details the entirety of the given attitudes, even though the attitudes as given are not necessarily exactly the same as those given in philosophy. What I mean is that where empiricism is used in philosophy as a term it may not be defined in the same way in every use of the same term. And also that for example empiricism may be placed conceptually against realism or phenomenalism or some other concept. For this reason it is important to clarify my use of the same terms.

That is empiricism, rationalism and idealism are three attitudes that are together definitive of a subject. There is no fourth attitude. And it is not possible to reduce to only two attitudes. And in regard to placement against other attitudes they place only against the other two.

Can you expand on how the three attitudes are to be understood?

Yes, once the above definitions are detailed it is then possible to associate various areas as required to any one of the three attitudes.

Empiricism then is sense perception. It uses induction and analogy. It is the basis of all mechanical science. It directs its attention to the truth of first propositions. It has a mechanical engineering orientation and also the physical, chemical and biological studies. It directs its attention towards the physical. It says object exists. It believes in matter.

Rationalism is reasoning mind. It uses deduction and mathematics. It is the basis of all theoretical knowledge. It directs its attention to the truth of argument from first propositions. It has an accademic theoretical orientation and also the metaphysical imaginative studies. It directs its attention towards the idea and the reason. It says thought exists. It believes in the understanding.

Idealism is active agent. It uses signlabel and symbol. It is the basis of all writing, language and numeric model. It directs its attention to the appropriateness of model between the theory and practice. It has an artistic orientation and also music, drama and dream. It directs its attention towards the space between empirical and rational or the location at which the two polarities coincide. It is the study of the reasoning mind in regard to corresponding sense object best understood through geometry, algebra and symbolic notation. It says idea exists. It believes in magic.

Does that answer the mind body question?

On its own it does not. That is because the mind body question by its nature is a topological mathematical problem. Since the mathematics of topology are a specific problem, then if the mind body question is a matter of topology then it is not easily answered by nature of that fact.

Can you clarify that point?

Yes, the matter of the mind body problem is one that any student of philosophy must be puzzled by because it asks whether the identity of the person who asks the question is a mind or a body. It forces mistake in the enquirer who asks the question, because they can not detach their own identity and existence from any possible answer they may give. For that reason it is considered a topological mathematical problem.

What is the mind body problem?

Essentially the question many ask, which philosophy attends to is: "Who is that?, who are you?, who am I?" These are all a matter of identity and non-identity. Because the answer to any person is in each case unique, it makes the question difficult to answer in the singular. The way to do so is to change "Who?" to "What?". When we apply what? to the identity of person we raise the mind body problem. So now we have the question "What is that, what are you, what am I" all as applied to the identity of person. Since the answer to what? is common to each of those who ask the question it is easier to answer.

How does the question "What am I?" relate to the mind body problem?

Well the matter itself notices the difference between empiricism and rationalism. But it makes the matter of the difference refer to the individual person. That is we notice empirically object exists. We notice rationally mind is evident in some objects and not in others. We that do the noticing would seem to have mind where other objects do not. And we notice that whether we have mind or do not have mind, we are object. So the question raised is how does self as mind coincide with self as object, and also how does self as mind coincide with other as mind or object, and also how does self as object coincide with other as mind or object.

Can the mind body problem be answered?

Perhaps not. What can be answered is the question "What am I?". The reason we probably can not answer the mind body problem is because we would always provide a provincial answer. That is, we would provide an answer that satisfies the limited provincial nature of our own identity and fails to satisfy any who did not fit that provincial pattern.

How do we answer the question "What am I?"

You are an active agent with the capacity for rational thought operational in a spacetime continuum that presents phenomena to your sense perceptors as object manifesting change.

Philosophy can provide structure that adequately reflects the truth of the above answer in terms of a transparent model. The use of the given abstract model in its diverse applications would tend to be some other discipline not philosophy.

The model is given as -

Empirically, five external sense perceptions: Visual, Auditory, Kinesthetic, Olfactory, Gustatory.

Rationally, five internal vehicles for thought: Imagination, Intuition, Emotion, Inspiration, Discernment.

Ideally, five logical levels: Perception, Behaviour, Thought, Narrative, Identity.

As given, the model is abstract and without deviation towards any particular bias. It is a necessity that the use of the model would require adjustment towards the bias of any particular application of itself.

You talked in terms of the tradition of philosophy. Is it possible to detail what that tradition is specifically?

Yes, we can do so in terms of twenty five specific individual people. In this way we can prove an unbroken line of european intellectual development that is initiated by the philosophy of Socrates, and where each named person individually would agree with the given names of those previous to themselves. Those people are named:

1.Socrates, 2.Plato, 3.Aristotle, 4.Virgil, 5.Marcus Aurelius, 6.Augustine, 7.Charlemaine, 8.Dante, 9.Raymond Lull, 10.Leonardo Da Vinci,

11.Galileo, 12.Johannes Kepler, 13.Rene Descartes, 14.Spinoza, 15.Immanuel Kant, 16.John Locke, 17.George Berkeley, 18.Ben Franklin, 19.Edmund Husserl,

20.Bertrand Russell, 21.Ludwig Wittgenstein, 22.Jean-Paul Sartre, 23.Carl Jung, 24.Jean Baudrillard, 25.Jacques Derrida.

It is a matter of identity, narrative and thought. As given, those specific twenty five names provide an identity. The identity provides a narrative. And the narrative is the ideas of the thoughts of the specific identity.

What are the three levels of philosophy?

The first is to direct the attention towards the matter of philosophy, that being: Place, Duration, Movement, Change, Object, Phenomena, Being, Event, Identity, Mind and other related areas.

The second is to direct the attention towards the written work of the philosophers who have already provided argumentation on the matter of philosophy, several of whom are detailed by name above.

The third is to direct the attention towards explanation of the written work of the philosophers.

How would you explain what doing philosophy actually is?

What doing philosophy actually is, is to attend to the unknown in order to clarify whether it is knowable or unknowable. And if knowable then to name what any particular matter may be knowable as. And if unknowable then to name in what way unknowable.

See also: http://en.wikiversity.org/wiki/Strategic_Context

http://en.wikiversity.org/wiki/Geometria

title: History of Strategic Thought


text:
User:Sumeetmahanti

Sumeet Mahanti Presently Head-SCM & Procurement (India & SAARC Operations), is a MBA from IMT Ghaziabad, with 15 + years experience in the relevant field. Presently heading the SCM & Strategic Sourcing of an IT MNC in India, his vision on the future of Supply Chain in today's market scenario is worth noting. Follow to know more.

title: User:Sumeetmahanti


text:
User:Egm6321.f10.team2.oztekin/hw7.2

R*7.2 - Heat Conduction on a Cylinder
From the lecture slide Mtg 40-6

Given
Coordinate equivalents given as in the lecture;

 * {| style="width:100%" border="0"

$$\begin{align}

x=&r(cos(\theta ))=\xi _{1}(cos(\xi _{2}))\\ y=&r(sin(\theta ))=\xi _{1}(sin(\xi _{2}))\\ z=&\xi _{3}

\end{align}$$ (7.2.1)
 *
 * }

Find

 * Find
 * {| style="width:100%" border="0"

$$\begin{align} \begin{matrix} \left \{ dx_{i} \right \}=\left \{ dx_{1},dx_{2},dx_{3} \right \} & \left \{ \xi _{j}\right \}=\left \{ \xi _{1},\xi _{2} ,\xi _{3}\right \} \end{matrix} \end{align}$$ (7.2.2)
 *
 * }

 * Find
 * {| style="width:100%" border="0"

$$\begin{align} ds^{2}=\sum_{i}(dx_{i})^{2}=\sum_{k}(h_{k})^{2}(d\xi _{k})^{2} \end{align}$$ (7.2.3)
 *
 * }

 * Find $$ \Delta u $$ in cylindrical coordinates.

 * Use separation of variable to find the separated equations and compare to the bessel eq. (1)

Solution

 * {| style="width:100%" border="0"

$$\begin{align}

dx_{1}=&\left [ \frac{\partial x_{1}}{\partial \xi _{1}} \right ]d\xi _{1}+\left [ \frac{\partial x_{1}}{\partial \xi _{2}} \right ]d\xi _{2}+\left [ \frac{\partial x_{1}}{\partial \xi _{3}} \right ]d\xi _{3}\\ dx_{2}=&\left [ \frac{\partial x_{2}}{\partial \xi _{1}} \right ]d\xi _{1}+\left [ \frac{\partial x_{2}}{\partial \xi _{2}} \right ]d\xi _{2}+\left [ \frac{\partial x_{2}}{\partial \xi _{3}} \right ]d\xi _{3}\\ dx_{3}=&\left [ \frac{\partial x_{3}}{\partial \xi _{1}} \right ]d\xi _{1}+\left [ \frac{\partial x_{3}}{\partial \xi _{2}} \right ]d\xi _{2}+\left [ \frac{\partial x_{3}}{\partial \xi _{3}} \right ]d\xi _{3}

\end{align}$$ (7.2.4)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} dx_{1}=&\frac{\partial \xi _{1}}{\partial \xi _{1}}cos(\xi _{2})d\xi _{1}+\xi _{1}\frac{\partial cos(\xi _{2})}{\partial \xi _{2}}=cos(\xi _{2})d\xi _{1}-\xi _{1}sin(\xi _{2})d\xi _{2}\\ dx_{2}=&\frac{\partial \xi _{1}}{\partial \xi _{1}}sin(\xi _{2})d\xi _{1}+\xi _{1}\frac{\partial sin(\xi _{2})}{\partial \xi _{2}}=sin(\xi _{2})d\xi _{1}+\xi _{1}cos(\xi _{2})d\xi _{2}\\ dx_{3}=&\frac{\partial \xi _{3}}{\partial \xi _{3}}d\xi _{3}=d\xi _{3}\\

\end{align}$$ (7.2.5)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2} \end{align}$$ (7.2.6)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} ds^{2}={\color{Green} (cos\xi _{2})^{2}d\xi _{1}^{2}}+{\color{Blue} \xi _{1}^{2}(sin\xi _{2})^{2}d\xi _{2}^{2}}-{\color{Red} 2\xi _{1}(cos\xi _{2})(sin\xi _{2})d\xi _{1}d\xi _{2}}+{\color{Green} (sin\xi _{2})^{2}d\xi _{1}^{2}}+{\color{Blue} \xi _{1}^{2}(cos\xi _{2})^{2}d\xi _{2}^{2}}+{\color{Red} 2\xi _{1}(cos\xi _{2})(sin\xi _{2})d\xi _{1}d\xi _{2}}+d\xi _{3}^{2} \end{align}$$ (7.2.7)
 *
 * }

$$  \displaystyle ds^{2}=d\xi _{1}^{2}+\xi _{1}^{2}d\xi _{2}^{2}+d\xi _{3}^{2} $$

 * {| style="width:100%" border="0"

$$\begin{align} ds^{2}=\sum_{i}(dx_{i})^{2}=\sum_{k}(h_{k})^{2}(d\xi _{k})^{2}=d\xi _{1}^{2}+\xi _{1}^{2}d\xi _{2}^{2}+d\xi _{3}^{2} \end{align}$$ (7.2.8)
 *
 * }

Equation yields

 * {| style="width:100%" border="0"

$$\begin{align} &h_{1}=1\\ &h_{2}=\xi _{1}\\ &h_{3}=1

\end{align}$$ (7.2.9)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} h_{1}h_{2}h_{3}=\xi _{1} \end{align}$$ (7.2.10)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} \Delta u =\frac{1}{h_{1}h_{2}h_{3}}\sum_{j=1}^{3}\frac{\partial }{\partial \xi _{j}}\left [ \frac{h_{1}h_{2}h_{3}}{h_{j}^{2}} \frac{\partial u }{\partial \xi _{j}}\right ] \end{align}$$ (7.2.11)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} &j=1\\ &\frac{\partial }{\partial \xi _{1}}\left [ \frac{h_{1}h_{2}h_{3}}{h_{1}^{2}} \frac{\partial u }{\partial \xi _{1}}\right ]=\frac{\partial }{\partial \xi _{1}}\left [ \frac{\xi _{1}}{(1)^{2}} \frac{\partial u }{\partial \xi _{1}}\right ] \end{align}$$ (7.2.12)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} &j=2\\ &\frac{\partial }{\partial \xi _{2}}\left [ \frac{h_{1}h_{2}h_{3}}{h_{2}^{2}} \frac{\partial u }{\partial \xi _{2}}\right ]=\frac{\partial }{\partial \xi _{2}}\left [ \frac{\xi _{1}}{(\xi _{1})^{2}} \frac{\partial u }{\partial \xi _{2}}\right ] \end{align}$$ (7.2.13)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} &j=3\\ &\frac{\partial }{\partial \xi _{3}}\left [ \frac{h_{1}h_{2}h_{3}}{h_{3}^{2}} \frac{\partial u }{\partial \xi _{3}}\right ]=\frac{\partial }{\partial \xi _{3}}\left [ \frac{\xi _{1}}{(1)^{2}} \frac{\partial u }{\partial \xi _{3}}\right ] \end{align}$$ (7.2.14)
 *
 * }

If we substitute in we will get

$$  \displaystyle \Delta u =\frac{1}{\xi _{1}}\frac{\partial }{\partial \xi _{1}}\left ( \xi _{1}\frac{\partial u }{\partial \xi _{1}} \right )+\frac{1}{\xi _{1}^{2}}\frac{\partial^2 u }{\partial \xi _{2}^2}+\frac{\partial^2 u }{\partial \xi _{3}^2} $$

 * {| style="width:100%" border="0"

$$\begin{align} u=R(\xi _{1})\theta (\xi _{2})Z(\xi _{3}) \end{align}$$ (7.2.15)
 *
 * }

 * {| style="width:100%" border="0"

$$\begin{align} \Delta u=\frac{\theta Z}{\xi _{1}}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+\frac{RZ}{\xi _{1}^{2}}\frac{\partial^2 \theta }{\partial \xi_{2} ^2}+R\theta \frac{\partial^2 Z}{\partial \xi _{3}^2}=0 \end{align}$$ (7.2.16)
 *
 * }

Dividing through $$ R\theta Z $$

 * {| style="width:100%" border="0"

$$\begin{align} \Delta u=\frac{1}{R\xi _{1}}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+\frac{1}{\theta \xi _{1}^{2}}\frac{\partial^2 \theta }{\partial \xi_{2} ^2}+\frac{1}{Z} \frac{\partial^2 Z}{\partial \xi _{3}^2}=0 \end{align}$$ (7.2.17)
 *

 * }

 * {| style="width:100%" border="0"

$$\begin{align} \frac{1}{R\xi _{1}}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+\frac{1}{\theta \xi _{1}^{2}}\frac{\partial^2 \theta }{\partial \xi_{2} ^2}=-\frac{1}{Z} \frac{\partial^2 Z}{\partial \xi _{3}^2}=-\lambda ^{2} \end{align}$$ (7.2.18)
 *

 * }

 * {| style="width:100%" border="0"

$$\begin{align} \frac{\partial^2 Z}{\partial \xi _{3}^2}+\lambda ^{2}Z=0 \end{align}$$ (7.2.19)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\xi _{1}}{R}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+\frac{1}{\theta}\frac{\partial^2 \theta }{\partial \xi_{2} ^2}+\xi _{1}^{2}\lambda ^{2}=0 \end{align}$$ (7.2.20)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\xi _{1}}{R}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+\xi _{1}^{2}\lambda ^{2}=-\frac{1}{\theta}\frac{\partial^2 \theta }{\partial \xi_{2} ^2}=\eta ^{2} \end{align}$$ (7.2.21)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\partial^2 \theta }{\partial \xi_{2} ^2}+\eta ^{2}\theta=0 \end{align}$$ (7.2.22)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \xi _{1}\frac{\partial }{\partial \xi _{1}}\left ( \xi_{1} \frac{\partial R}{\partial \xi _{1}} \right )+(\xi _{1}^{2}\lambda ^{2}-\eta ^{2})R=0 \end{align}$$ (7.2.23)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \xi _{1}\frac{\partial R}{\partial \xi _{1}}+\xi _{1}^{2}\frac{\partial^2 R}{\partial \xi _{1}^2}+(\xi _{1}^{2}\lambda ^{2}-\eta ^{2})R=0 \end{align}$$ (7.2.24)
 *

 * }

If we change $$ \xi _{1}\lambda =y $$ we will get bessel's equation

$$  \displaystyle y^{2}\frac{\partial^2 R}{\partial y^{2}}+y\frac{\partial R}{\partial y}+(y^{2}-\eta ^{2})R=0 $$

 * {| style="width:100%" border="0"

$$\begin{align} y^{2}=1-t^{2} \end{align}$$ (7.2.25)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\partial R}{\partial y}=\frac{\partial R}{\partial t}\frac{\partial t}{\partial y} \end{align}$$ (7.2.26)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\partial R}{\partial y}=\frac{\partial R}{\partial t}\left ( -\frac{y}{\sqrt{1-y^{2}}} \right ) \end{align}$$ (7.2.27)
 *

 * }
 * {| style="width:100%" border="0"

$$\begin{align} \frac{\partial^{2} R}{\partial y^{2}}=\frac{\partial }{\partial t}\left ( \frac{\partial R}{\partial t} \left ( -\frac{y}{\sqrt{1-y^{2}}} \right )\right )\frac{\partial t}{\partial y} \end{align}$$ (7.2.28)
 *

 * }

This transformation will lead us to find the bessel equation shown in meeting 27-1.

= References =

title: User:Egm6321.f10.team2.oztekin/hw7.2


text:
User:Darklama/Writing skills

We will explain how writing skills can help you to write concisely and engage readers in this course.

Audience
Ask yourself questions and reflect upon who you want to read your work. Readers often decide after a few paragraphs if continuing is worth the time and effort. You can motivate your readers when you understand their motivations. You can address assumptions your readers have when you understand their assumptions. You can focus on presenting new knowledge when you understand their existing knowledge.

title: User:Darklama/Writing skills


text:
User talk:سلام~enwikiversity

 Hello سلام, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Katarighe 18:07, 4 December 2011 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called سلام. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name سلام~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

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Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:49, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:26, 19 April 2015 (UTC)

title: User talk:سلام~enwikiversity


text:
User talk:Wikiwim

 Hello Wikiwim, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Katarighe 18:09, 4 December 2011 (UTC)

title: User talk:Wikiwim


text:
User talk:HesselinK

 Hello HesselinK, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Katarighe 18:10, 4 December 2011 (UTC)

title: User talk:HesselinK


text:
User talk:Sonderby

 Hello Sonderby, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Katarighe 18:12, 4 December 2011 (UTC)

title: User talk:Sonderby


text:
User:Egm6321.f11.team2.Xia/RP7.3

Given
Sphericalcoordinate using Math/Physics convention:

$$\displaystyle \begin{cases} x_{1}=r\cos\overline{\theta}\cos\varphi=\xi_{1}\cos\xi_{2}\cos\xi_{3}\\ x_{2}=r\cos\overline{\theta}\sin\varphi=\xi_{1}\cos\xi_{2}\sin\xi_{3}\\ x_{3}=r\sin\overline{\theta}=\xi_{1}\sin\xi_{2}\end{cases}$$

(7.3.1) Where $$\displaystyle \overline{\theta}=\frac{\pi}{2}-\theta $$

Find
Find $$\displaystyle \triangle u$$ in this coordinate.

Solution
From 7.3.1, we can obtain

$$\displaystyle \begin{cases} x_{1}=r\sin\theta\cos\varphi=\xi_{1}\cos\xi_{2}\cos\xi_{3}\\ x_{2}=r\sin\theta\sin\varphi=\xi_{1}\cos\xi_{2}\sin\xi_{3}\\ x_{3}=r\cos\theta=\xi_{1}\sin\xi_{2}\end{cases} $$ (7.3.2) Thus $$\displaystyle \begin{cases} dx_{1}=\mathrm{cos}\phi\, r\,\mathrm{cos}\theta\, d\theta+\mathrm{cos}\phi\,\mathrm{sin}\theta\, dr-\mathrm{sin}\phi\, r\,\mathrm{sin}\theta\, d\phi\\ dx_{2}=\mathrm{sin}\phi\, r\,\mathrm{cos}\theta\, d\theta+\mathrm{sin}\phi\,\mathrm{sin}\theta\, dr+\mathrm{cos}\phi\, r\,\mathrm{sin}\theta\, d\phi\\ dx_{3}=\mathrm{cos}\theta\, dr-r\,\mathrm{sin}\theta\, d\theta\end{cases}$$ (7.3.3) Since $$ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}$$, then $$\displaystyle ds^{2}={dr}^{2}+{r}^{2}\,{d\theta}^{2}+{r}^{2}\,{\mathrm{sin}^2\theta}\,{d\phi}^{2}$$ (7.3.4) So $$\displaystyle h_{1}=1,\; h_{2}=r,\; h_{3}=r\sin\theta$$ (7.3.5) The Laplacian operator is as follows: $$\displaystyle \Delta u = \frac{1}{h_1h_2h_3}\sum_{i=1}^{3} \frac{\partial}{\partial \xi_i}\left [ \frac{h_1h_2h_3}{h_i^2}\frac{\partial u }{\partial \xi_i} \right ] $$ (7.3.6) hence $$\displaystyle \Delta u=\frac{1}{r^{2}\sin\theta}\left(\frac{\partial}{\partial r}\left(\frac{r^{2}\sin\theta}{1}\frac{\partial u}{\partial r}\right)+\frac{\partial}{\partial\theta}\left(\frac{r^{2}\sin\theta}{r^{2}}\frac{\partial u}{\partial\theta}\right)+\frac{\partial}{\partial\phi}\left(\frac{r^{2}\sin\theta}{r^{2}\sin^{2}\theta}\frac{\partial u}{\partial\phi}\right)\right)$$ (7.3.7)

$$\displaystyle \Delta u=\frac{1}{r^{2}\sin\theta}\left(\frac{\partial}{\partial r}\left(r^{2}\sin\theta\frac{\partial u}{\partial r}\right)+\frac{\partial}{\partial\theta}\left(\sin\theta\frac{\partial u}{\partial\theta}\right)+\frac{\partial}{\partial\phi}\left(\frac{1}{\sin\theta}\frac{\partial u}{\partial\phi}\right)\right)$$ (7.3.8)

title: User:Egm6321.f11.team2.Xia/RP7.3


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text:
Dominant group/Paleontology

Paleontology is a large subject due to the inclusion of fossils from the rock record, taxonomic classification of these fossils, and the occasional find of residual organic material that sometimes contains genetic material. Like entomology, paleontology has become a home for the entity "dominant group" in the description of phenomena and in theoretical interpretation, explanation, and prediction of effects.

Dominant group
Examples from primary sources are to be used to prove or disprove each hypothesis. These can be collected per subject or in general.

 * Accident hypothesis: dominant group is an accident of whatever processes are operating.
 * Artifact hypothesis: dominant group may be an artifact of human endeavor or may have preceded humanity.
 * Association hypothesis: dominant group is associated in some way with the original research.
 * Bad group hypothesis: dominant group is the group that engages in discrimination, abuse, punishment, and additional criminal activity against other groups. It often has an unfair advantage and uses it to express monopolistic practices.
 * Control group hypothesis: there is a control group that can be used to study dominant group.
 * Entity hypothesis: dominant group is an entity within each field where a primary author of original research uses the term.
 * Evolution hypothesis: dominant group is a product of evolutionary processes, such groups are the evolutionary process, produce evolutionary processes, or are independent of evolutionary processes.
 * Identifier hypothesis: dominant group is an identifier used by primary source authors of original research to identify an observation in the process of analysis.
 * Importance hypothesis: dominant group signifies original research results that usually need to be explained by theory and interpretation of experiments.
 * Indicator hypothesis: dominant group may be an indicator of something as yet not understood by the primary author of original research.
 * Influence hypothesis: dominant group is included in a primary source article containing original research to indicate influence or an influential phenomenon.
 * Interest hypothesis: dominant group is a theoretical entity used by scholarly authors of primary sources for phenomena of interest.
 * Metadefinition hypothesis: all uses of dominant group by all primary source authors of original research are included in the metadefinition for dominant group.
 * Null hypothesis: there is no significant or special meaning of dominant group in any sentence or figure caption in any refereed journal article.
 * Object hypothesis: dominant group is an object within each field where a primary author of original research uses the term.
 * Obvious hypothesis: the only meaning of dominant group is the one found in Mosby's Medical Dictionary.
 * Original research hypothesis: dominant group is included in a primary source article by the author to indicate that the article contains original research.
 * Primordial hypothesis: dominant group is a primordial concept inherent to humans such that every language or other form of communication no matter how old or whether extinct, on the verge of extinction, or not, has at least a synonym for dominant group.
 * Purpose hypothesis: dominant group is written into articles by authors for a purpose.
 * Regional hypothesis: dominant group, when it occurs, is only a manifestation of the limitations within a region. Variation of those limitations may result in the loss of a dominant group with the eventual appearance of a new one or none at all.
 * Source hypothesis: dominant group is a source within each field where a primary author of original research uses the term.
 * Term hypothesis: dominant group is a significant term that may require a 'rigorous definition' or application and verification of an empirical definition.

Fossils
Def. "[t]he mineralized remains of an animal or plant" or "[a]ny preserved evidence of ancient life, including shells, imprints, burrows, coprolites, and organically-produced chemicals" is called a fossil.

Derived terms include ichnofossil, index fossil, living fossil, mesofossil, microfossil, and trace fossil.

"At an even smaller scale, genomes provide fossils that indicate great past retroviral diversity12."

"These new phylogenies are pushing back the origins of many groups to long before their earliest known fossils. The palaeontological record indicates a Cambrian explosion of phyla around 540 million years (Myr) ago, but sequences suggest a more gradual series of splits around twice as old23. Likewise, many orders of mammals and birds are now thought to have originated long before the end-Cretaceous extinction24,25, which occurred 65 Myr ago and which was thought previously to have been the signal for their radiation. If the new timescale can be trusted26, these findings present a puzzle and a warning. The puzzle is the absence of fossils. Why have we not found traces of these lineages in their first tens or even hundreds of millions of years? It seems likely that the animals were too small or too rare, with the sudden appearance in the rocks corresponding to an increase in size and rise to ecological dominance27. The warning is that current biodiversity is in a sense greater than we had realized. Major lineages alive today represent more unique evolutionary history than previously suspected — history that would be lost with their extinction."

Per the second image down on the right: "Subtaxa within taxa are often distributed unevenly. Uneven distribution of species among: a, eutherian orders, with rodents being the dominant group; b, rodent families, with murids being dominant; and c, murid genera."

"Although the sampling effect is biological in part — it requires both differences between species and an ecological mechanism making some species more abundant than others — the probabilistic component (more diverse communities have a greater chance of containing a species with particular properties) has made it controversial. Nevertheless, loss of species with key traits, as in the sampling effect, is not restricted to ecological experiments: logging, fishing, trapping and other harvesting of natural resources frequently remove particular organisms, often including dominant species."

Paleontology
Def. the "[s]tudy of the forms of life existing in prehistoric or geologic times" is called paleontology.

Geology
"In theory, "dominant group" in geology may have at least two meanings: (1) a dominant group of geology-based objects or (2) a dominant group in some way associated with geology." The fossils and their implications are here. The rocks themselves are in 'dominant group/geology'."

Mass Extinctions
"When dominance of particular ecological niches passes from one group of organisms to another, it is rarely because the new dominant group is "superior" to the old and usually because an extinction event eliminates the old dominant group and makes way for the new one. "

"The rise of dominant groups such as amphibians, reptiles, mammals and birds occurred by opportunistic expansion into empty ecological niches and the extinction of groups happened due to large shifts in the abiotic environment. "

On page 212 of a 1944 book by Simpson is "[i]n the history of life it is a striking fact that major changes in the taxonomic groups occupying various ecological positions do not, as a rule, result from direct competition of the groups concerned in each case and the survival of the fittest, as most students would assume a priori. On the contrary, the usual sequence is for one dominant group to die out, leaving the zone empty, before the other group becomes abundant." "Simpson noted that major extinctions provide opportunities (space, ecological niches, etc.) for later diversification by the survivors."

Ecological dominance
Ecological dominance is the degree to which a species is more numerous than its competitors in an ecological community, or makes up more of the biomass.

"The ecological dominance of diatoms under sporadic mixing conditions indicates that their long-term success in the Cenozoic reflects an increase in event scale turbulent energy dissipation in the upper ocean."

"In many paleontological studies, taxonomic diversity" carries with it "[t]he implicit assumption ... that more species in a lineage indicate greater biomass in the lineage as well."

Paleobotany
With respect to groups of vascular land plant in the Phanerozoic, "[f]ollowing initial invasion of the land, the diversification of each group coincides with a decline in species numbers of the previously dominant group."

“The Mesophytic types begin to appear towards the close of the Palaeozoic period. They come in very gradually, but become more numerous as we pass up through the Permian. It is not until Triassic times that they occupy the position of a dominant group.”

"This is the first such forest reconstruction in Asia for any time interval, it's the first of a peat forest for this time interval and it's the first with Noeggerathiales as a dominant group," Pfefferkorn said.

Holocene
The Holocene starts at ~11,700 b2k and extends to the present.

Actinopterygii
"A subclass of the Osteichthyes, the ray-finned fishes (Actinopterygii), have become the dominant group of fishes in the post-Paleozoic and modern world, with some 30,000 living species."

Arthropods
“No strong or dominant group of flies, like the Tachinide, Dolichopodidse, Syrphidae or Bombyliidae, has ever had in the past a larger average bodily size than is found among their living representatives.”

Extant brachiopods
"The two main extant brachiopod lineages, currently treated as subphyla (Williams et al.1996), comprise one numerically dominant group with a highly mineralised, hinged shell (articulate brachiopods), and one group with valves connected only by soft tissues (inarticulate brachiopods, comprising three lineages: craniids, discinids and lingulids)."

Teleosts
"The placoderms ... were replaced by the actinopterygians (ray-finned fishes), which ultimately produced the teleosts, the dominant group of modern fish."

Pleistocene
The Pleistocene dates from 2.588 x 106 to 11,700 b2k.

"Ahl al Oughlam lacks the diversity of murids found in East African sites of this age, but also fully lacks any arvicolid, the dominant group in Europe at that time. Remarkably, this original composition of North African rodent faunas remained virtually unchanged until the end of the Pleistocene ( Jaeger, 1975)."

Pliocene
The Pliocene ranges from 5.332 x 106 to 2.588 x 106 b2k.

"Primates (particularly cercopithecids) appear to be the most dominant group, followed by artiodactyls and carnivores, respectively. Among the artiodactyls, bovids and suids are dominant."

Miocene
The Miocene dates from 23.03 x 106 to 5.332 x 106 b2k.

Oligocene
The Oligocene dates from 33.9 ± 0.1 x 106 to 23.03 x 106 b2k.

"As the Earth began to cool, the tropical plants that had previously been found relatively widespread began to recede towards the equator where it was still warm. The general tropical plants began a transition to more forest like areas. The first grasses also appeared in the late Oligocene. The appearance of these grasses led to to evolution of various herbivore animals. With bodies low to the ground, animals would take advantage of the new grasses that appeared."

Alligators
"From the late Oligocene until the present, the family Alligatoridae remains the dominant group in North America in terms of both generic diversity and numbers of localities where it is found."

Foraminifera
"Signiﬁcantly, the dominant group of planktonic Foraminifera to emerge in the Oligocene were the globigerines, which today are largely restricted to cold-water masses (Cifelli, 1969)."

"Recurrent themes of pre-Cenozoic marine crises suggest that global temperature change also served as a major, and perhaps dominant, agent of extinction in these events: (1) Mass extinctions have frequently been concentrated in the tropics, which seem to have become a refrigerated trap from which there has been no escape; biotas previously occupying high latitudes have shifted equatorward, to replace disappearing tropical biotas. (2) Some crises were not instantaneous but followed protracted and pulsatile temporal patterns, as would be predicted for complex, global climatic crises. (3) Several mass extinctions coincided with recognized intervals of climatic cooling."

Perissodactyls
"Perissodactyls were the dominant group of large terrestrial browsers right through the Oligocene. However, the rise of grasses in the Miocene (about 20 million years ago) saw a major change: the even-toed ungulates with their more complex stomachs were better able to adapt to a coarse, low-nutrition diet, and soon rose to prominence. Nevertheless, many odd-toed species survived and prospered until the late Pleistocene (about 10,000 years ago) when they faced the pressure of human hunting and habitat change."

Eocene
The Eocene dates from 55.8 ± 0.2 x 106 to 33.9 ± 0.1 x 106 b2k.

"Penguins are by far the most dominant group of marine vertebrates in the Eocene La Meseta Formation (Seymour Island, Antarctica)."

Two "new species (Tonniornis mesetaensis and T. minimum) [were added and] a biostratigraphic unit, the Anthropornis nordenskjoeldi Biozone [was defined].

"This interval of strata, easily distinguishable by the numerous occurrence of penguin bones and the phosphatic brachiopod Lingula, is located nearly 30–35 m below the top of the 145 m-thick Submeseta Allomember. The highest morphological and taxonomic penguin diversity living sympatrically (organisms that live simultaneously in the same place), including giant and tiny species, is documented in this interval. Fossil penguins bones studied [...], recovered from rocks interpreted as shallow-marine deposits, accumulated between 34.2 and 36.13 Ma (late Late Eocene)."

"We selected Anthropornis nordenskjoeldi to identify the zone, as: (1) it is restricted to an interval of strata traceable through the Submeseta Allomember; and (2) it is numerically predominant over the other penguin species."

"On the basis of the body size, Anthropornis nordenskjoeldi was evidently the largest penguin known. Its hydrodynamic constraints suggest that it was a rather slow swimmer with speeds perhaps in the order 7–8 km h–1 (Jenkins 1985). The angled shape of the flippers, not straightened as in modern penguins, also suggest that A. nordenskjoeldi did not have the specialization to dive. The long neck of A. nordenskjoeldi probably favoured the capture of motile prey (fish) rather than krill and small squid."

Paleocene
The Paleocene dates from 65.5 ± 0.3 x 106 to 55.8 ± 0.2 x 106 b2k.

"Three stages are recognized in the Paleogene mammalian radiation: (1) the Paleocene flourishing of archaic groups, (2) the Eocene rising and development of modern major groups and (3) the Oligocene faunal reorganization. During the Paleocene, the mammalian radiation was dominated by the archaic groups and the faunas showed apparent endemism. The radiation was characterized by faunal turnovers due to the flourishing of different families in archaic groups. During this period, ancestral forms of modern glires emerged and the first Rodentiaformes appeared in the late Late Paleocene. Such faunal changes corresponded to the successive rise of temperature after the transition from the Mesozoic to the Cenozoic. The Initial Eocene Thermal Maximum resulted in a significant decrease of the archaic groups and the faunal composition became more similar to that of modern ones. At the beginning of the Eocene, Artiodactyla and Euprimates appeared and Rodentia and Perissodactyla began to differentiate. During the Eocene, Mixodontia, Arctostylopidae, Dinocerata, Pantodonta, Tillodontia and Creodonta disappeared in succession. Perissodactyla became the dominant group in the faunas. The faunal turnovers were characterized by the alteration of dominant families due to the appearance, differentiation and flourishing of families in modern orders. The severe cooling events at the Eocene–Oligocene transition resulted in the development of open grassland, that further contributed to the great mammalian faunal turnover. The perissodactyl‐dominant Eocene faunas were replaced by the rodent/lagomorph‐dominant Oligocene faunas. The appearance and radiation of hypsodont mammal groups characterized the mammalian evolution in the Oligocene."

Cretaceous
"The Cretaceous period is the third and final period in the Mesozoic Era. It began 145.5 million years ago after the Jurassic Period and ended 65.5 million years ago, before the  Paleogene Period of the Cenozoic Era."

Ammonoids
"Desmoceras predominates in the upper Albian–Cenomanian succession regardless of lithofacies, the family Gaudryceratidae is the second-most dominant group in each lithofacies, the abundance of Zelandites decreases offshore, and other groups, including Acanthoceratidae, are uncommon but occur in both inshore and offshore facies."

"The Labeceratidae represent the final evolutionary pulse of the Superfamily Ancylocerataceae which were the dominant group of Valanginian–Aptian heteromorph ammonites."

Bivalves
"The carbonate successions exposed in the two quarries contain a relatively abundant and diversified bivalve and ammonite fauna, with inoceramid bivalves representing the dominant group."

Enantiornithes
"Euenantiornithes is a superorder of Cretaceous birds. They are considered to contain the more advanced taxa of the Enantiornithes, the dominant group of birds during the late Mesozoic."

Sauropods
From Saltasaurus, "In the Cretaceous Period, sauropods in North America were no longer the dominant group of herbivorous dinosaurs, with the duck-billed dinosaurs, such as Edmontosaurus becoming the most abundant. However, on other landmasses such as South America and Africa (which were island continents much like modern Australia) sauropods, in particular the titanosaurs continued to be the dominant herbivores."

Tetanurans
"Shaochilong is the youngest known Laurasian allosauroid suggesting that basal tetanurans not tyrannosaurids, were still the dominant group of large-bodied theropods in Laurasian during the Mid-Cretaceous and that the rise of tyrannosaurids as the dominant group of large terrestrial predators was sudden and confined to the very end of the Cretaceous."

Jurassic
"The Jurassic Period takes place after the Triassic Period and before the Cretaceous Period. This period is well known for the reign of the dinosaurs of its time and the global tropical landscape."

"The Jurassic is a geologic period and system that extends from about 199.6±0.6 Ma (million years ago) to 145.5±4 Ma; that is, from the end of the Triassic to the beginning of the Cretaceous. The Jurassic constitutes the middle period of the Mesozoic Era, also known as the Age of Reptiles. The start of the period is marked by the major Triassic–Jurassic extinction event. However, the end of the period did not witness any major extinction event."

Ammonite subzone
"From this time on, perisphinctids spreading north out of the Tethys became the dominant group in the ammonite fauna. A general warming of the climate in Middle Oxfordian time is the most probable cause (see Gygi, 1986)."

Conifers
"Conifers (Gymnosperms) became the dominant group of plants in mid-Jurassic forests".

Ostracods
"Notable by their absence, however, are the metacopids and cytherids, while the Cypridacea are the dominant group with 53 % of the total number of specimens."

Saurischians
"The dominant herbivores of the Jurassic, the sauropodomorph saurischians evolved to larger forms and gave rise to the Neosauropoda".

Triassic
"Early neopterygian fishes (Fig. 13.9) shared the seas and fresh waters with the chondrosteans through most of the Triassic, Jurassic, and Cretaceous periods but gradually became the dominant group." "They presumably became dominant because of gradual but significant changes in structure that gave them a competitive edge over the chondrosteans. These changes culminated in the subdivision Teleostei, the dominant bony fishes today."

Archosaurs
"Since its origin in the Late Permian or Early Triassic, the archosaur clade has been a successful and often dominant group".

"The archosaurs became the dominant group during the Triassic period, though it took 30 million years before their diversity was as great as the animals that lived in the Permian."

Hybodonts
"During Early Mesozoic times, hybodonts were the dominant group of marine selachians, but, when neoselachian and actinopterygian diversity increased in the Middle and Late Jurassic, hybodonts gradually declined in marine habitats."

Sauria
"Sauria is a clade of reptiles that includes all living diapsids, as well as their common ancestor and all its extinct descendants. ... The ancestral saurian was probably a small lizard-like creature living in the Permian Period. This crown group is diagnosed by a number of details in skull and skeleton, and comprises the two important clades Lepidosauromorpha and Archosauromorpha."

Note: crown group is not a relative synonym for dominant group as crown is not a relative synonym for dominant.

"Obviously, other taxa shared the Earth with the reptiles and competed with them for food, but the Sauria were the dominant group."

Carboniferous
"There is evidence from the Upper Carboniferous, Mazon Creek biota of Illinois, USA, that the Limulina and Bellinurina occurred preferentially in different habitats. While the marine Essex biota yields specimens of Paleolimulus signatus (Limulina) and rarely Euproops, the euproopids (Bellinurina) are the dominant group in the brackish–freshwater Braidwood biota (Schram 1979c). The Bear Gulch Limestone has been described as forming a faunal continuum with the Essex biota (Schram 1979c). At first glance the presence of Paleolimulus in both the Bear Gulch and the Essex biota of Mazon Creek localities seems to support this suggestion. However, restudy of Paleolimulus longispinus by Anderson (1996) showed that the presence of a distinct opercular segment and six long, fixed spines and five short, moveable spines align these specimens with Rolfeia Waterston, 1985 rather than Paleolimulus. Rolfeia is known from the Tournaisian of Glencartholm, Scotland, and occurs in a marine–brackish depositional environment (Waterston 1985)."

Placoderm radiation
"The placoderms underwent a spectacular radiation during the Devonian (between 410 and 360 million years ago), but at the end of this period all placoderms—large, small, marine and freshwater—went extinct. They were replaced by the actinopterygians (ray-finned fishes), which ultimately produced the teleosts, the dominant group of modern fish."

Graptolites
For the Silurian of the Brabant Massif in Belgium, "[m]acrofossils are rare but graptolites provide a good but incomplete coverage." "The facies in the Silurian of the Brabant Massif is always deep neritic ... with no shallow marine sediments observed yet."

"[G]raptolites are nearly the only macrofossils present and until 1969 the sole basis for biostratigraphical dating". "Larvae and prosiculae of graptolites are often encountered in palynological preparations as are rhabdosomes in petrographical thin section".

"Some fossils such as Conularia, Dayia, Cardiola, Orthoceras, Siphocrinites, and some species of Chitinozoa (a.o. Margachitina margaritana, Desmochitina opaca) show the presence of a "less deep" environment at the following levels: upper Aeronian and lower Telychian, lower Wenlock, uppermost Wenlock and a level in the Gorstian. Since in all these levels graptolites are the dominant group of macrofossils, shallow marine conditions are excluded."

Placoderms
The placoderms surpassed the eurypterids as a large marine predator probably by the early to middle Silurian.

Rhynchonellides
"Although rhynchonellides have never been a dominant group of brachiopods, they are regarded as a successful order because they have first appeared in the early Ordovician, still survive in a wide range of marine environments today, and have left a longer palaeontological record than any other living articulated order, rich enough to allow inferences about their ancestral connections (Williams and Hurst, 1977; Ager, 1987)."

Echinoderms
"At the beginning of the Middle Ordovician the echinoderms became the dominant group of the benthos in many biotopes of most of the epicontinental seas."

Brachiopods
"The Brachiopoda were the dominant group of benthic filter feeding marine invertebrates from the early Cambrian, when they arose over 550 million years ago, until the end of the Permian period."

Mollusks
"Much of the carbonate mound at Tauwhareparae is fossiliferous and incorporates one dominant group: namely bathymodiolin mussels."

"These methods yielded conservative estimates of numerical dominants through the Phanerozoic because each numerically dominant group received the same score of “1” whether it dominated one shell bed or many shell beds per stratigraphic unit."

Hypotheses

 * 1) Dominant groups in paleontology are those that appear most numerous or splendid in the fossil record.
 * 2) Small monocellular organism probably constituted the most biomass throughout all history.

title: Dominant group/Paleontology


text:
User:Egm6321.f11.team2.Xia/RP7.9

Given
Consider the non-orthonormal basis $$ \{\mathbf{b}_{1},\mathbf{b}_{2},\mathbf{b}_{3}\}$$, expressed in the orthonomal basis $$ \{\mathbf{e}_{1},\mathbf{e}_{2},\mathbf{e}_{3}\}$$ as folllows: $$\displaystyle \mathbf{b}_{i}=A_{ij}\mathbf{e}_{j}$$ (7.3.2) here $$\displaystyle \mathbf{A}=\left[A_{ij}\right]=\left[\begin{array}{ccc} 5 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 5\end{array}\right]$$ and $$\displaystyle \mathbf{v}=-2\mathbf{e}_{1}+4\mathbf{e}_{2}-5\mathbf{e}_{3}$$ (7.3.3)

Find
$$\displaystyle{\mathbf v_i}\in\mathbb{R}^{3\times 1}$$ such that $$\displaystyle \mathbf{v}=v_i\mathbf b_i$$

Solution
From 7.3.2 and 7.3.3, we have $$\displaystyle \mathbf{v}=v_{i}A_{ij}\mathbf{e}_{j}$$ (7.3.4) $$\displaystyle \mathbf{\mathbf{A}}^{T}\left[\begin{array}{c} v_{1}\\ v_{2}\\ v_{3}\end{array}\right]=\left[\begin{array}{r} -2\\ 4\\ -5\end{array}\right]$$ (7.3.5) $$\displaystyle \left[A_{ij}\right]^{T}\left[\begin{array}{c} v_{1}\\ v_{2}\\ v_{3}\end{array}\right]=\left[\begin{array}{r} -2\\ 4\\ -5\end{array}\right]$$ (7.3.6) Since $$\displaystyle det(\mathbf{A})\neq 0$$

we have $$\displaystyle \left[\begin{array}{c} v_{1}\\ v_{2}\\ v_{3}\end{array}\right]=\left[A_{ij}\right]^{-T}\left[\begin{array}{r} -2\\ 4\\ -5\end{array}\right]=\left[\begin{array}{ccc} \frac{23}{80} & -\frac{11}{40} & \frac{3}{80}\\ -\frac{7}{40} & -\frac{1}{20} & \frac{13}{40}\\ \frac{3}{80} & \frac{9}{40} & -\frac{17}{80}\end{array}\right]\left[\begin{array}{r} -2\\ 4\\ -5\end{array}\right]$$ (7.3.7) thus $$\displaystyle \left[\begin{array}{c} v_{1}\\ v_{2}\\ v_{3}\end{array}\right]=\left[\begin{array}{r} -\frac{149}{80}\\ -\frac{59}{40}\\ \frac{151}{80}\end{array}\right]$$ (7.3.8)

title: User:Egm6321.f11.team2.Xia/RP7.9


text:
User:Davidthespecialone

Davidthespecialone 21:51, 4 December 2011 (UTC)

title: User:Davidthespecialone


text:
User talk:Davidthespecialone

Motivation and emotion
Hi there David - let me about your interest in Motivation and emotion and we can discuss a plan. Sincerely, James -- Jtneill - Talk - c 23:22, 4 December 2011 (UTC) i would like to learn more, i studied the 2010 handouts and it seems like a very interesting course.

title: User talk:Davidthespecialone


text:
User:Savannah~enwikiversity

Occupation: Student (Mechanical Engineering)

title: User:Savannah~enwikiversity


title: File:Photo(3).jpg


title: File:Photo(2).jpg


title: File:Photo(1).jpg


title: File:Pea1.s12.pythagorean.thm.2.svg


text:
User:EGM6321.f11.team1.pan/HW7

= R*7.7 Find the separated equation for the Laplace Equation in Parabolic coordinates= == Given == The Laplacian in parabolic coordinates given by
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle \nabla^2 u=\frac{1}{\mu^2+\nu^2}\left(\frac{\partial^2 u}{\partial \mu^2}+\frac{\partial^2 u}{\partial \nu^2}\right)$$
 * $$\displaystyle (Equation\;7.7.1)
 * $$\displaystyle (Equation\;7.7.1)
 * }
 * }

Find
Find the separated equation for the Laplace equation in Pararbolic coordinates.

Solution
Separation of variables: $$\displaystyle u(\mu,\nu)=U(\mu)V(\nu)$$ Substituting it into Equation (7.7.1), $$\displaystyle \Delta u=0=\frac{1}{\mu^2+\nu^2}\left(V \frac{\partial^2 U}{\partial \mu^2}+ U \frac{\partial^2 V}{\partial \nu^2}\right)$$ Cancel $$\displaystyle \frac{1}{\mu^2+\nu^2} $$ and $$\displaystyle UV$$, $$\displaystyle \frac{1}{U}\,\frac{\partial^2 U}{\partial \mu^2}+ \frac{1}{V}\,\frac{\partial^2 V}{\partial \nu^2}=0$$ Rearranging it, we can obtain that $$\displaystyle \frac{1}{U}\,\frac{\partial^2 U}{\partial \mu^2} = - \frac{1}{V}\,\frac{\partial^2 V}{\partial \nu^2}=k$$ Therefore, the separated equations are:

title: User:EGM6321.f11.team1.pan/HW7


title: File:Pea2.s12.rational.svg


text:
User:Egm6322.s12/Figures

Elastic bar:

Attraction of spheres:

Rational numbers:

title: User:Egm6322.s12/Figures


title: File:Image2789.jpg


text:
Reproductive health/Mammography

This page is being created as a stub topic. Its intent is to build open content in the subject area, for professionals and others interested. An associated wiki has been created at http://mammography.wikia.com/wiki/Mammography_wiki. An associated group has been created at http://groups.google.com/group/mammographytoday/—. The intent and purpose is to create a collaborative community passionate about learning in the content area of mammography, improving its use as a diagnostic tool, fomenting research into perfecting mammography as a diagnostic tool by enabling professionals to suggest trends, techniques, improvements in equipment, and procedures. In pursuit of this, please add structure and content to this stub topic. Consider your content as you provide it. Protect patient care information. Experienced professionals are especially encouraged to add content. Give those new to the profession a place where they can benefit from your years of experience. Carry your knowledge to the next generation. Welcome! Swgeek54 04:18, 5 December 2011 (UTC)

History of Mammography
Mammography is a division of Radiology which deals with detecting, and diagnosing diseases of the breast, specifically breast cancer. The genesis of radiology began with the discovery of x-rays byWilhelm Röntgen. Röntgen produced the first x-ray platein 1895. Diagnostic Radiology thus had its birth, from whence mammography developed.

title: Reproductive health/Mammography


text:
User talk:BBIndiana

 Hello BBIndiana, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --HappyCamper 06:16, 5 December 2011 (UTC)

About Learning theories
Hi there,

I'm just trying to get my head around what you are adding in POLT. Is this the beginnings of a book, is it already a book, or a theory or school of thought on Learning Theories? Historybuff 07:37, 5 December 2011 (UTC)

title: User talk:BBIndiana