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# Representation Theory - Science topic

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Suggest me some very new qualitative frameworks and Coding Frames for textual analysis so that these can be used to analysis data using the concepts of Representation Theory.

Let $p$ be a prime number, and let $\mathbb{F}_{p}$ be a finite

field of order $p$. Let $GL_{n}(\mathbb{F}_{p})$ denote the general linear

group and $U_{n}$ denote the unitriangular group of $n\times n$ upper

triangular matrices with ones on the diagonal, over the finite field $%

\mathbb{F}_{p}$. In fact $U_{n}$ is a Sylow $p$-subgroup of $GL_{n}(\mathbb{F}_{p})$ of order $p^{\frac{n(n-1)}{2}}$. Given $n_{p^{2}}$ be the number of elementary abelian p-subgroups of rank $2$ in $U_{n}$. How can we deduce the number of elementary abelian p-subgroups of rank $2$ in the whole linear group $GL_{n}(\mathbb{F}_{p})$?.

Conversely, given $N_{p^{2}}$ be the number of elementary abelian p-subgroups of rank $2$ in $GL_{n}(\mathbb{F}_{p})$. Is there a criterion deduces the number of elementary abelian p-subgroups of rank $2$ in $U_{n}$?.

In other words, what is the relationship between $N_{p^{2}}$ and $n_{p^{2}}$?.

Any help would be appreciated so much. Thank you all.

For ThCr

_{2}Si_{2}structure (space group I4/mmm) sample, e.g. CaCo_{2}As_{2}, Co atoms occupy the 4*d*site - site position (0, 0.5, 0.25). Assume that the propagation vector as (0,0,0) and that a antiferromagnetic structure occurs along the*c*-axis. According to irreducible representation analysis using BasIreps in FullProf, there is only one possible model as shown in Fig1. However, one journal paper presented another kind of antiferromagnetic structure as shown in Fig2 which is not included in the model from irreducible representation.So my question is that a magnetic structure model must agree with a model from irreducible representation theory?

Representations are about things other than themselves and are intentional in the sense of being about ‘this’ or ‘that’. Because the mental representations have content, which is related to belief, intention, thought, and action, they are also intentional in the sense of being purposive. Now we may ask: What is it that distinguishes items that serve as representations from other objects or events? And what distinguishes the various kinds of symbols from one another? As for the first question, there has been general agreement that the basic notion of a representation involves things like ‘standing for’, ‘being about’, ‘referring to’, and ‘un denoting’ something else. Some theorists have maintained that it is only the use of symbols that exhibits or indicates the presence of mind and mental states. Mental representation, like beliefs and thoughts, constitutes the broad domain of cognitive science. They explain how cognition takes place in the human mind. Cognitive science (including cognitive linguistics and cognitive psychology) has brought about a cognitive revolution in the study of mind. Here, we can undertake two important developments in cognitive science. One is the representational theory of mind. For, to accept the representational theory of mind is to accept that mental representations are very much like the inter representational states of a digital computer. The other is the adoption of a computational model of mind or computational theory of mind.

In turn, two questions have to be answered in this connection: What kinds of representational systems are employed in cognition? What is machine intelligence or artificial intelligent? Fodor has answered these questions in his computational representational theory of mind (CRTM in short). The computational representational theory of mind makes a strong assumption about mental processes: Mental processes are computational processes, i.e., formal operations defined over symbols. In Fodor’s view, “computational processes are both symbolic and formal. They are symbolic because they are defined over representations, and they are formal because they apply to representations in virtue of (roughly) the syntax of the representations.”[i] The theory purports to offer a solution to the problem raised by the compositionality of propositional attitudes like beliefs, thoughts, etc.; secondly, it proposes to vindicate the strong reading of the intentional realist casual thesis regarding the mental phenomena. Again, it may be noted that the CRTM is consequently based on two fundamental assumptions; the first is Fodors’ Language of Thought (LoT) hypothesis, and the second is the view that psychological explanation that is both intentional and nomological.

[i] Fodor, J. A.,

*Representations: Philosophical Essay on the Foundation of Cognitive Science,*The Harvester University Press, Sussex, 1981, p.226.Let R be a commutative ring with unity. Given two algebras A and A' over a field K, both with R-grading form. Prove that B:= A \otimes_R A' (the tensor product of A and A') has a R²-grading.

Any tip of how to prove this?

What would be the main importance you see on the study of Artinian/Noetherian Modules?

I’m planning to investigate Family's Social Representation in Colombia with Children's game and relate it with adult's answers . I could not find literature, Do you know what would be a good reference and what could be the most efficient method?

Why do we keep thinking that a "poor place" is a "dangerous place" (like cinema and media discourses)? What can we do to surpass this kind of 'paradigm' that seems to exists in researches about urban violence for example?

The only papers I found have Matroid Representations limited to matrix structures written in special occasions.

I want advice on readings.

When we consider two different representations of a C* algebra, physicists generally bother about whether they are "unitarily equivalent". Now, if the representations are different, the Hilbert spaces on which they act are also

different. So I think the right thing they worry about should be called isometric isomorphism instead of unitarity. (A linear operator which preserves the inner product in the sense that one is careful to confirm to the way the inner product

is defined in the appropriate vector space considered!)

Electronic voting is often presented as an advance for democracy, but it also raises a number of issues (secrecy, security...). Is a faster way to aggregate individual preferences a safer way?

I have looked at the ideas of gender schema and Stuart Hall's ideas on 'representation theories'. But I have not come across references to contemporary feminist theories in this context.

Unit vectors i, j, k are defined as the basis for orthogonal 3-space. My view is that these unit vectors are man-made and that Nature does not know about them. That is to say, the information they contain is in the minds of mathematicians, not in the machinery of Nature. I am therefore looking for a self consistent mathematical system, that asserts the orthogonal information of 3-space.

Is it possible that this man-defined orthogonality is false representation that enters General Relativity which then obstructs progress in quantising gravity?

Thanks to

*Number Theory*, we had been studying numbers and their properties since a*long*time now. Dealing with numbers usually involves trying to find out the existence of the certain special*magical powers*they possess, if any. My question rotates around some of the immediate clinical aspects:Is there a

**general**,**generic**,**genetic**manner in which numbers can be used as a memory storage unit? Is there a measure of how much information can be stored in numbers and representations of them? Is it possible to find how many numbers are there?Representation theory? What else? Key words: user generated content, collective identity, self-representation

I am doing my thesis on nationalism in social media. I have ideas on how to conduct my study (methods), but I don't have a concrete study framework yet. What theoretical framework can you suggest? My focus is on the posts of people that they deem as "nationalistic" and how it affects national identity in social media. I'm planning to do content analysis.

Whenever we invoke a representation for a group --using a matrix group, or group of differential operators -- are we converting a problem in group variables to one in arithmetical variables (field variables, actually)?

I have been observing the connections of differential geometry, representation theory and lie theory in general relativity, and was wondering what's essential in the view of a course on general relativity.

Let $G$ be a finite group of even order has only one non-principal irreducible character $\chi$ of degree $d$, $d\in \mathbb{N}$, with the following property (we name it $(*_d)$):

$(*_d)$: There exist $x,y\in G$ such that $o(x)=o(y)=2$ and $\chi(x)\neq \chi(y)$.

I know that $A_n$ ($n\geq 8$) has the property $(*_{n-1})$ and $S_n$ ($n\geq 4$) has the property $(*_1)$.

Now, for a suitable $d\in \mathbb{N}$, I have a question:

Is there any other solvable example of groups $G$ with the property $(*_d)$?

a) G has at least two distinct conjugacy classes which include at least two [non-involution] elements of group and inverses of them. In other words, there exist two conjugacy classes of G, C_1 and C_2, such that:

If a \in C_1, b \in C_2 then a^{-1} \in C_1, b^{-1} \in C_2

where the generated subgroups from these elements have the same cardinality. In other words:

Card( < a , a^{-1} > )= Card( < b , b^{-1} > ).

OR

b) G has at least two distinct conjugacy classes of involutions.