Classification Definition and 116 Threads

Wigner classified particles in function of the eigenvalues of P_\mu P^\mu and W_\mu W^\mu. Then, it can be proved that for massless particles spin values can be only \pm s_{max}. But for a particle with mass could have intermediate spin values. 1. If we think that a massless particle is the...

Checking to see whether semidirect products are isomorphic. Homework Statement I want to simplify this semidrect product (Z_7 \rtimes_{\bar{\alpha}} Z_3) \rtimes_{\alpha} Z_2, but I'm not sure how. In other words, I want to see if this is isomorphic to (for example) Z_7 \rtimes_{\alpha}...

Homework Statement I was trying to classify Z_7 \rtimes Z_6 \cong Z_2 \times Z_3, but I have questions about it... Homework Equations The Attempt at a Solution The possible homomorphisms are: 1) \alpha is trivial, so G \cong Z_7 \times Z_6 2) Kernel of \alpha = Z_3. So G...

Homework Statement Hello, I'm trying to learn how to classify reactions. I want to know how do I tell ionization, self protolysis and hydrolysis. Homework Equations NH4(aq) + H20(l) <--> NH3(aq) + H30(aq)+ This is hydrolysis why? How does it differ from this hydrolysis...

Homework Statement Hi there, I was wondering if anyone out there was familiar with image classification algorithms. I have been creating histograms of pixel intensity distributions. For example, suppose I have 100 images of a tiger and 100 images of a lion. I create 100 histograms using...

i read on a book that the matter can be classified as crystalline substances , amorphous substances or both of them depending on the % of packed crystalline part . please can you explain me what does it mean

Homework Statement I'm doing a course on numerical solutions of PDE and I am waaaay out of my depth, having not covered differential equations previously. I spoke to my lecturer about this and he said I would be fine as the course is on FDM/FEM and not analytic solutions but this is week 4 and...

In my research work, I recently have come across a system of three linear first order pde's whose characteristic polynomial has one real and two complex conjugate zeros. I have searched the available resources and could nowhere find out which category (elliptic/hyperbolic/parabolic) it falls...

Hi, I am an Engineering Student and my professor is insisting that we read about the different types and classifications of three-dimensional forces. I have been scouring the world wide web for more than 3 days now, even checked physics books but I can't find even one type or classification of...

In classification of the physics section of this site,there is nothing explicitly containing Optics or Photonics.Which part of physics do they belong to? Also why Atomic,solid state and computational physics are in one part? Thanks

Derive an expression for the number of impact of gas molecules on unit area in unit time in terms of the number of molecules per unit volume, n, and their mean speed, <c>. Explain the assumptions you make. A disc of radius "a" rotates with constant angular velocity "omega" in a gas at low...

This topic is quite confusing.. In the first place, how can we classify for example all O class stars would be having the same spectrum with the same absorbtion lines... Secondly, i just need a clarification on what do these absorbtion line reprsent and upon that how can we decide whether a star...

http://dl.dropbox.com/u/33103477/harvesting.png So am I right in saying the 2 steady states are: N_1=\frac{h}{r}, N_2=\frac{1-h}{\alpha} Now plugging in N_1 into the equation I get: \frac{-h^2 \alpha}{r} < 0 So N_1 is stable. But I can't quite figure out how to classify...

Given that the Classification Theorem says that every finite simple group is isomorphic to one of 4 broad categories of (specific) finite simple groups, does this mean that any conceivable symmetric: i) 2D form; or ii) 3D object is also isomorphic to one of these 4 categories. Otherwise...

When classifying an ODE do I just say whether its linear / non-linear and what order it is? EDIT: Example: x2x'' + e-xx = t3 where x is function of t. is this 2nd order, non linear and heterogeneous? Also, would dx/dt = logte-x be homogeneous because both terms contain the dependant...

I'm trying to understand the causal structure of Minkowskian spacetime and I was wondering whether something can be said about the relation between the classification of events and curves. To clarify: for Minkowskian inner product \eta with signature (-+++), two events p and q can be timelike...

According to Mathworld, if in y''+P(x)y'+Q(x)y=0, P diverges at x=x_0 quicker than \frac{1}{(x-x_0)} or Q diverges at x=x_0 quicker than \frac{1}{(x-x_0)^2} then x_0 is called an essential singularity. What I don't understand is that let's suppose Q diverges like \frac{1}{(x-x_0)^5}. In that...

Ok, so I got this equation: y^2 \frac{∂^2 u}{∂x^2} + 2xy \frac{∂^2 u}{∂x∂y} + x^2 \frac{∂^2 u}{∂y^2} = 0 A = y^2 B = xy C = x^2 Now I want to see what type it is, so I compute B^2 - A C = 0 which by definition is parabolic. However, according to an earlier statement in my book a...

I am working on classifying all groups of order less than or equal to 100. For most orders, this is fairly straightforward, since we can just utilize Cauchy's Theorem/Sylow's Theorems to show that the group can be expressed as a semi-direct product and then find the desired automorphism...

Suppose you have a PDE with an arbitrary number of independent variables (not necessarily two), and of order n. Is there a nice classification akin to the hyperbolic, parabolic, etc. Thanks

Let G be a group and Aut G the set of all automorphisms of G. What is Aut Z_{n} for arbitrary n\inN? Sol Let f\inAut Z_{n}. Since Z_{n}=<1>, f can be completely characterized by f(1), i.e., f(k) = f(1)^{m}, for k\inZ_{n} and m\inN. By these facts, it follows that f(1) must generate Z_{n}...

http://en.wikipedia.org/wiki/Sudarsky_extrasolar_planet_classification Several astrobiologists I know aren't aware of it. Could it just be that someone made a Wikipedia article out of research that isn't widely known yet?

Hi there: I was just searching about Gauge theories and stuff and I find it very confusing. My major complication is the classification. I'd like you to tell me some definitions and construct a "family tree". I guess it goes something like this: Gauge Theory: A Field Theory in which the...

I'm familiar with the classification of fixed points of linear dynamical systems in two dimensions; it's readily available in many a book, as well as good ol' Wiki (http://en.wikipedia.org/wiki/Linear_dynamical_system#Classification_in_two_dimensions). However, what happens with higher-order...

Please help somebody on this problem... When we topologically classify the defects in ordered media, we consider the character of the fundamental group of the associated order parameter space. To construct those groups, we circumscribe the line defects by circles and the point defects by...

Homework Statement P = [data(1:65,11:100) data(1:65,411:500)]; % Input, all together 180 data set, 65 dimension T = [ones(1,90) zeros(1,90); zeros(1,90) ones(1,90)]; % Actual output, first 90 data set belong to class I and the next 90 belong to class II net =...

Is there any good references of Petrov Classification? Thank you.

dear all, I don't quite get the difference between a metal, a semi metal and a semiconductor with zero gap. So far I thought that e metal was a material with a zero gap, that does not seem to me right. Can someone provide me a little explanation? Thanks, Eric.

Interesting finds. Continued... http://www.livescience.com/12883-plant-animal-mysterious-fossils-defy-classification.html

I have rather nasty vector partial diff eq which I think has been addressed before; however, when I vistied a few websites (other than Polyarin's site) to classify the equation the notation of these websites is not necessarily what I am accustomed to. I have attached the equation here & was...

Hi, all! As I'm new to biology and life science, I'm interested in the classification system of life. However it's hard for me to memorize those seemingly Latin words of all kinds of lives. For example, I've absolutely no idea what 'Escherichia' means in Escherichia coli. Do you know...

A while ago I heard the following two facts about semi-simple Lie groups (though I have a feeling they may have to be restricted to connected semi-simple Lie groups): 1. That semi-simple Lie groups are classified by their weight (and co-weight) and root (and co-root) lattices; 2. That all of...

OK recently I found a really old table stars based on partally on Yerkes Classification system with a small section on white dwarf stars. It has the stars organized into groups labeled DO, DA, DB, DF, DG, DK, and DM. However, I remember that the current classification system for white dwarf...

can you provide me eeg dataset for classifying epileptic brain and normal brain

Homework Statement Classify all groups of order 39 Homework Equations The Attempt at a Solution I can show that if the group of abelian, it is isomorphic to Z/3Z*Z/13Z. If the group is not abelian, there are two types of groups, they either follow the rule : x^3=e, y^13=e, and...

The complexified Lie algebra of the Lorentz group can be written as a direct sum of two commuting complexified Lie algebras of SU(2). It is being said, that this enables us to classify the irreducible representations of the Lorentz algebra with two half-integers (m,n). But can someone...

Hello PF readers, I've got trouble in finding neat examples of spectra of various stellar objects including quasars. Are there any sources of information that I could look for?(I would prefer to get the images of the spectra) I would use the examples of spectra to identify certain stellar...

Hello, What is Level 1 engineering drawing? What does it mean? Is there any particular section dealing about classification of engineering drawings in ASME Y 14 series. Please throw some light on this Thanks

This is a question from Hirsch's Differential Topology book: show that there is a bijective correspondence between K^k(S^n) \leftrightarrow \pi_{n-1}(GL(k)) , where K^k(S^n) denotes the isomorphism classes of rank k vector bundles over the sphere. The basic idea is that any vector bundle...

the schrodinger equation is sometimes called a wave equation and in my quantum mechanics text's they often show the wave equation comparing it to the schrodinger equation. i don't understand why they do this when it is of the same form as the heat equation, it's not second order in time like the...

Hello physics people. I love looking at the ICM program (http://www.mathunion.org/activities/icm/icm-2010-program-structure/) because I think it's the best classification system for mathematics out there. There are pretty much all the popular research topics listed and it is hard to argue...

Dear forum-members, Pestered by many (in my opinion, fundamental) questions and no literature at hand to answer them, I resort to posing my questions here. Let me start with the following. (Hopefully I have the correct subsection.) I am inspecting a dynamical, autonomous and conservative...

Hi, I've been reading about Petrov classification and I have a question (in fact this is an exercise from Wald's General Relativity): How can we prove that spherically symmetric spacetimes are algebraically special, using the fact that the Weyl tensor, as the principal null directions are...

Hi, can someone help me on a website for the classification of quadrics(ellipsoids,paraboloids,...) starting from the general second order equation. Thanks

[SOLVED] Particle Physics, perhaps a classification problem Homework Statement How are the classes of particles classified? The Attempt at a Solution Classes of particles should be bosons, leptons, hadrons and baryons. First, I had the idea that the particles are classified according to...

I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment. A: Well, the statement of the theorem is clear, that Every closed Surface is homeomorphic to: 1) a sphere, 2) the connected sum of g tori 3) or the connected sum of g...

Hi next one, bit confused with this problem: any hints on any of the parts would be greatly appreciated. QUESTION: --------------------------------------- let G be a group of order 8 and suppose that y \epsilon G has ord(y)=4. Put H = [1,y,y^2,y^3] and let x \epsilon G-H (i) show that H...

For exocrine glands, the portion of the gland that is described as simple or compound is the structure of the duct--not the secretory portion, right? Thank you.

I am looking for a table of spectral and luminosity classification that shows the breakdown of spectral classes, mass, luminosity, radius, and includes evolved stars. Has anyone seen something like this. I did find this: http://nrumiano.free.fr/Estars/classes.html It is helpful, but doesn't...

during my study on conics , I found a formula in the book regarding the classification of figure from the general equation of conics ax2+2hxy+by2+2gx+2fy+c=0 it was given that \Delta=abc+2fgh-af^{2}-{bg}^{2}-{ch}^{2} if \Delta \neq 0 then if h^{2}=ab...parabola h^{2}<ab...ellipse...