Regular Definition and 251 Threads

Hello, in group theory a regular action on a G-set S is such that for every x,y∈S, there exists exactly one g such that g⋅x = y. I noticed however that in the theory of Lie groups the definition of regular action is quite different (see Definition 1.4.8 at this link). Is there a connection...

I bought a water pitcher that purifies water. It supposedly filters out a lot of contaminants like lead. (It doesn't filter out fluoride but I knew this before I got it) It came with a little warning sticker saying that its important to use the product as specified, other wise you will be at...

So there was this question: Which sample demonstrates particles arranged in a regular geometric pattern? A. CO2(g) B. CO2(s) C. CO2(l) D. CO2(aq) E. None of the above I chose E because I thought that covalent molecules, when solid, would be arranged in a random pattern, especially since this...

This is actually for a wood shop project... but it certainly involves geometry! I am trying to build a real-world regular icosahedron. I know I need 20 equilateral triangles for the faces. But I do not know what the angles of the sides/thickness should be, to join those 20 triangles into a 3D...

Hello ! Homework Statement Consider a parametrized curve C(θ)=( (R+r)*cos(θ) - d*cos(θ(R+r)/r) ; (R+r)*sin(θ) - d*sin(θ(R+r)/r) ) Show that C is regular for d<r. Is it regular if d=r ? Homework EquationsThe Attempt at a Solution C'(θ)=( -(R+r)*sin(θ) +d*(R+r)/r*sin(θ(R+r)/r) ; (R+r)*cos(θ) -...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...

Hello the proof of the Spiser's book (introduction to theory of computation): PROOF We let R be a TM that decides REGULARTM and construct TM S to decide ATM. Then S works in the following manner. S = "On input (M, w), where M is a TM and w is a string: 1...

1. Homework Statement ##x^{2}y'' + (x^{2} + 1/4)y=0## 3. The Attempt at a Solution First I found the limits of a and b, which came out to be values of a = 0, and b = 1/4 then I composed an equation to solve for the roots: ##r^{2} - r + 1/4 = 0## ##r=1/2## The roots didn't differ by an...

See the image that I uploaded... I want to write the surface S (bounded by edges u, v and w) in terms of x, y and z, u, v and w and A, B and C. And I got it! See: S(A,B,C) = \sqrt{A^2+B^2+C^2} S(x,y,z) = \sqrt{\frac{1}{4}( (yz)^2 + (zx)^2 + (xy)^2 )} S(u,v,w) =...

Sturm-Liouville problem: \frac{d}{dx} (r(x) \frac{dX}{dx}) + q(x)X(x) + \lambda p(x) X(x) = 0 \quad x \in \left[a, b \right] a_1 X(a) + a_2X'(a) = 0 b_1 X(b) + b_2X'(b) = 0 r, r', q, p \in \mathbb{C} \forall x \in in \left[a, b \right] Theorem: Under the additional condition that r(a)>0 (or...

When an object becomes invisible when it undergoes “regular” or “diffused” reflection?

In the area of nutrition there's a huge amount of New Age pseudoscience so it's hard to know what's real from what's junk. Regarding this one particular issue I have to ask, is there any real scientific evidence to support the claim that whole wheat is better for your health than regular white?

Does a completely regular space imply the Dirac measure. From wikipedia we have the definition: X is a completely regular space if given any closed set F and any point x that does not belong to F, then there is a continuous function, f, from X to the real line R such that f(x) is 0 and, for...

Since the pressure a sphere exerts on a surface tends to infinity, how do you actually calculate it? My guess would be trying to see how many atoms of the surface (a straight line) and of the sphere collide. But this is very dependent on the materials and exterior factors. I have searched...

Homework Statement If I have a ball moving in a circular path (ball is connected to a string), as shown in this picture: http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/circularmotion/Images/cent_force_on_ball.gif should I say that the energy of the ball is both its kinetic...

First I would like to say that I'm sorry if this question has been asked before- I'm new here. I was reading QED by Richard Feynman, and he mentioned that any given antiparticle is just it's regular particle counterpart moving backwards in time. How is this possible? I thought that it was only...

A equilateral triangular lamina, has a moment of Inertia of I if the axis of rotation passes through the centroid of the triangle, perpendicular to it's plane. What is the moment of inertia of a regular hexagon(Again, through it's geometrical centre, perpendicular to the plane), provided that...

Hey! :o How can we find the regular expression of a language given by an automaton M?? Could you give some hints?? (Wondering) Which are the steps that we have to follow so that we convert an automaton into a regular expression?? (Wondering)

Hey! :o I want to prove that the language $$L=\{ww^R \mid w \in \{0, 1\}^{\star} \}$$ is not regular using the pumping lemma. I have done the following: We suppose that $L$ is regular and is recognized by a DFA $M$ with $k$ states. So, $M$ accepts the string $0^k110^k$. Since...

Hey! :o If $K$ is a set of natural numbers and $b$ is a natural number greater than $1$, let $$L_b(K)=\{w \mid w \text{ is the representation in base } b \text{ of some number in } K\}$$ Leading $0$s are not allowed in the representation of a number. For example, $L_2(\{3, 5\})=\{11, 101\}$...

Hey! :o Let $L=\{k |km \in K \text{ for some } m \in M\}$. How can we show that if $K$ is regular and $M$ is any language, then $L$ is regular?? (Wondering)

Hey! :o Let $$C_n=\{x \ \mid \ x \text{ is a binary number that is a multiple of } n\}$$ Show that for each $n \geq 1$, the language $C_n$ is regular. Could you give me some hints how we could show that?? Do we have to construct a NFA that accepts the language??

Hey! :o How can we show that the class of regular languages is closed under the following operation?? Let $L_1$ and $L_2$ be laguages over $\Sigma=\{0, 1\}$. The operation is: $$\{x \in L_1 | \text{ for some } y \in L_2, \text{ strings } x \text{ and } y \text{ contains equal numbers of }...

I was just googling something which led me to an old PF thread, i saw a few awarded members like @hootnany, @Kurdt, @Njorl @Enigma and many more.I don't see them around, What happened to them?? PS I'm sorry if i included someone who actually is still around(i haven't)

Im trying to construct a regular grid in a rectangular box in 3 dimensional space heres what i have to work with: x has a range between xmin and xmax y has a range beween ymin and ymax z has a range between zmin and zmax the total number of points is limited to a specific number n i want the...

Hi, I'm back with another question, but the opposite of last time. The question is: For each positive integer $n$, let ${L}_{n}$ = { ${a}^{k}$ $|$ $k$ is a multiple of $n$ } Show that for each $n$ the language ${L}_{n}$ is regular. As far as I understand you cannot use pumping lemma to prove...

Hi, I am struggling with the concept of proving languages are not regular. I know that I need to use pumping lemma to prove it by contradiction but I can't get my head around it. Here is one language that I need to prove is not regular. http://i.imgur.com/quD26In.png I know that is...

Hi, I'm trying to covert a NFA to a regular expression and I've manged to come up with an answer but I don't think that it is right. Here's the question - http://i.imgur.com/NUHxTXY.png And here's my workings -...

Hello everyone! :D I've been looking at the definition and proof of the Myhill-Nerode theorem for awhile now and cannot figure out what the notation is trying to tell me. Here are the languages I'm trying to apply it to, and then I'll explain what I think we're trying to do: Question: Prove...

Homework Statement Let truncn(L) = {w: wv exists in L, |v| = n} Show that trunc is regular if L is regular. The Attempt at a Solution By the definition of regular languages, L is regular if we can come up with a regular expression or a DFA for it. This question confuses me because what if...

The full title of this post is "Close Packing of Spheres in Regular Tetrahedral vs. Square Pyramidal Container" I'm not sure where this post belongs, but Greg Bernhardt suggested I just post it where I thought best, and he would find a place for it. So here goes: In 1611, Johannes Kepler...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings we read the following on page 57: https://www.physicsforums.com/attachments/3149I am trying to gain an understanding of representations. I would...

Hello everyone! I'm trying to design an NFA and then turn it into a DFA, and I'm not sure if I've done it correctly so far. Here is the question: "Present a transition diagram for an NFA for the language associated with the regular expression (1001 + 110 + 11)*. Your NFA must have no more than...

Hello! (Wave) Show,using the closure properties,that from the following languages over $\Sigma= \{ 0,1,2\}$,the first one is regular and the second one is context-free. $ \displaystyle{ L_1=\text{ the strings,that,when they contain at least one "000", } \\ \text{they contain also at least...

Greetings, I have two semi-related questions. 1. When making the Lagrangian formalism of electrodynamics, why is it that we use the Lagrangian density \mathcal{L}, rather than the plain old regular Lagrangian L? Is this something that is necessary, or is it more that it is just very...

My professor, in his handout (picture below), says the following about this diagram : I disagree with him partly. For \Delta_{mix} G/nRT<0 mixing is spontaneous and hence there solutions would be miscible. Hence at \beta=2.5 should we not expect the components to be fully miscible. ...

Hi!I have also an other question. Is the regular expression $\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*}\}\cap\{\{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}\}$ equal to this one: $\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}$ or is there a difference?

I have the following grammars and I have to check if they are regular. Could you tell me how I can check this? $G_1:$$$ I \to aK|bL$$ $$K \to bL| \varnothing$$ $$L \to dL|cK| \varnothing$$ $G_2:$$$ I \to KL$$ $$K \to aK|bK| \varnothing$$ $$L \to cL| dL| \varnothing$$ $G_3:$$$I \to II|(I)|...

Hello! :) I have a question: Suppose that $\Sigma=\{0,1\}$.Is the language $\{0^{m}1^{n}:m+n \geq 2\}$ regular? I tried to find a regular expression.I checked the case $m+n=2$ and I found that the possible words are $00,01,11$ .But..how can I continue? :confused:

Hello! :) I have a question.Given $\Sigma=\{1,2,4,5,7,9\}$ and $L=\{w:w \in \Sigma^{*},\text{ and w as a decimal gets divided completely by } 7\}$,is the language L regular?

Homework Statement Let \alpha : I =[a,b]→R^{2} be a rgular curve parametrized by arc length s. Let f:I→R be a differentiable function with f(a)=f(b)=0. For small values of \epsilon \alpha_{\epsilon}:=\alpha (s) + \epsilon f(s) N(s) defines a one parameter family of regular curves...

Homework Statement We are supposed to compute the magnitude of vectors that make up a regular hexagon. We are given the magnitude of one side (its magnitude is 1). We are also supposed to compute one of the interior angles. Homework Equations I feel like this isn't enough...

Hey all. I'm a high school freshman; so I'm not exactly 'wise' when it comes to education. I've been self teaching myself physics over the last couple of months from Sears and Zemansky's University Physics, 12th edition, and although I started out very badly, I now have a very good grasp over...

Hi everyone, I don't fully understand what is the regular method to state and solve problems in GR when no handy hints like spherical symmetry or homogeneity of time are assumed. If I find myself in arbitrary reference frame with coordinates x^0, x^1, x^2, x^3 the meaning of which is unknown...

Hello! :) Could you tell me if the language {as^{(n)}ms^{(n)}t:a,m,t \epsilon \Sigma ^{*} ,s \epsilon \Sigma,m does not contain s and n\geq 0} is regular?

Hello! I have to draw the DFA of the language of the following expressions: a){1^*\{00,010,\varnothing\}(01)^{*}} b)(\{\{1,0\}^{*},(\varnothing,2)^*\})^{*} Could you help me to find the languages that are meant,so I can draw the DFAs?

Hello! I need some help at the following exercise: The language L={l ε {a,b}*:the word l does not contain the subword bba} is regular.Which are the equivalence classes of the relation \approx_{L} ? Also,which is the smallest(as for the number of states) deterministic automata that recognize...

Consider the ODE y''+P(x)y'+Q(x)y=0. If \stackrel{limit}{_{x→x_{o}}}P(x) and \stackrel{limit}{_{x→x_{o}}}Q(x) converge, can you call x_{o} a 'regular singular point' besides calling it an 'ordinary point'? I am saying this because if \stackrel{limit}{_{x→x_{o}}}P(x) and...