Regular Definition and 269 Threads

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?

Show that languages are regular! Homework Statement Use the lemma: <<If the language L(A) of an automaton A has an infinite number of words,then there are words a,m,t ε Σ*,so that |at|≤|Σ_{k}|,and each word a m^{i}t,i≥0 is contained in L(A) >>(version of Pumping Lemma)and show that the...

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...

At first I just thought there was just algebra and college algebra, but trying to figure out what math I still need, I found all sorts of college maths, and I was curious, what do I expect beyond bigger numbers?

Given t\in Ithe arc length of a regular parametrized curve \alpha : I \to \mathbb{R}^3 from the point t_0 is by definition s(t) = \int^t_{t_0}|\alpha'(t)|dt where |\alpha'(t)| = \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2} is the length of the vector \alpha'(t). Since \alpha'(t) \ne 0 the arc length s...

Given t\in Ithe arc length of a regular parametrized curve \alpha : I \to \mathbb{R}^3 from the point t_0 is by definition s(t) = \int^t_{t_0}|\alpha'(t)|dt where |\alpha'(t)| = \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2} is the length of the vector \alpha'(t). Since \alpha'(t) \ne 0 the arc length s...

When expanding a function (for example the determinant of the space-time metric g) as a functional of a perturbation from the flat metric ##h_{\mu \nu}##, i.e. ##g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} ## i would think that the thing to do is to recognize that ##g_{\mu \nu}## and thus also...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Homework Statement How do you calculate the moment of inertia of a regular hexagonal plate of side a and mass M along an axis passing through its opposite vertices?Homework Equations Moment of inertia for a right triangle with an axis running along its base would be I = m h2 /6 where h and m...

Proving lemma about regular polygons? Homework Statement Can a n-1 sided regular polygon be inscribed in n sided regular polygon for \forall n \in \mathbb {N} \gt 3 Homework Equations N/A The area of n-1 sided regular polygon may be the largest of any n-1 polygon which is to be...

I'll be taking my first calculus class ever on this coming fall. I am pretty excited for it. I want to major in Chemical engineering, and when I have looked at the university class lists it says engineering for calculus and I am in a community college which means my calculus class will be a...

Homework Statement The only singularities of the differential equation y''+p(x)y'+q(x)y=0 are regular singularities at x=1 of exponents \alpha and \alpha', and at x=-1 of exponents \beta and \beta', the point at infinity being an ordinary point. Prove that \beta=-\alpha and \beta'=-\alpha'...

Homework Statement Consider the map \Phi : ℝ4 \rightarrow ℝ2 defined by \Phi (x,y,s,t)=(x2+y, yx2+y2+s2+t2+y) show that (0,1) is a regular value of \Phi and that the level set \Phi^{-1} is diffeomorphic to S2 (unit sphere) Homework Equations The Attempt at a Solution So I...

NOT including the prediction capabilities of the particular math equations of GR or SR. In particular, hard evidence such as, or close to; here's an electron, because we measured it directly, or saw it in an electron microscope. Or here's a cell under a microscope. Or this is a brain scan/MRI...

Since manifolds are locally compact Hausdorff spaces, manifolds are necessarily Tychonoff spaces. And a Tychonoff space is a topological space that is both Hausdorff and completely regular. This is cut and paste from wikipedia.org. Further, X is a completely regular space if given any closed...

Hello, it is known that "Every regular G-action is isomorphic to the action of G on G given by left multiplication". Is this true also when G is a Lie group? There is an ambiguous sentence in Wikipedia that is confusing me. It says: "The above statements about isomorphisms for regular, free...

In every top of a regular polygon with 2n tops there is written an integer number so the numbers written in two neighboring tops always differ by 1 ( the numbers are consecutive ) The numbers which are bigger than both of their neighbors are called ”mountains” and those which are smaller than...

So, I'm working a bit through munkres and I came across this problem Show that every locally compact Hausdorff space is regular. So, I think I've solved it, but there is something confusing me. I initially said that if X is locally compact Hausdorff, it has a 1-point compactification, Y...

I have got next interesting geometry example :-) I have got regular hexagon ABCDEF, when S (mark for area in Czech... and in the USA, British I don't know :D) 30cm2. In the hexagon is M. You know: ABM(S)=3cm2 and BCM(S)=2cm2. What is S of: CDM, DEM, EFM and FAM? So, about me... I don't...

Homework Statement Hello guys! I've never dealt with an ODE having 2 singularities at once, I tried to solve it but ran out of ideas. I must solve ##(x-2)y''+3y'+4\frac{y}{x^2}=0##. Homework Equations Not sure. The Attempt at a Solution I rewrote the ODE into the form...

Howdy, I came across a regular expression i couldn't get my head around. ' there \([^ ]*\)' echo "Howdy there neighbor" | sed 's/there \([^ ]*\)//' returns howdy. It's the subgroup that's a bit confusing. match any sentence which contains banana then a space and then a non-space character...

Homework Statement Hi! i want to ask somebody who are studying quantum mechanics about the definition of regular transformation. I guess there might be people who are not familiar with the notion. So, i'd like to let you know which book I'm referring to; "principles of quantum mechanics" ...

Let m : [0,L] → ℝ2 be a positively oriented C1 regular Jordan curve parametrized with arc length. Consider the function F : [a,b] x [a,b] → ℝ defined by F(u,v) = (1/2) ||m(u) - m(v)||2 Define a local diameter of m as the line segment between two points p = m(u) and q = m(v) such that: The...

Homework Statement Let m : [0,L] --> ℝ2 be a C2 regular closed curve parametrized with arc length, and define, for an integer n > 0 and scalar ε > 2 μ(u) = m(u) + εsin(2nπu/L)Nm(u) where Nm is the unit normal to m (1) Determine a maximum ε0 such that μ is a closed regular curve for...

On Math-Atlas, where does "regular" Algebra fit in? Where on the Math-Atlas does Algebra I and Algebra II fit? Should I assume "Algebra I and Algebra II" are essentially generalized, introductory courses that cover a subset of branches under the "Abstract Algebra" branch? I'm starting school...

I was wondering if anyone knew of a common technique for parametrizing a regular polygon with an arbitrary number of sides. I figured such a problem would be easy or at least be well documented online, but that doesn't seem to be the case. I started by assuming that the polygon was centered...

Homework Statement In a regular hexagon, ABCDEF, forces of magnitude 2N, 4N, 3N and 2N act along the lines AB, AC, AD and AF respectively. Find the equilbrant of the given forces and verify that is equal and opposite to their resultant. The Attempt at a Solution I realized that AB + BC...

Hi all, I am trying to understand the concept of Markov Chain (a scan copy of 2 pages is attached), before this text I already studied the notes on Markov Chains at: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf I am lil' confused at the...

Homework Statement 4 identical charges each equal to Q are placed at the 4 vertices of a regular triangular pyramid of each side equal to 'a'. Find the net electrostatic force on anyone charge. Homework Equations F = kQ^2/a^2 The Attempt at a Solution find the force due to each...

I plan to begin studying for the physics GRE no later than the beginning of August, but I hardly have any plans on studying for the regular GRE. After three years of physics I really can't imagine memorizing history dates and whatever other crap is on the regular GRE. Do grad schools really...

Homework Statement According to the question, i have to convert 3.60 * 105 to regular notation, without changing the number of significant figures, which is currently, as i understand, three. I'm just really unsure how to do this. Any help? Homework Equations Some said to write out...

Hello, I have been trying to solve the following problem about regular surfaces from Do Carmo's book of differential geometry of curves and surfaces, section 2-3, exercise 14. Homework Statement Problem: Let A\subsetS be a subset of a regular surface S. Prove that A is a regular surface...

I’m having trouble getting my head around this example and solution that was given as part of a revision pack for an upcoming exam. Any explanation would be gratefully received. Question: A simply supported regular I beam is 90mm wide and 120mm high. The top and bottom flanges are 10mm...

Hello, I'm a math tutor at a community college, and one of the students recently asked me why it is always true that a *regular* polygon (regular meaning equiangular and equilateral) has maximum area for any given perimeter. It makes perfect intuitive sense, but neither I nor any of the other...

Regular open sets,,,, If U is an open set in a topological space (X,τ),is it true that U=〖int〗_X 〖cl〗_X U?Justify.

Homework Statement Find the indicial equation and find 2 independent series solutions for the DE: xy''-xy'-y=0 about the regular singular point x=0 Homework Equations y=Ʃ(0→∞) Cnxn+r y'=Ʃ(0→∞) Cn(n+r)xn+r-1 y''=Ʃ(0→∞) Cn(n+r)(n+r-1)xn+r-2 The Attempt at a Solution Finding the...

Hello, I have a question regular values and smooth homotopies. Usually in giving the definition of regular value, they disregard the regular values whose inverse image is empty set (although they should be called regular values if we want to be able to say that set of regular values is dense for...

This question is in regards to higher dimensional algebraic geometry. The actual problem is very complicated so here is my question which is substantially simplified. Suppose {f_1,... f_k} is a set of quadratic polynomials and {g_1,...,g_l} is a set of linear polynomials in a polynomial ring...

can anyone hlep me with this qustion ? Consider the equation ε x^3 + x^2 - x - 6 = 0 ,ε > 0. (1) 1. Apply a naive regular perturbation of the form x~^{0}_{∞}Ʃ xn εn as ε→0+ do derive a three-term approximation to the solutions of (1). 2. The above perturbation expansion...

Does group velocity effect long linear waves generated by a paddle generating waves in deep water? I have developed a numerical wave tank in CFD at full scale, using a bottom hinged flap paddle that oscillates to produce regular waves, the domain is roughly three wavelengths long, and a beach...

Quick question. Suppose we have a manifold with a metric and a metric compatible symmetric connection. Suppose further that we have a smooth vector field V on this manifold. I see two ways to take the derivative of this vector field. I can regard my vector field as a vector-valued 0-form...

Dear Folks: In most textbooks on differential geometry, the regular theorem states for manifolds without boundaries: the preimage of a regular value is a imbedding submanifold. What about the monifolds with boundaries...

"unity" means just plain regular "1"? Im not sure whether this is a physics or math question, but in many physics problems, instead of saying "1", the problem will say "unity", like "the sine of theta is unity" or the "index of refraction is unity". I am assuming "unity" means just plain...

So any help would be really appreciated! I really have no idea where to start, and I can use any help. So essentially the problem is we have a regular polygon P inscribed in a unit circle. This regular polygon has n vertices. Fix one vertex and take the product of the lengths of diagonals...

There seem to be two definitions for a regular representation of a group, with respect to a field k. In particular, one definition is that the regular representation is just left multiplication on the group algebra kG, while the other is defined on the set of all functions f: G \to k . I do not...