Regular Definition and 251 Threads

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 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" ...

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...

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...

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...

I am not in the honors program at my University but I really want to get good at math so I was thinking about perhaps enrolling in an honors section for the Discrete math and Linear Algebra classes I'll be taking next fall. It seemed like the greater depth that these classes go would be really...

Homework Statement A uniform rod AB of mass M and length 2l attatched to a slider at A which is constrained to move along a smooth horizontal wire. The rod, which is subject to gravity, is free to swing in the vertical plane containing the wire. Using Ω (the angle between rod and vertical)...

Hi, I'm a undergraduate, major in physics at Weber State University in Utah. I have a very serious debate about whether is better for me to graduate here at Weber or make a transfer to the University of Florida (since am a resident in Florida). I began by getting my GED at seminole Sate...

Does anyone know if a set of homogeneous polynomials forms a reduced Grobner basis, then they form a regular sequence in the polynomial ring? Any references? All the references that I have looked at (so far) have not related the two. If this is not true, can you give me a counterexample...

I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string accepted by the DFA. Does anyone know of a "formal" proof that shows this is true in all cases...

ABCDEF is a regular hexagon with $\vec {BC}$ represents $\underline {b}$ and $\vec {FC}$ represents 2$\underline {a}$. Express, vector $\vec {AB}$, $\vec {CD}$ and $\vec {EC}$ in terms of $\underline {a}$ and $\underline {b}$. Before I start, I want to ask if we need to redefined $\underline...

Hi everyone! I am new to the forum but you have helped me many times in the past. I need your opinion about how much (roughly) brake torque can be produced by a regular car. I am developing a simplified vehicle model and I don't know how much torque to apply when the vehicle slows down. I...

Why is a quantum computer theoretically faster than a regular computer? Is it because of parallelization?

If dark matter is actually there and not just some flaw in our understanding or mathematics then how can galaxies be made of both and not just one or the other. If dark matter doesn't interact with anything else like light then how can a dwarf galaxy be made of "mostly dark matter"?I know its...

A is a square matrix such as: A^2 + A + I = 0 Which answer is correct ? a. A^-1 = A b. A^-1 = A^2 c. We can't tell if A is invertable d.A is not invertable e. A^-1 = A + I I have tried to play with the equation, I tried to multiply in A^-1 and to isolate it, but it didn't get me anywhere...I...

Homework Statement A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.200 m/s and acceleration -0.290 m/s2. Suppose it moves with constant acceleration for 5.80 s. Position of Particle after 5.80 Seconds - -3.4678 m. Velocity of Particle...

Homework Statement Why do transition metals tend to form +1/+2 ions? Take electron configurations into account so that I can better understand this "easy" concept.2. The attempt at a solution I think it has to do with the s orbitals. These, I think are valence electrons that are easily lost...

An electrically charged particle has an electric field centred around itself that extends far into space. That field has an energy density proportional to the electric field squared. By Einstein's E=mc^2 that energy density is equivalent to a mass density. Thus, as a charged particle...