Dimension Definition and 881 Threads

Homework Statement A car traveling at 25.43 m/s runs out of gas while traveling up a 17° slope. How far up the hill will it coast before starting to roll back down? Homework Equations Not sure on the equation to be used? The Attempt at a Solution

This confirms a beautiful result of Modesto's earlier paper, that LQG seems to coincide with two other very different types of quantum geometry/gravity on the business of dimensionality declining continuously with scale. Fractal-like microstructure of space time. As scale decreases the observed...

Purely from a non-mathematical perspective, could some/any/every-body answer my questions on the electromagnetic force in extra dimensions? άλφα) I am curious about how in the old Kaluza theory of the electromagnetic force the equation, which he found from his equations worked when it...

Homework Statement A box slides along a surface with a positive initial velocity. It the experiences an acceleration of -0.25m/s^2. After traveling 4.00 meters, its velocity is +0.50m/s. How long did it take for the boxto travel the 4.00 meters? Homework Equations \Deltax=Vot + 1/2 a t^2...

Suppose there is an extra compact spatial dimension in addition to familiar space dimensions x, y, and z. Let us suppose that matter is some kind of 3 dimensional surface moving in these 4 spatial dimensions, 4-space, in some cyclical manner. Let us suppose that from the shape of the surface we...

Hi there, I have a question. To me, measuring spatial dimensions is quite a bit different than measuring the time dimension. I was thinking the other day and it seemed very obvious to me what the main difference was. Time never goes the other way. A dimension defines two equal and...

could GR generalized to non-integer dimension?? let us suppose that the dimension of space time is NOT an integer then , could we generalize GR to obtain an expressions of Tensor, Covariant derivatives... in arbitrary dimensions ?? let us say 4.567898.. or similar, i mean GR in non integer...

My analysis textbook mentioned in passing that the range of the Hausdorff dimension is all nonnegative real numbers, i.e. for any nonnegative real number a, there's some compact subset of R^n whose Hausdorff dimension is exactly a. The problem is that I don't see how to prove this (and my...

Homework Statement A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. Homework Equations volume of a cone (1/3)(pi)(r^2)(h) = 30 SA of a cone pi(r)[sqrt(r^2 + h^2)] The Attempt at...

Homework Statement If {u1, u2,...,um} are nonzero pairwise orthogonal vectors of a subspace W of dimension n, prove that m \leq n. The Attempt at a Solution I look at all my notes but I still can't understand what this qurstion asks or what definitions I need to be using for this... I'm...

Are there any reference tables for what to use as the characteristic dimension of various shapes when calculating the Reynolds number? I am very interested in ballistics, and have done research and calculations for various ways of estimating the drag coefficient of various bullet shapes. I...

let g be the inverse function of f (not necessarily a bijective inverse function) If S is any subset of W then the pre-image of S is g(S) = {v ε V: f(v) ε S} Suppose that U is a subspace of W. Prove that g(U) is a subspace of V. Also prove that dim( g(U) )= dim( U intersect Im(f) ) +...

Homework Statement Let V be a vector space over C of dimenson n . We view V also as a vector space over R by restricting the scalar multiplication of C on V to R .Show that dimR(V) = 2n Homework Equations The Attempt at a Solution I have to show that if x1,...xn form a basis of V...

Let's say there is a water based heating device that has 3/4" connection nipples. The pipe that leads to the device is 5/4". If one ignores pressure- and head loss, does it make any difference how far from the device the pipe reduces from 5/4" to 3/4" ?

Homework Statement find a basis of the null space N(A) in R^5 of the matrix A = 1 -2 2 3 -1 -3 6 -1 1 -7 2 -4 5 8 -4 in M3*5 (R) and hence determine the dimension Homework Equations The Attempt at a Solution i found that A= 1 -2 2 3 1 0 0 1/5 2/5 -2/5 0 0 0 0 0 by...

Prove: the set of 3x3 symmetric matrices is a vector space and find its dimension. Well in class my prof has done this question, but I still don't quite get it.. Ok, first off, I need to prove that it's a vector space. The easy way is probably to prove that it contains the zero space and...

So I've been told that electromagnetic waves oscillate like flicking a rope up and down or a ripple in a pond. In the first example, from a side view, the rope can be considered to be a line, or 1-dimensional. However, once the ropes starts oscillating to represent waves, width must also be...

I don't know whether it was proved or can be prove. I don't know whether it is useful. maybe it can be used in string theory or some other things. any comment or address will be appreciated.

out of curiosity is there any theory on how dimensions that we exist in were created? or are they always said to have existed.

Homework Statement A motorcycle with a mass of m1 = 200 kg and a speed of v1 = 120 km/h collides with a car of mass m2 = 600 kg, traveling in a perpendicular direction to the motorcycle. After the collision, both vehicles travel in a direction that forms an angle of 60°. Find the initial...

I've had this on my mind for a while. I'm pretty confident that I have the right idea, but I can't find a formula that I could use to prove it to someone. So, here it is. Imagine a sphere of space-time with absolutely nothing inside of it. It is a large sphere, sun-size large. Now, take...

Earlier, I had a thought, and I have now been curious about the equation of this thought. Einstein's general relativity obviously states that objects curve and distort space. But the whole reason he came up with a cosmological constant was that he found that the curvature of all of the objects...

Homework Statement Let U, W be subspaces of a vector space V. Show that dim(U+W) = dim(U) + dim (W) - dim (U intersect W). Homework Equations The Attempt at a Solution I can see this picture-wise in a venn-diagram form. In adding U and W you count the elements in their...

Hello, I hope it's not the wrong forum for my question which is the following: Is there some list of Lie algebras, whose adjoint representations have the same dimension as their basic representation (like, e.g., this is the case for so(3))? How can one find such Lie algebras? Could you...

The claim was made tonight on a program about science fiction writers that HG Wells was aware of a geometry of 4 dimensions, and then made the leap of faith that time was a 4th dimension - ten years before Einstein came along. Did he really conceive of this before anyone else? I never read...

Homework Statement http://img410.imageshack.us/img410/8495/88748860vk8.png Homework Equations The Attempt at a Solution I don't know how to deal with the q1 part. q2 = u* =u x sqrt(... so that is clear. Normally I just substitute the expression for u in terms of u* (= f* )and t in terms of...

Homework Statement http://img21.imageshack.us/img21/613/70858934fn5.png Homework Equations Buckingham theoremThe Attempt at a Solution My question is what is the difference between question a and b? The sine doesn't influence the dimension. Or is it a question to trick me?

Just have a question if U,V and W are over the same field K does it mean that dim U = dim V = dim W ?

How do we calculate the dimension of a matrix? Is it the number of entries? Or is it the number of different entries? For instance if I have a matrix 2x2 the dimension would be 4 but if the matrix is simetrical it would be 3. Is this correct? Thanks for your help.

Homework Statement In the following exercises verify that the row rank is equal to the column rank by explicitly finding the dimensions of the row space and the column space of the given matrix. A = [1 2 1 ; 2 1 -1] Homework Equations The Attempt at a Solution All i can...

Homework Statement A commuter train travels between two downtown stations. Because the stations are only 1.30 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the travel interval Δt between the two stations by accelerating for a...

Kathy Kool buys a sport car that can accelerate at the rate of 4.90 m/s2. She decides to test the car by racing with another speedster, Stan Speedy. Both start from rest, but experienced Stn leaves the starting line 1.00 s before Kathy. Stan moves with a constant acceleration of 3.50 m/s2 and...

Homework Statement A runner hopes to compleate the 10,000m run in less than 30.0min. After running at a constant speed for exactly 27.0min there are still 1100m to go. The runner must then accelerate at 0.20 m/s^2 for how many seconds in order to achieve the desired time. *note* person does...

Hey everyone. I was recently on youtube, looking at 4-d objects, when I came across a comment which caught my eye: "You're forgetting Gravity. Without gravity there is no xyz and without two large bodies there is no concept of time. Therefore, gravity must be included as a dimension. They are...

can anybody tell me why in general phase transition is not possible in one dimension? and for a lattice gas at low temp. why it requires long range order to occur phase transition?

Homework Statement A runner hopes to complete the 10,000-m run in less than 30.0 min. After exactly 27.0 min, there are still 1100 m to go. The runner must then accelerate at 0.20 m/s2 for how many seconds in order to achieve the desired time? Homework Equations vf = vo + at avg...

Homework Statement Let V be a finite vector space, and A, B be any two linear operator. Prove that, rank A = rank B + dim(Im A \cap Ker B) The Attempt at a Solution Since rank A = dim I am A dim(Im B)+ dim(Ker B)=dim V dim(Im A + Ker B)=dim(Im A)+dim(Ker B)-dim(Im A \cap Ker B) It...

I have read a number of threads that argue the ontological status of time in physics. One of the most concrete "descriptions" of time in physics is offered by Huw Price. Huw Price suggests time is symmetrical, but the order of events in time are not. http://arxiv.org/abs/physics/0402040...

Homework Statement Claim: Matrices of trace zero for a subspace of M_n (F) of dimension n^2 -1 where M_n (F) is the set of all nxn matrices over some field F. Homework Equations Tr(M_n) = sum of diagonal elements The Attempt at a Solution I view the trace Tr as a linear...

Hi all! I´m trying to prove following two inequalities but I somehow got stuck: U, W are subspaces of V with dimV = n 1) dimV >= dim(U+W) 2) dim(U+W)>=dimU and dim(U+W)>=dimW Could you give me some hints? thanks in advance!

I am having trouble accepting two well known results of analysis as non contradictory. First, given a vector space equipped with norm ||.||, the unit ball is compact iff the space is finite dimensional. Second, the Arzela-Ascoli theorem asserts that given a compact set X, a set S contained...

Please help! i know how to do a elastic collisions in 1 dimension, but the 2D is too confusing...here is my problem: You have a blue ball with a mass of 1.5 kg moving with a speed of 4.5 m/s in a direction below the positive x-axis. You have a red ball with a mass of 3.6 kg moving with a...

Homework Statement What are the basis for the row space and null space for the following matrix? Find the dimension of RS, dim of NS. [1 -2 4 1] [3 1 -3 -1] [5 -3 5 1] Homework Equations dim RS + dim NS = # of columns The Attempt at a Solution I reduced the matrix into...

is time a "dimension" I have been trying to figure this one out for some time now. I have read much on the subject, but it seems to be dealt with in such a cavalier fashion. So, here goes... We speak of space-time as if it were something packaged. I have a problem with this. Let me list the...

Short version: What is the difference between the Lebesgue measure and the box counting dimension of a set? Long version: I was reading up on the definition of the Lebesgue measure, and the description of how to take the Lebesgue measure of a set (which I understood basically as "cover the...

Homework Statement Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 5.0 mi/h, the time to go one mile decreases by 13 s. What was your original speed in mi/hr? Homework Equations X (which in...

1. Kevin has a mass of 87kg and is skating with in-line skates. He sees his 22-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 3.4 m/s. Ignoring friction, find Kevin's speed just before he grabbed...

Homework Statement You are asked to consult for the city's research hospital, where a group of doctors is investigating the bombardment of cancer tumors with high-energy ions. The ions are fired directly toward the center of the tumor at speeds of 4.5 . To cover the entire tumor area, the...

hi, I am new to this forum and i have been having great difficulties with this question... Homework Statement An airplane with a speed of 81.6 m/s is climbing upward at an angle of 44.7 ° with respect to the horizontal. When the plane's altitude is 944 m, the pilot releases a package. 1)...

i know that idea would seem a bit weird but, let us suppose we have a surface or volume in d- dimension, here d can be any real number (fractional dimension) the question is that we do not know what value 'd' is \frac{\partial \phi}{\partial t} = D\,\Delta \phi D is a diffusion...