Property Definition and 635 Threads

well i tried the CRC handbook and online search of 2-methoxyethyl-2-methylpropanoate

Given a constant one-form k_1 \ dx + k_2 \ dy + k_3 \ dz in \bold{R}^{3} , and three points \vec{a}, \ \vec{b}, \ \vec{c} in \bold{R}^3 , prove that \int_{\vec{a}}^{\vec{c}} k_1 \ dx + k_2 \ dy + k_3 \ dz = \int_{\vec{a}}^{\vec{b}} k_1 \ dx + k_2 \ dy + k_3 \dz + \int_{\vec{b}}^{\vec{c}}...

What property of the magnet determines which side of it is North and which side is South? I know that we are unable to separate the poles of a magnet (ie cut a magnet in halves and we get two magnets). How come?

Hi, I am just wondering if the zero product property (ab=0 implies a=0 or b=0) can be proven on the integers, or is it directly axiomatic to the defining of the integers? Also, where might I find a definition of the integer axioms? Thanks a lot,

Homework Statement a system has the following property: Its response to a sum of inputs is the sum of its responses to the inputs. (a) Prove that the scaling property holds for any integer scaling factor (b) Prove that the scaling property holds for any rational scaling factor...

My question is stated in the title. I wonder is it that scientists are not able to explain the origin of magnetic moment of elementary particles and say that it's an intrinsic property just like mass.

Let \left\{x_{n}\right\} be a nonempty sequence of monotonically increasing rational numbers bounded from above. Prove that \left\{x_{n}\right\} has a least upper bound in \mathbb{R}. If we choose a monotonically decreasing sequence of upper bounds \left\{b_{n}\right\} with the property that...

hello! i am quite new to material engineering and so my question might seem a bit too obvious. her it is: i have a metal ring-(picture1(304 stainless steel)) i need to know what property of the metal defines the ring's resistance to "opening"- like shown in the second picture thank you very...

I read that a single electron, when passing two slits, would exhibit wave like distribution on target screen. This makes me wonder about the following. 1) Would this have anything to do with the interference by the slots? I understand that my question may be moot because such interference...

So I am looking at the proof for this in a linear algebra book and I half way get it: Theorem: If the all elements of the jth column of a determinate D are linear combinations of two columns of numbers, i.e., if D=\lambda b_{i}+uc{i} where lambda and mu are fixed numbers, then D is...

Given a positive whole number n, \exists N with the following property: if A is a subgroup of {1,2,...,N} with at least N/2 elements, then there is a positive whole number m<= N - n such that |A \cap{m+1, m+2,..., m+k}|>=k/2 \forall k = 1, 2, …, n.

Homework Statement The theorem about the closest point property says: If A is a convex, closed subspace of a hilbert space H, then \forall x \in H\,\, \exists y \in A:\,\,\,\, \| x-y\| = \inf_{a\in A}\|x-a\| I have to show that it is enough to show this theorem for x = 0 only, by...

Can anybody tell me what are Residual property and Excess property in thermodynamics for?

Prove that if the functions g:[a,b] --> R and h:[a,b] --> R are continuous, with h(x)\geq0 for all x in [a,b] then there is a point c in (a,b) such that \int h(x)g(x)dx = g(c) \int h(x)dx when the integrals go from a to b --- My immediate thought was Integral MVT, so I said \int...

So, I know the proof for a non-decreasing set using the continuity property, and I'm wondering if I have to use the intersection of all pairwise disjoint sets rather than the union, as seen in the non-decreasing proof. Any help would be greatly appreciated!

Someone please help me with this qiestion: Prove that for all integers a, b, and c, if a divides b but not c then a does not divide b + c, but the converse is false. Thanks.

What property of light does the photoelectric effect display?

I know this is elementary but I'm having trouble with proofs of some of the convolution properties: 1. f * (g * h) = (f * g) * h 2. (cf) * g = c(f * g) = f * (cg) Please show me the proofs step by step or lead me to a link where the detailed proofs are displayed. Sorry for such...

Is it possible for atoms of the same chemical element to have different chemical properties? My attempt Isotopes of an element differ from one another by the number of neutrons in the nucleus. They have same number of proton in the nuclei so they have the same chemical properties but not...

If gravity is a "property" of Mass, and mass is a "property" of matter, and matter is known to be composed of highly integral infinitessimal Force Fields, why jump to the conclusion of Gravitons, when one has not thoroughly defined Force Field. Of what are these force fields composed? Is the...

The adjoint of an operator A is defined as an operator A* s.t. <\phi|A\psi> = <A^{*}\phi|\psi>. How would you use the properties of inner products (skew-symmetry, positive semi-definiteness, and linearity in ket) to show that (cA)* = c*P* Note that I am using the conjugate and the...

Homework Statement Given x<y for some real numbers x and y. Prove that there is at least one real z satisfying x<z<y Homework Equations This is an exercise from Apostol's Calculus Vol. 1. The usual laws of algebra, inequalities, a brief discussion on supremum, infimum and the...

Homework Statement The nested set property: "If {F_k} is a decreasing sequence of non empty compact sets in a metric space (M,d), then their intersection is non empty." First I cooked up a proof of my own and then I read the one provided by the book. It seemed to me that they were perfectly...

If I put some kind of alcohol, can it destroy the property of vitamin C?

Hi When we fill a tumbler( of stainless steel) with water and then invert it ie empty it . The tumbler gets empty except a few drops of water. even if you keep the tumbler inverted for hours the water droplets do not fall down they remain stuck to the walls of the tumbler. I hope you...

Homework Statement I am to prove that P_n(-x)=(-1)^n*P_n(x) And, P'_n(-x)=(-1)^(n+1)*P'_n(x) Homework Equations The Attempt at a Solution I know that whether a Legendre Polynomial is an even or odd function depends on its degree.It follows directly from the solution of...

I have a pictorial example in a book here of a solid that behaves very strangely indeed. I would have called it 'biaxial metallicity' but I have no idea what the correct term is - the material is apparently metallic in one direction but not in another - that is, appears to obey the free or...

Hi there, I've been asked to prove that (R^2, S^1) has the homtopy extension property and then extend it to the general case: (R^n, S^(n-1)) here's where I've got so far, for (R^2, S^1) Let S^1=A, R^2=X well S^1 is contained in R^2, so by a theorem, if A contained in X, has a mapping...

so I'm having trouble with an integral. However I noticed an interesting property to it.int{gdu}=c*int{gd^2u} with the integral being from -infinity to positive infinity. The problem arose while I was trying to solve the schroedinger equation in the presence of a potential, I'm trying to...

I've bought a house! :smile: And have spent the last 2 weeks packing, moving in, unpacking, decorating, and buying and building furniture! It's all very scary, and I'm now tied down with a mortgage until 2037, but it's great fun! I think I probably qualify for entry in the world...

Homework Statement Show that a superadditive function has the following property: For any superadditive function g on XxY (cartesian product): f(x) = min { y' : y' = argmin g(x,y) } is nonincreasing in x. Homework Equations if g(x,y) is a superadditive on XxY, x in X, y in Y, x1 >=...

Hi, Why is it that if A is m×n-matrix and B is n×m matrices such that m<n, then AB is m×m and BA is n×n matrix. Then the following is true: pAB(t) = t^(m-n)*pBA(t) where pAB(t) and pBA(t) are characteristic polynomials of AB and BA thanks

A Wikipedia article says: "The surface of the inner core exhibits rapid variations in properties at scales at least as small as 1 km. This is puzzling, since lateral temperature variations along the inner core boundary are known to be extremely small (this conclusion is confidently constrained...

Here is the question: -------- Let f: \mathbb{R} \rightarrow \mathbb{R} satisfy f(x+y) = f(x)f(y) \ \forall x,y \in \mathbb{R}.Let a = f(1) > 0. Show that f(r)=a^r \ \forall r \in \mathbb{Q}. --------- This question actually has multiple parts to it. I have already proved the following...

Homework Statement Prove the reflective property of the ellipse. Homework Equations x^2/a^2 + y^2/b^2 = 1 (equation of ellipse) tan theta = m2-m1/(1+m1m2) m = (y1-y0)/(x1-x0) The Attempt at a Solution I apologize if this is to simple for this forum, not sure where else to put it...

This has to do with the wedge product ^ on alternating tensors. I can't seem to prove w ^ n = (-1)^kl * n ^ w. where w is a k alternating tensor and n is an l alternating tensor. I know w ^ n = (k+l)!/(k! l!) * Alt(w x n) where x is the tensor product. Now, Alt(wxn) (v_1,...,v_k+l) =...

Why the charge on the drum in a photocopier disappears when light shines upon it? My solution says that it's because the drum is photosensitive. but what is "photosensitive" property ?

Hello, Recently, I've come across a textbook question based on permutation. I've even got the answer to that, but i want to verify my steps, because each time i solved the question, i realized how tricky it was, and i had to modify my approach. Heres my final approach, please spot any...

They decided to build a big ass highway in my back yard and my property value is going to tank. Now we have to move out of our dreamhouse :mad:. My parents asked me if I wanted to say, but I told them its a nice house, but I can't justify loosing that much money just because I think its nice...

x(t) = sigma (from m = -infinity to infinity) zm e^(j*m*omega*t) now my book says that using orthonormality property, we can calculate zm by calculating scalar product of x(t) and em(t) (where em(t) = e^(j*m*omega*t)) hows that possible?? please feel free to move the thread if its in wrong...

My test here asks me to: "Use log5 2 =0.4307 and log5 3=0.6826 to approximate the value of log5 12." According to my textbook I would solve this by subtracting (using the quotient property): 0.6826-0.4307. That = 0.2519. But that number isn't right! log5 12=1.544 (about) Which I found...

when we normally see the "stress -strain" curve is having stress on y-axis and strain on x axis. that mean stress is the response of the structure and strain is the input can i say the following stress -strain curve,stress in the x-axis and strain in the y axis. because when i apply a...

i wanted the techinical information. bending property of solid pipe and hollow pipe with same diameter. which will bend more and why ? i wanted the technical answer please help me out :smile:

Yes, the same questions as in the topic. What gives particles their property, like charge, structure, what to interact with, amount of energy and all the like? And also another question, are 2 protons the same? From a visible world, me may easily conclude that no 2 things exactly alike. Even...

Sir, It is said that it is possible to distinguish between transverse and longitudinal waves by studying the property of polarization. Also it is said that longitudinal waves cannot be polarized but transverse waves can be polarized. Are they true?

If f:S \to R is a continuous function on a surface S, we define \int\limits_{}^{} {\int\limits_S^{} {fdS} } = \int\limits_{}^{} {\int\limits_D^{} {\left( {fo\Phi } \right)} } \left\| {\frac{{\partial \Phi }}{{\partial u}} \times \frac{{\partial \Phi }}{{\partial v}}} \right\|dudv...

i have a couple questions which i didnt want to continue on posting in the other thread or else it would get extremely hard to follow. 1. recall that the Intersecting Secants Property states that if two secants AB and CD intersect at an external point P, then PA x PB = PC x PD. well, i need...

In my econ homework, I was asked to prove that: A set C is convex iff a C + b C = (a+b) C for all nonnegative scalars a and b. All that I'm given is that the definition of a convex set is, for x,y elements of a convex set C: (1-a) x + a y exists in C, for 0<a<1 My thoughts were to first...

Hi dudes, don't be put off by the clumsy notation here. I was wondering about these particular exponent towers and this curious property of theirs... Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p. e.g. for p=2. tower part...

What are your thoughts, in general terms, on the notion of time as an emergent property? In what ways could time be a product and side effect of some other, move fundamental process or entity? I've been thinking on it, and I thought some other people's thoughts would be useful. Thanks!