Property Definition and 608 Threads

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...

x(t) = sigma (from m = -infinity to infinity) z[SIZE="1"]m e^(j*m*omega*t) now my book says that using orthonormality property, we can calculate z[SIZE="1"]m by calculating scalar product of x(t) and e[SIZE="1"]m(t) (where e[SIZE="1"]m(t) = e^(j*m*omega*t)) hows that possible?? please feel...

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?

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!

Colligative property of ice cream HELP! How is the colligative property in effect during the manufacture of ice cream, and in the ice cream??

Let X be a space. Let \mathcal{D} be a collection of subsets of X that is maximal with respect to the finite intersection property. Show that if X satisfies the T_1 axiom, there is at most one point belonging to: I = \bigcap _{D\in \mathcal{D}}\bar{D} A collection of subsets has the...

sec 0 = 1/cos 0 Write the quotient property expressing tan 0 as a quotient of two other trigonometric functions...is there someone that please lead me in the right direction? Bryce

I had this question on a test today. Prove that if a function f:X-->Y is injective, then f(X\setminus A) \subset Y\setminus f(A), \forall A \subset X. This is how I did it: If x_1 is in A, then y_1=f(x_1) is in f(A). Because the function is injective, we can pick (cut Y into pieces) f(A) and...

Another question: Prove that if a set E in R has a finite infimum and e > 0 is any positive number, then there is a point a in E such that inf E <= a < inf E + e. The first part, inf E <= a, is obvious from the definition of infimum. I am having trouble showing that a < inf E + e, even...

I got a material property data for a steel as follows. 1.0.2% of proof load 358kg 2.0.2% of proof stress 28.64(kg/sqmm) My questions are 1)what is proof load 2)what is 0.2% of proof load. Why 0.2%? Why not 0.3% 3)How this proof load is arrived while testing the specimin in a...

Hello everyone, does anyone know the proof of the dot products communative property (a)(b) = (b)(a) or any websites that show the dot products communative property? or other properties? Thanks! The book only shows the distributed property.

How do I prove that when a function f is continuous on a closed bounded interval [a,b], it is uniformly continuous on that interval? Actually, I have found some proofs to this but I have not tackled about compact, Heine-Borel theorem, metric spaces, sequences and series, etc. in my class..

"property" vs "characteristic" OK, semantic hair-splitting time. The two words "property" and "characteristic" mean essentially the same thing, but they are often distinguished from each other in textbooks. For example, with waves there are two sets of attributes (yet another synonym) "the...

Why is the vanishing of a cyclic integral the property of a state function?

I'm not sure where this thread would go, but here it is... I am reading about the property of satisfiability. And trying to get some things straight. I saw different kinds of logics (porpositional, relational) being tested for satisfiability. I've read about models and formal systems. The...

Hi all Recently my roomates and I moved out of a duplex we rented. The security deposit was $2000. Our landlord said we did not clean the house at all (which is a huge lie) and charged us $1000, another $800 for removal of furniture (everyone says they took everything so no one knows what...

I can't remember for the life of me how to read Themodynamic property tables! I want to find answers to questions for example: What is the internal energy of 1kg of saturated steam at 10 bar or 3kg of water at 130C Can anyone help or know of any good websites which has information on how...

This ruling makes me very nervous. http://news.yahoo.com/s/ap/20050623/ap_on_go_su_co/scotus_seizing_property_10;_ylt=AjD7WnZAJ_f_VjRE9mHYjPduCM0A;_ylu=X3oDMTBiMW04NW9mBHNlYwMlJVRPUCUl I must admit nothing but pure contempt for developers, mostly because of the power they already have in...

quick question WOULD high melting points and boiling points be a property of petrolium aka crude oil.

I was thinking about x=0.999.. so 10x=9.999... therefore 10x-x=9 when I asked myself does the distributive property apply to an infinite number of terms since 0.9999...= sum(9/10^(-k), k=1,2...)? Maybe I'm confused about what "=" means.

Hi, I need help with this proof relating to strictly upper-triangular matrices. Let A be an n x n strictly upper triangular matrix. Then the (i,j-th entry of AA = A^2 is 0 if i >= j - 1. Here's what I have. Pf: Let B = A^2. The (i,j)-th entry of B is given by b_{ij} =...

So I've been thinking lately about what physics is really about. Isn't it true that at the end of the day physics is just a logical construction for us to understand the material world? Nobody has ever litterly 'seen' enities like energy, charge, electrons or even time and space. Simply...

Recall that every point (x, y) in the plane is described by its radius- vector r = xi + yj. A planar curve [gamma] has the following geometric property: at every point on the curve the radius vector and the tangent intersect at a fixed angle [alpha]. 1. Derive a first order differential...

I need to prove that if I := [0, 1/n], the element 0 belongs to all I(n) and the archimedian property to show that 0 is the only common point. so basically, I need to prove the intersection from 1 to infinite of I(n) = {0}. the book says to use the archimedian property that if t > 0, then...

Hi, I'm having a bit of trouble with this question. Use the property |integral over c of f(z)dz|<=ML to show |integral over c of 1/(z^2-i) dz|<=3pi/4 where c is the circle |z|=3 traversed once counterclockwise thanks in advance for any tips.

Consider N vectors, V_1 ... V_N, (not all zero) in an N-dimensional space. Project these vectors to a 2-dimensional plane, P. Let us denote the results for the i'th vector as (a_i,b_i) in Cartesian coordinates defined on the plane. We will be interested in considering these coordinates as a...

Show that the diophantine equation x^2 - y^2= n is solvable in integers iff n is odd or 4 divides n.

Hi, I've spent dozen of hours searching by my-self and dozen of hours searching on the Web. Now I need help. Who could provide a proof for this binomial property ? I need it for another proof. Thanks Tony Let: F_n=2^{2^n}+1 , n \geq 2 . Prove: F_n \text{ prime } \Longrightarrow F_n...

Hi, I fail finding a proof (even in MathWorld, in my Mathematic dictionary or on the Web) for the following property of Chebyshev polynomials: (T_i o T_j)(x) = (T_j o T_i)(x) = T_ij(x) when x is in ] -inf ; + inf [ Example : T_2(x) = 2x^2-1 T_3(x) = 4x^3-3x T_3(T_2(x)) = T_2(T_3(x)) =...

I am presently taking my first course in signals and systems and I have been charged with proving the scaling property of the impulse function; that: delta(a(t-to)) = 1/abs(a)*delta(t-to) I am seriously miffed and need some help.