Property Definition and 608 Threads

Hi, I've found this property of Strenght Field Tensors: $$F_{\mu}^{\nu}\tilde{F}_{\nu}^{\lambda}=-\frac{1}{4}\delta_{\mu}^{\lambda}F^{\alpha\beta}\tilde{F}_{\alpha\beta}$$ Where $$\tilde{F}_{\mu\nu}=\frac{1}{2}\varepsilon_{\mu\nu\alpha\beta}F^{\alpha\beta}, \qquad \varepsilon_{0123}=1$$ I've...

I'm pondering something about properties of integrals. What can we say about the following limit? ##\lim_{t\to\infty} \int_t^{\infty } f(x) \, dx## On one hand, the 'gap' from the lower to upper integration limit diminishes, so that would suggest the limit is always 0. But what if f is an...

Is it possible to change a fundamental property of a particle? If that can be done, will it's twin particle's state also be altered accordingly?

2019 is the smallest number that can be expressed as sum of 3 squares of prime number in 6 different ways 2019 = $7^2+11^2+43^2$ = $7^2 + 17^2 + 41^2$ = $13^2+13^2 + 41^2$ = $11^2+23^2+37^2$ = $17^2 + 19^2 + 37^2$ =$ 23^2+23^2+31^2$

In Hebrew, one explain to me that: "Transitivity is a property (or attribute - I don't which word is correct) of property". So, (1) Which word is correct? (2) Why Transitivity is not standalone by itself? (3) Are there relations of other kind, that no standalone by themselves?

Hello all - I am after a little help and was hoping I could find the answer here! A property is worth $550,000 and the bank requires 20% equity is kept in the house. To buy a second property (say $600,000 for arguments sake) the bank requires a 35% deposit. I want to calculate how much I need...

I am trying to gain a very basic understanding of voltage. I understand amps and resistance, but not voltage. I am thinking of a copper wire that is used in a basic electrical circuit to light a light bulb. Is the voltage of this wire an inherent property of copper at a given temperature...

Hello! (Wave) I want to show that $\ell$ is the infimum of a set $A$ iff $\ell$ is a lower bound of $A$ and for each $\epsilon>0$ there exists an $a \in A$ such that $\ell+\epsilon>a$. I have thought the following so far for the direction "$\Leftarrow$". Let $\ell$ be a lower bound of $A$ such...

Homework Statement Give an example of the associative property of vector addition using vectors in Cartesion form. Homework Equations (u+v)+w=u+(v+w) The Attempt at a Solution I can't figure out how to get the arrow on top of my work so I wrote it without it. I'm somewhat confused on why I...

Firstly, please note that I am talking about the period BEFORE electricity and magnetism were unified. So I am NOT seeking for answers based on Ampere atomic current model of magnets. I have read the following statement about the property of magnets at two different places. One from here: and...

Homework Statement I’m being asked to prove if and why (what instances in which) T<0 for the Laplace transform property of time shifting doesn’t hold. Homework Equations L{f(t-T)}=e^-aT* F(s) The Attempt at a Solution I know that for T<0 there are instances where the property cannot hold, but...

Is the notion of emergent property one that is useful within physics proper?

Homework Statement Let G be a group, and H a subgroup of G. Let a and b denote elements of G. Prove the following: 1. ##Ha = Hb## iff ##ab^{-1} \epsilon H##. Homework Equations Let ##e_H## be the identity element of H. The Attempt at a Solution Proof: <= Suppose ##ab^{-1} \epsilon H##. Then...

We can denote the jacobian of a vector map ##\pmb{g}(\pmb{x})## by ##\nabla \pmb{g}##, and we can denote its determinant by ##D \pmb{g}##. We were asked to prove that ##\sum_j \frac{\partial ~ {cof}(D \pmb{g})_{ij}}{\partial x_j} = 0## generally holds so long as the ##g_i## are suitably...

Say I have ##log_5(x)=log_5\left(\frac{2x+3}{2x-3}\right)## This means that the value of the LHS and RHS are equal. I take this to mean that "5 raised to some exponent is equal to both x and ##\frac{2x+3}{2x-3}##. I can now write this as ##x=\frac{2x+3}{2x-3}## because since the function is...

I am trying to prove that if two groups are isomorphic then one is abelian iff the other is abelian. This is a simple task, but I am a little confused about how to write it up. Suppose that ##\phi : G \to H## is an isomorphism. Let ##a,b \in G##. Then ##ab = ba \implies \phi (a) \phi (b) = \phi...

Out of curiosity, I'm trying to find functions of a real variables such that ##f(x)f(-x) = 1##. One obvious example is ##f(x) = e^x##, and all other exponential functions. Are there any other examples? How would I go about generating them?

Homework Statement Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and...

Many books sometimes for example define energy as quantity and sometimes as property. Also the definition of energy is the ability to do work or the meter of the ability to do work ? we define for example force as a quantity or as some quality and then we quantify this ?

With regard to the real number system, what is the importance of the Archimedean property and the property that the rationals are dense in ##\mathbb{R}## (which is a consequence of the Archimedean property)? Related to this, what is the most general structure for which the Archimedean property...

Homework Statement Homework Equations Laplace and then inverse laplace. The Attempt at a Solution Laplace of U(t-to) = 1/s e^(-tos) x(t)-->X(s) Laplace inverse 1/s means integration. e^(-tos) means delay on x(t) by to. I think answer should be C Book answer is D. How am I wrong?

Homework Statement Going from ln|\frac {y-2} {y+2}| = 4x + c_2 to \frac {y-2} {y+2} = \pm e^{4x+c_2} Meaning, why is is \pm e^{4x+c_2}? Homework EquationsThe Attempt at a Solution I know that for log, you take the absolute value because ln(x) has restriction x>0 but I'm failing to...

I searched through previous posts, but did not see this question posted - but I was wondering if mass and matter are different entities. I was reading a book that said something to the effect "if this entire paper clip was converted to energy using E=mc2"... but can a proton (what I see as...

I've heard that the average homeowner in the state of Massachussetts (MA) pays about $15,000 in state property taxes per year. I believe that the standard deduction on Federal income taxes is $6,400 per year. State property taxes can be itemized on Federal income taxes. It seems to me that...

Homework Statement Let g be a primitive root for ##\mathbb{Z}/p\mathbb{Z}## where p is a prime number. b) Prove that ##\log_g(h_1h_2) = \log_g(h_1) + \log_g(h_2)## for all ##h_1, h_2 \epsilon \mathbb{Z}/p\mathbb{Z}##. Homework Equations Let x, denoted ##\log_g(h)##, be the discrete logarithm...

Hello, Please I don't get how a Magnetometer property measurement system (MPMS) and a Superconductor quantum interference device (SQUİD) are working, can someone explain it ? Thank you very much

Hey! :o Two of the properties of the exterior product are the following: - Let $\psi_1, \ldots , \psi_k, n_{1}, \ldots , n_{\ell}\in V^{\star}$ then it holds that $$\left (\psi_1\land \ldots \land \psi_k\right )\land \left (n_1\land \ldots \land n_{\ell}\right )=\psi_1\land \ldots \land...

Can we consider temperature in general as "property" without even been associated to well defined states of matter. Like the boiling and melting points.

My book says that the real numbers are complete in the sense that they satisfy the least upper bound property. So it is the case that completeness and satisfying the l.u.b. property are equivalent by definition, or is it the case that satisfying the l.u.b. property implies completeness, meaning...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with yet a further issue/problem with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with yet a further issue/problem with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with another issue/problem with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with another issue/problem with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested Intervals Theorem ... ...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested Intervals Theorem ... ...

If we have a bottle with a fluid A of X density, and in the bottom of this bottle it magically spawns the same amount of fluid B with X/2 density, fluid B should rise in fluid A until they both change positions and fluid B floats in A. Wich property of the fluids are the ones that determinates...

Homework Statement I am trying to follow the attached solution to show that ##T_{p}f(\tau+1)=T_pf(\tau)## Where ##T_p f(\tau) p^{k-1} f(p\tau) + \frac{1}{p} \sum\limits^{p-1}_{j=0}f(\frac{\tau+j}{p})## Where ##M_k(\Gamma) ## denotes the space of modular forms of weight ##k## (So we know that...

In how many different ways can we arrange three letters A, B, and C? There are three candidates for the third position that leaves the two remaining letters for the second position and so 3 times 2 is 6 and One is the multiplicative identity I am astonished by The commutative property of...

An absolute value property is $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##. Is this true for the case ##a=0##? I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction. How can this property...

By commutative, we know that ##ab = ba## for all a,b in G. Thus, why do we need to prove separately that ##a^n b^m = b^ma^n##? Isn't it the case that ##a^n## and ##b^m## are in fact elements of the group? So shouldn't the fact that they commute automatically be implied?

In an attempt to explain why a matt surface of aluminium is a better emitter/absorber of blackbody radiation than shiny surface of aluminium, my university lecturer suggested to me that: By brushing a metal surface to create a matt finish, the surface of the metal becomes rougher. Rougher means...

Homework Statement Consider a real valued function f which satisfies the equation f (x+y) = f (x) . f (y) for all real numbers x and y. Prove: f ((x + y) / 2) ≤ 1/2 (f(x) + f(y)) Homework Equations Not sure The Attempt at a Solution Please give me a hint to start solving this question. I...

Homework Statement Let G be an abelian group of order n, and let k be an nonnegative integer. If k is relatively prime to n, show that the subgroup generated by a is equal to the subgroup generated by ak Homework EquationsThe Attempt at a Solution I'm not sure where to start. I know that we...

I encountered this in http://calcchat.com/book/Calculus-10e/8/4/7/ How come the above expression equals the below? What I know it should be 4 ln(x/(4+sqrt(16-x^2))) which means the -1 becomes the power of that thing inside ln. Please help me. I really don't get it.

What is the least multiple of 2016 such that the sum of its digits is 2016. I think the answer must be a 225 digit long number ending in 8 but do not know the exact value nor how to prove it. Any ideas. Thanks beforehand.

Homework Statement I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...). Can someone please help me out where I've gone wrong: struggling to spot it...

https://www.sciencedaily.com/releases/2016/11/161130082804.htm Is there any other detection's to back this up?By studying the light emitted from an extraordinarily dense and strongly magnetized neutron star, astronomers may have found the first observational indications of a strange quantum...

Homework Statement If two differentiable functions are linearly dependent on the interval I, then their Wronskian is identically zero on I. Homework EquationsThe Attempt at a Solution We start with the definition of linearly dependence for two functions. ##y_1 = Cy_2## ##\displaystyle...

Homework Statement Prove: If p is prime and m, n are positive integers such that p divides mn, then either p divides n or p divides m. Is anyone willing to look through this proof and give me comments on the following: a) my reasoning within the strategy I chose (validity, any constraints or...

I'm sure that I am not the first one to notice this, but I found that for angles between 0 and 90 degrees, tan(90-10^n) approximately equals 5.7296*10^(-n+1). Is that purely a coincidence?