Properties Definition and 1000 Threads

Homework Statement We assume from ODE theory that given a smooth A: I → gl(n;R) there exists a unique smooth solution F : I → gl(n;R), defined on the same interval I on which A is defined, of the initial value problem F' = FA and F(t0) = F0 ∈ gl(n;R) given.(i) Show that two solutions Fi : I →...

Homework Statement Let γ : I → R3 be an arclength parametrized curve whose image lies in the 2-sphere S2 , i.e. ||γ(t)||2 = 1 for all t ∈ I. Consider the “moving basis” {T, γ × T, γ} where T = γ'. (i) Writing the moving basis as a 3 × 3 matrix F := (T, γ × T, γ) (where we think of T and etc...

I want to clarify the relations between a few different sets of operators in a conformal field theory, namely primaries, descendants and operators that transform with an overall Jacobian factor under a conformal transformation. So let us consider the the following four sets of...

Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...

Are the physical properties of a particle spread out through the wave function in bohmian mechanics? This is from wikipedia "Also, unlike in classical mechanics, physical properties (e.g., mass, charge) are spread out over the wavefunction in de Broglie–Bohm theory, not localized at the position...

I am looking for resources on the physical properties of the various components that make up the human body. As an example of what I am looking for; If we look at the finger, we know it has bones, skins, nails, blood etc. What are the various physical properties of these different parts...

Hi, I was reading up on the properties on various materials but never quite found out what I was looking for. My question is this , I found out an explanation why diamond is the best thermal conductor even though its not a metal and why other materials that would be similar to diamond like glass...

Let U be a universal set, and let C be any subset of U. Let R be the relation on P(U) defined by A R B if $A \cap C = B \cap C$. Determine whether the relation is reflexive, symmetric, and/or transitive. Prove you answer.

In the Standard Model, for any particle, I have only found properties related to electromagnetic and gravitational (in fact mass does not necessarily mean it is a property related to gravity, but to emergy)forces like charge and mass. Why there isn't anything about the other two interactions...

I am trying to model fluid flow and losses through a component (e.g., pipe) using REAL GAS properties since 1) I have access to RefProp from NIST, and 2) I am dealing with refrigerants, which are far from ideal. I have seen nowhere an analysis of fluid flow losses (e.g., drag, friction...

As I understand it, the properties of a particle exist in superposition in the wave function until a measurement forces a the wave function to "collapse" to one possibility, and the particle continues to have that value for the property until it interacts again with something else. But for...

So a Bose Einstein condensate is another state of matter at temperatures below those where a solid state exists. The temperature is reduced so much, that the quantum wave states overlap and become one single object. So what are the properties of this object? Is it more rigid than solids...

I've been reading Elitzur although with a number of questions, some likely too obvious that they aren't spelled out in the literature based on my searching. To ensure I understand some key details of masers, I thought I'd ask a few (simple) questions if that's all right. 1. Is there a maximum...

do we know what the proportions of antimatter is compared to matter ?? like does gravity electromagnetism the strong and weak forces exc...as well as other thing like does it react to it self the same way matter does to it self??

Given the property, [A,BC] = [A,B]C+B[A,C], is it true that, if B=C, then [A,B]C+B[A,C]=[A,B]C+B[A,B]=[A,B](C+B)? I apologize if I have posted in the wrong forum.

Uni mini projects: to design a reflective silencer plate: properties and calculations involved? as i am very new to this field and i need to design a simple piece of reflective silencer plate(perforation max 60%) is there any rule/equation that can help me to decide/calculate: the position...

Hey all, So the question in Jackson 1.4 is that I have 3 spheres that all have a total charge Q on them, but each sphere has different material properties. For instance, I have a conducting sphere, a sphere with a uniform charge distribution, and one with a charge distribution that has a...

The gamma matrices ##\gamma^{\mu}## are defined by $$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}.$$ --- There exist representations of the gamma matrices such as the Dirac basis and the Weyl basis. --- Is it possible to prove the relation...

I'm writing a story involving multiple sentient species, interstellar travel, and a long history of colonisation. My main character is a Human living on the planet "Tender", whose ancestors colonised it from the planet "Ardel" a few centuries ago. Is it possible to arbitrarily write up the...

What properties of waves caused the photoelectric effect to indicate the fact that light was quantized. Why couldn't it be explained by light waves being emitted at the same frequency. I am a little confused about why light couldn't still be a wave. Couldn't the photoelectric effect be explained...

Hi everyone. Very orderly forum you have here. I'd like to ask a few philosophical questions which are very fundamental to QM. Firstly I assume we all agree that a fundamental particle - imagine an electron or quark - has multiple inherent properties which are all separable from each other, such...

Dear Experts, I am studying about a Stanford University innovation, using Molybdenum Disulphide and solar radiation to disinfect water at a very quick rate. I am unable to find details about photo sensitive properties of Molybdenum Disulphide. What is the work function of molybdenum...

What are the thermal properties of ice cream? any helpful journals or pdfs for this kind of study? thank you ☺

Homework Statement [/B] Question: Use the properties of logarithms to rewrite and simplify the logarithmic expression. 1. log_{5}\dfrac{1}{250} Homework Equations Product Property: log_{a}(uv) = log_{a}u + log_{a}v Quotient Property: log_{a}\dfrac{u}{v} = log_{a}u - log_{a}v Power Property...

It is perfectly fine to do the following: ##\displaystyle{\int_{-\infty}^{\infty}\ d\phi\ e^{-\phi^{2}/2}e^{-\lambda \phi^{4}/4!} = \int_{-\infty}^{\infty}e^{-\phi^{2}/2}\sum\limits_{n=0}^{\infty}}\frac{(-\lambda\phi^{4})^{n}}{(4!)^{n}\...

I've been trying to prove a couple of properties of integrals using the Riemann sum definition: $$\int_{a}^{b}f(x)dx:=\lim_{n\rightarrow\infty}\sum_{i=1}^{n}f(x^{\ast}_{i})\Delta x$$ where the interval ##[a,b]## has been partitioned (such that ##a=x_{1}<x_{2}<\cdots <x_{i-1}<x_{i}<\cdots...

Homework Statement I want to proof, using the axioms of a vector space, that: ##(\alpha - \beta)\overrightarrow a = \alpha \overrightarrow a - \beta \overrightarrow a## Homework Equations Definition vector space: The Attempt at a Solution ##(\alpha - \beta)\overrightarrow a = (\alpha +...

Hi, I am trying to figure out why a term like ## L \sim i \bar \psi_L \sigma^{\mu\nu}G_{\mu\nu}^a t^a \psi_R + h.c=## ##= i \bar \psi_L \sigma^{\mu\nu}G_{\mu\nu}^a t^a \psi_R - i \bar \psi_R \sigma^{\mu\nu}G_{\mu\nu}^a t^a \psi_L ## violates CP by looking at all the terms composing the...

My text of physics, Gettys's, proves that the magnetic field on the axis of a solenoid, in whose loops, of linear density ##n## (i.e. there are ##n## loops per length unit), a current of intensity ##I## flows, has the same direction as the loops' moment of magnetic dipole and magnitude ##\mu_0...

We say about an element that this element is solid, liquid and gaseous in nature...(like we say oxygen and nitrogen are gaseous)...My question is that how can we say that an ELEMENT is solid, liquid or gaseous...From what I understand, elements are kind of ''represented'' by their atoms...So how...

Homework Statement Let ##A## be an n × p matrix and ##B## be an p × m matrix with the following column vector representation, B = \begin{bmatrix} b_1 , & b_2, & ... & ,b_m \end{bmatrix} Prove that AB = \begin{bmatrix} Ab_1 , & Ab_2, & ... & , Ab_m \end{bmatrix} If ##A## is represented...

Homework Statement A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\quad =\quad ? Homework Equations Various cross product and dot product properties The Attempt at a Solution I've only managed to get so far, don't really know what to do next A\cdot...

Doing my undergrad thesis on a ramjet and am confused about scramjets. A ramjet's diffuser slows down supersonic inlet flow to low subsonic to allow combustion. But a scramjet's diffuser first slows the flow down, then speeds it back up in the "diverging" section for supersonic combustion. Why...

What are some properties of materials that are related to the fact that the crystal structure of said material is the hexagonal close-packed structure?

Thruth, Space is a strange place. I wonder what properties we haven't discovered yet. Because the space wraps everything...

I am just curious whether the formulas that apply to 'magnets', such as the formula for the magnetic field of a dipole (as brought up in my previous thread), apply to both electromagnets and permanent magnets, and other types? Is the magnetic fields exhibited by these different forms of...

I know when we see an object then the frequencies of photons reflected from the object carry the information about the colors. Frequencies of visible spectrum helps us to visualize colors. However which properties of photons help us to estimate distance,speed,size,width,height,depth, plainness...

Homework Statement Find what x is I don't understand what to do with (3x-23). Homework Equations Angles centered at a point: a+b+c+d=360 https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf (here is a pdf of the textbook, Exercise 4A, 3i.)[/B]The Attempt at a Solution...

Scalar Product is defined as ##\mathbf A \cdot \mathbf B = | \vec A | | \vec B | \cos \theta##. With the construct of a triangle, the Law of Cosines is proved. ##\mathbf A## points to the tail of ##\mathbf B##. Well, ##\mathbf C## starts from the tail of ##\mathbf A## and points to somewhere...

I'm trying to make a pizza oven, but rather than brick or refractory, steel. I want to use a hemisphere and have it fed by pellets. I've been told by people on wood oven forums that I won't get the heat needed. I'm wanting 900 F at the hearth of the oven, using pellets for heat (roughly 8000...

Mod note: moved from a homework section What properties do prime numbers exhibit which can be used in proofs to define them? Like rational numbers have a unique property that they can be expressed as a quotient of a/b. Even numbers have a unique property of divisibility by 2 and thus they can be...

Homework Statement I am unsure if the first statement below is true. Homework Equations \frac{\partial \psi^*}{\partial x} \frac{\partial^2 \psi}{\partial x^2}=\frac{\partial^2 \psi}{\partial x^2}\frac{\partial \psi^*}{\partial x} Assuming this was true, I showed that \int \frac{\partial...

Homework Statement I would just like to know if this statement is true. Homework Equations \frac {\partial^2 f}{\partial x^2} \frac{\partial g}{\partial x}=\frac{\partial g}{\partial x} \frac {\partial^2 f}{\partial x^2} The Attempt at a Solution I've thought about this a bit and I haven't...

If you want to define a covariant derivative which transforms correctly, you need to define it as ##\nabla_i f_j = \partial_i f_j - f_k \Gamma^k_{ij}##, where ##\Gamma^k_{ij}## has the transformation property ##\bar{\Gamma}^k_{ij} = \frac{\partial \bar{x}_k}{\partial x_c}\frac{\partial...

Hi, is anybody able to tell me if any of the below ingredients contain any bleaching properties to surfaces/fabrics and/or irritable to skin? Any advice is greatly appreciated. 2,2-dimethyl-1,3-dioxolan-4- ylmethanol (>85%)CAS-NO: 100-79-8 EINECS-No. : 202-888-7

An electron displays both wave and particle like properties. Does it exhibit these at the same time or at different times?

It has always struck me that extensive quantities (kinetic energy, volume, momentum, angular momentum, mass, entropy, ...) could be defined as measures (https://en.wikipedia.org/wiki/Measure_(mathematics)) whereas intensive quantities are fields. Are there known ressources that put emphasis on...

Do (i), (ii) and (iii) apply to conditionally convergent series as well? I feel like they don't. But the book seems to say that they do because it doesn't "state otherwise".

Hi In calculation the mechanical properties of graphene nanoribbons by tight binding methods should band structure graphene calculated by the DFT and tight binding methods fitted to calculate b parameter. In the tight binding methods hopping parameter changes as follow: t'_{ppsigma}=t_{ppsigma}...

I'm trying to better understand RSA and Diffie-Hellman exchange and the modulus math that they are base on, there are some questions I have about there properties for which I am unable to find concise explanations about. I'm generally interested in how the commutative, associative...