Term Definition and 775 Threads

We are working with series currently, and some of the problems ask you to create a general term and write it in series summation form. Some of it is a no-brainer, but other ones, I'm at a loss as to how they expect us to get the answer without a ton of trial and error. For example, there is...

I'm sort of stumped here , do i do this? (1+3x) \left( \frac{1+3x}{1+2x} \right)^2 = (1+3x) \left( \frac{3}{2} - \frac{1}{2(2x+1)} \right)^2 (1+3x) \left( \frac{3}{2} \right)^2 \left( 1 + \frac{-1}{3(2x+1)} \right)^2 and then apply the binomial theorem formula on the squared term above...

TL;DR Summary: the peaks and valleys vs. the peaks A. He felt this interminable wave was an abstract view of the universe: one end connected to the endless past, the other to the endless future, and in the middle only the ups and downs of random chance—without life, without pattern, the peaks...

LBM model for phase change- relevant equations found here. Also here. #Thermal LBM #solves 1D 1 phase phase-change #D2Q5 Lattice nx=100 # the number of nodes in x direction lattice direction ny=5 # the number of nodes in y...

For part(a) of this problem, The solution is, a. 160 J In part (a), are they referring to the simi-circular path from R to S instead of the path from R back to R? I though the closed path would be the path from R to R, or the path from S to S, where both give W = 0 since ##W = P(V_f - V_i) =...

I mean, what's "general relativity but without the cosmological constant term" (##G_{\mu \nu}=\kappa T_{\mu \nu}##) called?

From my physical problem, I ended up having a sum that looks like the following. S_N(\omega) = \sum_{q = 1}^{N-1} \left(1 - \frac{q}{N}\right) \exp{\left(-\frac{q^2\sigma^2}{2}\right)} \cos{\left(\left(\mu - \omega\right)q\right)} I want to know what is the sum when N \to \infty. Here...

$$ln{x/t}=lnk +aln[S_2O^{2-}_8] $$ From the above equation,I made a table with the experimental data of the two terms ##ln{x/t}## and ##ln[S_2O^{2-}_8] ##Bur I didn't mention units for them as I had known that even if k had unit,##lnk ## wouldn't have had.But my teacher pointed out...

I am trying to reproduce the results from this paper. On page 10 of the paper, they have an equation: $$ \frac{S}{T}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+11.3 c_0^3+21.5 c_0 c_1^2+10.7 c_0 \dot{c_0}{}^2+3.32 c_0 \dot{c_1}{}^2+6.64 \dot{c_0} c_1 \dot{c_1} \tag{B12} $$ where they...

The eigenvalue for this ##H_0## is given by ##\hbar \omega(n+1) ; (n_x+n_y = n)## At the ground state, ##nx = ny = 0## so the eigenvalue is simply ##\hbar\omega## Next we turn the perturbation potential on and I know that the first order shift in the energy is the expectation value of the...

I got the same result apart from that extra x in the second term? I have boiled it down to that it must have come from maybe the x hat j hat and z hat part of the product rule? Any help would be grateful thank you!

I've solved further Term Symbol problems. The task is: derive the term symbols of the ground states of the following atoms: a) H, b) F, c) Cu, d) F- , e) P, f) Na, g) Sc Why is the d-orbital considered here in g)? Why isn't the s orbital taken into account here? The 4s orbital is energetically...

Hi everyone! I can't solve a problem. It is about the following task. How exactly should I proceed here? Task A): What levels result from a 4F term? How many states are there at each level? I tried many ways but none of them helped me to solve this problem. However, I have some basic ideas...

What I guess (based on experience) is it's asking about this. Table student-: Name Roll Grades Table Teacher-: Salary Experience Subjects Taught This is database schema according to my guess. Is this the context used here? A rather loose definition could be a "schematic of database". Would...

In a discussion, looking for source material. I'm not sure how to categorize this, let alone cite some authority on it. They aren't "disabled people"; they are "people with disabilities". They aren't "homeless people"; they are "people experiencing homelessness". The logic is that they are...

Visualize a lid to a toddler snack cup. Making an entry into an object which is to be placed in nature which can be used by humans but not easily by animals, would the curves used in some toddler snack cups be more durable and flexible without being floppy, or would straight line radii from the...

Hello there, for the above question I have no issue finding the term symbols but I am a little unsure about employing Hund's rules to the electron configuration, particularly those referring to the energies based on the total angular momentum J. These state: - In a less than ##\frac12##-filled...

Im having a issue with studying physics. When I receive a HW problem I dive deep into the problem in a holistic way. I tend to start solving problems that are related to the HW problem but are not the HW problem itself. For instance, I received a pendulum problem and was asked to find its...

So this is the circuit. And here i tried to calculate Uout/ Uin , any suggestion how to simplify this term?? I used Uout= Uin * (1+ Z2/Z1)

The 3rd and 4th terms of an arithmetic sequence are 13 and 18. respectively. What is the 50th term of the sequence! a, 248 b. 250 c. 253 d, 258 e, 763 b the common difference is 5 so $5\cdot 50=\boxed{250}$ basically these are easy but I still seem to miss the goal posts

My working...i need to arrange this in an array, ##[2, 9, 28, 65, 126]## ##[ 7, 19, 37, 61 ]## ##[ 12...

The term approximating basis is used by author Harry Floyd David is his book Fourier Series and Orthogonal Functions on page 56: So I have looked in other books on functional analysis, harmonic analysis...and even on Google and I cannot find any other text reference that uses this term. This...

I don't understand what the question is asking. the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.

I would like to solve a coupled system of two PDEs using Comsol for the following geometry: Equation 1 (valid for 0⩽Z⩽bm): The initial and boundary conditions are: Tm(r,t→0)=20 Tm(r→rw,t)=70 Tm(r→∞,t)=20 However, for bm⩽Z⩽bm+b2, the equation to solve is: With the following initial and...

When something is described as say 7 billion light years away would't it be more accurate to 7 billoin years ago?

I need to work out the maximum thermal energy which can be stored within an area, and to do this I need to convert the specific heat capacity (which measures by mass) to measure instead by volume. Is there a common measurement term I can search for (in the same way as I might search "specific...

In the following page (which, despite examining a question that comes up in science fiction, raises valid scientific questions): http://pages.erau.edu/~andrewsa/sci_fi_projects_spring_2015/Project_1/Eilts_Mitchell/Enders%20Game%20Eilts/Enders%20Game%20Eilts/index_Eilts.html I encountered the...

I think I've got the numerator part figured out, but I'm really stuck on what to do with those negative phases in the last term and how to get this to all come together in the end. I feel like I must have made a mistake somewhere, but can't find it. Thanks in advance for the help!

It's been a long time since I've had a need for my math knowledge and as a result, sadly, a lot has been forgotten. I had a thought the other day and it has been bugging me ever since. What is the mathematical term for when you continually divide any number by 2 until you no longer get a whole...

Whereas a singularity is everything together, is there a name for a proposed end state after a Big Bang or something similar? Is there a name for that situation (hypothetical or not) where each elemental particle is so far from every other elemental particle that nothing affects anything...

I have heard many times that it does not matter where you put the zero to calculate the potential energy and then ##L=T-V##. But mostly what we are doing is taking potential energy negative like in an atom for electron or a mass in gravitational field and then effectively adding it to kinetic...

Hi, I'm a Portuguese translator working on a documentary about black holes and there is a specific bit of dialogue between Stephen Hawking and his colleagues that I'm having a hard time translating. Basically, Hawking says: "So, it could be the F plus minus term takes this away." Is this the...

I guess it could be called a cuboid, but the corresponding circular shape called a spheroid has the dimension in 2 of the axes as the same. Perhaps it is called rectoid or rectohedron?

Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but it involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for lattices with this...

Currently, I am reading about counter term renormalization used to eliminate the infinities in the loop calculations involved in QFT calculations. I found somewhere that the insertion of mass counter terms in one loop diagrams is equivalent to the derivative of one loop diagram multiplied with...

$\tiny{act.al.4}$ The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term of the sequence? $a.\ {248}\quad b.\ {250}\quad c.\ {253}\quad d.\ {258}\quad e.\ {263}$ ok according to Sullivan's textbook $a_1=a\quad a_n=a_{n-1}+d$ so $d=5$ and $a_1=3$ and...

In considering possible scenarios invoked to explain the origin of life, I find myself searching for a general term which can be applied to the first units on the way to becoming living cells. Currently, I am using the term "entity", but am unsatisfied with it because I consider it about the...

I'm trying to derive the path integrals, but this step got me confused: Consider the propagator $$K_{q_{j+1},q_j}=\langle q_{j+1}|e^{-iH\delta t}|q_j\rangle $$ Knowing that ##\delta t## is small, we can expand it as $$K_{q_{j+1},q_j}=\langle q_{j+1}|(1-iH\delta t-\frac 1 2 H² \delta...

If the Summary is not clear, the following is an example translated from: https://telecombloger.ru/7335 '... air conditioning systems. For example, the efficiency of a compressor is about 85%. The remaining 15% is spent on friction, oil movement, overflows, heating, etc. The efficiency of the...

Hello, I am learning about solutions of the Schrodinger equation including the term of rotational energy (i.e. L^2 /2I, in its quantized form) and I was wondering if there should be another quantum term describing vibrational states of hadrons or any other composite subatomic particle, in...

I'm not a statistician, but this has been bothering me for a bit. Suppose we have the simple model Y= aX + b + U where Y,X and U are taken to be random variables representing the explanatory variable, the independent variable and the error term respectively. In the case of a stochastic...

Hey! 😊 Question 1: We consider $\frac{2n-1}{n+7}$. For which $n$ is this term an integer? I have done the following: We set $n+7=m \Rightarrow n=m-7$. Then we get $$\frac{2n-1}{n+7}=\frac{2(m-7)-1}{(m-7)+7}=\frac{2m-15}{m}$$ So $m$ has to be a divisor of $15$, i.e. $m\in \{1,3,5,15\}$...

find the square root of ## a+b+√(2ab +b^2)## let ##√[a+b+√(2ab +b^2)]= ±(√x +√y)## then, ##a+b+√(2ab +b^2)= x+y+ 2√(xy)## where ##a+b=x+y##.......1 ##(b+a)^2-a^2=4xy## .....2 from 2, ##a^2=(b+a)^2-4xy## ##a=√[x+y)^2-4xy]## ##a=√[x^2-2xy+y^2]## ##a=x-y## therefore...

Seems like "spike" should be the Word of 2020; I hear it repeatedly in every newscast. But I think it is being used incorrectly. To me, a "spike" in some statistic means an unusually high value, over a short time period, and with a rapid return to the prevailing value. So, if you plotted...

It is expected from civilised folks to use respectful terms for others. I personally find “kicked out” a very derogatory and insulting remark :-) . How do you see that? (Especially if it is from someone who is classified as civil and meant for someone who is also civil).

Ampere´'s law with the correction term I have a infinite cylinder with radius R with a current density , and magnetic field . I have to proof that it is acceptable to discard the correction term of term of ampere's law, while calculating the magnetic field, as long as it obeys the following...

I derive the quadratic form of Dirac equation as follows $$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$ And I need to find the form of the spin dependent term to get the final expression $$g...

I have read in several places (e.g., https://physics.stackexchange.com/questions/257035/confusion-in-understanding-of-quantum-fluctuations-and-vacuum-energy) that "quantum fluctuations" is an expression to be consigned to the sixth or eighth Circle of Dante's Inferno. OK, I can sympathize with...

I am trying to understand the term ##min_k## ##T_k ## in the following algorithm. At other place they said that it represents min load on any machine but I can’t understand the usage of variable ‘k’ which is not assigned any value. Some body please guide me ,what value is assigned to k in the...

I can’t understand the term Summation of (j tj). Are we multiplying j and tj. But the text is not talking about multiplying, it says”Total processing time Somebody please guide me. Zulfi.