What are general ways to handle simplex dynamics?

I want to know if there's any general method to investigate a linear system restrained by a standard simplex. It's hard for me to start with such a system because if I directly regard it as...

02 March 2014 1,696 3 View

Why are physicists concerned with velocity fields instead of position in fluid mechanics?

Navier-Stokes equation describes the evolutionary law of fluid velocity. Essentially, it is a special form of Newton's second law. But why not position here? People don't care about trajectories...

02 March 2014 828 5 View

How can I solve this Noether's theorem problem?

Noether's (first) theorem states that if a Lagrangian L admits a continuous symmetry, then some quantities are conserved. So I want to know if there's any inverse problem like this: Given one or...

02 March 2014 6,888 17 View

On representation of expansion in fluid flow - can anyone help?

In Helmholtz original thesis On integrals of the hydrodynamical equations, which express vortex-motion, he mentioned in the first section that the change undergone by an arbitrary infinitesimal...

08 September 2013 2,839 3 View

Is Taylor expansion related to Helmholtz decomposition?

The Taylor expansion of a vector field $f(x)$ to the order of one is $$f(x)=f(x_0)+Jf(x_0)\cdot\Delta x+o(\Delta x)$$ where $Jf$ is Jacobian of the vector field and $\Delta x=x-x_0$. Suppose we...

08 September 2013 4,801 0 View

Is autonomous dynamical system equivalent to a higher-order ode?

We know that a higher-order ode can be converted to a dynamical system by replacing each higher-order derivative by a new variable. What about the inverse problem? Does a dynamical system convert...

07 August 2013 9,005 11 View

How to solve this pde system analytically?

07 August 2013 1,958 4 View

Can someone advise on a proof of Poincare lemma?

Poincare lemma states that every smooth closed form in contractible subset is exact. The assumption actually represents a set of pdes that dd=0. Could Frobenius theorem be used to say that the...

07 August 2013 312 1 View

Does Markov process have something to do with thermodynamics?

I want to know if a Markov process far from equilibrium corresponds to a non-equilibrium thermodynamics process or whether they have something in common?

04 May 2013 9,926 7 View

What tools are generally employed in classical mechanics describing dissipative systems?

It seems Hamiltonian systems handle conservative systems because of invariant Hamiltonian and Lagrangian mechanics does so for it is equivalent to Hamiltonian mechanics. Is there anything a like...

04 May 2013 3,375 8 View

Binary Logistic Generalized Linear Mixed model in SPSS. Is it doable?

I want to analyses the proportion of swimming sperm of three species of fish in two salinities. To analyse the proportion of swimming sperm in a Generalized Linear Model, I would use a Binary...

03 March 2021 2,297 3 View

Could you recommend any books about Number Theory?

Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.

03 March 2021 7,174 5 View

Arena simulation - how do i model the following model in ARENA (see description) (new to ARENA)?

Hello, I'm fairly new to ARENA and I have the following problem: I have two queues in which, in each queue, a different order type arrives (both having an arrival rate of exponential 10). Order...

02 March 2021 2,431 3 View

Do I need to do linear regression before running mediation analysis using PROCESS MACRO by Hayes ?

I just wanted to check if I need to run a linear regression separately if I am using PROCESS MACRO to run mediation analysis. Thank you.

02 March 2021 4,359 3 View

What analysis to choose with a large neste dataset and clearly skewed or kurtotic distributions?

Hello! I have a dataset of n=3000 nested within 8 countries with approximately 200 or 400 responses in each country. I originally planned to perform multilevel modelling with 4 dependent variables...

02 March 2021 6,865 1 View

How to classify strictly upper triangular matrices by similarity?

Let F be a field. Consider U, the set of n times n strictly upper triangular matrices in F. For X, Y in U, we call them similar if there exists some S, which is non-degenerate and upper...

01 March 2021 2,957 8 View

Is CD44 degraded in lysosome together with hyaluronan after CD44 mediated endocytosis of hyaluronic acid?

Also when RHAMM binds hyaluronic acid, they get internalized, will RHAMM also be degraded? Or both CD44 and RHAMM will be transferred back to the cell membrane? Asking for breast cancer cell line...

01 March 2021 8,169 2 View

Why is the sum of the elements in a row in a Q matrix equal to zero?

When explaining substitution models, the substitutions are expressed as Q matrix. Why is the sum of the elements in a row zero?

28 February 2021 3,864 3 View

Distribution of particles in metal matrix?

How would define the "good" and "poor" distribution of particles within the matrix. Is there a quantitative solution to assess the distribution of the particles, which then having denotation of...

28 February 2021 7,397 8 View

How to find a correlation between coordinates in a curvilinear coordinate system?

Hello. I have a skewed elliptical coordinate system (I use alternative elliptical coordinates). And I need to determine connections between coordinates in order to fetch a covariance matrix of...

28 February 2021 364 3 View