Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).

We prove that the following three conditions together imply the concavity of the sequence Pn iˆ0 aibi= Pn iˆ0 ai : concavity of fbng, log-concavity of fang and nonincreasing of f…bn ÿ bnÿ1†=…anÿ1=an ÿ anÿ2=anÿ1†g. As a consequence we get necessary and sufficient conditions for the concavity of the sequences fSnÿ1…x†=Sn…x†g and fSn…x†=Sn…x†g for any nonnegative x, where Sn…x† is the nth partial ...

A representation of a group is a realization of its elements in terms of matrices that takes the group operation into matrix multiplication. The groups of permutations (symmetric groups) were among the first families of groups for which the representations were classified in the work of Frobenius, Schur and Young around 1900. It was found that the irreducible representations of the nth permutat...

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive nth-order Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochas...

Let V be the standard two-dimensional representation of the algebraic group G = SL(2,C), and write Vn = SymnV for the irreducible (n+1)-dimensional representation of G on the nth symmetric tensor power of V . Also write Wn = V ⊗n for the nth tensor power of V (which has dimension 2n). Then, as virtual representations, it is known that each Vn can be written in terms of W0, . . . , Wn as Vn = Wn...

We are interested in a nonlinear boundary value problem for (|u′′|p−2u′′)′′ = λ|u|p−2u in [0,1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n− 1 zero points in (0,1). Eigenvalues of the ...

For any initial state of the M/D/c queueing system this paper presents explicit expressions for the transient distributions of the number of customers in the system at time t > 0, the virtual waiting time for a customer arriving at time t > 0, the queue length at the service intitiation of the nth customer, and the waiting time of the nth customer to be served after t = 0. The analysis requires...