Lerch’s formulae for Euler quotients in the rings Z and Fq[t] have already been studied. In this paper, we extend the study of these quotients to number fields and the Carlitz module. In the number fields case, we prove a version of Lerch’s formula for OKHil , the ring of integers of the Hilbert class field of a number field K. In the Fq[t] case, we replace the usual multiplication in Fq[t] wit...

For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...

The purpose of this paper is to show that algorithms in a diverse set of applications may be cast in the context of relations on a finite set of operators in Hilbert space. The Cuntz relations for a finite set of isometries form a prototype of these relations. Such applications as entropy encoding, analysis of correlation matrices (Karhunen-Loève), fractional Brownian motion, and fractals more ...

Decision-making is a crucial aspect of emergency response during mass casualty incidents (MCIs). MCIs require rapid decisions to be taken by geographically-dispersed teams in an environment characterized by insufficient information, ineffective collaboration and inadequate resources. Despite the increasing adoption of decision support systems in healthcare, there is limited evidence of their va...

Let Hc be the rational Cherednik algebra of type An−1 with spherical subalgebra Uc = eHce. Then Uc is filtered by order of differential operators with associated graded ring grUc = C[h ⊕ h∗]W , where W is the n-th symmetric group. Using the Z-algebra construction from [GS] it is also possible to associate to a filtered Hcor Uc-module M a coherent sheaf Φ̂(M) on the Hilbert scheme Hilb(n). Using ...

For a polynomial ring, R, in 4n variables over a field, we consider the submodule of R corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with variable entries (which corresponds to the Cauchy-Fueter operator in partial differential equations) and let Mn be the corresponding quotient module. We compute many homological properties of Mn includi...

We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gröbner basis of a finitely generated difference-differential module and we use this to compute the bivariate difference-differential dimension polyomial of the module with respect to the natural bifiltration of the ring of difference-differential operators. An overview regarding ...

For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.

We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group. This has applications to shift-invariant spaces and wavelet theory. One of the main findings in this paper is that whenever a shift-invariant subspace in L2(R...