We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher label. This solves a problem posed by Shin and Zeng in a recent article. We also provide a generalization of this identity that translates to a formula for t...

Accuracy of the quarter-point and transition elements is investigated on oneand two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the str...

Let E be a cyclic algebraic number eld of a prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.

Let E be a cyclic algebraic number field of prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.

(1) Introduction.-For arithmetic subgroups r of algebraic semisimple groups defined over the rational numbers Q, and of Q-rank one, M. S. Raghunathan has given a criterion for all classes in certain cohomology groups associated to r to be representable by square integrable forms (cf. ref. 11). In the present note we announce a generalization of Raghunathan's criterion for arbitrary Q-rank (cf. ...

Inverse Scattering methods for solving integrable nonlinear p.d.e. found their limits as soon as one tried to solve with them new boundary value problems. However, some of these problems, e.g. the quarter-plane problem, can be solved (e.g. by Fokas linear methods), for related linear p.d.e., (e.g. LKdV). It is shown here that a nonlinear algebraic inverse scattering method, which we already app...

This paper studies categories of definable subassignments with some category equivalences to semi-algebraic and constructible subsets arc spaces algebraic varieties. These lead the identity certain Grothendieck rings, which allows us compare motivic measure Cluckers-Loeser that Denef-Loeser for classes subassignments.

We show that certain finite groups do not arise as the automorphism group of the square of a finite algebraic structure, nor as the automorphism group of a finite, 2-generated, free, algebraic structure.