New asymmetric generalizations of the Filbert and Lilbert matrices

Periodica Mathematica Hungarica - Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with...     

The infinity Laplacian, Aronsson's equation and their generalizations

The infinity Laplace equation arose originally as a sort of Euler-Lagrange equation governing the absolute minimizer for the variational problem of minimizing the functional ess-sup The more general functional ess-sup leads similarly to the so-called Aronsson equation

In this paper we show that these PDE operators and various interesting generalizations also appear in several other contexts seemingly quite unrelated to variational problems, including two-person game theory with random order of play, rapid switching of states in control problems, etc. The resulting equations can be parabolic and inhomogeneous, equation types precluded in conventional variational problems.

     

Finite Shmidt's groups and their generalizations

There are considered direct generalizations of finite Shmidt's groups, i.e., finite nonnilpotent groups, whose all proper subgroups are nilpotent. As corollaries, there are proved assertions confirming the dependence of the structure of the entire group on the presence of some system of Shmidt's groups. In particular, it is proved that a finite group is dispersive, if all its Shmidt's subgroups are upper-solvable.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 963–968, July–August, 1991.     

On biharmonic maps and their generalizations

We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove that a weak limit of biharmonic maps into a sphere is again biharmonic. The proof of regularity can be adapted to biharmonic maps on the Heisenberg group, and to other functionals leading to fourth order elliptic equations with critical nonlinearities in lower order derivatives.Received: 6 February 2003, Accepted: 12 March 2003, Published online: 16 May 2003Mathematics Subject Classification (2000): 35J60, 35H20Pawel Strzelecki: Current address (till September 2003): Mathematisches Institut der Universität Bonn, Beringstr. 1, 53115 Bonn, Germany (email: strzelec@math.uni-bonn.de). The author is partially supported by KBN grant no. 2-PO3A-028-22;he gratefully acknowledgesthe hospitality of his colleagues from Bonn,and the generosity of Humboldt Foundation.     

k-th record times and their generalizations

A series of asymptotic results are given for the k-th record times and for their generalizations, the so-called k_n-record times. All possible limiting distributions are obtained for some generalizations of the k-th record variables. These distributions are closely related with the corresponding limit distributions of the extremal order statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 115–121, 1986.     

Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

Approximation by simple partial fractions and their generalizations

We consider a multiple interpolation by Padé simple partial fractions and propose a method for calculating the values of rational functions and polynomials on the basis of approximation by special rational functions (their numerator and denominator are represented as the differences between two simple partial fractions). We obtain an extrapolation formula for an analytic function h(z) in a neighborhood of the origin. For an extrapolation tool we use the expressions Σ _k λ _k h(λ _k z), where λ _k are calculated by a certain algorithm and are independent of the choice of h. Bibliography: 17 titles.     

Some properties of Bernoulli polynomials and their generalizations

In this work, we investigate some well-known and new properties of the Bernoulli polynomials and their generalizations by using quasi-monomial, lowering operator and operational methods. Some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the (generalized) Bernoulli polynomials.     

A note on generalizations of strict diagonal dominance for real matrices

We investigate classes of real square matrices possessing some weakened from of strict diagonal dominance of a real matrix whose diagonal entries are all positive. The intersection of each one of these classes with the set of all real matrices, with nonpositive off-diagonal elements, coincides with the set of all nonsingular M- matrices.