On the existence and regularity of solutions of a quasilinear mixed equation of Leray-Lions type

Our aim in this article is to study the existence and regularity of solutions of a quasilinear elliptic-hyperbolic equation. This equation appears in the design of blade cascade profiles. This leads to an inverse problem for designing two-dimensional channels with prescribed velocity distributions along channel walls. The governing equation is obtained by transformation of the physical domain to the plane defined by the streamlines and the potential lines of fluid. We establish an existence and regularity result of solutions for a more general framework which includes our physical problem as a specific example.     

A multi-frequency inverse source problem

This paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies. Rigorous stability estimates are established when the background medium is homogeneous. It is shown that the ill-posedness of the inverse problem decreases as the frequency increases. Under some regularity assumptions on the source function, it is further proven that by increasing the frequency, the logarithmic stability converts to a linear one for the inverse source problem.     

The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. The coefficients of polynomial invariants are integers if is a finite Galois extension of Q, and A is a scalar extension of some finite-dimensional semisimple Hopf algebra over Q. Furthermore, we show that our polynomial invariants are indeed tensor invariants of the representation category of A, and recognize the difference between the representation category and the representation ring of A. Actually, by computing and comparing polynomial invariants, we find new examples of pairs of Hopf algebras whose representation rings are isomorphic, but whose representation categories are distinct.     

Hypergeometric systems of Gelfand-type equations and series in orthogonal polynomials

We describe multivariable hypergeometric series in orthogonal polynomials. These series are solutions of special systems of Gelfand-type equations. The difference andq-analogs are also given.     

Characteristic functional equations of polynomials and the morera-carleman theorem

Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.     

A survey of pseudo (v,k, λ)-designs

This work is an attempt to give a complete survey of all known results about pseudo (v, k, )-designs. In doing this, the author hopes to bring more attention to his conjecture given in Section 6; an affirmative answer to this conjecture would settle completely the existence and construction problem for a pseudo (v, k, )-design in terms of the existence of an appropriate (v, k, )-design.     

Linear algorithms for testing the sign stability of a matrix and for findingZ-maximum matchings in acyclic graphs

Summary Ann×n real matrixA=(a _ij ) isstable if each eigenvalue has negative real part, andsign stable (orqualitatively stable) if each matrix B with the same sign-pattern asA is stable, regardless of the magnitudes ofB's entries. Sign stability is of special interest whenA is associated with certain models from ecology or economics in which the actual magnitudes of thea _ij may be very difficult to determine. Using a characterization due to Quirk and Ruppert, and to Jeffries, an efficient algorithm is developed for testing the sign stability ofA. Its time-and-space-complexity are both 0(n ²), and whenA is properly presented that is reduced to 0(max{n, number of nonzero entries ofA}). Part of the algorithm involves maximum matchings, and that subject is treated for its own sake in two final sections.     

A mixed finite element method for solving the nonstationary stokes equation

Summary This paper deals with a mixed finite element method for approximating a fourth order initial value problem arising from the nonstationary Stokes problem. For piecewise linear shape functions error estimates are given with convergence rates similar to the elliptic case. Some numerical computations will illustrate the theoretical results.     

Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider the Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds.