Abstract. New variants of the QZ algorithm for solving the generalized eigenvalue problem are proposed. An extension of the small-bulge multishift QR algorithm is developed, which chases chains of many small bulges instead of only one bulge in each QZ iteration. This allows the effective use of level 3 BLAS operations, which in turn can provide efficient utilization of high performance computin...

Applying Baxter’s method of the Q-operator to the set of Sekiguchi’s commuting partial differential operators we show that Jack polynomials P (1/g) λ (x1, . . . , xn) are eigenfunctions of a one-parameter family of integral operators Qz. The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct an integral ...

Continuation methods are a well-known technique for computing several stationary solutions of problems involving one or more physical parameters. In order to determine whether a stationary solution is stable, and to detect the bifurcation points of the problem, one has to compute the rightmost eigenvalues of a related, generalized eigenvalue problem. The recently developed Jacobi-Davidson QZ me...

Incessant malaria endemicity in the tropics and subtropical regions and the recent work done on the synthesis of metal drug complexes of antimalarial drugs and the evaluation of their antimalarial activities in vitro, has led to the development of this study. Quinine-Zinc complex (QZ) was synthesized using a modification of Singla and Wadhwa method. Melting point determination, TLC analysis, in...

The applicability or terminating condition for the ordinary case of Zeilberger’s algorithm was recently obtained by Abramov. For the qanalogue, the question of whether a bivariate q-hypergeometric term has a qZ-pair remains open. Le has found a solution to this problem when the given bivariate q-hypergeometric term is a rational function in certain powers of q. We solve the problem for the gene...

This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=\frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions zero order in the complex plane $\mathbb{C}$. We give logarithmic lemma, second fundamental theorem, defect relation, Picard theorem and five-value sense $q$-difference operator. By using this theory, we investigate growth entire solutions line...

We prove the equidistribution of subsets (R/Z)n defined by fractional parts (Z/qZ)n that are constructed using Chinese Remainder Theorem.