In this paper we study the parallel solution of the discrete time Lyapunov equation Two parallel ne and medium grain algorithms for solving dense and large order equa tions A X A X B B on a shared memory multiprocessor are presented They are based on Hammarling s method and directly obtain the Cholesky factor of the solution The parallel algorithms work following an antidiagonal wavefront In or...

In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z 's popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations thus far have either failed to provide a calculus (e.g. the draft standard 3]) or have fallen back on informal descriptions at a s...

The core of the Rice dHPF compiler for High Performance Fortran is a practical, executable, equa-tional framework for data parallel program analysis and optimization. This framework, based on abstract operations on sets of integers, greatly simpliies the implementation of many key analysis, optimization and code generation tasks (even with a general computation partitioning model), and yet enha...

We present two learning inference control heuristics for equa-tional deduction. Based on data about facts that contributed to previous proofs, evaluation functions learn to select equations that are likely to be of use in new situations. The rst evaluation function works by symbolic retrieval of generalized patterns from a knowledge base, the second function compiles the knowledge into abstract...

The initial-boundary value problem for the time-dependent Ginzburg-Landau equa, tions that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented. Keywords-Superconductivity, Timedependent Ginzburg-Landau equa...

National legal and political regulation in the field of energy efficiency is closely connected to minimizing consumption buildings. Within framework implementing Directive 2018/844/EU on performance buildings Europe, practice its application differs from country country. This study aims reveal differences indicators an energy-efficient building European states. To that end, analysis was made co...

Based on the N-soliton solutions of $$(2+1)$$ -dimensional Sawada–Kotera equation, collisions among lump waves, line and breather waves are studied in this paper. By introducing new constraints, wave does not collide with other forever, or stays collision forever. Under condition velocity resonance, soliton molecules consisting a wave, any number derived for first time. In particular, interacti...

Under the well-known bilinear method of Hirota, specific expression for N-soliton solutions (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada(gCDGKS) equation in fluid mechanics is given. By defining a novel restrictive condition on solutions, resonant Y-type and X-type soliton are generated. new proposed constraint, combined with velocity resonance module method, mixed solitons l...

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each the preceding equations, a Galilean type transformation between these $u_2$ previously known $u_2^{\prime}$ generated zero seed is given. We present several explicit formulas single-soliton for $u_2...