László L. Stachó

Bicircular projections and characterization of Hilbert spaces

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

A global strategy for determining reaction paths: I. General theory of a procedure finding Fukui's intrinsic reaction coordinate

SummaryThe aim of this paper is to give a well-parallelizable curve variational method of finding Fukuis IRC and locating saddle points or other stationary points on potential energy surfaces of chemical reactions, based upon Mezeys theory on catchment regions of the gradient field in mass weighted coordinates.

Mathematical foundation of a global strategy for searching reaction paths

For the determination of reaction paths and critical points on the potential energy hypersurface of chemical reactions, a rigorous mathematical background for the theory of a global searching procedure based on the catchment regions of the gradient field is given.

Uniform primeness of the Jordan algebra of symmetric operators

In this note we establish the best possible constant for the general lower estimate for the Jacobson McCrimmon operator on the algebra of symmetric operators acting on a Hilbert space.

An algorithm for determining dynamically defined reaction paths (DDRP)

SummaryA numerically stable and well-parallelizable curve variational algorithm is described for determining tangent curves of vector fields between two given stationary points. In particular, the method is suitable for finding reaction paths and saddle points on potential energy hypersurfaces (PHS). The stability of the procedure is illustrated by an artificial mathematical function, showing phases of following the reaction on the PHS.

Dynamically defined reaction path (DDRP) method

Abstract Brief accounts of the theoretical background of the dynamically defined reaction path (DDRP) method and algorithm are presented. By employing mathematical functions used for testing reaction path-following algorithms and by simple chemical examples, applications of the procedure have been illustrated.

Experiences and practical hints on using the DDRP method, illustrated by the example of the H 2 + H reaction

By using the dynamically defined reaction path (DDRP) method and starting from various initial polygons, the intrinsic reaction coordinate (IRC) of the H2 + H → H + H2 reaction has been calculated. The numerical stability of the method is illustrated by the evolution phases of the reaction path. Techniques and experiences on the parameter choice and effects of the parameter values on the stability and computer time consumption are discussed.

Procedure for determining dynamically defined reaction path

Abstract A practical computational program and pertinent sections of the code illustrated by flow-charts for a searching procedure to determine dynamically defined reaction paths have been discussed.

FAST MEASUREMENT OF HYPERSPACE VECTORS IN NOISE-BASED LOGIC

We propose a method to determine single hyperspace vectors (product strings of noise-bits) by classical means with the same effectiveness as the results using time shifted noise-based logic. A system of binary linear equations based on the amplitudes of the hyperspace vector and the reference noise-bits is set up and solved after enough independent information is collected. The resulting error probability (the chance of getting no answer) has approximately an exponential decay with the time of measurement.

On the Elber–Karplus reaction path-following method and related procedures

Abstract It is shown through a mathematical proof and by using simple test examples that the fundamental principles of the method of Elber and Karplus (EK) for determining reaction paths are incorrect. Therefore the method, including its improved versions, and the results obtained with the algorithms based on the stategy of EK, even when they are in concordance with experimental data, should be accepted with reservations.