Numerical enclosure for each eigenvalue in generalized eigenvalue problem

An algorithm for enclosing all eigenvalues in generalized eigenvalue problem Ax=λBx is proposed. This algorithm is applicable even if A∈C^n×n is not Hermitian and/or B∈C^n×n is not Hermitian positive definite, and supplies nerror bounds while the algorithm previously developed by the author supplies a single error bound. It is proved that the error bounds obtained by the proposed algorithm are equal or smaller than that by the previous algorithm. Computational cost for the proposed algorithm is similar to that for the previous algorithm. Numerical results show the property of the proposed algorithm.     

Existence test for solution of nonlinear systems applying affine arithmetic

A computational test is proposed for existence of solution in nonlinear systems. In this test, an interval inclusion of Newton mapping is estimated applying affine arithmetic. Numerical examples are presented to show the efficiency of this test.     

Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rough set based rule induction from two decision tables

We study rule induction from two decision tables as a basis of rough set analysis of more than one decision tables. We regard the rule induction process as enumerating minimal conditions satisfied with positive examples but unsatisfied with negative examples and/or with negative decision rules. From this point of view, we show that seven kinds of rule induction are conceivable for a single decision table. We point out that the set of all decision rules from two decision tables can be split in two levels: a first level decision rule is positively supported by a decision table and does not have any conflict with the other decision table and a second level decision rule is positively supported by both decision tables. To each level, we propose rule induction methods based on decision matrices. Through the discussions, we demonstrate that many kinds of rule induction are conceivable.     

Gaussian Estimates of Order α and L p -Spectral Independence of Generators of C 0-Semigroups

We prove L^p-spectral independence for generators of C₀-semigroups estimated by the positive C₀-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C₀-semigroup .     

Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Michael addition of N-isobutylidene-t-butylamine to dimethyl methoxymethylenemalonate and a new synthesis of some fused pyrazole derivatives from the adduct

N-Isobutylidenemethylamine reacted with dimethyl methoxymethylenemalonate to afford the N-alkylation product 3a exclusively. Exchanging the N-substituent of the Schiff's base from methyl to t-butyl altered the course of the reaction, allowing Michael addition to take place predominantly. The Michael adduct 4c on reaction with hydrazinoalkanols 6a,b, 6c,d and 6e gave tetrahydropyrazolo[5,1-b]oxazoles 9a,b , tetrahydro-pyrazolo[5,1-b][1,3]oxazines 9c,d and hexahydropyrazolo[5,1-b][1,3]oxazepine 9e , respectively.     

Lipid A and related compounds. XXXVII. Determination of favorable binding linkages of lipid A analog to antigen moiety for synthetic vaccines

For the determination of favorable binding linkages of lipid A analog as a synthetic immunoadjuvant to the antigen moiety for synthetic vaccines, new N-acylated L-serine-containing D-glucosamine analogs (Type A, B, C) were synthesized and their mitogenicities were examined. Among chemically synthesized compounds (6-15, 30), compound 8 for Type B exhibited the most potent mitogenicity.