Random oscillations in the Van der Pol system under the action of a broadband random process

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1517–1521, November, 1998.     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.     

Algebraic cycles and topology of real Enriques surfaces

For a real Enriques surface Y we prove that every homology class in H₁(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y.     

The Categories of Yetter—Drinfel’d Modules, Doi—Hopf Modules and Two-sided Two-cosided Hopf Modules

We show that the two-sided two-cosided Hopf modules are in some case generalized Hopf modules in the sense of Doi. Then the equivalence between two-sided two-cosided Hopf modules and Yetter—Drinfeld modules, proved in [8], becomes an equivalence between categories of Doi—Hopf modules. This equivalence induces equivalences between the underlying categories of (co)modules. We study the relation between this equivalence and the one given by the induced functor.     

Syntomic regulators and special values of p-adic L-functions

In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map, and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters. Oblatum 14-V-96 & 9-X-97     

The Nonexistence of Ternary [38, 6, 23] Codes

It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n₃(6,23) = 38> or 39 and d₃(38,6) = 22 or 23 and (ii) n₃(6,24) = 39 or 40 and d₃(39,6) = 23 or 24, this implies that n₃(6,23) = 39, d₃(38,6) = 22, n₃(6,24) = 40 and d₃(39,6) = 23, where n3<>(k,d) and d<>3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3).     

Minimal forms wit respect to function fields of conics

Summary LetF be a field of characteristic ≠2, and let ϱ be an anisotropic conic overF. Anisotropic quadratic forms φ overF which become isotropic over the function fieldF(ϱ), but which do not contain proper subforms becoming isotropic, are calledF(ϱ)-minimal forms. It is investigated how upper bounds for the dimension ofF(ϱ)-minimal forms depend on certain properties and invariants of the fieldF. The existence of fieldsF and conics ϱ such thatF containsF(ϱ)-minimal forms of arbitrarily large (odd) dimension is proved. During the work on this article, the first author was a postdoc at the Institute for Experimental Mathematics, University of Essen, Germany, supported by a grant from the Deutsche Forschungsgemeinschaft This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.     

Formal orthogonal polynomials and Hankel/Toeplitz duality

For classical polynomials orthogonal with respect to a positive measure supported on the real line, the moment matrix is Hankel and positive definite. The polynomials satisfy a three term recurrence relation. When the measure is supported on the complex unit circle, the moment matrix is positive definite and Toeplitz. Then they satisfy a coupled Szeg recurrence relation but also a three term recurrence relation. In this paper we study the generalization for formal polynomials orthogonal with respect to an arbitrary moment matrix and consider arbitrary Hankel and Toeplitz matrices as special cases. The relation with Padé approximation and with Krylov subspace iterative methods is also outlined.This research was supported by the National Fund for Scientific Research (NFWO), project Lanczos, grant #2.0042.93.     

On a class of maximally hypoelliptic operators

The maximal hypoellipticity of the operator X ₁ ^2m , ... X _k ^2m is proved, where X_j are first-order pseudodifferential operators and m is a natural number. It is assumed that the set of these operators and their first-order commutators is an elliptic system. The results obtained generalize the well-known results of Hormander, Oleinik, and Radkevich, Kohn, Helffer, and Nourrigat, and Rothshield and Stein. Bibliography: 9 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 3–26, 1994.     

Heterocycles from carbohydrate precursors. Part XIX. The X-ray crystal structure determination of the reaction product of 4-(2-acetoxyethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methylhydrazine

X-ray crystallographic data show that the product obtained in the reaction of 4-(2-acetoxy-ethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methyl-hydrazine is the bicyclic compound 2,6-dimethyl-3,4-dioxo-2,3,4,6,7,8-hexahydropyridazino-[4,3-c]pyridazine 4-(p-bromophenylhydrazone) ( 10 ) and not as originally suggested 1-methyl-3-(1-methylpyrazolin-3-yl)-4,5-pyrazoledione 4-(p-bromophenylhydrazone) ( 8 ).