A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

Computational analysis of supersonic turbulent boundary layers over rough surfaces using the k–ω and the stress–ω models

The influence of surface roughness in the prediction of the mean flow and turbulent properties of a high-speed supersonic (M = 2.7, Re/m = 2 × 10⁷) turbulent boundary layer flow over a flat plate is numerically investigated. In particular, the performance of the k–ω and stress–ω turbulence models is evaluated against the available experimental data. Even though the performance of these models have been proven satisfactory in the computation of incompressible boundary layer flow over rough surfaces, their validity for high-speed compressible has not been investigated yet. It is observed from this study that, for smooth surface, both k–ω and stress–ω models perform very well in predicting the mean flow and turbulence quantities in supersonic flow. For rough surfaces, both models matched the experimental data fairly well for lower roughness heights but performed unsatisfactorily for higher roughness conditions. Overall the performance of the k–ω model is better than the stress–ω model. The stress–ω model does not show any strong advantages to make up for the extra computational cost associated with it. The predictions indicate that the ω boundary conditions at the wall in both models, especially the stress–ω model, need to be refined and reconsidered to include the geometric factor for supersonic flow over surfaces with large roughness values.     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.     

Rotational discontinuity in magnetohydrodynamics

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 3, pp. 3–18, May–June, 1993.     

Mechanical properties of irradiated silicone compounds

The change in the mechanical properties of silicone compounds subjected to irradiation with electrons and x rays has been investigated. The compounds contained the fillers ZnO and SiO₂ and, moreover, Be₂O₃ and Fe₂O₃. It is shown that as a result of prolonged irradiation the capacity of the compounds for high elastic deformation is reduced by a factor of 5–6, the true strength values are reduced by a factor of 2–3, and the stiffness of the compounds increases by a factor of 2–3. The compound containing Be₂O₃ proved to be the more radiation-resistant material.Institute of the Chemical Industry, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 610–615, July–August, 1973.     

Decomposing the complete graph into cycles of many lengths

For all oddv 3 the complete graph onvK _v vertices can be decomposed intov – 2 edge disjoint cycles whose lengths are 3, 3, 4, 5,...,v – 1. Also, for all oddv 7,K _v can be decomposed intov – 3 edge disjoint cycles whose lengths are 3, 4,...,v – 4,v – 2,v – 1,v. Research supported by Australian Research Council grant A49130102     

Calibrated Embeddings in the Special Lagrangian and Coassociative Cases

Every closed, oriented, real analytic Riemannian3–manifold can be isometrically embedded as a specialLagrangian submanifold of a Calabi–Yau 3–fold, even as thereal locus of an antiholomorphic, isometric involution. Every closed,oriented, real analytic Riemannian 4–manifold whose bundle of self-dual2–forms is trivial can be isometrically embedded as a coassociativesubmanifold in a G₂-manifold, even as the fixed locus of ananti-G₂ involution.These results, when coupledwith McLean's analysis of the moduli spaces of such calibratedsubmanifolds, yield a plentiful supply of examples of compact calibratedsubmanifolds with nontrivial deformation spaces.     

Apparatus for fatigue testing glass-reinforced plastic specimens in symmetrical tension-compression at acoustic frequencies

The characteristics of an electromechanical apparatus for fatigue testing glass-reinforced plastic specimens in symmetrical tension-compression at loads up to 10–40 kN and acoustic frequencies on the interval 300–5000 Hz are described.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 525–528, May–June, 1972.     

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsváth–Szabó contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thurston–Bennequin plus rotation number of any Legendrian realization of the knot. We use it to demonstrate the first systematic construction of prime knots in contact manifolds other than S³ with negative maximal Thurston–Bennequin invariant. Perhaps more interesting, our invariant provides a criterion for an open book to induce a tight contact structure. A corollary is that if a manifold possesses contact structures with distinct non-vanishing Ozsváth–Szabó invariants, then any fibered knot can realize the classical Eliashberg–Bennequin bound in at most one of these contact structures.     

A certain ill-posed Cauchy problem for first-order and second-order differential equations with operator coefficients

Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 702–706, May–June, 1994.     

A multidimensional inverse problem for an equation with memory

Translated from Sibirskii Zhurnal, Vol. 35, No. 3, pp. 574–582, May–June, 1994.     

Distribution of integral points on certain two-sheeted hyperboloids

Yu. V. Linnik's investigations [Vestn. Leningr. Univ., No. 2, 3–23; No. 5, 3–32; No. 8, 15–27 (1955)] are refined and generalized to indefinite ternary quadratic forms of a sufficiently general form (to forms contained in the form x₁x₃—x ₂ ² ]. The method of investigation is improved. The presentation is substantially simplified.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 87–141, 1980.     

Rings with locally defined torsions

Translated from Algebra i Logika, Vol. 30, No. 3, pp. 369–377, May–June, 1991.     

On nilpotent groups having an almost regular automorphism of prime order

Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 630–632, May–June, 1994.     

Intuitionistic theory of algebraic systems and heyting-valid analysis

Translated from Algebra i Logika, Vol. 30, No. 3, pp. 320–332, May–June, 1991.     

Quality properties of solutions of diffenetial inequalities of a special form

Volgograd. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 78–90, May–June, 1992.     

Stability problems in certain inverse problems of reconstruction of convex compacta from their projections

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 50–57, May–June, 1992.     

Self-adjoint extensions of a Schrödinger opertor with singular potential

Kiev. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 60–69, May–June, 1991.     

Varieties whose countable embeddability skeletons are semilattices

Translated fromAlgebra i Logika, Vol. 32, No. 3, pp. 288–307, May–June, 1993.     

The cauchy problem,the dirichlet problem,and some inverse problems for the one-velocity Peierls equation of the theory of radiation transport in a homogeneously absorbing and scattering medium with isotropic sources

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 3, pp. 551–572, May–June, 1995.