Eigenschaften von vollstaendigen Systemen orthogonaler lateinischer Quadrate,die bestimmte affine Ebenen repraesentieren

A set of n-1 mutually orthogonal Latin squares of order n is a model of an affine plane with exactly n points on a line and every affine plane with n points on a line can be represented by n-1 mutually orthogonal Latin squares ([1]). In this paper we investigate properties of finite planes through the complete set of mutually orthogonal Latin squares representing the plane and mainly — vice versa — properties of the squares representing a fixed plane. The results are based on the geometrical configurations which hold in the planes. For presumed definitions and theorems which are not specially referred to see [4], [7], [3] or [6].     

Non rank 3 strongly regular graphs with the 5-vertex condition

Three new strongly regular graphs on 256, 120, and 135 vertices are described in this paper. They satisfy thet-vertex condition — in the sense of [1] — on the edges and on the nonedges fort=4 but they are not rank 3 graphs. The problem to search for any such graph was discussed on a folklore level several times and was fixed in [2]. Here the graph on 256 vertices satisfies even the 5-vertex condition, and has the graphs on 120 and 135 vertices as its subgraphs. The existence of these graphs was announced in [3] and [4]. [4] contains M. H. Klin's interpretation of the graph on 120 vertices. Further results concerning these graphs were obtained by A. E. Brouwer, cf. [5].     

Linear homeomorphisms of non-classical Hilbert spaces

Let K be a complete infinite rank valued field. In [4] we studied Norm Hilbert Spaces (NHS) over K i.e. K-Banach spaces for which closed subspaces admit projections of norm ≤ 1. In this paper we prove the following striking properties of continuous linear operators on NHS. Surjective endomorphisms are bijective, no NHS is linearly homeomorphic to a proper subspace (Theorem 3.7), each operator can be approximated, uniformly on bounded sets, by finite rank operators (Theorem 3.8). These properties together — in real or complex theory shared only by finite-dimensional spaces — show that NHS are more ‘rigid’ than classical Hilbert spaces.     

Fastalgebren mit zweiseitigem bzw. kommutativem Inzidenzgruppoid

In this paper it is shown that a nearalgebra (F,H) — in the sense of [4] — is an algebra (a commutative algebra), if its incidencegroupoid F^*/H^* is twosided (commutative).

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Herrn Professor Martin Barner zum 65. Geburtstag     

Arcs and k-sets with large nucleus — set in Hall planes

In this paper we give k-sets (k>-q+1) of the Hall planes with q-q nuclei. This shows that the results of BICHARA — KORCHMÁROS [1] and WETTL [16] cannot be extended to non-desarguesian planes. We construct some inherited arcs in the Hall planes as well. For example complete (q–1)-arcs of the Hall planes of odd order will be constructed.     

Refined linear theory of elastic anisotropic multilayer shells. Part 2

On the basis of the refined linear theory of elastic anisotropic multilayer shells of arbitrary shape derived in [1] it is established that a number of theorems of the linear theory of elasticity have analogues in the theory of multilayer anisotropic shells.For Part 1 see [1].Institute of Fluid Mechanics, Bucharest. Translated from Mekhanika Polimerov, No. 1, pp. 100–109, January–February, 1976.     

The Combinatorial Quantum Cohomology Ring of <Emphasis Type="Italic">G</Emphasis>/<Emphasis Type="Italic">B</Emphasis>

A purely combinatorial construction of the quantum cohomology ring of the generalized flag manifold is presented. We show that the ring we construct is commutative, associative and satisfies the usual grading condition. By using results of our previous papers [12, 13], we obtain a presentation of this ring in terms of generators and relations, and formulas for quantum Giambelli polynomials. We show that these polynomials satisfy a certain orthogonality property, which—for G = SL_n( )—was proved previously in the paper [5].     

Large spaces between the zeros of the Riemann zeta-function and random matrix theory II

We develop the theory set out in Part 1 [R.R. Hall, Large spaces between the zeros of the Riemann zeta-function and random matrix theory, J. Number Theory 109 (2004) 240–265] and in particular provide a lower bound (and almost sure evaluation) for Λ(7). The square of this number is rational, as were the previous values, but still rather surprizing.     

Bewegungsgruppen aufn-dimensionalen Quadriken

Ohne ZusammenfassungVon beweistechnischen Änderungen abgesehen ist dies — in Verbindung mit [3] — die Habilitationsschrift des Verfassers.     

Soliton attraction law

Soliton coordinates are determined for the Korteweg — de Vries equation. In this case, the center of mass of solitons moves uniformly. The two-soliton attraction law is established.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 686–688, May, 1995.The principal results of this paper were presented at the Congress of Mathematical Physics, July 1994 [2].     

A double obstacle problem arising in differential game theory

A Hamilton–Jacobi equation involving a double obstacle problem is investigated. The link between this equation and the notion of dual solutions—introduced in [S. As Soulaimani, Infinite horizon differential games with asymmetric information, PhD thesis; P. Cardaliaguet, Differential games with asymmetric information, SIAM J. Control Optim. 46 (3) (2007) 816–838; P. Cardaliaguet, C. Rainer, Stochastic differential games with asymmetric information, Appl. Math. Optim. 59 (1) (2009) 1–36] in the framework of differential games with lack of information—is established. As an application we characterize the convex hull of a function in the simplex as the unique solution of some nonlinear obstacle problem.     

Iterationsverfahren höherer Ordnung in Banach-Räumen

The Newton process for operator equations in say a linear normed complete space converges under certain hypothesis about the Fréchet-derivatives of the operator with at least the order two. There are different ways to improve this Newton process. For instance you obtain a process of order three if you add a correction element containing the second Fréchet-derivative of the operator [1]. In the following note we will generalize this idea. In a recursive manner — by adding higher derivatives — we will construct iterative processes of any orderk (k > 1). A general theorem due toCollatz provides us error estimates for this processes. Last we will illustrate the processes by several examples.     

Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II

This paper is the second part of [12]. Using the comparison theorems which were proved in the first part, the asymptotic normality of the estimator — in a model of a series of several samples — of the correlation function of a stationary Gaussian random process in spaces of continuous functions with weights is established. A method for constructing functional confidence intervals for an unknown correlation function in these spaces is described.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 579–583, May, 1991.     

High order algebraically stable Runge-Kutta methods

In Burrage and Butcher [3] the concept of Algebraic Stability was introduced in the study of Runge-Kutta methods. In this paper an analysis is made of the family ofs-stage Runge-Kutta methods of order 2s—2 or more which possesses this property.     

Realizations and LP

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 (4) (2008) 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. (The second of these is actually weaker than just stated, but this is not the place for a detailed formulation.) The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode (Eds.), Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223].     

Quantum -modules and generalized mirror transformations

In the previous paper [Hiroshi Iritani, Quantum D-modules and equivariant Floer theory for free loop spaces, Math. Z. 252 (3) (2006) 577–622], the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c₁(M) of the tangent bundle is nef. In this paper, even when c₁(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum D-module under certain conditions on the ambient toric variety. The proof is based on a mirror theorem of Coates and Givental [T. Coates, A.B. Givental, Quantum Riemann — Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (1) (2007) 15–53]. The reconstruction procedure here gives a generalized mirror transformation first observed by Jinzenji in low degrees [Masao Jinzenji, On the quantum cohomology rings of general type projective hypersurfaces and generalized mirror transformation, Internat. J. Modern Phys. A 15 (11) (2000) 1557–1595; Masao Jinzenji, Co-ordinate change of Gauss–Manin system and generalized mirror transformation, Internat. J. Modern Phys. A 20 (10) (2005) 2131–2156].     

Auslander-Reiten quivers of local,orders of finite lattice type

The classification of the Auslander-Reiten quivers of the local orders of finite lattice type is completed. For this purpose, it is shown—using the results of [7]—that to the list of the known Auslander-Reiten quivers of the local Bäckström orders of finite lattice type [11], [14] and of the local Gorenstein orders of finite type and their minimal overorders [18] one has to add two remaining types of valued translation quivers to obtain a complete list of all Auslander-Reiten quivers of the local orders of finite lattice type.     

Interpolation between sequence transformations

Levin's sequence transformation [1] and a structurally very similar sequence transformation [4] behave quite differently in convergence acceleration and summation processes. In particular, it was found recently that Levin's transformation fails completely in the case of the strongly divergent Rayleigh-Schrödinger and renormalized perturbation expansions for the ground state energies of anharmonic oscillators, whereas the structurally very similar sequence transformation gives very good results [14,17]. For a more detailed investigation of these phenomena, a sequence transformation is constructed which — depending on a continuous parameter — is able to interpolate between Levin's transformation and the other sequence transformation. Some numerical examples, which illustrate the properties of the interpolating sequence transformation, are presented.