Construction of Pseudorandom Binary Sequences Using Additive Characters

In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Second term of the logarithmic asymptotics of path integrals

In the survey results are presented related to the construction of asymptotic expansions of Green's function of the Cauchy problem for the heat equation. The basic attention is devoted to the first two terms of the logarithmic asymptotics which are obtained locally by probabilistic methods and globally by the method of convolution of the sequence of asymptotic solutions over small time.Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 19, pp. 127–154, 1982.     

Computations in choice groupoids

Defining achoice as a mapping of the subsets of a setX into their respective subsets, a one-to-one (and naturally) corresponding binary operation,sequential choice, is identified under which the power set ofX is closed as achoice groupoid. A complete logical diagram is given, exhibiting all the implications between conjunctions of the seven conditions: (1) idempotence, (2) consistency, (3) absorbence, and (4) homomorphism of a choice, and (5) commutativity, (6) associativity, and (7) path-independence of the corresponding sequential choice.     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

On the continuity of midpoint hull convex set-valued functions

Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399).     

Using “quasiphotons” to compute wave fields in an elastic medium

Quasiphoton solutions are constructed for longitudinal and transversal waves in an elastic medium. The quasiphotons are then applied to determine the fields of nonstationary high-frequency point sources in a medium with parameters dependent on two Euclidean coordinates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 89–103, 1985.     

A characterization of probability distributions by mean values

Let (X) be a measurable complex function onR;X, Y, Z be i.i.d. random variables; and (t, u, v)=E(tX+uY+nZ), wheret, u, vR. In this paper we describe a class of function (x) such that the distribution ofX, Y, Z is determined by the funetion (t, u, v). The main result is a generalization of the author's characterization of normal and stable distributions.     

Surfaces and the second homology of a group

LetG be a group andK(G, 1) an Eilenberg—MacLane space, i.e. ₁(K(G,1))G, _i (K(G,1))=0,i1. We give a purely algebraic proof that the second homology groupH ₂(G)=H ₂(G,)H ₂(K(G,1)) is isomorphic to the group of stable equivalence classes of continuous mapsFK(G,1) inducing surjections on fundamental groups (resp. surjections, whereF{F _g=closed orientable surface of genusg,g}. As a corollary we obtain an algebraic proof of the well-known isomorphismH ₂(G)₂(K(G,1)) (2-dimensional bordism group).     

A class of general systems of KdV type I

We consider some wide class of general systems of Korteweg-de Vries equations which contain nonlinear terms with derivatives of higher order, we have proved the existence of generalized solution for this system and the asymptotic behavior ast and blow up property of the solution are discussed.     

Metric Density and Quasimobius Mappings

We study the notion of -density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between -density and homogeneous density is established. We also characterize -dense spaces as arcwise connected metric spaces in which arcs are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of ⁿ in terms of -density.     

A Framework for Evaluating Knowledge-Based Interestingness of Association Rules

In Knowledge Discovery in Databases (KDD)/Data Mining literature, interestingness measures are used to rank rules according to the interest a particular rule is expected to evoke. In this paper, we introduce an aspect of subjective interestingness called item-relatedness. Relatedness is a consequence of relationships that exist between items in a domain. Association rules containing unrelated or weakly related items are interesting since the co-occurrence of such items is unexpected. Item-Relatedness helps in ranking association rules on the basis of one kind of subjective unexpectedness. We identify three types of item-relatedness – captured in the structure of a fuzzy taxonomy (an extension of the classical concept hierarchy tree). An item-relatedness measure for describing relatedness between two items is developed by combining these three types. Efficacy of this measure is illustrated with the help of a sample taxonomy. We discuss three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items. These mechanisms utilize the relatedness of item-pairs and other aspects of an association rule, namely its structure, distribution of items and item-pairs. We compare our approach with another method from recent literature.     

A new characterization of <Emphasis Type="Italic">PSU</Emphasis>(<Emphasis Type="Italic">p,q</Emphasis>)

Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.     

Staircase kernels for orthogonald-polytopes

LetS be a finite union of boxes inR ^d . Forx inS, defineA _x ={yx is clearly visible fromy via staircase paths inS}, and let KerS denote the staircase kernel ofS. Then KerS={A _x x is a point of local nonconvexity ofS}. A similar result holds with clearly visible replaced by visible and points of local nonconvexity ofS replaced by boundary points ofS.Supported in part by NSF grant DMS-9207019.     

Averaging of Systems with Slow Variables

We justify the averaging method for systems with delay described by both slow and fast variables. The results obtained are applied to the analysis of one problem in control theory.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Applying a fuzzy relation to describe influence of flux behaviour in a printed coil

Summary Being a subject of expectedly fuzzy character, an attempt is made to apply fuzzy functions, more precisely fuzzy relations to investigate the problem of flux distortion in a printed coil.

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Zusammenfassung Da die Vorgänge in einer gedruckten Spule sich aus einer Vielzahl schwerer erfaßbarer Einzeleinflüsse zusammensetzen, die insbesondere den Magnetfluß verzerren, lag es nahe, den Versuch zu machen, die Fuzzy Functions (die logische Algebra, gemäß [1]) darauf anzuwenden. Die Fuzzy Functions sind gedacht für das Beschreiben von Vorgängen, oder Ereignissen, die im Ansatz ein breit gefächertes (fuzzy) Verhalten, ohne scharfe Grenzen aufweisen; siehe Fig. 4.Dieser gefächerten logischen Funktion entspricht eine reguläre mathematische Kurvenschar, die meßtechnisch nachgewiesen werden muß.Im vorliegenden Falle ergab sich eine Korrekturfunktion (5), die es gestattet, die Induktivität gedruckter Spulen, in einem weiten Bereich von Abmessungen und Windungen, mit einer Genauigkeit von –2% bis +5% zu bestimmen.

     

Convex Separable Minimization Subject to Bounded Variables

A minimization problem with convex and separable objective function subject to a separable convex inequality constraint and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. Convex minimization problems subject to linear equality/linear inequality constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix.     

Evolution of weak discontinuity waves in self-similar flows and formation of secondary shocks. The “point explosion model”

In this paper we consider a quasi-linear hyperbolic system in two independent variables (space and time), to evaluate the critical time for weak discontinuity waves travelling in self-similar flows like those generated by a point explosion.The evolutionary law for weak perturbations is given in function of the adiabatic index of the unperturbed medium whose mass density distribution follows a power law of the radial distance.We proved that secondary shocks can occur if appropriate conditions on the amplitude of the initial perturbations are satisfied.The condition of non-impact between a weak perturbation and the primary shock is discussed. In connection to this problem we have computed, for several combinations of both the adiabatic index and the wave strength, the relative position within the fluid at which the secondary shock forms.

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Riassunto Viene considerato un sistema iperbolico quasi-lineare in due variabili indipendenti (spazio e tempo), per calcolare il tempo critico per onde di discontinuità deboli viaggianti in fluidi autosimilari come quelli che vengono generati da una esplosione puntiforme.Viene data la legge evolutiva delle perturbazioni deboli in funzione dell'indice adiabatico del mezzo imperturbato in cui la densità varia secondo una legge di potenza della distanza radiale.Si trova che la formazione di onde d'urto secondarie è possibile se le ampiezze delle perturbazioni iniziali soddisfano determinate condizioni.E'discussa anche la condizione di non-impatto tra l'onda di discontinuità e l'urto primario. In relazione a quest'ultimo problema, viene calcolata, per diverse combinazioni dell'indice adiabatico e della forza dell'onda, la posizione relativa entro il fluido in cui si forma l'urto secondario.

     

The automorphism groups of the congruence group and of some of its subgroups in finite Euclidean planes

In the affine plane over a Galois field GF(q), q ; 3(4), q = p, of congruence transformations, of motions and of the generation of all point reflections respectively. Then we determine the groups AutC, AutM, AutM and obtain the following results: 1. Aut C is isomorphic to the product of the augmented group of similarities (generated by similarities, quasi reflections, quasi rotations 2) and the group of collineations which are induced by the automorphism of GF(q) operating on the coordinates. 2. AutM– AutC. 3. AutM– group of affinities of the affine space of dimension 2 over the prime field. 4. Moreover for any desarguesian affine plane Aut Dil (Dil = group of dilatations) is isomorphic to (the full collineation group).Lecture delivered at the Haifa Geometry conference 1983In my lecture I called these transformations semi-. To avoid confusion I follow here a suggestion of E. Schröder.