Serge Kruk

American University | AU · Department of Computer Science

We build a database of genus 2 curves defined over $\mathbb Q$ which contains all curves with minimal absolute height $h \leq 5$, all curves with moduli height $\mathfrak h \leq 20$, and all curves with extra automorphisms in standard form $y^2=f(x^2)$ defined over $\mathbb Q$ with height $h \leq 101$. For each isomorphism class in the database, an...

We build a database of genus 2 curves defined over $\Q$ which contains all curves with minimal absolute height $\h \leq 5$, all curves with moduli height $\mH \leq 20$, and all curves with extra automorphisms in standard form $y^2=f(x^2)$ defined over $\Q$ with height $\h \leq 101$. For each isomorphism class in the database, an equation over its m...

In this paper, an inverse biharmonic axisymmetric elasticity problem is solved by invoking measured out-of-plane surface deformation values at discrete locations around a preloaded bolt head, in order to calculate the underhead contact stress and joint clamp load that would have caused that out-of-plane surface deformation. Solution of this type of...

In this paper, an inverse bi-harmonic axisymmetric elasticity problem is solved by invoking measured out-of-plane surface deformation values at discrete locations around a preloaded bolt head, in order to calculate the under head contact stress and joint clamp load that would have caused that out-of-plane surface deformation. Solution of this type...

We consider multiple alldifferent predicates of size 2 arranged in a cycle structure and fully characterize all of the facet-inducing inequalities of the convex hull of all integer solutions. The facet-inducing inequalities in the case of n such predicates fall into one of three classes: (1) x i ≥0, for all i∈S={1,2,⋯,n}; (2) 2x i +x i+1 +⋯+x i+m-2...

In the context of constraint programming, we present a search technique used for optimization problems where the objective function includes an linear assignment problem on variables declared to be all different. We show that by solving a simple minimum cost flow problem, at certain nodes of the search tree, we can guide the search very effectively...

We explore the properties of the comb structure of the multiple alldifferent predicates by presenting two classes of facet-inducing inequalities of the convex hull of feasible integer solutions. Since the number of these facets is exponential, we sketch an algorithm that adds facet-inducing inequalities to a linear programming formulation for a giv...

We explore the properties of the comb structure of the multiple all - different predicates by presenting two classes of facet-inducing inequalities of the convex hull of integer solutions. Since the number of these facets is exponential, we sketch an algorithm that adds facet-inducing inequalities to a linear program formulation for a given comb st...

The convex feasibility problem under consideration is to find a common point of a countable family of closed affine subspaces and convex sets in a Hilbert space. To solve such problems, we propose a general parallel block-iterative algorithmic framework in which the affine subspaces are exploited to introduce extrapolated over-relaxations. This fra...

This work models, analyzes, and simulates the process of adhesive bonding between a rod or a slab and an object. The process is assumed to be quasistatic and the model consists of an evolution equation for the rod, a nonstandard boundary condition describing the adhesive traction, and an ordinary differential equation for the adhesive evolution. Th...

For the purpose of large scale computing, we are inter-ested in linking computers into large interconnection networks. In order for these networks to be useful, the underlying graph must possess desirable properties such as a large number of vertices, high connectivity and small diameter. In this paper, we are interested in the alternating group gr...

The class of (n; k)-star graphs and their unidirectional ver- sion were introduced as generalizations of star graphs and unidirectional star graphs respectively. In this paper, we substantially improved previously known bound for the the diameter of unidirectional (n; k)-star graphs. The previous bound was 10k 5 for small k and 5k+5b(n 1)=2c for la...

The convex feasibility problem asks to find a point in the intersection of finitely many closed convex sets in Euclidean space. This problem is of fundamental importance in the mathematical and physical sciences, and it can be solved algorithmically by the classical method of cyclic projections.In this paper, the case where one of the constraints i...

Various interconnection topologies such as the star graph, alternating group graphs and split-stars are alternatives to the hypercubes. They are advantageous over the hypercubes in many ways. Directed versions of these graphs were studied. In this short note, we make several remarks on the diameter in directed alternating group graphs and directed...

hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other instit...

Thesis (Ph. D.)--University of Waterloo, 2001. Includes bibliographical references.