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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Polynomial Equations"”.
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The roots of polynomial equations
Not available
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Exploiting chordal structure in systems of polynomial equations
… chordality might also help solve systems of polynomials. We propose a new technique, which we refer to as chordal elimination, that relies in elimination theory and Gröbner bases. Chordal elimination can be seen as a generalization of sparse linear algebra. Unlike the linear case, the …
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Simplification of radicals with applications to solving polynomial equations.
Thesis: M.S., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1977
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Geometric Properties of Over-Determined Systems of Linear Partial Difference Equations
… coefficient systems of partial difference equations (a discretization of a system of linear partial differential equations) satisfying some collection of scalar polynomial equations to systems defined over the coordinate ring of an algebraic variety. This motivates the extension of …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
… background: Finding integer solutions to polynomial equations (called as Diophantine problems) have been of great interest to humanity since antiquity. These fundamental problems have been driving significant developments in modern number theory and algebraic geometry. An algebraic variety …
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New Techniques for Polynomial System Solving
Since any encryption map may be viewed as a polynomial map between finite dimensional vector spaces over finite fields, the security of a cryptosystem can be examined by studying the difficulty of solving large systems of multivariate polynomial equations. Therefore, algebraic attacks lead to the …
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Studies of some classes of algebraically defined graphs
… graphs whose adjacency is governed by systems of polynomial equations over various fields. In certain contexts, point-line incidence graphs of finite geometries called generalized quadrangles have these algebraically defined graphs as induced subgraphs. At present, if its order is odd, there is …
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Using wave attenuation techniques for monitoring of stress levels
… can be expressed by simplified second order polynomial equations.
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Polynomial systems : graphical structure, geometry, and applications
Solving systems of polynomial equations is a foundational problem in computational mathematics, that has several applications in the sciences and engineering. A closely related problem, also prevalent in applications, is that of optimizing polynomial functions subject to polynomial constraints. In …
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Finite Geometry and Computer Algebra, with Applications
… and finding associated canonical forms for polynomial functions. We deal with some quite complex cases, in particular with the case of line (complement) generated figures of , where it was originally uncertain if the results would be forthcoming. During this work we develop some new …
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Mathematical Methods for Image Based Localization
… of Gröbner basis techniques to solve systems of polynomial equations are presented. The new strategies improve the numeric stability with several orders of magnitudes, compared to previous state of the art. This framework is then applied in the next three papers to solve several geometrical pose …
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Unprovability and phase transitions in Ramsey theory
… as a vast introduction to the Atlas of prefixed polynomial equations. We begin with the necessary definitions, present some specific members of the Atlas, discuss several issues and give technical details.
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Development of a semivolatile aerosol dichotomous sampler
… four performance parameters were expressed in polynomial equations. Utilizing an optimization procedure, values for the major parameters giving the best performance were determined and used as the base model for optimizing minor parameters. Five minor parameters were then investigated for their …
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Spatial reasoning for computer aided design, manufacturing and process planning
… etc. GCS/SF can be expressed as a set of polynomial equations, with the feasible configurations corresponding to common roots of the polynomials. Using known results in algebraic geometry, this work maps properties of Grobner bases to the GCS/SF domain. The mapping allows to determine …
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CFD Modeling and Simulation of Natural Circulation in Helium- Cooled Very High Temperature Reactors
… using pressure and temperature-dependent polynomial equations to realistically simulate buoyancy-driven convection. Three heat input scenarios (230W, 330W, and 580W) were analyzed, revealing a direct correlation between increased thermal input and enhanced flow velocity and temperature …
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Polynomial continuation in the design of deployable structures
Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of …
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An analytic approach to problems connected with plane tree enumeration
… problem to an analytic problem. A system of polynomial equations is created, each of which is satisfied by F and an additional set of generating functions related to the desired set of trees.</p> <p>The following chapter begins with the analytic problem created previously. A process is …
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Diagnosis, synthesis and analysis of probabilistic models
… The rates in the pCTMCs are expressed by polynomials over reals with parameters and the main question is to find all the parameter values (forming a synthesis region) with which the specification is satisfied. We first present a symbolic approach where the intersection points are computed …
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Real root counting for parametric polynomial systems and applications.
Polynomial systems appear in many different fields of study. Many important problems can be reduced to solving systems of polynomial equations and usually the coefficients involve parameters. This thesis is devoted to finding practical ways to solve such problems from two fields, the studies of …
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