Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 17 of 17 for “"characteristic polynomial"”.
-
Fixed order controller design via linear programming
… to time domain specifications. The interval polynomial search algorithm is formulated to maximize the interval characteristic polynomial within the design domain defined by the design parameters on the s-plane. The Edge Theorem is applied to ensure the performance and stability of the …
-
Spectra of Hypergraphs
… to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally. We apply this notion to the 'adjacency hypermatrix' of a uniform hypergraph, and prove a number of natural analogues of basic results in Spectral Graph Theory.</p>
-
The Divisibility and Modular Properties of Kth-Order Linear Recurrences Over The Ring of Integers of an Algebraic Number Field With Respect to Prime Ideals
… = 1 are called unit sequences. Let f be the characteristic polynomial of the recurrence defined by (1). Let D be the discriminant of f. An ideal M is a maximal divisor of the kth-order recurrence (w) if the maximal number of successive terms of (w) it divides is k - 1.
-
Higher-Order Lucas Sequences and Dickson Polynomials
… = D^M_k where D^M_k is a higher-order Dickson polynomial. We first examine the cases where M has projective orders 3, 4, and 6. For the order 3 case, we find that M has entries in, at worst, a quadratic extension of F. This is also true for the orders 4 and 6, but requires a restriction on the …
-
The number of zeros of linear recurring sequences over finite fields
… elements, based on an irreducible minimal polynomials of degree <italic>d<italic> and order <italic>m<italic> as the characteristic polynomial. I prove upper and lower bounds on the cardinality of the set of number of zeros. The set is determined when <italic>t= …
-
On the best principal submatrix problem
… (\(n-k\))'th coefficient of the max-algebraic characteristic polynomial of \(A\). It has been shown that any coefficient can be found in polynomial time if it belongs to an essential term. One application of BPSM is the job rotation problem: Given workers performing a total of \(n\) jobs, where …
-
Inversion for subbottom sound velocity profiles in the deep and shallow ocean
… coefficients, another for the zeros of the AR characteristic polynomial.
-
Arithmetic Properties Related to Isogeny Criteria for Elliptic Curves and Drinfeld Modules
… Phi_1 and Phi_2 have the same Frobenius trace or characteristic polynomial of the Frobenius is bounded above asymptotically by a function of x. We prove bounds with a power saving dependent upon a generalization of the open image theorem for Drinfeld modules of Pink and Rütsche.
-
Design of Two-axis Multivariable Control Systems
… These loci relate directly to the closed loop characteristic polynomial of the system and conditions are derived for an unambiguous indication of stability. The method is applicable to systems having a high degree of interaction and is extended to nonlinear systems by means of describing …
-
Properties and Recent Applications in Spectral Graph Theory
… to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel …
-
Built-In Schemes for Test Pattern Generation and Fault Location
… efficient technique that uses irreducible polynomial-primitive element pair to generate distinct subsequences of test patterns. It is shown that for the given characteristic polynomial the hardware cost remains the same irrespective of the number of seeds required to generate the test …
-
Pole-placement with minimum effort for linear multivariable systems
… poles according to a successive change of their characteristic polynomial coefficients.
-
Inversion for subbottom sound velocity profiles in the deep and shallow ocean
… coefficients, another for the zeros of the AR characteristic polynomial. The decimation of the pressure field defined in a discrete range grid is analyzed as a tool to improve AR estimation. The nonlinear eigenvalue inverse problem of estimating the svp from a sequence of eigenvalues is solved …
-
Machine Learning Coupled Potential Energy Surfaces
… by learning the nuclear coordinate dependent characteristic polynomial coefficients of the potential matrix instead, which enables the construction of smooth, accurate machine learning models even at seams of conical intersections. The proposed approach is first validated at the ab initio …
-
Stability and efficiency properties of implicit Runge-Kutta methods
… when using this implementation are those whose characteristic polynomial of the Runge-Kutta matrix has a single real s-fold zero. Based on this criterion a family of methods, called singly-implicit methods, is constructed, and results concerning their maximum attainable order and stability …
-
On Gaussian Multiplicative Chaos
… unitary ensemble, the absolute powers of the characteristic polynomial, when suitably normalised, converge in distribution to multiplicative chaos on the support of the limiting spectral distribution as the size of the matrix goes to infinity, and the limit is independent of the choice of the …
-
Species and Hyperplane Arrangements
… In the first part, we extend the study of characteristic elements of a hyperplane arrangement from the linear to the affine case. We present the basic properties of these elements and apply them to derive numerous results about the characteristic polynomial of an arrangement, from …