The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant [22], rigidity and ...
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Methods for deciding quantifier-free non-linear arithmetical conjectures over R are crucial in the formal verification of many real-world systems and in formalised mathematics. While non-linear (rational function) ari...
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ISBN:
(纸本)9783642026133
Methods for deciding quantifier-free non-linear arithmetical conjectures over R are crucial in the formal verification of many real-world systems and in formalised mathematics. While non-linear (rational function) arithmetic over R is decidable, it is fundamentally infeasible: any general decision method for this problem is worst-case experiential in the dimension (number of variables) of the formula being analysed. This is unfortunate;as many practical applications of real algebraic decision methods require reasoning about high-dimensional conjectures. Despite their inherent infeasibility, a number of different decision methods have been developed, most of which have "sweet spots" - e.g., types of problems for which they perform much better than they do in general. Such "sweet spots" can in many cases be heuristically combined to solve problems that are out of reach of the individual decision methods when used in isolation. RAHD ("Real algebra in High Dimensions") is a theorem prover that works to combine a. collection of real algebraic decision methods in ways that exploit their respective "sweet-spots." We discuss high-level mathematical and design aspects of RAHD and illustrate its use on a number of examples.
A number of problems in system theory, signal processing, and computeralgebra fit into a generic structured low-rank approximation problem. Several problems of this type are reviewed and efficient local optimization ...
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A number of problems in system theory, signal processing, and computeralgebra fit into a generic structured low-rank approximation problem. Several problems of this type are reviewed and efficient local optimization methods for solving them are outlined.
This paper provides a fast algorithm for Grobner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing...
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ISBN:
(纸本)9781424443123
This paper provides a fast algorithm for Grobner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Groumlbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.
Using the framework of formal theory of partial differential equations, we consider a method of computation of the m-Hilbert polynomial (i.e. Hilbert polynomial with multivariable), which generalizes the Seiler's ...
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Using the framework of formal theory of partial differential equations, we consider a method of computation of the m-Hilbert polynomial (i.e. Hilbert polynomial with multivariable), which generalizes the Seiler's theorem of Hilbert polynomial with single variable. Next we present an approach to compute the number of arbitrary functions of positive differential order in the general solution, and give a formally well-posed initial problem. Finally,as applications the Maxwell equations and weakly over determined equations are considered.
We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and...
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ISBN:
(纸本)9781424446452
We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over the ancestor relation. While the characterizations are in general non-effective, we are able to use them to formulate necessary conditions for definability and provide new proofs that a number of languages are not definable in these logics.
作者：
Wenjuan ChenSchool of Mathematics
Shandong University Jinan 250100 Shandong China School of Science University of Jinan Jinan 250022 Shandong China
In order to show the applications of intuitionistic fuzzy sets and generalize the concepts of fuzzy Lie sub-superalgebras and fuzzy ideals of Lie superalgebras, the theory of intuitionistic fuzzy Lie superalgebras is ...
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In order to show the applications of intuitionistic fuzzy sets and generalize the concepts of fuzzy Lie sub-superalgebras and fuzzy ideals of Lie superalgebras, the theory of intuitionistic fuzzy Lie superalgebras is introduced in this paper. By defining Z2-graded intuitionistic fuzzy vector subspaces, intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals of a Lie superalgebra are given. Some examples are utilized to show the definitions of intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals. The relations between intuitionistic fuzzy Lie sub-superalgebras (intuitionistic fuzzy ideals) and Lie sub-superalgebras (ideals) are also investigated.
The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from alg...
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We investigate the joint moments of the 2k-th power of the characteristic polynomial of random unitary matrices with the 2h-th power of the derivative of this same polynomial. We prove that for a fixed h, the moments ...
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We investigate the joint moments of the 2k-th power of the characteristic polynomial of random unitary matrices with the 2h-th power of the derivative of this same polynomial. We prove that for a fixed h, the moments are given by rational functions of k, up to a well-known factor that already arises when h = 0. We fully describe the denominator in those rational functions (this had already been done by Hughes experimentally), and define the numerators through various formulas, mostly sums over partitions. We also use this to formulate conjectures on joint moments of the zeta function and its derivatives, or even the same questions for the Hardy function, if we use a "real" version of characteristic polynomials. Our methods should easily be applied to other similar problems, for instance with higher derivatives of characteristic polynomials. More data and computer programs are available as expanded content.
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