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Displacement Structure and Completion Problems
SIAM Journal on Matrix Analysis and Applications, 1995This paper proves that the displacement equation, defined in terms of solvability of the time-invariant Lyapunov equation, has a Pick solution \(R(t)\) iff there exists a certain upper triangular contraction operator. This has applications to positive completion problems and the Hermite- Fejér interpolation problem and can be combined with embeddings ...
Tiberiu Constantinescu +2 more
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Hierarchies of complete problems
Acta Informatica, 1976An attempt is made to present a framework for the diverse complete problems that have been found. A new concept--a Hierarchy of Complete Problems is defined. Several hierarchies in various domains such as graph theory, automata theory, theorem proving and games are established.
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The Completion of a Problem of Kloosterman
American Journal of Mathematics, 1946See the joint review in [\textit{A. E. Ross}, Am. J. Math. 68, 29--46 (1946; Zbl 0060.11001)].
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Normal Matrices and the Completion Problem
SIAM Journal on Matrix Analysis and Applications, 2002Let \(M_n({\mathbf F}) \) be the algebra of \(n\times n\) matrices over a field \({\mathbf F}\), where \({\mathbf F}\) is either the field of real numbers \({\mathbf R}\) or of complex numbers \({\mathbf C}\). An inverse problem for matrices (IPFM) is the problem of existence of a matrix \(A\) from a certain class belonging to a given variety ...
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On a completion problem for Latin arrays [PDF]
Australas. J Comb., 2022 In this paper, the authors prove that every \(n\times n\) partial Latin array is \(n\)-completable. That is, there exists a partition of its cells into \(n\) parts so that each part constitutes a completable partial Latin square. It gives rise to the proof of \textit{J. Kuhl} and \textit{M. W. Schroeder}'s conjecture [Graphs Combin. 32, No. 1, 241--256
Kevin Akers +5 more
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Average Case Complete Problems
SIAM Journal on Computing, 1986Many interesting combinatorial problems were found to be NP-complete. Since there is little hope to solve them fast in the worst case, researchers look for algorithms which are fast just “on average,” This matter is sensitive to the choice of a particular NP-complete problem and a probability distribution of its instances.
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Completeness for Parity Problems
2005In this talk we shall review recent work on holographic algorithms and circuits. This work can be interpreted as offering formulations of the question of whether computations within such complexity classes as NP, ⊕P, BQP, or #P, can be efficiently computed classically using linear algebra.
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1991
Besides the description of program properties, programming logics are also expected to provide appropriate tools for proving the existence of these properties at concrete programs. Therefore, an appropriate calculus is required to permit the proof of formulas of the descriptive language.
Tamás Gergely, László Úry
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Besides the description of program properties, programming logics are also expected to provide appropriate tools for proving the existence of these properties at concrete programs. Therefore, an appropriate calculus is required to permit the proof of formulas of the descriptive language.
Tamás Gergely, László Úry
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The problem of complete heart block
The American Journal of Surgery, 1963Abstract The experience with fifty-three cases of complete heart block at the University of California Medical Center in a ten-year period was reviewed. Of twenty-two nonsurgical cases, the average survival time from onset of disease under medical management without benefit of the artificial pacemaker was nineteen months, in contrast to one death in ...
D L, BRUNS +3 more
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A Note on Matrix Completion Problems
Algebra Colloquium, 2012Matrix completion problems are an important subclass of problems in matrix theory. An important question in matrix completion problems was posed by Oliveira in 1975, where the author proposed the description of the characteristic polynomial of a partitioned matrix of the form A = [Ai,j], i, j ∈ {1,2} (whose entries are in a field and A1,1, A2,2 are ...
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