Results 311 to 320 of about 3,729,724 (366)

Constant solutions of polynomial equations

International Journal of Control, 1991
Abstract A necessary and sufficient condition is given for the equation AX + BY = C in polynomial matrices to have a constant solution pair X, Y and also for X to be non-singular. A sufficient condition is then established under which the equation with A and B fixed has a constant solution for each C from a given class. Applications to the construction
V. Kučera, P. Zagalák
semanticscholar   +2 more sources

An Atomic Insight into the Chemical Origin and Variation of Dielectric Constant in Liquid Electrolytes.

Angewandte Chemie, 2021
Dielectric constant is a crucial physicochemical property of liquids in tuning solute-solvent interactions and solvation microstructures. Herein the dielectric constant variation of liquid electrolytes regarding to temperatures and electrolyte ...
N. Yao, Xiang Chen, Xin Shen, Rui Zhang, Zhongwang Fu, Xia‐Xia Ma, Xue‐Qiang Zhang, Bo‐Quan Li, Qiang Zhang   +8 more
semanticscholar   +1 more source

Polynomial maps with constant Jacobian

Israel Journal of Mathematics, 1979
It has been long conjectured that ifn polynomialsf 1, …,f n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf 1, …,f n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically.
M. Razar
semanticscholar   +3 more sources

Exact matching of random graphs with constant correlation

Probability theory and related fields, 2021
This paper deals with the problem of graph matching or network alignment for Erdős–Rényi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem.
Cheng Mao, M. Rudelson, K. Tikhomirov
semanticscholar   +1 more source

On polynomial controllability with polynomial state for linear constant systems

IEEE Transactions on Automatic Control, 1986
Summary: We prove that for linear, reachable, time independent dynamic systems, control at any given time may be achieved with the additional requirements that both the input and the state be polynomial functions of time. The proof is constructive and elementary, and yields a bound on the degree.
A. Ailon, L. Baratchart, J. Grimm, G. Langholz   +3 more
semanticscholar   +3 more sources

John constants for polynomials

Complex Variables, Theory and Application: An International Journal, 1996
Let g be some set of non-constant analytic functions in the unit disk D, and for f e dg define The quantity where g u is the set of univalent functions in g, is called the John constant of g. We discuss where T k consists of the trinomials In particular, we find We also establish a conjecture of Rahman and Szynal for univalent trinomials in T ...
openaire   +1 more source

Polynomial Constants Are Decidable

2002
Constant propagation aims at identifying expressions that always yield a unique constant value at run-time. It is well-known that constant propagation is undecidable for programs working on integers even if guards are ignored as in non-deterministic flow graphs. We show that polynomial constants are decidable in non-deterministic flow graphs.
Markus Müller-Olm, Helmut Seidl
openaire   +1 more source

A polynomial-time classical algorithm for noisy quantum circuits

arXiv.org
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the computational basis)
Thomas Schuster, Chao Yin, Xun Gao, Norman Y. Yao   +3 more
semanticscholar   +1 more source

Quasi-polynomial mappings with constant Jacobian

Izvestiya: Mathematics, 2021
Abstract The famous Jacobian conjecture (JC) remains open even for dimension . In this paper we study it by extending the class of polynomial mappings to quasi-
openaire   +2 more sources

Constant-round interactive proofs for delegating computation

Electron. Colloquium Comput. Complex., 2016
The celebrated IP=PSPACE Theorem of Lund et-al. (J.ACM 1992) and Shamir (J.ACM 1992), allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity of extremely complicated statements (as long as they can be evaluated
Omer Reingold, Ron D. Rothblum, G. Rothblum   +2 more
semanticscholar   +1 more source