Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Supersymmetric structures for second order differential operators
2012
Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.
On monadic quantale algebras: basic properties and representation theorems
2010
Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
Free sequences and the tightness of pseudoradial spaces
2019
Let F(X) be the supremum of cardinalities of free sequences in X. We prove that the radial character of every Lindelof Hausdorff almost radial space X and the set-tightness of every Lindelof Hausdorff space are always bounded above by F(X). We then improve a result of Dow, Juhasz, Soukup, Szentmiklossy and Weiss by proving that if X is a Lindelof Hausdorff space, and $$X_\delta $$ denotes the $$G_\delta $$ topology on X then $$t(X_\delta ) \le 2^{t(X)}$$ . Finally, we exploit this to prove that if X is a Lindelof Hausdorff pseudoradial space then $$F(X_\delta ) \le 2^{F(X)}$$ .
Symmetric and asymmetric cryptographic key exchange protocols in the octonion algebra
2019
AbstractWe propose three cryptographic key exchange protocols in the octonion algebra. Using the totient function, defined for integral octonions, we generalize the RSA public-key cryptosystem to the octonion arithmetics. The two proposed symmetric cryptographic key exchange protocols are based on the automorphism and the derivation of the octonion algebra.
Post‐processing of Gauss–Seidel iterations
1999
A Note on Perturbations of Stochastic Matrices
2000
Cardinal estimates involving the weak Lindelöf game
2021
AbstractWe show that if X is a first-countable Urysohn space where player II has a winning strategy in the game $$G^{\omega _1}_1({\mathcal {O}}, {\mathcal {O}}_D)$$ G 1 ω 1 ( O , O D ) (the weak Lindelöf game of length $$\omega _1$$ ω 1 ) then X has cardinality at most continuum. This may be considered a partial answer to an old question of Bell, Ginsburg and Woods. It is also the best result of this kind since there are Hausdorff first-countable spaces of arbitrarily large cardinality where player II has a winning strategy even in the weak Lindelöf game of countable length. We also tackle the problem of finding a bound on the cardinality of a first-countable space where player II has a wi…
On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms
2011
The application of a Method of Lines to a hyperbolic PDE with source terms gives rise to a system of ODEs containing terms that may have very different stiffness properties. In this case, Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful as high order time integrators because they allow an explicit handling of the convective terms, which can be discretized using the highly developed shock capturing technology, together with an implicit treatment of the source terms, necessary for stability reasons. Motivated by the structure of the source term in a model problem introduced by LeVeque and Yee in [J. Comput. Phys. 86 (1990)], in this paper we study the preservation of ce…
Rationalizability of square roots
2021
Abstract Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots i…
On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids
2007
In this paper we discuss a system of partial differential equations describing the steady flow of an incompressible fluid and prove the existence of a strong solution under suitable assumptions on the data. In the 2D-case this solution turns out to be of class C^{1,\alpha}.