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In this paper, we study the Cauchy problems for certain regularized models to the incompressible viscoelastic flow in n space dimensions with n = 2, 3. Firstly, we establish a regularity condition for the solution under del u is a...
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In this paper, we study the Cauchy problems for certain regularized models to the incompressible viscoelastic flow in n space dimensions with n = 2, 3. Firstly, we establish a regularity condition for the solution under del u is an element of L-1(0, T; L-infinity(R-n)). Furthermore, we obtain a regularity condition to the smooth solution for the inviscid regularized models in two space dimensions. Finally, we prove a global existence result of classical solutions for a three-dimensional incompressible Oldroyd-alpha model with fractional diffusion.
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Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new...
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Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective by transforming the positions of the elements in the regularity conditions, some new regularity conditions (collectively referred to as transposition regularity) are obtained, and the concepts of various transposition regular semigroups are introduced (L1/L2/L3, R1/R2/R3-transposition regular semigroups, etc.). Their relations with completely regular semigroups and left (right) regular semigroups, proposed by Clifford and Preston, are analyzed. Their properties and structures are studied from the aspects of idempotents, local identity elements, local inverse elements, subsemigroups and so on. Their decomposition theorems are proved respectively, and some new necessary and sufficient conditions for semigroups to become completely regular semigroups are obtained.
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This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Frechet and pro...
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This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Frechet and proximal subdifferentials of the distance function from a closed subset in a Riemannian manifold are represented by corresponding normal cones of the set.
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In this article, we discuss when one can extend an r-regular graph to an r + 1 regular by adding edges. Different conditions on the number of vertices n and regularity r are developed. We derive an upper bound of r, depending on n...
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In this article, we discuss when one can extend an r-regular graph to an r + 1 regular by adding edges. Different conditions on the number of vertices n and regularity r are developed. We derive an upper bound of r, depending on n, for which, every regular graph G(n, r) can be extended to an r + 1-regular graph with n vertices. Presence of induced complete bipartite subgraph and complete subgraph is discussed, separately, for the extension of regularity.
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This work concerns regularization (or explosion suppression) and stabilization of randomly switching dynamic systems by selecting suitable input functions. Starting with a randomly switching system modulated by a continuous-time M...
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This work concerns regularization (or explosion suppression) and stabilization of randomly switching dynamic systems by selecting suitable input functions. Starting with a randomly switching system modulated by a continuous-time Markov chain, our aim is to find a feedback control (input function) so that the system becomes stable. But before addressing the stabilization issue, another problem needs to be resolved first. Because of the fast growth in the continuous state variable, the solution of the system has a finite explosion time with probability one. To ensure the existence of global solutions, a feedback control (a noise perturbation) is added to make the system regular. Then another feedback control (a second perturbing noise) is added to ensure the stability of the resulting systems. Owing to the nonlinearity, closed-form solutions are often virtually impossible to obtain. Thus, a discrete-time approximation algorithm is constructed. Under simple conditions, a suitably interpolated sequence of the discrete-time algorithm is shown to converge to the limit switching diffusion. Finally, regularization and stabilization of the approximating sequence are dealt with.
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We show regularization effect of nonlinear gradient noise to the solution of 1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale noise at the extremum poin...
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We show regularization effect of nonlinear gradient noise to the solution of 1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale noise at the extremum points of the process.
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In this paper, regular cryptogroups are constructed by left and right regular bands and a family of groups and homomorphisms satisfying some conditions.
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We present algebras that axiomatise the equational theories of two variants of omega-regular expressions. The first algebra simplifies a two-sorted infinitary axiomatisation by Wagner. Its completeness is established relatively to...
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We present algebras that axiomatise the equational theories of two variants of omega-regular expressions. The first algebra simplifies a two-sorted infinitary axiomatisation by Wagner. Its completeness is established relatively to Wagner's completeness result. The second one is based on one-sorted algebras proposed by Park and Cohen. Its completeness is derived from our first result.
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We introduce a symmetry property for unit-regular rings as follows: a ∈ R is unit-regular if and only if aR ⊕ (a ? u)R = R (equivalently, Ra ⊕ R(a ? u) = R) for some unit u of R if and only if aR ⊕ (a ? u)R =(2a ? u)R (equival...
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We introduce a symmetry property for unit-regular rings as follows: a ∈ R is unit-regular if and only if aR ⊕ (a ? u)R = R (equivalently, Ra ⊕ R(a ? u) = R) for some unit u of R if and only if aR ⊕ (a ? u)R =(2a ? u)R (equivalently, Ra ⊕ R(a ? u) = R(2a ? u)) for some unit u of R. Let M and N be right R-modules and α, β ∈ Hom(M, N) such that α + β is regular. It is shown that αS ⊕ βS =(α + β)S, where S = End(M) if and only if Tα ⊕ Tβ = T(α + β), where T = End(N). We also introduce partial order α ≤⊕β and minus partial order α ≤?β for any α, β ∈ Hom(M, N); they translate into module-theoretic language defined in a ring in [7] and [8]. We analyze some relationships between ≤⊕ and ≤? on the endomorphism rings of the modules M and N.
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There are two well-known map representations of hypermaps, namely the Walsh andthe Vince map representations, that are dual to each other. They correspond to normal sub_x0002_groups of index two of a free product Γ = (C2×C2)?C2 ...
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There are two well-known map representations of hypermaps, namely the Walsh andthe Vince map representations, that are dual to each other. They correspond to normal sub_x0002_groups of index two of a free product Γ = (C2×C2)?C2 which decompose as “elementary”free product C2 ? C2 ? C2. However, Γ has three normal subgroups that decompose as “elementary” free product C2 ? C2 ? C2, the third of these subgroups giving the less knownPetrie-path map representation. By relaxing the “elementary” free product condition to freeproduct of rank 3, and under the extra condition “words of smaller length” on the generators, we prove that the number of map representations of hypermaps increases to 15 (up toa restrictedly dual), all of which are described in this paper.
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