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University of Texas Rio Grande Valley
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
A New Integrable Two-Component System With Cubic Nonlinearity, Junfeng Song, Changzheng Qu, Zhijun Qiao
A New Integrable Two-Component System With Cubic Nonlinearity, Junfeng Song, Changzheng Qu, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, a new integrable two-component system, mt=[m(uxvx−uv+uvx−uxv)]x,nt=[n(uxvx−uv+uvx−uxv)]x, where m=u−uxx and n=v−vxx, is proposed. Our system is a generalized version of the integrable system mt=[m(u2x−u2)]x, which was shown having cusped solution (cuspon) and W/M-shape soliton solutions by Qiao [J. Math. Phys. 47, 112701 (2006). The new system is proven integrable not only in the sense of Lax-pair but also in the sense of geometry, namely, it describes pseudospherical surfaces. Accordingly, infinitely many conservation laws are derived through recursion relations. Furthermore, exact solutions such as cuspons and W/M-shape solitons are also obtained.
When Is Hyponormality For 2-Variable Weighted Shifts Invariant Under Powers?, Raul E. Curto, Jasang Yoon
When Is Hyponormality For 2-Variable Weighted Shifts Invariant Under Powers?, Raul E. Curto, Jasang Yoon
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Abstract. For 2-variable weighted shifts W(α,β) ≡ (T1, T2) we study the invariance of (joint) khyponormality under the action (h, ℓ) 7→ W (h,ℓ) (α,β) := (T h 1 , T ℓ 2 ) (h, ℓ ≥ 1). We show that for every k ≥ 1 there exists W(α,β) such that W (h,ℓ) (α,β) is k-hyponormal (all h ≥ 2, ℓ ≥ 1) but W(α,β) is not k-hyponormal. On the positive side, for a class of 2-variable weighted shifts with tensor core we find a computable necessary condition for invariance. Next, we exhibit a large nontrivial class for which hyponormality …
Mathematical Modeling And Computation Of Channel Flow Over Discrete Structures, Rolando J. Olivares, Daniel N. Riahi
Mathematical Modeling And Computation Of Channel Flow Over Discrete Structures, Rolando J. Olivares, Daniel N. Riahi
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper mathematical modeling and computation of channel flow over small discrete structures are carried out under some reasonable conditions. A mathematical model for such a flow problem, which is based on a relevant system of partial differential equations and Fourier analysis, is studied using perturbation and nonlinear stability methods, and the resulting flow solutions over two types of discrete structures are computed under both stable and unstable conditions. It was found, in particular, that for a subcritical domain with the Reynolds number R slightly less than its critical value Rc, which is defined as the value below which …
Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev
Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.