Mathematics Commons^™

Global Solutions To The Lake Equations With Isolated Vortex Regions, Chaocheng Huang

Mathematics and Statistics Faculty Publications

The vorticity formulation for the lake equations in R² is studied.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Yi Li

In this paper, we study the following Duffing-type equation: x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Mathematics and Statistics Faculty Publications

In this paper, we study the following Duffing-type equation:

x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu

Mathematics and Statistics Faculty Publications

No abstract provided.

On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

A simple method is provided to construct a general class of individual and simultaneous confidence intervals for the effects in orthogonal saturated designs. These intervals use the data adaptively, maintain the confidence levels sharply at 1 - α at the least favorable parameter configuration, work effectively under effect sparsity, and include the intervals by Wang and Voss (2001) as a special case.

The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi

Yi Li

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_1,t = u_1,xx − u^α₁ u^β₂, u_2,t = du_2,xx+ u^α₁ u^β₂ with non-negative initial data, where the exponents α,β satisfy 1<α,β<2, α+β = 3 and the constant d>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi

Mathematics and Statistics Faculty Publications

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_1,t = u_1,xx − u^α₁ u^β₂, u_2,t = du_2,xx+ u^α₁ u^β₂ with non-negative initial data, where the exponents α,β satisfy 1<α,βd>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Yi Li

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Yi Li

No abstract provided.

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Mathematics and Statistics Faculty Publications

No abstract provided.

An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.