Theta Subgroups and the Solvability of FiniteGroups

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＤｅｆｉｎｉｔｉｏｎＡｌｌｇｒｏｕｐｓｔｒｅａｔｅｄａｒｅｆｉｎｉｔｅ．Ｉｎ［１］，Ｎ．Ｐ．ＭｕｋｈｅｒｊｅｅａｎｄＰ．Ｂｈａｔｔａｃｈａｒｙａｄｅｆｉｎｅｄｔｈｅｃｏｎｃｅｐｔｏｆθ－ｐａｉｒｓａｓｓｏｃｉａｔｅｄｔｏａｍａｘｉｍａｌｓｕｂｇｒｏｕｐＭｏｆａｇｒｏｕｐＧａｓｆｏｌｌｏｗｓ：ａθ－ｐａｉｒｆｏｒＭｉｓａｎｙｐａｉｒｏｆｓｕｂｇｒｏｕｐｓ（Ｃ，Ｄ）ｏｆＧｓｕｃｈｔｈａｔ（１）ＤＧ，Ｄ＜Ｃ，（２）〈Ｍ，Ｃ〉＝Ｇ，〈Ｍ，Ｄ〉＝Ｍａｎｄ（３）Ｃ／Ｄ…     

Modules Characterized by Injectivity Clases

ＭｏｄｕｌｅｓＣｈａｒａｃｔｅｒｉｚｅｄｂｙＩｎｊｅｃｔｉｖｉｔｙＣｌａｓｅｓＷａｎｇＤｉｎｇｇｕｏ（王顶国）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ，Ｓｈａｎｄｏｎｇ，２７３１６５）Ａｂｓ...     

The Projection onto a Direct Product of Convex Cones

ＴｈｅＰｒｏｊｅｃｔｉｏｎｏｎｔｏａＤｉｒｅｃｔｒｏｄｕｃｔｏｆＣｏｎｖｅｘＣｏｎｅｓＬｉｕＷｅｉ（刘维）ａｎｄＳｈｉＮｉｎｇｚｈｏｎｇ（史宁中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｅａｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃ...     

Equivalent Representations of Complex Positive Definite Matrices

ＥｑｕｉｖａｌｅｎｔＲｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆＣｏｍｐｌｅｘＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｔｒｉｃｅｓ￥ＰａｎｇＭｉｎｇｘｉａｎ（逄明贤）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｊｉ...     

Hybrid Finite Element Method for Two-phase Miscible Displacement in Porous Media

ＨｙｂｒｉｄＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｆｏｒＴｗｏ┐ｐｈａｓｅＭｉｓｃｉｂｌｅＤｉｓｐｌａｃｅｍｅｎｔｉｎＰｏｒｏｕｓＭｅｄｉａ＊）ＬｉａｎｇＤｏｎｇ（梁栋）ＣｈｅｎｇＡｉｊｉｅ（程爱杰）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

A Chaotic System May be Simple

ＡＣｈａｏｔｉｃＳｙｓｔｅｍＭａｙｂｅＳｉｍｐｌｅＬｉａｏＧｏｎｇｆｕ（廖公夫）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）ＦａｎＱｉｎｊｉｅ（范钦杰）（Ｄｅｐａｒｔｍｅｎｔｏｆ...     

Invariant Kahler Metrics and Curvatures on a Class of Pseudoconvex Domains

（童武）（殷慰萍）ＩｎｖａｒｉａｎｔＫａｈｌｅｒＭｅｔｒｉｃｓａｎｄＣｕｒｖａｔｕｒｅｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＴｏｎｇＷｕＹｉｎＷｅｉｐｉｎｇ（Ｄａｐｔ．ｏｆＭａｔｈ．，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉ...     

A Characterization of a Class of Symmetric(0,1)Matrices

ＡＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆａＣｌａｓｓｏｆＳｙｍｍｅｔｒｉｃ（０，１）ＭａｔｒｉｃｅｓＬｉＷｅｎ（黎稳）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｇｕａｎｚｈｏｎ，５１０６３１...     

Closed Geodesics and Non一Differentiability of the Metric in Infinite－Dimensional Teichmuller Spaces

ＣｌｏｓｅｄＧｅｏｄｅｓｉｃｓａｎｄＮｏｎ一ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆｔｈｅＭｅｔｒｉｃｉｎＩｎｆｉｎｉｔｅ－ＤｉｍｅｎｓｉｏｎａｌＴｅｉｃｈｍｕｌｌｅｒＳｐａｃｅｓＬｉｚｈｏｎｇ（李忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

Some Spectral Properties of Metapositive Definite Matrice

ＳｏｍｅＳｐｅｃｔｒａｌＰｒｏｐｅｒｔｉｅｓｏｆＭｅｔａｐｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｔｒｉｃｅｓＬｉＺｈｕｘｉａｎｇ（李竹香）ＬｕＨｏｎｇｂｉｎ（吕洪斌）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇ...     

The Existence of Almost Periodic Solution and Periodic Solutions

In this paper, it is obtained that a periodic system has an almost periodic solution if it has a solution x=\phi(t) uniformly stable with respect to \Omega_\phi ,and has a periodic solution if x=\phi(t) is weakly uniformly asymptotically stable with respect to \Omega_\phi. Meanwhile, it is also obtained that a uniformly almost periodic system has an almost periodic solution if it has a solution x=\phi(t) uniformly asymptotically stable with respect to A_\phi^j.     

Stable Periodic Solutions of Periodic Systems of Differential Equations

An infinitely differentiable periodic two-dimensional system of differential equations is considered. It is assumed that there is a hyperbolic periodic solution and there exists a homoclinic solution to the periodic solution. It is shown that, for a certain type of tangency of the stable manifold and unstable manifold, any neighborhood of the nontransversal homoclinic solution contains a countable set of stable periodic solutions such that their characteristic exponents are separated from zero.     

Linearized stability in periodic functional differential equations with state-dependent delays

In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with state-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable.     

Periodic billiard paths in right triangles are unstable

A stable periodic billiard path in a triangle is a billiard path which persists under small perturbations of the triangle. This article gives a geometric proof that no right triangles have stable periodic billiard paths.      

Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay

In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.     

Replicate periodic windows in the parameter space of driven oscillators

In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.     

Some new results for a logistic almost periodic system with infinite delay and discrete delay

A nonautonomous logistic almost periodic system with infinite delay and discrete delay is considered. Our result shows that the system is globally asymptotically stable under the condition for the boundedness of the system. By using almost periodic functional Hull theory and new computational techniques, we show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution under the condition for the boundedness of the system. Some recent results are improved, and an open question is answered.     

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on n letters, where n is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.     

Bifurcation and stability of forced convection in tightly coiled ducts: stability

A numerical study is made on the stability of multiple steady flows and heat transfer in tightly coiled ducts by examining their responses to finite random disturbances. It is found that possible physically realizable fully developed flows evolve, as the Dean number increases, from a stable steady symmetric 2-cell flow at lower Dean numbers to a temporal periodic oscillation, a temporal intermittent oscillation, another temporal periodic oscillation, the co-existence of stable steady symmetric 2-cell flow and temporal oscillating flows (either periodic or aperiodic), and the co-existence of three stable steady 2-cell flows (either symmetric or asymmetric) and aperiodic oscillating flows.