FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach

The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory.

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-pointed, non-convex and non-closed into a finite union of disjoint strictly supported pointed convex cones, we discuss the continuous perturbations of the decision space. Several sufficient conditions for the continuity of the sets of majorly efficiellt points and solutions are given.

The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Differential Equations

In ordinary differential equations, structural stability of hyperbolic fixed points is a classical result, but the proof of this result in [2] has same small mistake. In this paper,we will correct the above mistake by using the Hartman theorem and its idea.

Stability of Triangular Points of the Generalized Photogravitational Robes Restricted Three-Body Problem

The linear stability of the triangular points was studied for the Robes restricted three-body problem when the bigger primary (rigid shell) is oblate spheroid and the second primary is radiating. The critical mass obtained depends on the oblateness of the rigid shell and radiation of the second primary as well as the density parameter k. The stability of the triangular points depends largely on the values of k. The destabilizing tendencies of the oblateness and radiation factors were enhanced when k > 0 and weakened for k .

Stability of Collinear Points in the Generalized Photogravitational Robes Restricted Three-Body Problem

In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.

Stability Analysis of a SDOF Mechanical Model with Distinct Critical Points: II. Catastrophe Theory Approach

In a recent publication [1], the fully nonlinear stability analysis of a Single-Degree-of Freedom (SDOF) model with distinct critical points was dealt with on the basis of bifurcation theory, and it was demonstrated that this system is associated with the butterfly singularity. The present work is the companion one, tackling the problem via the Theory of Catastrophes. After Taylor expanding the original potential energy function and introducing Padè approximants of the trigonometric expression involved, the resulting truncated potential is a universal unfolding of the original one and an extended canonical form of the butterfly catastrophe potential energy function. Results in terms of equilibrium paths, bifurcation sets and manifold hyper-surface projections fully validate the whole analysis, being in excellent agreement with the findings obtained via bifurcation theory.

A FIXED POINT APPROACH TO THE STABILITY OF A GENERALIZED APOLLONIUS TYPE QUADRATIC FUNCTIONAL EQUATION

Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed.The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation.The slip for viscous fluid is considered.The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate.The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method.Dual solutions are obtained for the velocity,skin friction coefficient,temperature,and Nusselt number subject to sundry flow parameters,magnetic parameter,Darcy-Forchheimer number,thermal radiation parameter,suction parameter,and dimensionless slip parameter.In this research,the main consideration is given to the engineering interest like skin friction coefficient(velocity gradient or surface drag force)and Nusselt number(temperature gradient or heat transfer rate)and discussed numerically through tables.In conclusion,it is noticed from the stability results that the upper branch solution(UBS)is more reliable and physically stable than the lower branch solution(LBS).

A Fixed Point Approach to the Fuzzy Stability of a Mixed Type Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.

1-Methyl-3-octylimidazolium Polyoxomolybdate Ionic Liquid with Low Melting Point and High Stability:Preparation and Photocatalytic Activity

The polyoxometalate（POM）-imidazole ionic liquid（IL） [C8mim]2[Mo6O19]（C8mim=1-methyl-3-octylimi- dazolium） with a low melting point of 82.6 °C was successfully prepared and characterized by FTIR, XPS, NMR, TG and so on. The polyoxomolybdate-based IL has high stability, and its decomposing temperature reaches 321 °C, which is higher than that of 1-alkyl-3-methylimidazolium halides IL. Further photocatalytic performances of the IL were measured via degrading dye rhodamine B（RB） in aqueous solution under the UV light irradiation. The experiments show that the conversion of RB reaches 80.5% after 90 min under UV-light and the degradation efficiency depends on the pH value of the solution, irradiation time and the dosage of the IL and so on.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

STABILITY AND SUPERSTABILITY OF JORDAN HOMOMORPHISMS AND JORDAN DERIVATIONS ON BANACH ALGEBRAS AND C~＊-ALGEBRAS： A FIXED POINT APPROACH

Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.

Fixed Points and Asymptotic Properties of Neutral Stochastic Delay Differential Equations

This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.

Singularities of the Moduli Space of n Unordered Points on the Riemann Sphere

We classify the nite groups associated to the orbifold singularities of the moduli space of n≥5 unordered points on the Riemann sphere.

Different Thermal Stabilities of Cation Point Defects in LaAlO_3 Bulk and Films

Using the first-principles method, we investigate the thermal stability of cation point defects in LaAlO3 bulk and films. The calculated densities of states indicate that cation vacancies and antisites act as acceptors. The formation energies show that cation vacancies are energetically favorable in bulk LaAIO3 under O-rich conditions, while the AILa antisites are stable in reducing atmosphere. However, the same behavior does not appear in the case of LaAlO3 films. For LaO-terminated LaAlOa fihns, La or AI vacancies remain energetically favorable under O-rich and O-deficient conditions. For an AlO2-terminated surface, under O-rich condition the La interstitial atom is repelled from the outmost layer after optimization, which releases more stress leading to the decrease of total energy of the system. An AI interstitial atom has a smaller radius so that it can stay in distorted films and becomes more stable under O-deficient conditions, and the Al interstitial atoms can be another possible carrier source contribution to the conductivity of n-type interface under an ultrahigh vacuum. La and Al antisites have similar formation energy regardless of oxygen pressure. The results would be helpful to understand the defect structures of LaAlOa-related materials.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

Accelerated RHSS Iteration Method for Stabilized Saddle-Point Problems

For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.

InSe单层中点缺陷的第一性原理研究

InSe是Ⅲ-Ⅵ族化合物中的主要成员,由于其具有优异的电学性能,在太阳能电池、固体电池组等领域受到广泛的关注.光电材料及器件的优良特性由电子结构决定,而Ⅲ-Ⅵ族化合物中的点缺陷对电子结构具有重要的调控,且单层InSe中点缺陷的Perdew-Burke-Ernzerhof(PBE)和Heyd-Scuseria-Ernzerhof(HSE)对比研究尚且缺乏.本文基于密度泛函理论的第一性原理计算,对单层InSe的硒空位、铟空位、溴替代硒、硫替代硒、碲替代硒、镓替代铟、锡替代铟和铊替代铟的缺陷形成能和稳定性进行了研究.结果表明:在缺铟和富铟条件下,硫替代硒和镓替代铟的缺陷形成能低且可以有效的降低体系总能,提高体系的稳定性.溴替代硒具有较小的缺陷形成能,但较大的体系总能表明溴替代硒的缺陷体系不稳定.在缺铟条件下易形成铊替代铟缺陷;在富铟条件下易形成碲替代硒缺陷.上述研究结果有助于理解点缺陷对Ⅲ-Ⅵ族化合物稳定性的影响,同时也为未来实验上设计基于InSe的高效的光电子器件提供理论依据.