Differential Independence of <Emphasis Type="Italic">Γ</Emphasis> and <Emphasis Type="Italic">ζ</Emphasis>

In a celebrated theorem H?lder proved that the Euler Γ-function is differential transcendental, i.e. Γ(z) is not a solution of any (non-trivial) algebraic ordinary differential equation with coefficients that are complex numbers; and we extend his methods to the Riemann ζ-function. Moreover, we conjecture that Γ and ζ are differential independent, i.e. Γ(z) is not a solution of any such algebraic differential equation—even allowing coefficients that are differential polynomials in ζ(z). However, we are able to demonstrate only the partial result that Γ(z) and ζ(sin 2πz) are differential independent.     

Solitary waves for power-law regularized long-wave equation and <Emphasis Type="Italic">R</Emphasis>(<Emphasis Type="Italic">m</Emphasis>,<Emphasis Type="Italic">n</Emphasis>) equation

This paper integrates the regularized long-wave equation with power-law nonlinearity using the solitary-wave ansatz. A few of the conserved quantities are calculated by using the 1-soliton solution. This technique is then extended to obtain the solitary-wave solution of the R(m,n) equation and a conserved quantity is also calculated for this generalized equation.     

On the L_p intersection body

In this paper,by using the Brunn-Minkowski-Firey mixed volume theory and dual mixed volume theory,associated with L_p intersection body and dual mixed volume,some dual Brunn-Minkowski inequalities and their isolate forms are established for L_p intersection body about the normalized L_p radial addition and L_p radial linear combination.Some properties of operator Lp are given.     

A new method for calculating hysteretic <Emphasis Type="Italic">K</Emphasis>(<Emphasis Type="Italic">S</Emphasis>) relationship

A new method for calculating the hysteretic relationship between hydraulic conductivity (K) and suction (S) is proposed. This method uses the experimental (K–S) data of the main wetting and drying branches and predicts satisfactorily the scanning drying and wetting curves. The proposed method is applicable to those porous media where the hysteretic Θ–S relationship complies with the independent domain concept.     

2<Emphasis Type="Italic">T</Emphasis>-periodic solution for<Emphasis Type="Italic">m</Emphasis> order neutral type differential equations with time delays

Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1), the better result cannot be found by using the same method. Foundation item: the Natural Science Foundation of Yunnan Education Committee (990002) Biography: ZHANG Bao-sheng (1962-)     

Inequalities relating to Lp-version of Petty＇s conjectured projection inequality

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.     

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.     

L-leap-accelerating the stochastic simulation of chemically reacting systems

Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems,in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap.The L-leap method can better satisfy the leap condition.Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.     

Motion of a Graph by <Emphasis Type="Italic">R</Emphasis>-Curvature

We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in R ^d , by the continuum limit of a class of infinite particle systems. We also show that weak solutions of the partial differential equation are viscosity solutions and give the uniqueness result on both weak and viscosity solutions.     

Variational Analysis of the Asymptotics of the <Emphasis Type="Italic">XY</Emphasis> Model

In this paper we consider the XY (N-dimensional possibly anisotropic) spin-type model and, by comparison with a Ginzburg–Landau-type functional, we perform a variational analysis in the limit when the number of particles diverges. In particular we show how the appearance of vortex-like singularities can be described by properly scaling the energy of the system through a Γ-convergence procedure. We also address the problem in the case of long-range interactions and solve it in two dimensions.     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Infinitely many solutions of p-Laplacian equations with limit subcritical growth

We discussed a class of p-Laplacian boundary problems on a bounded smooth domain,the nonlinearity is odd symmetric and limit subcritical growing at infinite.A sequence of critical values of the variational functional was constructed after the general- ized Palais-Smale condition was verified.We obtain that the problem possesses infinitely many solutions and corresponding energy levels of the functional pass to positive infinite. The result is a generalization of a similar problem in the case of subcritical.     

Reduction of<Emphasis Type="Italic">K</Emphasis><Subscript>I</Subscript> and<Emphasis Type="Italic">K</Emphasis><Subscript>II</Subscript> by the shape-memory effect in a TiNi shape-memory fiber-reinforced epoxy matrix composite

Shape-memory TiNi fiber-reinforced/epoxy matrix composites have been fabricated, and the suppression of crack-tip stress intensity and the change in fracture toughness have been systematically investigated. Stress-strain data for these composite specimens with notches at various angles and different crack lengths in the transverse direction have been measured in tensile tests. The stress intensity factor at the crack tip is experimentally determined from photoelastic fringe patterns. The decreases inK values are attributed to the compressive stress field in the matrix induced when the pre-strains of the TiNi fiber contract to their initial length upon heating above the austenitic final temperature. We present the influences of the pre-strain of TiNi fibers and the compressive domain size between a crack tip and fiber on theK value.     

Optimal harvesting for an age-dependent <Emphasis Type="Italic">n</Emphasis>-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur＇s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.     

Application of the probabilistic fracture mechanics method of predicting the fatigue life of tubular joints

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<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in J ₂ relative dynamics. Working with the Hamiltonian model of the relative motion including the J ₂ perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J ₂ invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo simulation. The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science Foundation of China (60535010).     

HAMILTON OPERATORS AND HOMOTHETIC MOTIONS IN R^3

Quaternion is a division ring. It is shown that planes passing through the origin can be made a field with the quaternion product in R3. The Hamiltonian operators help us define the homothetic motions on these planes. New characterizations for these motions are investigated.     

Effects of measurement techniques on the experimental characterization of crack tip opening angle-Δ<Emphasis Type="Italic">a</Emphasis> resistance curves

One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental, surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced.