Pseudo S-Asymptotically(ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type

In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example.

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.

ON THE LIMITABILITY OF SOLUTIONS OF SOME DIFFERENCE EQUATIONS

We investigate limitability by the Cesaio (C, 1) and the Abel (A) methods of solutions of some third and fourth order difference equations. Also some results contained in [2],[3] are improved.

Evaluation of C and P Factors in Universal Soil Loss Equation on Trapping Sediment: Case Study of Santubong River

Universal Soil Loss Equation (USLE) is the most comprehensive technique available to predict the long term average annual rate of erosion on a field slope. USLE was governed by five factors include soil erodibility factor (K), rainfall and runoff erodibility index (R), crop/vegetation and management factor (C), support practice factor (P) and slope length-gradient factor (LS). In the past, K, R and LS factors are extensively studied. But the impacts of factors C and P to outfall Total Suspended Solid (TSS) and % reduction of TSS are not fully studied yet. Therefore, this study employs Buffer Zone Calculator as a tool to determine the sediment removal efficiency for different C and P factors. The selected study areas are Santubong River, Kuching, Sarawak. Results show that the outfall TSS is increasing with the increase of C values. The most effective and efficient land use for reducing TSS among 17 land uses investigated is found to be forest with undergrowth, followed by mixed dipt. forest, forest with no undergrowth, cultivated grass, logging 30, logging 10^6, wet rice, new shifting agriculture, oil palm, rubber, cocoa, coffee, tea and lastly settlement/cleared land. Besides, results also indicate that the % reduction of TSS is increasing with the decrease of P factor. The most effective support practice to reduce the outfall TSS is found to be terracing, followed by contour-strip cropping, contouring and lastly not implementing any soil conservation practice.

Complete solution of the diophantine equation A^2x^4-By^2=1 and some related problems

We prove that diophantine equation in title has at most one positive integer solution for any positive integers A>1, B>1. It follows that Lucas problem is very simple to solve and a recent result of Bennett is very simple to prove.

A General Hermitian Nonnegative-Definite Solution to the Matrix Equation <i>AXB</i>= <i>C</i>

We derive necessary and sufficient conditions for the existence of a Hermitian nonnegative-definite solution to the matrix equation AXB = C. Moreover, we derive a representation of a general Hermitian nonnegative-definite solution. We then apply our solution to two examples, including a comparison of our solution to a proposed solution by Zhang in [1] using an example problem given from [1]. Our solution demonstrates that the proposed general solution from Zhang in [1] is incorrect. We also give a second example in which we derive the general covariance structure so that two matrix quadratic forms are independent.

Accuracy of glomerular filtration rate estimation equations in patients with hematopathy

Renal dysfunction is a common side-effect of chemotherapeutic agents in patients with hematopathy. Although broadly used, glomerular filtration rate(GFR) estimation equations were not fully validated in this specific population. Thus, this study was designed to further assess the accuracy of various GFR equations, including the newly 2012 CKD-EPI equations. Referring to ^(99m)Tc-DTPA clearance method, three Scr-based(MDRD, Peking, and CKD-EPI_(Scr)), three Scys C-based(Steven 1, Steven 2, and CKD-EPI_(Scys C)), and three Scr-Scys C combination based(Ma, Steven 3, and CKD-EPI_(Scr-Scys C)) equations were included. Bias, P_(30), and misclassification rate were applied to compare the applicability of the selected equations. A total of 180 Chinese hematological patients were enrolled.Mean bias, absolute mean bias, P_(30), misclassification rate and Bland-Altman plots of the CKD-EPI_(Scr-Scys C) equation were 7.90 mL/minute/1.73 m^2, 17.77 mL/minute/1.73 m^2, 73.3%, 38% and 79.7 mL/minute/1.73 m^2, respectively.CKD-EPI_(Scr-Scys C) predicted the most precise eGFR both in lymphoma and leukemia subgroups. Additionally, CKDEPI_(Scys C) equation in the rGFR■90 mL/minute/1.73 m^2 subgroup and Steven 2 equation in the rGFR<90 mL/minute/1.73 m^2 subgroup provided more accurate estimates in each subgroup. The CKD-EPI_(Scr-Scys C) equation could be recommended to monitor kidney function in hematopathy patients. The accuracy of GFR equations may be closely related with GFR level and kidney function markers, but not the primary cause of hematopathy.

THE GLOBAL AND LOCAL C^(2)-SOLUTIONS FOR THE WAVE EQUATION □u = G(u_t, Du) IN THREE SPACE DIMENSIONS

Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Operator Semi-group of Density Evolution Equation for a Repairable Redundant System with Two Same Components

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.

C_0-Semigroup Method of the Density Evolution Equation for M/M/∞ Model

In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.

On C^(1 ,α) Regularity for Monge- Ampre Equation

In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both degenerate and nondegenerate cases.

ON THE EXISTENCE OF SOLUTIONS TO D＇－VALUED STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING EVOLUTION DRIFT

In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.

C1-Conforming Quadrilateral Spectral Element Method for Fourth-Order Equations

This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.

C-Bézier基函数在稳态线弹性方程求解中的应用

用有限元方法求解稳态线弹性方程,以C-Bézier基函数作为参考元上的形函数,通过选取适当的形状参数,在步长不变的情况下,所得到的数值解精度比传统的Lagrange基函数在L∞、L 2范数下高3个数量级以上,在H 1半范数下高2~6个数量级,充分说明了C-Bézier基函数在求解稳态线弹性方程时具有更好的逼近效果。

Tensor-Centric Warfare I: Tensor Lanchester Equations

We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, inspired by the contemporary debate in defence and military circles around how to best utilize information and communications systems in military operations, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). Despite attracting considerable interest and spawning several efforts to develop sound theoretical frameworks for informing force design decision-making, the development of good frameworks for analytically modeling combat remains anything but decided. Using a simple combat scenario, we first develop a tensor generalization of the Lanchester square law, and then extend it to also include the Lanchester linear law, which represents the effect of suppressive fire. We also add on-off control inputs, and discuss the results of a simple simulation of the final model using our small scenario.

HLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

We study Hlder continuous solutions for the second order integro-differential equations with infinite delay （P1）： u′′（t）＋cu′（t）＋∫t-∞β（t-s）u′（s）ds＋∫t-∞γ（t-s）u（s）ds = Au（t）-∫t-∞δ（t-s）Au（s）ds ＋ f（t）on the line R, where 0 〈 α 〈 1, A is a closed operator in a complex Banach space X, c ∈ C is a constant, f ∈ Cα（R,X） and β,γ,δ∈L1（R＋）.Under suitable assumptions on the kernels β, γ and δ, we completely characterize the Cα- well-posedness of （P_1） by using operator-valued Cα-Fourier multipliers.

^(60)CO-r射线辐射辣椒(甜椒)种子诱变效应研究

采用60CO-r射线1-5万伦琴对辣椒(甜椒)种子进行辐射处理,结果表明:对辣椒(甜椒)品种之间发芽率和出苗率影响很大,随着辐射剂量增加,辣椒(甜椒)的发芽率和出苗率逐渐降低。辣椒在1万伦琴低剂量处理,辣椒植株茎粗、茎高、地上部鲜重与对照差别不大,个别植株有所增加,但变异频率很低。当剂量增加,出苗率降低,变异频率增加;在4万伦琴的剂量以上,处于半致死剂量;最适宜的辐射剂量2万伦琴。甜椒在3万伦琴的剂量以上,处于半致死剂量;最适宜的辐射剂量1.5-2万伦琴。

EG7564C-RS点阵液晶的开发应用

介绍了EPSONEG7564C-RS点阵液晶和Motorola16位单片机MC68HC16Z1的硬件连接电路以及在该液晶上的画点程序和图片显示程序。该程序可以在液晶任意位置上显示任意字符、图片,其设计方案可应用于各种选用点阵液晶显示的微型仪器的界面设计中。

复变函数中C.-R方程的教学过程分析

在复变函数中,C.-R.V方程,即柯西-黎曼方程是讨论函数解析性的核心内容,也是研究柯西积分定理的基础,本文针对实际教学中学生的学习情况对C.-R.方程的教学过程做了进一步分析与优化。