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.

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.

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.

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.

Fe-28Mn-10Al-0.8C的热压缩行为及微观组织结构转变

通过Gleeble-3500热模拟机研究了铸态Fe-28Mn-10Al-0.8C低密度高强钢在850~1050℃温度范围和0.01~10 s^(-1)应变速率范围内的热压缩行为和组织转变。实验结果表明,Fe-28Mn-10Al-0.8C钢的动态回复(DRV)和动态再结晶(DRX)行为与变形温度、应变和应变速率直接相关。基于双曲正弦函数和线性拟合,实验钢的可用活化能(Q)为454.64 kJ/mol。给出了实验钢在热压缩变形过程中的组织演变和动态再结晶过程:变形温度的升高或应变速率的降低,可促进奥氏体的动态再结晶和晶粒长大;随着应变速率的增加,会得到更细小的奥氏体动态再结晶晶粒。

基于C-A-C理论的健康科普视频对用户持续使用意愿的影响研究

目的为了提高用户对健康科普视频的持续使用意愿,使设计人员准确掌握健康科普视频的用户需求,优化健康科普视频设计与开发。方法基于C-A-C理论,构建健康科普视频、情绪唤醒和用户持续使用意愿的理论模型,应用结构方程模型论证健康科普视频中博主形象气质、专业性、信息质量、互动质量因素与用户情绪唤醒和持续使用意愿的路径关系。结果健康科普视频中博主形象气质、专业性、信息质量、互动质量对用户情绪唤醒和持续使用意愿具有正向影响作用。结论健康科普视频博主形象气质、专业性、信息质量、互动质量作为影响用户情绪和持续使用意愿的关键因素,能够帮助设计人员从用户视角提高用户情绪唤醒和持续使用意愿,为健康科普视频的设计和创新提供理论和实践参考。

一种估算MICP加固砂土体渗透系数的简便方法

基于Kozeny-Carman(K-C)方程和微生物诱导碳酸钙沉淀(Microbial Induced Carbonate Precipitation,MICP)技术原理,提出一种MICP加固砂土体渗透系数的简便算法.MICP产生的碳酸钙填充土体孔隙,采用电镜成像法得到碳酸钙晶体的粒径,推导得固化砂土体的孔隙比和颗粒平均比表面积.将固化砂土体的孔隙比和颗粒平均比表面积代入K-C方程,得到预测MICP加固砂土体渗透系数的简便算法,并经已有文献试验数据和研究结果验证,结果表明:孔隙比减小和颗粒平均比表面积增大导致MICP固化砂土渗透系数显著降低,算例一土体的渗透系数最终下降了93%-97%,算例二碳酸钙含量达到10%时,渗透系数下降了67%-92%;MICP固化砂土的渗透系数下降速率开始加固时最大,随着碳酸钙含量逐渐增加,渗透系数下降速率逐渐减小;初始渗透系数越大的土体,加固效果越明显,渗透系数的下降速率和下降幅值更大;该算法简便可靠,能较为快速和准确预测MICP加固砂土体的渗透系数,为工程实践提供了理论依据.

Improving Cardiovascular Risk Assessment to Optimize Therapy

Background: Quantifying ten-year cardiovascular risk can be challenging. Different online risk calculators provide different risk estimates and online risk calculators use only one point in time. However, risk factors occur over the lifetime of the individual. Purpose: This manuscript provides three solutions to improving ten-year cardiovascular risk assessment in individuals at intermediate risk. Methods: Measuring Lipoprotein(a)—Lp(a) is recommended for assessing cardiovascular risk in all individuals who are in the intermediate risk category by standard online risk calculators. Lp(a) is primarily determined by genetic inheritance. It has the undesirable properties of being proatherosclerotic, proinflammatory, and prothrombotic. Measuring apolipoprotein B (apo B) provides a good index of the number of atherosclerotic particles present. Studies have demonstrated that small, dense LDL cholesterol particles are more atherogenic than larger, less dense LDL cholesterol particles. Measuring high sensitivity C-reactive protein (hsCRP) provides a good estimation of the degree of inflammation in the vascular system. Inflammation is a critical component of heart attacks and strokes. It is increased in diabetes and obesity. Treatment to reduce inflammation results in a reduction of cardiovascular events, independent of lipid values. Results: The above three risk factors should be measured in all patients with an intermediate risk score. Routine assays are readily available at a reasonable cost. They are independent risk factors for cardiovascular disease. Their recommendation is based on the pathophysiology of atherosclerotic cardiovascular disease. Successful therapy will result in the decrease of each of these risk factors. Conclusion: The recommended approach will improve the assessment of cardiovascular risk and guide the physician and patient to the correct treatment recommendations.