Existence and Uniqueness of Solutions for a Class of Reaction-diffusion Systems

61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-…     

On the M/G/1 retrial queueing system with linear control policy

Summary This paper is concerned with the study of a newM/G/1 retrial queueing system in which the delays between retrials are exponentially distributed random variables with linear intensityg(n)=α+nμ, when there aren≥1 customers in the retrial group. This new retrial discipline will be calledlinear control policy. We carry out an extensive analysis of the model, including existence of stationary regime, stationary distribution of the embedded Markov chain at epochs of service completions, joint distribution of the orbit size and the server state in steady state and busy period. The results agree with known results for special cases.     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

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The null controllability of thermoelastic plates and singularity of the associated minimal energy function

We consider the null controllability problem for thermoelastic plates, defined on a two dimensional domain Ω, and subject to hinged, clamped or free boundary conditions. The uncontrolled partial differential equation system generates an analytic semigroup on the space of finite energy. Consequently, the concept of null controllability is indeed appropriate for consideration here. It is shown that all finite energy states can be driven to zero by means of just one L2((0,T)×Ω) control be it either mechanical or thermal. The singularity, as T↓0, of the associated minimal energy function is the main object studied in the paper. Singularity and blow-up rates for minimal energy function are not only of interest in their own right but are also of critical importance in Stochastic PDEs. In this paper, we establish the optimal blow-up rate for this function. It is shown that the rate of singularity is the same as for finite-dimensional truncations of the model. In view of sharp estimates available in the finite dimensional setting [Math. Control Signals Systems 9 (1997) 327], the singularity rates provided in this paper are optimal.     

Existence and stability of bounded solutions for a system of parabolic equations

In this paper we study the existence and the stability of bounded solutions of the following non-linear system of parabolic equations with homogeneous Dirichlet boundary conditions:

     

光束旋转90°多程放大系统的波前误差校正

光束通过神光-Ⅲ原型装置四程放大系统发生了90°旋转和扩束。在四程放大系统腔镜处放置变形镜校正系统像差是一种新的自适应光学方案，推导出被校正像差与变形镜面形之间的数学关系。理论推导表明，在扩束比大于1的前提下，腔镜处变形镜可以校正系统输出的任意类型的像差，且变形镜对应的面形唯一。理论分析和计算仿真说明该方案的校正能力与像差类型和扩束比有关，扩束比增大将增强变形镜校正像散的能力，但系统旋光消像散的能力也将减弱。     

Adaptive modeling, adaptive data assimilation and adaptive sampling

For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical–biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling.     

The development of an integrated platform to identify breast cancer glycoproteome changes in human serum

Protein glycosylation represents one of the major post-translational modifications and can have significant effects on protein function. Moreover, changes in the carbohydrate structure are increasingly being recognized as an important modification associated with cancer etiology. In this report, we describe the development of a proteomics approach to identify breast cancer related changes in either concentration and/or the carbohydrate structures of glycoprotein(s) present in blood samples. Diseased and healthy serum samples were processed by an optimized sample preparation protocol using multiple lectin affinity chromatography (M-LAC) that partitions serum proteins based on glycan characteristics. Subsequently, three separate procedures, 1D SDS-PAGE, isoelectric focusing and an antibody microarray, were applied to identify potential candidate markers for future study. The combination of these three platforms is illustrated in this report with the analysis of control and cancer glycoproteomic fractions. Firstly, a molecular weight based separation of glycoproteins by 1D SDS-PAGE was performed, followed by protein, glycoprotein staining, lectin blotting and LC–MS analysis. To refine or confirm the list of interesting glycoproteins, isoelectric focusing (targeting sialic acid changes) and an antibody microarray (used to detect neutral glycan shifts) were selected as the orthogonal methods. As a result, several glycoproteins including alpha-1B-glycoprotein, complement C3, alpha-1-antitrypsin and transferrin were identified as potential candidates for further study.     

Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

O Introduction We consider the orbital instability of standing waves for the Klein-Gordon-Zakharov system with different propagation speeds in three space dimensions