Modelling the steady-state effluent characteristics of the TNCU process under different return mixed liquid

The Activated Sludge Model No. 2d (ASM2d) was employed and modified to predict the effluent qualities of the modified enhanced biological phosphate removal (EBPR) system – TNCU. The TNCU process was composed of anaerobic/anoxic/oxide (A2O) process and rotating biological contactors (RBC) in each reactor. There were three modifications for the model in this study: (1) the biosorption effect of the soluble COD, (2) the ammonification of the organic nitrogen in influent wastewater, and (3) the growth of the heterotrophic organisms in the anaerobic tank. The influent wastewater qualities were fixed, the ratios of return sludge and SRT were 0.5 and 11 days, and the model plant was operated at three different mixed liquid recycling ratios (MLRR, 0.5, 1.25, 2). When a steady state was reached, the comparisons between the measured values and the model predicted values in each test were made. It shows a good consistency between them. According to the consistent results, the biosorption effect of the soluble COD and the ammonification of the organic nitrogen in influent wastewater were the important effects in activated sludge system. Additionally, the heterotrophic organisms might grow in the anaerobic tank. The heterotrophic organisms, phosphorus accumulating organisms and autotrophic organisms would decrease in the anaerobic tanks because the lysis reactions were the major reactions in the anaerobic tanks. They would increase in the aerobic tanks. Furthermore, it was indirectly proved that the denitrifying PAOs existed in the EBPR system.     

Log-det approximation based on uniformly distributed seeds and its application to Gaussian process regression

Maximum likelihood estimation (MLE) of hyperparameters in Gaussian process regression as well as other computational models usually and frequently requires the evaluation of the logarithm of the determinant of a positive-definite matrix (denoted by C hereafter). In general, the exact computation of is of O(N³) operations where N is the matrix dimension. The approximation of could be developed with O(N²) operations based on power-series expansion and randomized trace estimator. In this paper, the accuracy and effectiveness of using uniformly distributed seeds for approximation are investigated. The research shows that uniform-seed based approximation is an equally good alternative to Gaussian-seed based approximation, having slightly better approximation accuracy and smaller variance. Gaussian process regression examples also substantiate the effectiveness of such a uniform-seed based log-det approximation scheme.     

Iterative process for G-multi degree reduction of Bézier curves

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.     

A note on iterative process for G-multi degree reduction of Bézier curves

In the paper [A. Rababah, S. Mann, Iterative process for G²-multi degree reduction of Bézier curves, Applied Mathematics and Computation 217 (2011) 8126-8133], Rababah and Mann proposed an iterative method for multi-degree reduction of Bézier curves with C¹ and G²-continuity at the endpoints. In this paper, we provide a theoretical proof for the existence of the unique solution in the first step of the iterative process, while the proof in their paper applies only in some special cases. Also, we give a complete convergence proof for the iterative method. We solve the problem by using convex quadratic optimization.     

Weighted integral inequalities for solutions of the A-harmonic equation

We prove the parametric versions of -weighted integral inequalities for differential forms satisfying the A-harmonic equation. These results can be considered as extensions of the classical inequalities for Sobolev functions.     

K-theory of reduced C*-algebras and rapidly decreasing functions on groups

We associate to any length function L on a group a space of rapidly decreasing functions on (in the l ² sense), denoted by H _L (). When H _L () is contained in the reduced C*-algebra C _r ^* () of (), then it is a dense *-subalgebra of C _r ^* () and we prove a theorem of A. Connes which asserts that under this hypothesis H _L () has the same K-theory as C _r ^* (). We introduce another space of rapidly decreasing functions on (in the l ¹ sense), denoted by H _L ^1, (), which is always a dense *-subalgebra of the Banach algebra l ¹(), and we show that H _L ^1, () has the same K-theory as l ¹().     

Approximation and decomposition properties of some classes of locally D.C. functions

We study the connexion between local and global decompositions of some important subclasses of locally d.c. functions (functions which locally split as a difference of two convex functions). Then we tackle the problem of regularizing such functions by the Moreau-Yosida process and prove in particular that the class of lower-C ² functions fits well this approximation procedure.     

C-GV triviality of function germs and Newton polyhedra

We provide estimates on the degree of C l GV determinacy ( G is one of Mather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C l G triviality of function germs given by M.A.S.Ruas.     

Approximation Presentations of Modules and Homological Conjectures

In this article we give a sufficient condition of the existence of 𝕎 ^t -approximation presentations. We also introduce property (W ^k ). As an application of the existence of 𝕎 ^t -approximation presentations we give a connection between the finitistic dimension conjecture, the Auslander–Reiten conjecture, and property (W ^k ).     

具有常余维数2k+4不动点集的(Z2)k作用

本文通过构造上协边环MO_*的一组生成元决定了J_*,k^2k+4.     

Abelian and Tauberian theorems for a new trigonometric method of summation

We first introduce a new trigonometric method of summation and then prove some Abelian and Tauberian theorems for this method.     

The newton filtration and d-determination of bifurcation problems related to C0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

Harmonic Functions,Entropy, and a Characterization of the Hyperbolic Space

Let (M ⁿ ,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ ₀ of its universal covering satisfies λ ₀≤(n−1)²/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. The author was partially supported by NSF Grant 0505645.     

The L-L estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

We first obtain the L^p-L^q estimates of solutions to the Cauchy problem for one-dimensional damped wave equation

     

半空间MHD方程组弱解的L~2衰减

该文利用Stokes算子的谱表示及能量估计的方法研究半空间MHD方程组初边值问题弱解的L~2衰减.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

An Asymptotic Expansion for the Distribution of Hotelling'sT-Statistic under Nonnormality

In this paper we obtain an asymptotic expansion for the distribution of Hotelling'sT²-statisticT²under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariatet-statistic. Our method is to use the Edgeworth expansion and to expand the characteristic function ofT².