生物吸附剂Bio-matrix去除废水中重金属的研究

[目的]研究生物吸附剂Bio-matrix对常规重金属Cu^(2+)、Ni^(2+)、Cr^(3+)的吸附性能。[方法]考察不同温度、吸附剂投加量、吸附时间、p H对吸附量的影响,并分析了Bio-matrix对Cu^(2+)的等温吸附情况。[结果]Bio-matrix吸附剂对Cu^(2+)的吸附效果优于Ni^(2+)和Cr^(3+),温度对吸附量影响较小,3 h可达到吸附平衡,单位吸附量随p H的升高先增大后减小,在p H 4左右时对重金属的单位吸附量最大,Bio-matrix对Cu^(2+)的吸附等温线与Freundlich方程有较好的拟合性,饱和吸附量为19.3 mg/g。[结论]该研究为Bio-matrix作为生物吸附剂去除废水中重金属提供了可行途径。

Functional N-Representability in 2-Matrix,1-Matrix,and Density Functional Theories

The N-representability conditions on the reduced second-order reduced density matrix (2-RDM), impose restrictions not only in the context of reduced density matrix theory (RDMT), but also on functionals advanced in one-matrix theory such as natural orbital functional theory (NOFT), and on functionals depending on the one-electron density such as those of density functional theory (DFT). We review some aspects of the applications of these N-representability conditions in these theories and present some conclusions.

Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices

In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.

The Number of Digraphs with Cycles of Length <i>k</i>

In this note, we show that the number of digraphs with n vertices and with cycles of length k, 0 ≤ k ≤ n, is equal to the number of n × n (0,1)-matrices whose eigenvalues are the collection of copies of the entire kth unit roots plus, possibly, 0’s. In particular, 1) when k = 0, since the digraphs reduce to be acyclic, our result reduces to the main theorem obtained recently in [1] stating that, for each n = 1, 2, 3, …, the number of acyclic digraphs is equal to the number of n × n (0,1)-matrices whose eigenvalues are positive real numbers;and 2) when k = n, the digraphs are the Hamiltonian directed cycles and it, therefore, generates another well-known (and trivial) result: the eigenvalues of a Hamiltonian directed cycle with n vertices are the nth unit roots [2].

New Mehrotra's second order predictor-corrector algorithm for P_*(κ) linear complementarity problems

It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_＊（κ） linear complementarity problems.This paper presents an extension of the recent variant of Mehrotra＇s second order algorithm for linear optimijation.It is shown that the iteration-complexity bound of the algorithm is O（4κ ＋ 3）√14κ ＋ 5 nlog（x0）Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization.

SOME PROPERTIES OF A CLASS OF INTERCHANGE GRAPHS

Abstract Let U(R,S) denote the class of all (0,1) m×n matrices having row sum vector R and column sum vector S. The interchange graph G(R,S) is the graph where the vertices are the matrices in U(R,S) and two vertices representing two such matrices are adjacent provided they differ by an interchange. It is proved that G(R,(1,1,...,1)) is a generalized Cartesian product of some Johnson Scheme graphs. Furthermore, its connectivity, diameter and transitivity (vertex ,edge ) are also determined.

AN ASYMPTOTICAL O((k + 1)n^3L) AFFINE SCALING ALGORITHM FOR THE P_*(k)-MATRIX LINEAR COMPLEMENTRITY PROBLEM

Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity problem (LCP). Form using high-order correctors technique and rank-one updating, the iteration complexity and the total computational turn out asymptotically O((kappa + 1)root nL) and O((kappa + 1)n(3)L) respectively.

On relations between R_aR_b transformation and canonical diagonal form of λ-matrix

RaRb transformation over λ-matrix is defined and explored. Relations between Ra Rb transforma tion over λ-matrix and canonical diagonal form of λ-matrix are investigated and some results are

On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with H_(+) -Matrices

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix.Theoretical analysis gives the choice of parameter matrix involved based on the H-compatible splitting of the sys-tem matrix.Moreover,in actual implementation,the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied.Numeri-cal experiments show that the method is efficient and further verify the convergence theorems.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the Hausdorff measure of the sets of finitetype of the one-sided symbolic space are

ON THE SPECTRUM OF SINGULAR HAMILTONIAN DIFFERENTIAL SYSTEMS

In this paper, we study a bounded-below singular Hamiltonian system. Sufficient and necessary conditions are obtained for the existence and the number of eigenvalues on the left-axis. The main results of this paper are the extension and improvement of Weyl spectral theorem for singular sccond order differential equations.

(0,1)-MATRICES AND GENERALIZED ULTRAMETRIC MATRICES

In this paper, using a graph theoretic approach, we give a necessary and sufficient condition for a (0,1)-matrix to be a nonsingular generalized ultrametric matrix.

Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

Linear complementarity problems have drawn considerable attention in recent years due to their wide applications.In this article,we introduce the two-step two-sweep modulus-based matrix splitting(TSTM)iteration method and two-sweep modulus-based matrix splitting type II(TM II)iteration method which are a combination of the two-step modulus-based method and the two-sweep modulus-based method,as two more effective ways to solve the linear complementarity problems.The convergence behavior of these methods is discussed when the system matrix is either a positive-definite or an H+-matrix.Finally,numerical experiments are given to show the efficiency of our proposed methods.

Directional H^(2) Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation

This study aimed to specialise a directional H^(2)(DH^(2))compression to matrices arising from the discontinuous Galerkin(DG)discretisation of the hypersingular equation in acoustics.The significantfinding is an algorithm that takes a DG stiffness matrix andfinds a near-optimal DH^(2) approximation for low and high-frequency problems.We introduced the necessary special optimisations to make this algorithm more efficient in the case of a DG stiffness matrix.Moreover,an automatic parameter tuning strategy makes it easy to use and versatile.Numerical comparisons with a classical Boundary Element Method(BEM)show that a DG scheme combined with a DH^(2) gives better computational efficiency than a classical BEM in the case of high-order finite elements and hp heterogeneous meshes.The results indicate that DG is suitable for an auto-adaptive context in integral equations.

Design and preparation of an ultra-high temperature ceramic by in-situ introduction of Zr_(2)[Al(Si)]_(4)C_(5) into ZrB_(2)-SiC:Investigation on the mechanical properties and oxidation behavior

Novel ZrB_(2)-matrix composites were designed and prepared by in-situ introducing SiC and Zr_(2)[Al(Si)]_(4)C_(5) simultaneously for the first time.The obtained composites were dense and showed good mechanical properties,especially the strength and toughness,706 MPa and 7.33 MPa·m^(1/2),respectively,coupled with high hardness of 21.3 GPa,and stiffness of 452 GPa.SiC and Zr_(2)[Al(Si)]_(4)C_(5) constituted a reinforcing system with synergistic effects including grain refinement,grain pull-out as well as crack branching,bridging,and deflection.Besides,the oxidation results of the composites showed that the oxidation kinetics followed the parabolic law at 1600℃,and the oxidation rate constants increased with the increase of Zr_(2)[Al(Si)]_(4)C_(5) content.The formation and evolution model of the oxidation structure was also investigated,and the oxide scale of the composite exhibited a three-layer structure.