Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type

In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.     

Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping

Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm.     

Fixed points and graph images for minimal maps on the once punctured torus

A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point.     

Allocating fixed costs and common revenue via data envelopment analysis

An issue of considerable importance involves the allocation of fixed costs or common revenue among a set of competing entities in an equitable way. Based on the data envelopment analysis (DEA) theory, this paper proposes new methods for (i) allocating fixed costs to decision making units (DMUs) and (ii) distributing common revenue among DMUs, in such a way that the relative efficiencies of all DMUs remain unchanged and the allocations should reflect the relative efficiencies and the input-output scales of individual DMUs. To illustrate our methods, numerical results for an example are described in this paper.     

Vector Preisach hysteresis modeling: Measurement, identification and application

The paper presents a Preisach model to simulate the vector hysteresis properties of ferromagnetic materials. The vector behavior has been studied using a single sheet tester with a disk-shaped specimen at low frequency. The locus of the magnetic flux density vector has been controlled by a digital measurement system. An inverse vector Preisach hysteresis model has been developed and identified by applying the measured data. Finally, the inverse model has been inserted into a finite element procedure through the fixed point technique and the reduced magnetic scalar potential formulation to simulate the measurement system. The applicability of the measurement system as well as the developed model has been proven by comparing measured and simulated results.     

污泥的超声破解实验研究

本文在测量超声破解污泥试验所用反应器声场的基础上,主要研究了复频超声作用下,超声频率和换能器位置对污泥破解效果的影响。在此基础上采用两个同相换能器,以污泥滤液COD、NH₃-N、TP的增量,首次研究了复频超声破解污泥的效果,且详细探讨了影响复频超声破解污泥的影响因素（不同频率组合、不同功率组合、不同时间组合）。实验结果与理论分析符合较好,从而说明超声是一种有效的破解污泥的方法,进而对超声处理污泥的规律进行研究,这将为超声处理污泥提供一定的实验基础。     

Adsorption and photochemical behaviors of the novel cationic xanthene derivative on the clay surface

Novel tetra-cationic xanthene derivative (Flu) was synthesized. Its adsorption and photochemical behaviors on the clay surface were investigated. Fluorescence quantum yield (?_f) and fluorescence lifetime were 0.50 and 2.9 ns for Flu/clay complex. ?_f of Flu was enough high (>0.1) even at high density conditions (0.080 molecules nm⁻²). It is supposed that the strong interaction between clay and Flu by the ‘Size-Matching Effect’ realizes the highly emissive clay complexes at high density adsorption condition by a suppression of a molecular aggregation, which tends to decrease the photochemical activity.     

Comparative study of analytical methods for the determination of chromium in groundwater samples containing iron

Determination of chromium in groundwater samples containing iron may pose analytical problems due to sorption and fixation of chromium species onto Fe(III) hydroxides. Parks et al. (Water Res. 2004, 38, 2827) hypothesized that chromium species trapped inside Fe(III) hydroxides i.e. “fixed chromium” may not be soluble by HNO₃ digestion (APHA method 3030 B). In such cases, hydroxylamine digestion is required to release “fixed chromium”. To verify the hypothesis, we carried out this study on groundwater samples containing chromium and iron, using different methods of APHA and EPA. The results showed the presence of “fixed chromium”, ranged between 0.1 and 19.2 μg L^{− 1}, contributing 0.2 to 14.1% towards true total chromium. Digestion of samples with HNO₃ released Cr(III) bound to organic complexes, but not the “fixed chromium”. The hydroxylamine digestion released “fixed chromium”, but not the Cr(III) bound to organic complexes. Microwave digestion of samples with HNO₃ + HCl was effective for the release of both “fixed” and “Cr(III)-organic complexes”. Cr(III) was only adsorbed onto suspended matter, whereas Cr(VI), and Cr(III)-organic complexes were not adsorbed onto suspended matter due to their solubility. Sample pH, buffering capacity, and matrix have a significant influence on the adsorption and fixation of chromium species onto Fe(III) hydroxides.     

On Impulsive Hyperbolic Differential Inclusions with?Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases. Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.     

Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

In this note, we establish a sufficient condition for the controllability of a first-order semilinear differential system with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed-point theorem combined with operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article. Y.K. Chang was supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10801065), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) of Lanzhou Jiaotong University. J.J. Nieto was supported by Ministerio de Educacion y Ciencia-FEDER Project MTM2007-61724, and by Xunta de Galicia-FEDER Project PGIDIT05PXIC20702PN.