Abstract:
In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.

Abstract:
We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings in Banach spaces. The strong convergence theorems for weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings are derived under some suitable assumptions. The main results in this paper develop, extend, and improve the corresponding results of Matsushita and Takahashi (2005) and Qin and Su (2007). 1. Introduction Throughout this paper, without other specifications, we denote by the set of real numbers. Let be a real reflexive Banach space with the dual space . The norm and the dual pair between and are denoted by and , respectively. Let be proper convex and lower semicontinuous. The Fenchel conjugate of is the function defined by We denote by the domain of , that is, . Let be a nonempty closed and convex subset of a nonlinear mapping. Denote by , the set of fixed points of . is said to be nonexpansive if for all . In 1967, Brègman [1] discovered an elegant and effective technique for the using of the so-called Bregman distance function (see, Section 2, Definition 2.1) in the process of designing and analyzing feasibility and optimization algorithms. This opened a growing area of research in which Bregman's technique is applied in various ways in order to design and analyze iterative algorithms for solving not only feasibility and optimization problems, but also algorithms for solving variational inequalities, for approximating equilibria, for computing fixed points of nonlinear mappings, and so on (see, e.g., [1–25], and the references therein). Nakajo and Takahashi [26] introduced the following modification of the Mann iteration method for a nonexpansive mapping in a Hilbert space as follows: where and is the metric projection from onto a closed and convex subset of . They proved that generated by (1.2) converges strongly to a fixed point of under some suitable assumptions. Motivated by Nakajo and Takahashi [26], Matsushita and Takahashi [27] introduced the following modification of the Mann iteration method for a relatively nonexpansive mapping in a Banach space as follows: where , for all , is the duality mapping of and is the generalized projection (see, e.g., [2, 3, 28]) from onto a closed and convex subset of

Abstract:
A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorithms for solving the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover, strong convergence theorems of these iterative sequences generated by the corresponding algorithms are proved under suitable conditions. As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main results in this paper develop, improve, and unify some well-known results in the literature. 1. Introduction Generalized mixed quasivariational inclusion problems, which are extensions of variational inequalities introduced by Stampacchia [1] in the early sixties, are among the most interesting and extensively investigated classes of mathematics problems and have many applications in the fields of optimization and control, abstract economics, electrical networks, game theory, auction, engineering science, and transportation equilibria (see, e.g., [2–5] and the references therein). For the past few decades, existence results and iterative algorithms for variational inequality and variational inclusion problems have been obtained (see, e.g., [6–14] and the references cited therein). Recently, some new problems, which are called to be the system of variational inequality and equilibrium problems, received many attentions. Ansari et al. [2] considered a system of vector variational inequalities and obtained its existence results. In [3], Pang stated that the traffic equilibrium problem, the spatial equilibrium problem, the Nash equilibrium, and the general equilibrium programming problem can be modeled as a system of variational inequalities. Verma [15] and J. K. Kim and D. S. Kim [16] investigated a system of nonlinear variational inequalities. Cho et al. [17] introduced and studied a new system of nonlinear variational inequalities in Hilbert spaces and obtained the existence and uniqueness properties of solutions for the system of nonlinear variational inequalities. In [18], Peng and Zhu introduced a new system of generalized mixed quasivariational inclusions involving -monotone operators. Very recently, Qin et al. [19] studied the approximation of solutions to a system of variational

Abstract:
Short-term power load forecasting is one of the most important issues in the economic and reliable operation of electricity power system. Taking the characteristics of randomness, tendency, and periodicity of short-term power load into account, a new method (SSA-AR model) which combines the univariate singular spectrum analysis and autoregressive model is proposed. Firstly, the singular spectrum analysis (SSA) is employed to decompose and reconstruct the original power load series. Secondly, the autoregressive (AR) model is used to forecast based on the reconstructed power load series. The employed data is the hourly power load series of the Mid-Atlantic region in PJM electricity market. Empirical analysis result shows that, compared with the single autoregressive model (AR), SSA-based linear recurrent method (SSA-LRF), and BPNN (backpropagation neural network) model, the proposed SSA-AR method has a better performance in terms of short-term power load forecasting. 1. Introduction Short-term power load forecasting is one of the most important issues in economic and reliable operation of power system. Many operating decisions related to electricity power system such as unit commitment, dispatch scheduling of the generating capacity, reliability analysis, security assessment, and maintenance scheduling of the generators are based on the short-term power load forecasting. In recent years, domestic and foreign scholars have done many studies in the field of short-term power load forecasting. Currently, the short-term power load forecasting method can be divided into two categories, that is, load-series-based forecasting method and affecting-factors-based forecasting method. Although the power load shows the random and uncertain characteristic, it also has an apparent tendency. Therefore, the load-series-based forecasting method is based upon the internal structure of the short-term power load series, which includes ARIMA, ARMAX [1, 2], neural networks [3, 4], gray prediction model [5, 6], wavelet analysis [7, 8], and other forecasting methods. However, these methods have some shortcomings: the load-series-based forecasting method can only be used for data fitting and is not suitable for the treatment of regularity; the neural network method has the problem that the relation between the input variables cannot be expressed explicitly; the grey prediction model is used for the case of the little sample data; the wavelet analysis forecasting method transforms the original sequence by the orthogonal wavelets to get the subsequences of different frequency-domain

Abstract:
In this paper, ZnS one-dimensional (1D) nanostructures including tetrapods, nanorods, nanobelts, and nanoslices were selectively synthesized by using RF thermal plasma in a wall-free way. The feeding rate and the cooling flow rate were the critical experimental parameters for defining the morphology of the final products. The detailed structures of synthesized ZnS nanostructures were studied through transmission electron microscope, X-ray diffraction, and high-resolution transmission electron microscope. A collision-controlled growth mechanism was proposed to explain the growth process that occurred exclusively in the gas current by a flowing way, and the whole process was completed in several seconds. In conclusion, the present synthetic route provides a facile way to synthesize ZnS and other hexagonal-structured 1D nanostructures in a rapid and scalable way.

Abstract:
The neutron-drip-line nucleus $^{23}$N is investigated in a three-body model consisting of a $^{21}$N core and two valence neutrons. By solving the Faddeev equations with the realistic neutron-neutron potentials and the neutron-core potentials, we calculate the ground state properties of $^{23}$N and also find that there is a new excited state with two-neutron separation energy at about 0.18 MeV. The properties, such as the two-neutron separation energies, are obtained with a good agreement with experiments. By calculating the root-mean-square matter radii, the average distances between the valence neutrons, and the average distances between the core and the center-of-mass of the neutron pair, we show that the excited state of $^{23}$N has a clear halo structure. The correlation density distributions of the three-body system are also calculated to analyze its geometric configuration. At last, we find that the excited state of $^{23}$N has a very small binding energy, a large radius and distribution, and a triangular shape similar with the ground state. These roperties of the excited state indicate that it can be an Efimov state.

We give a study result to analyze a rather different, semi-analytical numerical
algorithms based on splitting-step methods with their applications to mathematical
finance. As certain subsistent numerical schemes may fail due to producing
negative values for financial variables which require non-negativity preserving.
These algorithms which we are analyzing preserve not only the
non-negativity, but also the character of boundaries (natural, reflecting, absorbing,
etc.). The derivatives of the CIR process and the Heston model are
being extensively studied. Beyond plain vanilla European options, we creatively
apply our splitting-step methods to a path-dependent option valuation.
We compare our algorithms to a class of numerical schemes based on Euler
discretization which are prevalent currently. The comparisons are given with
respect to both accuracy and computational time for the European call option
under the CIR model whereas with respect to convergence rate for the
path-dependent option under the CIR model and the European call option
under the Heston model.

Abstract:
The CODE V optical design software is used to design a TV micrometric lens for a centering item with an inner adjusting focus. The lens is composed of four lenses. It has a symmetric structure with positive and negative focal lengths. Its focal length, numerical aperture and field of view are 17.20 mm, 0.063 and 16.82° respectively. The lens operates in the waveband from 486 nm to 656 nm. Its total optical length is 68 mm. It has the maximum distortion of 1.13% in the full field of view and the modulation transfer function greater than 0.64 at a space frequency of 60 lp/mm. The design result shows that the system has good imaging quality and a compact structure which meet the practical requirements.