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Oral squamous cell carcinoma (OSCC) accounts for over 90% of malignant neoplasms of the mouth. In Taiwan, OSCC is the fourth most common male cancer and the fourth leading cause of male cancer death. Resistin (RETN) is an adipokine that is associated with obesity, inflammation, and various cancers. Here, we examine the association between four single nucleotide polymorphisms (SNPs) of theRETNgene (rs3745367, rs7408174, rs1862513, and rs3219175) and OSCC susceptibility as well as clinical outcomes in 935 patients with OSCC and in 1200 cancer-free healthy controls. We found that, in 1465 smokers,RETNpolymorphisms carriers with the betel-nut chewing habit had a 6.708–10.882-fold greater risk of having OSCC compared toRETNwild-type carriers without the betel-nut chewing habit. Patients with OSCC who had A/A homozygous ofRETNrs3219175 polymorphism showed a high risk for an advanced tumor size (> T2), compared to those patients with G/G homozygotes. In addition, A/T/G/G haplotype significantly increased the risks for OSCC by 1.376-fold. This study is the first to examine the risk factors associated withRETNSNPs in OSCC progression and development in Taiwan.

By using a new hybrid method, a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of Bregman strongly nonexpansive mappings in a reflexive Banach space is proved.

With the further development of oilfield, liquid-gas separation has become an essential problem. Cylindrical cyclone separators are popular in the industrial process due to the advantage that they are simple, compact, and inexpensive to manufacture. In this paper, a three-dimensional turbulence model including Reynolds stress model was established to describe the mixture flow field in the separator. Through the numerical simulation, the separation efficiency was investigated under different parameter cases such as separator length, gas phase outlet diameter, and inlet shape. It can be indicated from the simulation results that the separation efficiency decreases with the increase of the separator length, and the separation efficiency increases firstly and then decreases with the increase of the gas phase outlet diameter as well as the liquid phase outlet. Furthermore, the rectangular inlet is more suitable than the circular inlet with the separation efficiency changing from 66.45% to 79.04%. In the end, the optimal geometrical structure was presented with separation efficiency of 86.15%.

The purpose of this paper is to propose an algorithm for solvingthe split common fixed point problems for total asymptotically strictly pseudocontractive mappingsin infinite-dimensional Hilbert spaces. The results presented in the paper improve and extend some recent results of Moudafi (2011 and 2010), Xu (2010 and 2006), Censor and Segal (2009), Censor et al. (2005), Masad and Reich (2007), Censor et al. (2007), Yang (2004), and others.

The purpose of this paper is first to introduce the concept oftotal quasi-ϕ-asymptotically nonexpansive mappingwhich contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results.

The purpose of this paper is to use a new hybrid algorithm for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for an infinite family of quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

In this paper, we prove some existence theorems for random vector variational inequalities and an existence theorem for the random noncooperative vector equilibrium under suitable assumptions.

The purpose of this paper is to introduce the concept oftotal asymptotically nonexpansive mappingsand to prove someΔ-convergence theorems of the iteration process for this kind of mappings in the setting ofhyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.

The study of variational inequalities and related problems with applications constituted a rich topic of intensive research efforts within the latest 50 years. Variational inequalities problems have been found with an explosive growth in theoretical advances, algorithmic development, and applications across all the disciplines of pure and applied sciences. Analysis of these problems requires a blend of techniques from convex analysis, nonlinear functional analysis, and numerical analysis. As a result of interaction between different branches of mathematical and engineering sciences, we now have a variety of techniques to suggest and analyze various algorithms for solving variational inequalities and related optimization problems with applications. We received 12 research papers in the research fields.This special issue includes 7 high-quality peer-reviewed papers, where five papers are related to variational inequalities and the other two papers are regarding Fourier transform and satellite data transmission scheduling problems. The aim of this special issue has been to present the newest and generalized coverage of the fundamental and constructive ideas, concepts, and important issues in the accepted original research articles as well as comprehensive review articles stimulating the continuing efforts to numerical analysis for variational inequality problems. In the paper by Z. B. Liu et al. a system of generalized variational inequalities has been set up for set-valued mappings by using surjectivity theorem of pseudomonotone and coercive operators. Convergence results for total asymptotically nonexpansive mappings are given by L. C. Zhao et al. in the set of hyperbolic spaces. Equilibrium problems andmonotone inclusion problems are studied by H. C. Wu and C. Z. Cheng. Moreover, generalized mixed equilibrium problems and fixed point problems are studied by P. Phuangphoo and P. Kumam. Provided by L. Xie et al. methods for variational inequalities are even applied to solve order-optimization problems in Banach spaces. Satellite data transmission scheduling problems are given by H. Xu et al. Fast Fourier transform is also studied by J. Huang et al.

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.

In this paper, we prove some common fixed point theorems for compatible mappings of type(A)in metric spaces and probabilistic metric spaces Also, we extend Caristi's fixed point theorem and Ekeland's variational principle in metric spaces to probabilistic metric spaces.

Humans are not natural hosts ofDirofilaria; however, pulmonary or subcutaneous infections may occur through mosquitoes transmission. Patients presenting with simple subcutaneous nodules may not seek early medical attention, and hence systemic involvement through hematogenous spread may occur. Definitive diagnosis of Dirofilaria infection is made by histopathological examinations of the infected tissues. We report a patient with an incidental diagnosis of Dirofilaria infection confirmed by histopathological findings of a subcutaneous nodule on the right thigh. The source of infection remains unknown.

The purpose of this paper is to study the strong and weak convergence theorems of the implicit iteration processes for an infinite family of Lipschitzian pseudocontractive mappings in Banach spaces.

The main purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi--asymptotically nonexpansive mappings, and null spaces of finite family of -inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. The results presented in the paper improve and extend the corresponding results announced by some authors.

Some new coincidence point and fixed point theorems for multivalued mappings in complete metric space are proved. The results presented in this paper enrich and extend the corresponding results in [5-16, 20-25, 29].