Abstract:
Let L be a positive line bundle over a compact complex projective manifold X and K be a compact subset of X which is regular in a sense of pluripotential theory. A Fekete configuration of order k is a finite subset of K maximizing a Vandermonde type determinant associated with the power L^k of L. Berman, Boucksom and Witt Nystr\"om proved that the empirical measure associated with a Fekete configuration converges to the equilibrium measure of K as k tends to infinity. Dinh, Ma and Nguyen obtained an estimate for the rate of convergence. Using techniques from Cauchy-Riemann geometry, we show that the last result holds when K is a real nondegenerate C^5-piecewise submanifold of X such that its tangent space at any regular point is not contained in a complex hyperplane of the tangent space of X at that point. In particular, the estimate holds for Fekete points on some compact sets in R^n or the unit sphere in R^{n+1}.

Abstract:
Let $X$ be a compact K\"ahler manifold of dimension $n.$ Let $T$ and $S$ be two positive closed currents on $X$ of bidegree $(p,p)$ and $(q,q)$ respectively with $p+q\le n.$ Assume that $T$ has a continuous super-potential. We prove that the wedge product $T \wedge S,$ defined by Dinh and Sibony, is a positive closed current.

Abstract:
The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral position.

Abstract:
The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for nonzero meromorphic functions on $\mathbb{C}^l.$ The second is to improve the definition of the non-integrated defect relation of H. Fujimoto \cite{F2} and to show two theorems on the new non-integrated defect relation of meromorphic maps from a closed submanifold of $\mathbb{C}^l$ to a compact complex manifold. The third is to give a unicity theorem for meromorphic mappings from a Stein manifold to a compact complex manifold.

Abstract:
Background. While HIV infection among men who have sex with men (MSM) in Vietnam has received increasing attention, most studies focus on HIV knowledge and established risk factors such as injection drug use. This paper proposes to address HIV risk among MSM from an integrated approach to preventive care that takes into account syndemic conditions such as substance use, mental health, and stigma, the latter of which prevents MSM from accessing health services. Method. Current studies related to MSM in Vietnam from 2000 onwards, gathered from peer-reviewed as well as non-peer-reviewed sources, were examined. Results. HIV and STI prevalence among MSM varied significantly by location, and yet HIV prevalence has increased significantly over the past few years. Most studies have focused on sexual risk behaviors, paying little attention to the broad spectrum of sexual health, including noninjecting drug use, heavy alcohol consumption, high rates of mental health distress and anxiety, and stigma. Conclusion. Future research and interventions targeting MSM in Vietnam should address their vulnerability to HIV from an integrated approach that pays attention to both sexual health and syndemic conditions. 1. Introduction Research studies have shown that men who have sex with men (MSM) have unique health-care needs and that interventions focusing on this group should address these needs [1, 2]. MSM have been significantly affected by HIV epidemics all over the world. Research on MSM has found that the epidemics are reemerging in many wealthy countries and that many developing countries are paying more attention to the HIV epidemic among MSM [3]. A critical study on MSM in developing countries showed that the possibility of MSM being HIV infected was much higher than that of the general population [4]. In Asia, an association between HIV infection and drug use, including both injection and noninjection use, has been found [5]. However, non-injection drug use has been an increasingly important risk factor for HIV infection among MSM, whereas injecting drug use is thought to have a limited impact on the spread of HIV among this group [6]. Recreational drug use, especially the use of ecstasy and methamphetamines and alcohol use, is becoming increasingly common and is an important factors contributing to unprotected receptive anal intercourse [5, 7, 8]. The impact of substance use and myriad syndemic conditions has resulted in an alarming increase in HIV infection in Southeast Asia [9]. There are a number of studies on HIV infection among MSM in Vietnam, yet

Abstract:
Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d>2 odd. Here V is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a. We show for generic potentials V that the number of resonances of -Delta+V with modulus less than r is approximatively equal to a constant times a^dr^d.

Abstract:
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider G\"{o}del's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.

Abstract:
This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a resolution principle for our logic to resolve on two clauses having contradictory linguistic truth values. Since linguistic information is uncertain, inference in our linguistic logic is approximate. Therefore, we introduce the concept of reliability in order to capture the natural approximation of the resolution inference rule.

Abstract:
Myocardial infarction is the leading cause of death in developed countries. Cardiac cell therapy has been introduced to clinical trials for more than ten years but its results are still controversial. Tissue engineering has addressed some limitations of cell therapy and appears to be a promising solution for cardiac regeneration. In this review, we would like to summarize the current understanding about the therapeutic effect of cell therapy and tissue engineering under purview of functional and structural aspects, highlighting actual roles of each therapy towards clinical application. 1. Introduction Ischemic heart disease is the principal cause of chronic heart failure in developed countries. In the USA alone, it causes 400,000 deaths annually [1]. The currently available therapies (i.e., pharmacological, interventional, and surgical methods) are unable to revitalize dead myocardium. Therefore, they cannot halt or reverse the development of congestive heart failure (CHF). Though cardiomyocytes in nonmammalian vertebrate species, like zebrafish, can restore the injured myocardium through proliferation and differentiation, this mechanism is not significant in humans [2]. Cardiac transplantation, the sole definitive therapy with long-term effect for end-stage HF so far, remains limited due to the scarcity of heart donors [3]. Myocardial restoration therapies, including cardiac cell therapy and cardiac tissue engineering, sound promising for a failing heart [4] as their ultimate goals are to regenerate the injured myocardium by robust and viable cells or artificial tissues. Although 10 years passed since Menasche et al. launched the first clinical trial [5], cardiac cell therapy has not become a well-established medical treatment for postmyocardial infarction (MI) patients. Delivery of cell suspensions to the myocardium is limited by various factors, such as insufficient cell retention and survival [6]. The introduction of cell-cell mechanical interaction systems, in the form of either cell sheets or biomaterial scaffolds [7] has addressed the issues related to poor cell retention and survival. Moreover, this strategy may offer a three-dimensional homogeneous cell delivery plus structural support (scaffold) to the myocardial area of ischemic injury [7]. Yet, there are no clinical studies of this approach. Though both cardiac cell therapy and tissue engineering have resulted in some improvement of function and structure of the injured heart, it would still be a laborious mission to reproduce the “real” myocardium. In this review, we would like to summarize

Abstract:
This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative integers. The obtained results can be applied to study Rees algebras of homogeneous ideals and their diagonal subalgebras. The Hilbert polynomial is computed explicitly in the following cases: (1) R is a bigraded polynomial ring of the above type; (2) R is the Rees algebra of an ideal generated by a homogeneous regular sequence; (3) R is the Rees algebra of the ideal generated by the maximal minors of a generic (r-1) by r matrix.