Abstract:
Let be a time scale with . We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale , , which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques. 1. Introduction Let be a time scale with , we consider the existence of positive solutions, in this paper, for a nonlinear boundary value problem of second-order dynamic equation on a time scale as follows: Research for the existence of solutions to the dynamic boundary value problem is rapidly growing in recent years. A great many existence results of positive solutions have been established for problem (1.1), see [1–5] and the references therein. The main tool used by them is the fixed point theorem in cones, and the key conditions in these papers do not depend on the first eigenvalue, , of the following linear problem: and the corresponding existence conditions are not optimal. In 2006, for , ,？？ ,？？ with for , Luo and Ma [6] obtained the existence of at least one positive solution to problem: under the condition？(H) if either or , where and is the first eigenvalue of the linear problem: The approaches adopted by Luo and Ma [6] are based on global bifurcation techniques. They obtained the existence of at least one positive solution by considering the branches of solutions, which bifurcate from one point. The key conditions in [6] depend on the first eigenvalue of the corresponding linear problem and the condition (H) is optimal! In this paper, we will use the following assumptions.？(A1) is continuous and there exist functions , such that ？for some functions with ？？ uniformly for , and ？for some functions with ？？ uniformly for .？(A2) for .？(A3) There exists a function such that Obviously, (A1) means that is not necessarily linearizable at and . We consider the existence of positive solutions of problem (1.1) in this paper by using bifurcation techniques. The difference from [6] is that the branches of positive solutions under consideration now bifurcate from not one point, but an interval. Our main idea is from [7], in which they considered positive solutions of fourth-order boundary value problems for differential equations. The main tool we will use is the following global bifurcation theorem for problems which is not necessarily linearizable. Theorem A (Rabinowitz, [8]). Let be a real reflexive Banach space. Let be completely continuous such that , for all . Let be such that is an isolated solution of the equation for , and , where , are

Abstract:
Let be a time scale and ,∈, <2(). We study the nonlinear fourth-order eigenvalue problem on , Δ4()=？()((),Δ2()), ∈[,2()], ()=Δ(())=Δ2()=Δ3(())=0 and obtain the existence and nonexistence of positive solutions when 0<≤？ and >？, respectively, for some ？. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.

Abstract:
With the advent and increasing popularity of new communication technologies, social media tools have been widely used in corporate organization-public communication. The extant literature on social media use in public relations practice has largely centered on the ways social media tools have transformed the practice of public relations in the United States. Limited studies have examined the role of social media in China. The present study represents one of the first to investigate the measurement and challenges of social media use in Chinese public relations practice. Based on 18 in-depth interviews with public relations executives, this paper concludes that traditional quantitative methods of social media production and message exposure have been utilized to measure social media campaigns, accompanied by the growing use of methods focused on intangible impact of public relations (e.g., online publics’ awareness, advocacy, and participation). Challenges unique to China’s social media landscape are also identified. Theoretical and practical implications are discussed.

Abstract:
By defining a new terminology, scatter degree, as the supremum of graininess functional value, this paper studies the existence of solutions for a nonlinear two-point dynamic boundary value problem on time scales. We do not need any growth restrictions on nonlinear term of dynamic equation besides a barrier strips condition. The main tool in this paper is the induction principle on time scales.

Abstract:
We study a certain singular second-order m-point boundary value problem on a time scale and establish the existence of a solution. The proof of our main result is based upon the Leray-Schauder continuation theorem.

Abstract:
The miniature chromosome maintenance (MCM) complex is a group of proteins that are essential for DNA replication licensing and control of cell cycle progression from G1 to S phase. Recent studies suggest that MCM7 is overexpressed and amplified in a variety of human malignancies. MCM7 genome sequence contains a cluster of miRNA that has been shown to downregulate expression of several tumor suppressors including p21, E2F1, BIM and pTEN. The oncogenic potential of MCM7 and its embedded miRNA has been demonstrated vigorously in in vitro experiments and in animal models, and they appear to cooperate in initiation of cancer. MCM7 protein also serves as a critical target for oncogenic signaling pathways such as androgen receptor signaling, or tumor suppressor pathways such as integrin α7 or retinoblastoma signaling. This review analyzes the transforming activity and signaling of MCM7, oncogenic function of miRNA cluster that is embedded in the MCM7 genome, and the potential of gene therapy that targets MCM7.

Abstract:
Let $mathbb{T}$ be a time scale with $0,T in mathbb{T}$. We investigate the existence and multiplicity of positive solutions to the nonlinear second-order three-point boundary-value problem $$displaylines{ u^{Delta abla}(t)+a(t)f(u(t))=0,quad tin[0, T]subset mathbb{T},cr u(0)=eta u(eta),quad u(T)=alpha u(eta) }$$ on time scales $mathbb{T}$, where 0, 0less than $alpha$ less than $frac{T}{eta}$, 0 less than $eta$ less than $frac{T-alphaeta}{T-eta}$ are given constants.