ALBERT

Description: In this article we consider the global behavior of the following system of piecewise linear difference equations: x n + 1 = | x n | − y n − b and y n + 1 = x n + | y n | where b is any positive real number and the initial condition ( x 0 , y 0 ) is an element of R 2 . By mathematical induction and direct computations we show that the solution to the system is eventually one of two particular prime period 3 solutions or the unique equilibrium solution.

Description: Spectral analysis of a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions depending on an eigenvalue parameter with spectral singularities was first studied by Aygar and Bohner (Appl. Math. Inf. Sci. 9(4):1725-1729, 2015). The main goal of this paper is to construct the principal vectors corresponding to the eigenvalues and the spectral singularities of this BVP. These vectors are important to get the spectral expansion formula for this BVP.

Description: In this paper, we consider the Barnes-type q-Euler polynomials which are derived from the fermionic p-adic q-integrals and investigate some identities of these polynomials. Furthermore, we define the Barnes-type q-Changhee polynomials and numbers, and we derive some identities related with the Barnes-type q-Euler polynomials and the Barnes-type q-Changhee polynomials.MSC: 11B68, 11S40.

Description: We study, for a given process X , the conditions under which ν-similarity is provided, relations between similarity and ν-similarity of processes, and we analyze (doubly) limiting conditional distributions. We present sufficient conditions for the existence of at least one ν-similar process to a given one. Moreover, recursive formulas for birth and death rates of ν-similar processes are formulated. We apply differential equations and uniqueness of solutions to such equations to derive the main results of the paper. Finally, an example illustrates the applications of our results.MSC: 60J80, 42C05, 60J85.

Description: Background: Tree thinking refers to an approach to evolution education that emphasizes reading and interpreting phylogenetic trees. We studied the relationship between introductory biology students’ tree-thinking ability and their acceptance of evolutionary theory. Results: Comparisons between a semester in which interpretation of phylogenetic trees and related concepts were taught as stand-alone topics versus one in which tree thinking was used as an organizing framework for the course curriculum found significant increases in students’ ability to read and interpret trees in both semesters, but only in the tree thinking semester was there a significant increase in students’ scores on the Measure of the Acceptance of the Theory of Evolution (MATE) instrument. Over four additional semesters, the Tree Thinking Concept Inventory (TTCI) was used to assess students’ tree-thinking abilities before and after the course. We found that MATE posttest scores correlated with gains in tree-thinking ability. These increases in MATE posttest scores were predominantly due to students’ reporting greater acceptance of the scientific evidence supporting evolutionary theory. Conclusions: Increased acceptance of evolution in a tree-thinking versus non-tree-thinking semester and significant positive correlations between TTCI and MATE scores indicate there is a relationship between tree-thinking ability and acceptance of evolution. This result suggests that, as a framework to connect different forms of data and investigate a variety of biological phenomena, tree thinking can promote greater acceptance of the evidence and scientific validity of evolutionary theory in introductory biology students.

Description: We investigate the hyper-order of solutions of two class of complex linear differential equations. We investigate the growth of solutions of higher order and certain second order linear differential equations, and we obtain some results which improve and extend some previous results in complex oscillations.MSC: 30D35, 34M10.

Description: We establish an explicit formula for q-analog of Morley’s congruence.MSC: 11B68, 11B65, 11B83.

Description: ObjectivesDespite substantial public health efforts to increase HIV testing, testing rates have plateaued in many countries and rates of repeat testing for those with ongoing risk are low. To inform policies aimed at increasing uptake of HIV testing, we identified characteristics associated with individuals’ willingness-to-accept (WTA) an HIV test in a general population sample and among two high-risk populations in Moshi, Tanzania. Methods: In total, 721 individuals, including randomly selected community members (N = 402), female barworkers (N = 135), and male Kilimanjaro mountain porters (N = 184), were asked in a double-bounded contingent valuation format if they would test for HIV in exchange for 2000, 5000 or 10,000 Shillings (approximately $1.30, $3.20, and $6.40, respectively). The study was conducted between September 2012 and February 2013. Results: More than one quarter of participants (196; 27 %) stated they would be willing to test for Tanzania Shilling (TSH) 2000, whereas one in seven (98; 13.6 %) required more than TSH 10,000. The average WTA estimate was TSH 4564 (95 % Confidence Interval: TSH 4201 to 4927). Significant variation in WTA estimates by gender, HIV risk factors and other characteristics plausibly reflects variation in individuals’ valuations of benefits of and barriers to testing. WTA estimates were higher among males than females. Among males, WTA was nearly one-third lower for those who reported symptoms of HIV than those who did not. Among females, WTA estimates varied with respondents’ education, own and partners’ HIV testing history, and lifetime reports of transactional sex. For both genders, the most significant association was observed with respondents’ perception of the accuracy of the HIV test; those believing HIV tests to be completely accurate were willing to test for approximately one third less than their counterparts. The mean WTA estimates identified in this study suggest that within the study population, incentivized universal HIV testing could potentially identify undiagnosed HIV infections at an incentive cost of $150 per prevalent infection and $1400 per incident infection, with corresponding costs per quality adjusted life year (QALY) gained of $70 for prevalent and $620 for incident HIV infections. Conclusions: The results support the value of information about the accuracy of HIV testing, and suggest that relatively modest amounts of money may be sufficient to incentivize at-risk populations to test.

Description: In this paper, we study an epidemic model with stage structure and latency spreading in a heterogeneous host population. We show that if the disease-free equilibrium exists, then the global dynamics are determined by the basic reproduction number  R 0 . We prove that the disease-free equilibrium is globally asymptotically stable when R 0 ≤ 1 ; and there exists a unique endemic equilibrium which is globally asymptotically stable when R 0 〉 1 . The global stability of the endemic equilibrium is also proved by using a graph-theoretic approach to the method of Lyapunov functions. Finally, numerical simulations are given to illustrate the main theoretical results.

Description: In this paper, we study the existence and uniqueness of positive solutions for a class of higher-order nonlocal fractional differential equations with Riemann-Stieltjes integral boundary conditions. We firstly convert the problem to an equivalent integral equation, and then by applying a fixed point theorem of a sum operator, the existence and uniqueness of positive solutions is established. Furthermore, an iterative scheme to approximate the solution is constructed and an example is given to illuminate the application of the main results.