Open Journal of mathematical Sciences (OMS)

In this paper, we study the existence of positive solutions for boundary value problem of sixth-order elastic beam equation of the form \(-u^{(6)}(t)=q(t)f(t,u(t),u^{‘}(t),u^{”}(t),u^{”’}(t),u^{(4)}(t),u^{(5)}(t)),~~0<t<1,\) with conditions \(u(0)=u^{‘}(1)=u^{”}(0)=u^{”’}(1)=u^{(4)}(0)=u^{(5)}(1)=0,\) where \(f\in C([0,1]\times[0,\infty)\times[0,\infty)\times(-\infty,0]\times(-\infty,0]\times[0,\infty)\times[0,\infty)\rightarrow [0,\infty))\). The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. We give sufficient conditions that allow us to obtain the existence of positive solution. The main tool used in the proof is the Leray-Schauder nonlinear alternative and Leray-Schauder fixed point theorem. As an application, we also give example to illustrate the results obtained.

In this paper we establish a fixed point theorem for generalized weakly contractive mappings in the setting of \(b\)-metric spaces and prove the existence and uniqueness of a fixed point for a self-mappings satisfying the established theorem. Our result extends and generalizes the result of Cho [1]. Finally, we provided an example in the support of our main result.

In this paper we have introduced the concept of pseudo-valuations on JU-algebras and have investigated the relationship between pseudo-valuations and ideals of JU-algebras. Conditions for a real-valued function to be a pseudo-valuation on JU-algebras are given and results based on them have been shown. We have also defined and studied pseudo-metric on JU-algebras and have proved that \(\vartheta\) being a valuation on a JU-algebras \(A\), the operation \(\diamond\) in \(A\) is uniformly continuous.

This paper studies some properties of the Fourier multiplier operators on a compact group when the underlying multiplication functions (the symbols) defined on the dual object take values in a Banach algebra. More precisely, boundedness properties for such Fourier multiplier operators for the space of Bochner strong integrable functions and for the (vector) \(p\)-Fourier spaces are investigated.

Since the emergence of the avian influenza A(H7N9) in the year 2013 in China, several researches have been carried out to investigate the spread. In this paper, a mathematical model describing the transmission dynamics of avian influenza A(H7N9) between human and poultry proposed by Li et al. [1] is modified by introducing re-infections into the susceptible human compartment. The method of next generation matrix is used to calculate the reproduction number. We also establish the local and global stability of the equilibria using Lyapunov functions. Finally, we use numerical simulations to validate our results.

Let \(G\) be a simple graph with vertex set \(V(G)\) and edge set \(E(G)\). A mapping \(g:V (G)\rightarrow\{1,2,…t\}\) is called \(t\)-coloring if for every edge \(e = (u, v)\), we have \(g(u) \neq g(v)\). The chromatic number of the graph \(G\) is the minimum number of colors that are required to properly color the graph. The chromatic polynomial of the graph \(G\), denoted by \(P(G, t)\) is the number of all possible proper coloring of \(G\). Dendrimers are hyper-branched macromolecules, with a rigorously tailored architecture. They can be synthesized in a controlled manner either by a divergent or a convergent procedure. Dendrimers have gained a wide range of applications in supra-molecular chemistry, particularly in host guest reactions and self-assembly processes. Their applications in chemistry, biology and nano-science are unlimited. In this paper, the chromatic polynomials for certain families of dendrimer nanostars have been computed.

In this paper, Petrović’s inequality is generalized for \(h-\)convex functions on coordinates with the condition that \(h\) is supermultiplicative. In the case, when \(h\) is submultiplicative, Petrović’s inequality is generalized for \(h-\)concave functions. Also particular cases for \(P-\)function, Godunova-Levin functions, \(s-\)Godunova-Levin functions and \(s-\)convex functions has been discussed.

Inspired by the observation that adjacent vertices need possess their own characteristics in terms of total coloring, we study the smarandachely adjacent vertex total coloring (abbreviated as SAVTC) of a graph \(G\), which is a proper total coloring of \(G\) such that for every vertex \(u\) and its every neighbor \(v\), the color-set of \(u\) contains a color not in the color-set of \(v\), where the color-set of a vertex is the set of colors appearing at the vertex or its incident edges. The minimum number of colors required for an SAVTC is denoted by \(\chi_{sat}(G)\). Compared with total coloring, SAVTC would be more likely to be developed for potential applications in practice. For any graph \(G\), it is clear that \(\chi_{sat}(G)\geq \Delta(G)+2\), where \(\Delta(G)\) is the maximum degree of \(G\). We, in this work, analyze this parameter for general subcubic graphs. We prove that \(\chi_{sat}(G)\leq 6\) for every subcubic graph \(G\). Especially, if \(G\) is an outerplanar or claw-free subcubic graph, then \(\chi_{sat}(G)=5\).

In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form \(\frac{d}{dt} \Biggl[r(t) \frac{d}{dt} \biggl [x(t)+p(t)x(t-\tau)\biggr]\Biggr]+q(t)G\bigl(x(t-\sigma_1)\bigr)+v(t)H\bigl(x(t-\sigma_2)\bigr)=0, \;\; t \geq t_0,\) under the assumptions \(\int_{0}^{\infty}\frac{d\eta}{r(\eta)}=\infty\) and \(\int_{0}^{\infty}\frac{d\eta}{r(\eta)}<\infty\) for \(|p(t)|<+\infty\). Two illustrative examples are included.

This study investigate movements of molecule on the biological cell via the cell walls at any given time. Specifically, we examined the movement of a particle in tiling, i.e. in hexagonal and square tiling. The specific questions we posed includes (i) whether particles moves faster in hexagonal tiling or in square tiling (ii) whether the starting point of particles affect the movement toward attainment of stationary distribution. We employed the transitional probabilities and stationary distribution to derive expected passage time to state \(j\) from state \(i\), and the expected recurrence time to state \(i\) in both hexagonal and square tiling. We also employed aggregation of state symmetries to reduce the number of state spaces to overcome the problems (i.e. the difficulty to perform algebraic computation) associated with large transition matrix. This approach leads to formation of a new Markov chain \(X_t\) that retains the original Markov chains properties, i.e. by aggregation of states with the same stochastic behavior to the process. Graphical visualization for how fast the equilibrium is attained with different values of the probability parameter \(p\) in both tilings is also provided. Due to difficulties in obtaining some analytical results, numerical simulation were performed to obtains useful results like expected passage time and recurrence time.