In this study, we first introduce the co-ordinated trigonometrically $\rho$-convex functions. Then we establish some Hermite-Hadamard type inequalities for this kind of functions. We also give refinement of the obtained inequalities by using the result given by Budak. The inequalities obtained in this study provide generalizations of some result given in earlier works.

This paper deals with the problem of finding an upper bound for the maximal modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates involve the maximal modulus of the polynomial in some disk, the degree, the coefficients and the radii of the disks.

In this paper, we introduce generalized exponential rational function method (GERFM) to obtain an exact satisfies satisfies solutions for the Biswas-Milovic (BM) equation with quadratic-cubic and parabolic nonlinearities. A wide range of closed solutions are acquired. The most important feature of the new method is that it is very effective and simple. The main merits of the proposed is that it gives more general solutions with some free parameters and can be applied to other types of nonlinear partial differential equations.Some interesting Figures for the physical features of some of the obtained solutions are also presented.

Let $\overline{p}_{k, -2}(n)$ counts the number of overpartition pairs of $n$ with 2-color in which one of the colors appears only in parts that are multiples of $k$. We establish several infinite families of congruences modulo powers of $2$ and $3$ for $\overline{p}_{k, -2}(n)$ where $k= 2$ and $3$. For example, for all $n \geq 0$ and $\alpha\geq0$, we have $$\overline{p}_{2, -2}(16\cdot 3^{4\alpha+2}n+34\cdot 3^{4\alpha+1})\equiv 0 \pmod{128},$$ $$\overline{p}_{3, -2}(6\cdot 25^{\alpha+2}n+20\cdot 25^{\alpha+2})\equiv 0 \pmod{27}.$$

In this paper, we deal with the uniqueness problem for the $k$-th derivative of power of meromorphic function and obtain some results which improve and supplement the previous theorem given by V.H. An and H.H. Khoai.

In 1920s R. L. Moore introduced upper semicontinuous and lower semicontinuous decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in 1950s. In this paper we consider lower semicontinuous decompositions $\mathcal D$ of a topological space $X$ such that the decomposition spaces $X/\mathcal D$ are Alexandroff spaces. If the associated proset (preordered set) of the decomposition space $X/\mathcal D$ is a poset, then the decomposition map $\pi:X \to X/\mathcal D$ is a continuous map from the topological space $X$ to the poset $X/\mathcal D$ with the associated Alexandroff topology, which is nowadays called a poset-stratified space. As an application, we capture the face poset of a real hyperplane arrangement $\mathcal A$ of $\mathbb R^n$ as the associated poset of the decomposition space $\mathbb R^n/\mathcal D(\mathcal A)$ of the decomposition $\mathcal D(\mathcal A)$ determined by the arrangement $\mathcal A$. We also show that for any locally small category $\mathcal C$ the set $hom_{\mathcal C}(X,Y)$ of morphisms from $X$ to $Y$ can be considered as a poset-stratified space, and that for any objects $S, T$ (where $S$ plays as a source object and $T$ as a target object) there are a covariant functor $\mathfrak{st}^S_*: \mathcal C \to \mathcal Strat$ and a contravariant functor $\mathfrak{st}^*_T$ $\mathfrak{st}^*_T: \mathcal C \to \mathcal Strat$ from $\mathcal C$ to the category $\mathcal Strat$ of poset-stratified spaces. We also make a remark about Yoneda's Lemmas as to poset-stratified space structures of $hom_{\mathcal C}(X,Y)$.

We developed a numerical scheme to solve the nonlinear fractional (NF) generalized seventh order KdV (sKdV) equation with time-space-fractional using the shifted Jacobi collocation method. Basically, a time-space collocation approximation for temporal and spatial discretizations is employed efficiently to tackle these equations. The convergence and stability analyses of the suggested basis functions are presented in-depth. The validity and efficiency of the proposed method are investigated and verified through numerical examples.

In this article, we discuss the uniqueness problems of differential-difference polynomials of hyper order $(\geq 1)$ meromorphic functions sharing a small function and prove some results, which generalise and improve the results due to Y. Liu, J. P. Wang and F. H. Liu.

In this work, we consider the Cauchy problem for a wave equations with frictional and displacement dependent damping terms with nonlinear memory in multi-dimensional space $\mathbb{R}^{n}$, $n\geq 1$, we will prove the existence and uniqueness of the local solution and the nonexistence of global weak solutions theorems for any dimension space.

Boehmians, being the specific class of the generalized functions (the theory of distributions), are exposed to applications within mathematics and beyond. This paper is involved into the investigation of the $Z$ - transform for integrable Boehmians.

In this paper we describe a feasible construction of universal set of quantum gates using monodromy matrices of Fuchsian system. Fuchsian systems are considered as Schrödinger type equations and it is shown that such quantum systems are exactly solvable. We also show that dynamics of trapped cold ions may be described by a Fuchsian system which also describes the critical points of logarithmic potential associated with equilibrium positions of trapped ions in line geometry. Two different approaches to the inverse problem are also discussed.

In this paper, we approximate a family of functions with a tri-symmetric left invariant mean property by tri-cubic functions in Lipschitz spaces.

An enveloping associative superalgebra $\Lambda [L,\alpha ,\beta ]$ and its groups of cohomologies are defined and it is proved that there exists Frobenius multiplication of the Quillen algebraic $K$-functors of $\Lambda [L,\alpha ,\beta ]$. These results generalize corresponding results for Lie $p$-algebras which were proved by the author earlier.

In this paper, we introduce new symmetric endomorphism operators on appropriate infinite product series. The main results show that after direct calculations, the proposed operators are qualified to obtain new generating functions for second-order recurrence sequences.