In this paper, we provide an attractive analytic solution for Maxwell's equation for a given set of smooth periodic functions as initial condition with demonstrative examples. The complexity of the solution is comparable to the Fourier expansions of the initial functions.
Suppose that u is the potential function of a complete Kähler-Einstein metric on a bounded strictly convex domain in $\mathbb{C}^n$. We prove that u itself is strictly convex.
We establish the short-time existence and uniqueness of non-decaying solutions to the generalized Surface Quasi-Geostrophic equations in Hölder-Zygmund spaces $C^r(\mathbb{R}^2)$ for $r>1$ and uniformly local Sobolev spaces $H_{ul}^s(\mathbb{R}^2)$ for $s>2$.
Using Gegenbauer polynomials and the zonal harmonic functions we build an explicit representation formula for the Green function with Neumann boundary conditions in the annulus.
This work is devoted to study the relation between regularity and decay of solutions of some dissipative perturbations of the Korteweg-de Vries equation in weighted and asymmetrically weighted Sobolev spaces.
We show that the recent work by G{é}rard-Kappeler-Topalov can be used in order to construct new non degenerate invariant measures for the Benjamin-Ono equation on the Sobolev spaces H s , s > --1/2.
In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.
In this article, we establish the existence of solutions to the fractional $p-$Kirchhoff type equations with a generalized Choquard nonlinearities without assuming the Ambrosetti-Rabinowitz condition.
The paper shows the summability of formal solutions of some linear q-difference-differential equations by using q-Laplace and q-Borel summation method.
The plundering, looting and neglect of archaeological and heritage sites are quite common in many parts of the world. Turkey is one such country that has a poor record of preservation of archaeological and heritage sites, particularly those of minority ethnic groups and from the prehistoric and ancient periods. In other words, those which are not part of the national/official past of Turkey. The main reason for this is that Turkish formal education neglects the prehistoric and ancient past, and ‘others’ the past of minority groups. This paper will examine and discuss how and to what extent archaeology and heritage related topics are presented in formal education in Turkey, i.e., national, minority groups, prehistoric and ancient pasts and antiquities by analysing the curriculum and textbooks from 2013. Specifically, this paper will demonstrate that history education in schools has a major impact on the development and re-configuration of heritage perception, which can either lead to the protection or neglect of heritage.
We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek-Ricci spaces. Applying these estimates we prove the $L^p$-boundedness of Littlewood-Paley-Stein operators.
A generalization of the Emden-Fowler equation is presented and its solutions are investigated. This paper is devoted to asymptotic behavior of its solutions. The procedure is entirely based on a previous paper by the author.
Using a mixture of classical and probabilistic techniques we investigate the convexity of solutions to the elliptic pde associated with a certain generalized Ornstein-Uhlenbeck process.