ترغب بنشر مسار تعليمي؟ اضغط هنا

Notes on the zeros of the solutions of the non-homogeneous Airys equation

73   0   0.0 ( 0 )
 نشر من قبل Federico Zullo
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Federico Zullo




اسأل ChatGPT حول البحث

We present some observations on the distribution of the zeros of solutions of the nonhomogeneous Airys equation. We show the existence of a principal family of solutions, with simple zeros, and particular solutions, characterized by a double zero in a given position of the complex plane. A recursion, describing the distribution of the zeros, is introduced and the limits of its applicability are discussed. The results can be considered a generalization of previous works on the distribution of the zeros for the solutions of the corresponding homogeneous equation



قيم البحث

اقرأ أيضاً

78 - Jayanta Sarkar 2020
In this article, we study certain type of boundary behaviour of positive solutions of the heat equation on the upper half-space of $R^{n+1}$. We prove that the existence of the parabolic limit of a positive solution of the heat equation at a point in the boundary is equivalent to the existence of the strong derivative of the boundary measure of the solution at that point. Moreover, the parabolic limit and the strong derivative are equal.
99 - Alexander Lytchak 2008
We discuss some properties of Jacobi fields that do not involve assumptions on the curvature endomorphism. We compare indices of different spaces of Jacobi fields and give some applications to Riemannian geometry.
138 - Ruiming Zhang 2015
In this work we verify the sufficiency of a Jensens necessary and sufficient condition for a class of genus 0 or 1 entire functions to have only real zeros. They are Fourier transforms of even, positive, indefinitely differentiable, and very fast dec reasing functions. We also apply our result to several important special functions in mathematics, such as modified Bessel function $K_{iz}(a), a>0$ as a function of variable $z$, Riemann Xi function $Xi(z)$, and character Xi function $Xi(z;chi)$ when $chi$ is a real primitive non-principal character satisfying $varphi(u;chi)ge0$ on the real line, we prove these entire functions have only real zeros.
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-an alogues of the q-integral transform and further apply to some general special functions such as : the exponential functions, the q-trigonometric functions, the q-hyperbolic functions and the Heaviside Function. Some further results involving convolutions and differentiations are also obtained.
We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Instead of a vector field grad u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove existence and unique ness for solutions of the equation P div P=0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only if the domain is a tubular neighbourhood of a regular closed curve. The idea of the proof is to apply a generalized method of characteristics introduced in Jabin, Otto, Perthame, Line-energy Ginzburg-Landau models: zero-energy states, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002), to a suitable vector field m satisfying P = m otimes m. This formulation provides a useful approach to the analysis of stripe patterns. It is specifically suited to systems where the physical properties of the pattern are invariant under rotation over 180 degrees, such as systems of block copolymers or liquid crystals.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا