Related papers: A More General Linear Projectile Problem
The purpose of this paper is to extend the analysis of gravitational instability of the Linet - Tian solution to the case $\Lambda > 0$. A fundamental difference brought about by $\Lambda >0$, as compared to $\Lambda<0$ is in the structure…
Starting from basic physical principles, we present a novel derivation linking the global wind power to measurable atmospheric parameters. The resulting expression distinguishes three components of the atmospheric power (the kinetic power…
In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $\gamma_e >0$ governing whether the flow is increased or decreased as it crosses…
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an…
We address the dusty wind problem, from the point where dust formation has been completed and outward. Given grain properties, both radiative transfer and hydrodynamics components of the problem are fully defined by four additional input…
Exact analytic solutions for one-dimensional elastic lumped line under affection of external force inclined to the axe of line is analyzed. It is shown that in this case an inclined wave being described by implicit function propagates along…
Plane waves are regarded as the general solution of the wave equation. However the plane wave expansion of standing waves by means of complex phasors leads to a theory in which the time coordinate does not receive the same treatment as the…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation…
This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…
Motivated by the search for potentially exactly solvable time-dependent string backgrounds, we determine all homogeneous plane wave (HPW) metrics in any dimension and find one family of HPWs with geodesically complete metrics and another…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
Accurate wind speed and direction forecasting is paramount across many sectors, spanning agriculture, renewable energy generation, and bushfire management. However, conventional forecasting models encounter significant challenges in…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
By introducing new weighted vector fields as multipliers, we derive quantitative pointwise estimates for solutions of defocusing semilinear wave equation in $\mathbb{R}^{1+3}$ with pure power nonlinearity for all $1<p\leq 2$. Consequently,…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
Within the traditional frame of reduced MHD, a new rigorous perturbation expansion provides the equation ruling the nonlinear growth and saturation of the tearing mode for any current gradient. The small parameter is the magnetic island…