Related papers: Buffon's problem with a pivot needle
We study the dual of Philo's shortest line segment problem and find the optimal line segments passing through two given points, with a common endpoint, and with the other endpoints on a given line. This problem is dual, in a…
Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the…
There is well-known problem of geometric probability which can be quote as the Broken Spaghetti Problem. It addresses the following question: A stick of spaghetti breaks into three parts and all points of the stick have the same probability…
A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…
We deal with the Brill-Noether problem for stable vector bundles of slope between one and two.
Prostate cancer diagnosis continues to encounter challenges, often due to imprecise needle placement in standard biopsies. Several control strategies have been developed to compensate for needle tip prediction inaccuracies, however none…
The Probe Method is an analytical reconstruction scheme for inverse obstacle problems utilizing the Dirichlet-to-Neumann map associated with the governing partial differential equation. It consists of two distinct parts: Side A and Side B.…
We show that the problem of covering a set of points in the plane with a minimum number of guillotine cuts is NP-complete. To that end, first we present a new NP-completeness proof for the problem of covering points with disjoint line…
Let $\Cant_n$ be the $n$-th generation in the construction of the middle-half Cantor set. The Cartesian square $\K_n = \Cant_n \times \Cant_n$ consists of $4^n$ squares of side-length $4^{-n}$. The chance that a long needle thrown at random…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
In a previous work we investigated the existence of Hopf degenerate bifurcation points for a differential delay equation modeling leukemia and we actually found Hopf points of codimension two for the considered problem. If around the…
In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…
In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…
We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.
In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…
In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…
The Lambert problem consists in connecting two given points in a given lapse of time under the gravitational influence of a fixed center. While this problem is very classical, we are concerned here with situations where friction forces act…
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as…