An extremal problem for the neighborhood Lights Out game

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Symmetric Matrices over F_2 and the Lights Out Problem

We prove that the range of a symmetric matrix over F2 contains the vector of its diagonal elements. We apply the theorem to a generalization of the “Lights Out” problem on graphs.

Lights out.

An Extremal Problem for Polynomials

Let f(z) = z" Hbe a polynomial such that the level set E = {z : |/(z)| < 1} is connected. Then max{|/'(z)| : z e E} < 2<1/")-1n2 , and this estimate is the best possible. The following question was asked in [1, Problem 4.8]. Let f be a polynomial of degree n, (1) f{z)~z», z^oo. Put Ef = {z : \f(z)\ < 1} , and assume that Ef is connected. Is it true that (2) max{\f'(z)\:z£Ef}. Pommerenke ...

MATHEMATICAL MODELLING FOR DICE FINDER GAME PROBLEM

Play is often episodic and mission-centric, with a series of challenges culminating in a final puzzle or enemy that must be overcome. Multiple missions played with the same characters may be related to each other in a plot arc of escalating challenges. The exact tone, structure, pace and end (if any) vary from game to game depending on the needs and preferences of the players, as in [9]. "THE C...