An analytic problem whose solution follows from a simple algebraic identity

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

An Optimization Problem with a Surprisingly Simple Solution

Suppose you and n of your friends play the following game. A random number from the uniform distribution on [0, 1] will be generated. This number is called the target. Each of you will independently guess what the target number will be and the person whose guess is closest will be declared the winner. In order to investigate an optimal strategy for this game, we need to assume something about y...

An analytic solution for the perspective 4-point problem

An Algebraic Solution to the Spectral Factorization Problem

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...

A Simple Solution to Friedman's Fourth Problem

It is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of fo...