We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n + 1)-th order differential equation and give a simple method for obtaining the differential equation. Also we determine the exponents of the differential equation and derive a bound for the degree of the polynomials, whic...

We present certain results on the direct and inverse spectral theory of Jacobi operator with complex periodic coefficients. For instance, we show that any $N$-th degree polynomial whose leading coefficient is $(-1)^N$ Hill discriminant finitely many discrete $N$-periodic Schrödinger operators (Theorem 1). Also, in case where spectrum a closed interval prove result 2) which analog Borg's Theorem...

We construct the exact solution of one (anti)instanton in N = 1 2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1 2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), the SU(2) part of the solution is given by the standard (anti)instanton, but the U(1) field strength also turns out nonzero. The solution is SO(4) rotationall...

Let Th be the complete binary tree of height h. Let M be the infinite grid graph with vertexset Z, where two vertices (x1,y1) and (x2,y2) of M are adjacent if and only if|x1-x2| + |y1-y2| = 1. Suppose that T is a tree which is a subdivision of Th and is also isomorphicto a subgraph of M. Motivated by issues in optimal VLSI design, we show that the point expansionration(T)<lb...

We construct the exact solution of one (anti)instanton in N = 1 2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1 2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), the SU(2) part of the solution is given by the standard (anti)instanton, but the U(1) field strength also turns out nonzero. The solution is SO(4) rotationall...

For every nite n > 1, the embedding property fails in the class of all n-dimensional cylindric type algebras which satisfy the following. Their boolean reducts are boolean algebras and two of the cylindriications are normal, additive and commute. This result also holds for all subclasses containing the representable n-dimensional cylindric algebras. This considerably strengthens a result of S. ...