Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

Gessel walks are lattice walks in the quarter plane N2 which start at the origin (0, 0) ∈ N2 and consist only of steps chosen from the set {←,↙,↗,→}. We prove that if g(n; i, j) denotes the number of Gessel walks of length n which end at the point (i, j) ∈ N2, then the trivariate generating series G(t;x, y) = X n,i,j≥0 g(n; i, j)xyt is an algebraic function.

0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...

Using number theory on function fields and algebraic number fields we prove results about Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional additive cellular automata on finite square grids. For example, we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three.

Let K be an arbitrary field and X a square matrix over K. Then X is sum of two square nilpotent matrices over K if and only if, for every algebraic extension L of K and arbitrary nonzero α ∈ L, there exist idempotent matrices P 1 and P 2 over L such that X = αP 1 - αP 2.

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

Abstract The paper aims to generalize Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen’s identity. The general contiguous variation of Clausen’s identity is found. The related Chaundy’s identit...

place is a part of geographical space and a base for establishment of social relations. each place is unique according to its specific properties, functions and history. meanwhile, some places find symbol identity due to their especial historical events and properties and this identity would be maintained in the minds and moved to the other generations. for example azadi tower in tehran and sav...