This article analyzes the behavior of a Brownian fluctuation process under mixed strategic game setup. A variant compound motion has been newly proposed, which is called Shifted Fluctuation Process to predict turning points stochastic process. evolves until it reaches one step prior point. The Game constructed based on this new find optimal moment actions. Analytically tractable results are obt...

A standard barely set-valued tableau of shape λ is a filling the Young diagram with integers 1,2,…,|λ|+1 such that are increasing in each row and column, every cell contains one integer except two integers. Counting tableaux closely related to coincidental down-degree expectations (CDE) lower intervals Young’s lattice. Using q-integral techniques we give formula for number arbitrary shifted sha...

The purpose of this dissertation is to study certain classes of permutations and plane partitions of truncated shapes. We establish some of their enumerative and combinatorial properties. The proofs develop methods and interpretations within various fields of algebraic combinatorics, most notably the theory of symmetric functions and their combinatorial properties. The first chapter of this the...

When the Schur function sλ corresponding to a partition λ is defined as the generating function of the column strict tableaux of shape λ it is not at all obvious that sλ is symmetric. In [BK] Bender and Knuth showed that sλ is symmetric by describing a switching rule for column strict tableaux, which is essentially equivalent to the jeu de taquin of Schützenberger (see [Sü]). Bender and Knuth’s...

The purpose of this note is to give a counterexample to the conjectured large N asymptotics of character values χ R (U) of irreducible characters of SU (N), which appears in papers of Gross-Matytsin [M, GM] and Kazakov-Staudacher-Wynter [KW, KSW, KSW2, KSW3]). Asymptotics of characters are important in the large N limit of Y M 2 (2D Yang-Mills theory). Our counterexample consists of one special...

We present an exact expression for the 2 error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines , and bandlimited signal expansions. The formula takes the simple form of a Parseval’s-like relation, where the Fourier c...