In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindström–Gessel–Viennotmethod and the Jacobi-Trudi identity together with elementary observations. After some preparations, this point of view provides “graphical proofs” for classical determinantal identities like the Cauchy-Binet formula, Dodgson’s condensation fo...

Derivatives of a solution of an ODE Cauchy problem can be computed inductively using the Faà di Bruno formula. In this paper, we exhibit a noninductive formula for these derivatives. At the heart of this formula is a combinatorial problem, which is solved in this paper. We also give a more tractable form of the Magnus expansion for the solution of a homogeneous linear ODE.

In this paper, we prove that the semigroup [Formula: see text] generated by the Cauchy problem of the evolution p-Laplacian equation [Formula: see text] ([Formula: see text]) is continuous form a weighted [Formula: see text] space to the continuous space [Formula: see text]. Then we use this property to reveal the fact that the evolution p-Laplacian equation generates a chaotic dynamical system...

This paper investigates higher order wave-type equations of the form [Formula: see text], where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. Using methods from harmonic analysis, we first establish global pointwise time-space estimates for a class of oscillatory integrals that appear as the fundamental solu...

By studying the distances of a point to the sides, respectively the vertices of an equilateral triangle, certain new identities and inequalities are deduced. Some inequalities for the elements of the Pompeiu triangle are also established.

In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions Gλ which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these functions in analogy with Schur functions. In particular we will describe: • a Pieri and dual-Pieri formula for ribbon functions, • a ribbon Murnaghan-Nakayama formula, • ribbon Cauchy and dual Cauchy identities, • and...

We use the Cauchy-Crofton formula to show that every Q-bounded definable cell in an O-minimal expansion of a field F ≥ R satisfies the Whitney arc property.

Extensions of Sherman’s theorem to convex functions of higher order and to real weights are obtained by using Taylor’s formula. New upper bounds for Sherman’s difference and generalized inequalities are established. Some related Cauchy-type means are discussed.