Related papers: Multiples of Pfister forms
This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…
We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…
In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology. For applications, we show…
Motivated by amplitude calculations in string theory we establish basic properties of homotopy invariant iterated integrals on affine curves.
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
For the principal eigenvalue with bilateral Dirichlet boundary condition, the so-called basic estimates were originally obtained by capacitary method. The Neumann case (i.e., the ergodic case) is even harder, and was deduced from the…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
Consideration is given to the methods of gaining experimental data on the substances which constitute a part of multicomponent samples to be measured. The methods are applicable to the samples comprising an arbitrary number of components;…
We prove non-trivial upper and lower bounds for the "Spectrum of Singularities" of Fourier Series with polynomial frequencies. The Spectrum of Singularities of a function f gives the Hausdorff dimension of the set of points with a given…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to…
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these numbers to the Betti tables of the multi-parameter…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…