Related papers: Examples Concerning Abelian and Cesaro Limits
In this note we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
In the paper we pursue the analysis from the section 5 of the Talagrand's paper "Sample boundedness of stochastic processes under increment conditions." Ann. Probab. 18, No. 1, 1-49. In particular we give the proof of some Sobolev…
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery,…
This paper is mainly concerned with the existence of extremals for the Adams inequality. We first establish an upper bound for the classical Adams functional along of all concentrated sequences in $W^{m,\frac{n}{m}}_{\mathcal{N}}(\Omega)$,…
We establish an explicit lower bound for the N\'eron-Tate height on elliptic curves with complex multiplication, for nontorsion points defined over the maximal abelian extension of a number field. Building on a strategy developed by…
New upper and lower bounds on the Castelnuovo-Mumford regularity are given in terms of the Hilbert coefficients. Examples are provided to show that these bounds are in some sense nearly sharp.
We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.
This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an…
We establish the slope equality and give an upper bound of the slope for finite cyclic covering fibrations of an elliptic surface including bielliptic fibrations of genus greater than 5. We also give an upper bound of the slope for triple…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
We give upper bounds for triples of subsets of a finite group such that the triples of elements that multiply to 1 form a perfect matching. Our bounds are the first to give exponential savings in powers of an arbitrary finite group.…
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the "inclusion" between operators becomes a full equality.
For the trace of Besov spaces $B^s_{p,q}$ onto a hyperplane, the borderline case with $s=\frac{n}{p}-(n-1)$ and $0<p<1$ is analysed and a new dependence on the sum-exponent $q$ is found. Through examples the restriction operator defined for…
We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equations
Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.
We introduce subclasses of exact categories in terms of admissible intersections or admissible sums or both at the same time. These categories are recently studied by Br\"ustle, Hassoun, Shah, Tattar and Wegner to give characterisations of…