Related papers: Notes on Laver Tables

We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.

We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…

In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…

This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.

We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side result, the inverse of two special…

In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.

We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…

These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.

We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of non-uniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…

This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when…