Related papers: Sudo-Lyndon
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…
This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It…
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
Creating a new Ontology: a Modular Approach
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
In this paper, we obtain new results on the critical points of a polynomial, these results are useful to the Sendov conjecture.
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We present in this paper our solver for logic grid puzzles. The approach used by our algorithm mimics the way a human would try to solve the same problem. Every progress made during the solving process is accompanied by a detailed…
We derive a relative version of the slicing Bennequin inequalities for cobordant Legendrian knots, and review a few proofs of the result.
Inspired by the relation between the hadronic decay of the tau lepton and the electron-positron annihilation into hadrons, we derive new tests of perturbative QCD. We design a set of commensurate scale relations to test the self-consistency…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.
A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…