Related papers: The order conjecture fails in S

We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns {12345,12354} and {45123,45213} that extends the list of 10 related conjectures proved in the literature in a series of papers. To achieve our goals, we prove…

Assuming the abc conjecture with $\epsilon=1/6$, we use elementary methods to show that only finitely many $s$-Cullen numbers are repunits, aside from two known infinite families. More precisely, only finitely many positive integers $s$,…

Let $f$ be an entire almost periodic function with zeros in a horizontal strip of finite width; for example, any exponential polynomial with purely imaginary exponents is such a function. Let $\mu$ be the measure on the set of zeros of $f$…

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…

This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on…

Let $F_{\omega_1}$ be the countable admissible ordinal equivalence relation defined on ${}^\omega 2$ by $x \ F_{\omega_1} \ y$ if and only if $\omega_1^x = \omega_1^y$. It will be shown that $F_{\omega_1}$ is classifiable by countable…

We investigate how the sentence choice semantics (SCS) for propositional superposition logic (PLS) developed in \cite{Tz17} could be extended so as to successfully apply to first-order superposition logic(FOLS). There are two options for…

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…

We give a full description of the functions $F$ of degree 2 and conductor 1 in the general framework of the extended Selberg class. This is performed by means of a new numerical invariant $\chi_F$, which is easily computed from the data of…

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for…

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…

We investigate deformations of the shuffl e Hopf algebra structure Sh(A) which can be de fined on the tensor algebra over a commutative algebra A. Such deformations, leading for example to the quasi-shuffl e algebra QSh(A), can be…

We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context:…

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…

Recently, G. Mason has produced a counterexample of order 128 to a conjecture in conformal field theory and tensor category theory in [Ma]. Here we easily produce an infinite family of counterexamples, the smallest of which has order 72.

Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…

The shuffle of a non-empty countable set $ S $ of linear orders is the (unique up to isomorphism) linear order $ \Xi(S) $ obtained by fixing a coloring function $ \chi: \mathbb{Q} \to S $ having fibers dense in $ \mathbb{Q} $ and replacing…

We prove the completeness of a first-order analogue of the Fischer Servi logic $\mathsf{FS}$ with respect to its expected birelational semantics. To this end we introduce the notion of the $\textit{trace model}$ and, much like in a…

Let $f$ and $g$ be transcendental entire functions, each with a bounded set of singular values, and suppose that $f$ and $g$ are affinely equivalent (that is, $g \circ \phi= \psi\circ f$, where $\phi,\psi:\C\to\C$ are affine). We show that…

For a unitary local system of rank one on a complete hyperbolic threefold of finite volume which has only one cusp, we will compare the order of the Alexander invariant at t=1 and one of Ruelle-Selberg L-function at s=0. Our result may be…