Related papers: Polarized relations at singulars over successors

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\omega_1,\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language…

The main result is that for lambda strong limit singular failing the continuum hypothesis (i.e. 2^lambda > lambda^+), a polarized partition theorem holds.

Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.

We prove that if there is a dominating family of size ${\aleph}_{1}$, then there is are ${\aleph}_{1}$ many compact subsets of ${\omega}^{\omega}$ whose union is a maximal almost disjoint family of functions that is also maximal with…

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…

Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by $\S_A(f)$, $\A_A(f)$ and $\I_A(f)$, respectively, the `verbal' subspace, subalgebra, and ideal, in $A$, generated by the set of all…

We study the generalized dominating number $\mathfrak{d}_{\mu}$ at a singular cardinal $\mu$ of cofinality $\kappa$. We show two lower bounds: in ZFC, $\mathrm{cf}([\mu]^\kappa,\subseteq) \leq \mathfrak{d}_{\mu}$, and under mild…

In the present paper, we derive formulas of complex and $\ell$-adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of variables. We provide an algebraic proof of these formulas by…

We give elementary proofs for the Apagodu-Zeilberger-Stanton-Amdeberhan-Tauraso congruences $$\sum\limits_{n=0}^{p-1}\dbinom{2n}{n} \equiv\eta_{p}\mod p^{2},$$ $$\sum\limits_{n=0}^{rp-1}\dbinom{2n}{n}…

Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…

The paired Hayman's conjecture of different types are considered. More accurately speaking, the zeros of a pair of $f^nL(z,g)-a_1(z)$ and $g^mL(z,f)-a_2(z)$ are characterized using different methods from those previously employed, where $f$…

Let F be a field of characteristic not 2 and assume all algebras are over F. We establish several conjugacy theorems for the special linear Lie algebra sl_2 over an F-algebra which is a UFD. We find the structure of the full automorphism…

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf…

We extend the state models for Jones and Alexander polynomials of classical links to state models of 2-variable polynomials in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular…

Consider the Dirichlet-type space on the bidisk consisting of holomorphic functions $f(z_1,z_2):=\sum_{k,l\geq 0}a_{kl}z_1^kz_2^l$ such that $\sum_{k,l\geq 0}(k+1)^{\alpha_1} (l+1)^{\alpha_2}|a_{kl}|^2 <\infty.$ Here the parameters…

Using the analytical expressions for the genuine eigenfunctions $\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry…

We prove: $\mathbf{Theorem}$ Let $K$ be a universal class. If $K$ is categorical in cardinals of arbitrarily high cofinality, then $K$ is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also…

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the…

A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…

Two proper polynomial maps $f_1, \,f_2 \colon \mC^n \lr \mC^n$ are said to be \emph{equivalent} if there exist $\Phi_1,\, \Phi_2 \in \textrm{Aut}(\mC^n)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. In this article we investigate proper…