Algebraic Bethe ansatz for $$\mathfrak o_{2n+1}$$ -invariant integrable models

Theoretical and Mathematical Physics - We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction...     

$$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras: triangulated surfaces and friezes

Journal of Algebraic Combinatorics - By viewing $$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras as triangulated surfaces, we find all cluster variables in terms of either (i) the frieze...     

$${\mathcal {W}}_\infty $$ W ∞ -transport with discrete target as a combinatorial matching problem

Archiv der Mathematik - In this short note, we show that given a cost function c, any coupling $$\pi $$ of two probability measures where the second is a discrete measure can be associated to a...     

Divisibility of certain $$\ell $$ -regular partitions by 2

The Ramanujan Journal - For a positive integer $$\ell $$ , let $$b_{\ell }(n)$$ denote the number of $$\ell $$ -regular partitions of a nonnegative integer n. Motivated by some recent conjectures...     

Compact operators and integral equations in the $${\cal H}{\cal K}$$ ℋ K space

Czechoslovak Mathematical Journal - The space $${\cal H}{\cal K}$$ of Henstock-Kurzweil integrable functions on [a, b] is the uncountable union of Fréchet spaces $${\cal H}{\cal K}$$ (X). In...     

$$\Gamma $$ Γ -evaluations of hypergeometric series

The Ramanujan Journal - In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $$\Gamma $$ -functions and exponential functions of linear...     

An $$\mathcal{O}(m\log n)$$ algorithm for the weighted stable set problem in claw-free graphs with $$\alpha ({G}) \le 3$$

Mathematical Programming - In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G(V, E) with $$\alpha (G) \le 3$$ in time $$\mathcal{O}(|E|\log...     

$$\aleph _0$$ -categoricity of semigroups II

Semigroup Forum - A countable semigroup is $$\aleph _0$$ -categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into...     

The $${\mathbb {Q}}$$ Q -Korselt set of $$\mathrm {pq}$$ pq

Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus...     

Toward logarithmic extensions of $$\widehat{s\ell }(2)_k $$ conformal field models

For positive integers p = k + 2, we construct a logarithmic extension of the conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a butterfly resolution of a three-boson realization of . The currents W⁻(z) and W⁺(z) of a W-algebra acting in the kernel are determined by a highest-weight state of dimension 4p − 2 and charge 2p − 1 and by a (θ=1)-twisted highest-weight state of the same dimension 4p − 2 and opposite charge −2p+1. We construct 2p W-algebra representations, evaluate their characters, and show that together with the p−1 integrable representation characters, they generate a modular group representation whose structure is described as a deformation of the (9p−3)-dimensional representation R _p+1⊕ℂ²⊗R _p+1ʕR _p−1⊕ℂ² R _p−1⊕ℂ³ R _p−1, where R _p−1 is the SL(2, ℤ)-representation on integrable-representation characters and R _p+1 is a (p+1)-dimensional SL(2, ℤ)-representation known from the logarithmic (p, 1) model. The dimension 9p − 3 is conjecturally the dimension of the space of torus amplitudes, and the ℂⁿ with n = 2 and 3 suggest the Jordan cell sizes in indecomposable W-algebra modules. We show that under Hamiltonian reduction, the W-algebra currents map into the currents of the triplet W-algebra of the logarithmic (p, 1) model. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 291–346, December, 2007.     

On $$\ell $$-regular bipartitions modulo $$\ell $$

Let \(B_\ell (n)\) denote the number of \(\ell \)-regular bipartitions of n. In this paper, we prove several infinite families of congruences satisfied by \(B_\ell (n)\) for \(\ell \in {\{5,7,13\}}\). For example, we show that for all \(\alpha >0\) and \(n\ge 0\),

$$\begin{aligned} B_5\left( 4^\alpha n+\frac{5\times 4^\alpha -2}{6}\right)\equiv & {} 0 \ (\text {mod}\ 5),\\ B_7\left( 5^{8\alpha }n+\displaystyle \frac{5^{8\alpha }-1}{2}\right)\equiv & {} 3^\alpha B_7(n)\ (\text {mod}\ 7) \end{aligned}$$

and

$$\begin{aligned} B_{13}\left( 5^{12\alpha }n+5^{12\alpha }-1\right) \equiv B_{13}(n)\ (\text {mod}\ 13). \end{aligned}$$

     

Fibred multilinks and singularities $${f \overline g}$$

In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:

Some remarks on Kida’s formula when $$\mu \ne 0$$ μ ≠ 0

The Ramanujan Journal - Kida’s formula in classical Iwasawa theory relates the Iwasawa $$\lambda $$ -invariants of p-extensions of number fields. Analogue of this formula was subsequently...     

On the quantum $$\mathfrak{osp}(1|2\ell)$$ Toda chain

Theoretical and Mathematical Physics - The orthosymplectic Lie superalgebra $$\mathfrak{osp}(1|\,2\ell)$$ is the closest superanalogue of standard Lie algebras. We demonstrate that the...     

First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

Characterizations of $$\sigma$$ -Solvable Finite Groups

Mathematical Notes - All the groups considered in this paper are finite, and $$G$$ always denotes a finite group; $$\sigma$$ is a partition of the set $$\mathbb{P}$$ of all primes, i.e.,...     

$${\cal K}$$-Convexity1 in $$\Re^{n}$$

We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of -convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or joint setup costs. We derive some basic properties of -convex functions. We conclude the paper with some suggestions for future research. Support from Columbia University and University of Texas at Dallas is gratefully acknowledged. Helpful comments from Qi Feng are appreciated.     

n-APR tilting and $$\tau $$ τ -mutations

Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that...     

Multiplicative updates for convolutional NMF under $$\beta $$ β -divergence

Optimization Letters - We generalize the convolutional NMF by taking the $$\beta $$ -divergence as the contrast function and present the exact multiplicative updates for its factors in closed form....     

Beckman-Quarles type theorems for mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{C}^n $$

Summary. Let We say that preserves the distance d 0 if for each implies Let A _n denote the set of all positive numbers d such that any map that preserves unit distance preserves also distance d. Let D _n denote the set of all positive numbers d with the property: if and then there exists a finite set S _xy with such that any map that preserves unit distance preserves also the distance between x and y. Obviously, We prove: (1) (2) for n 2 D _n is a dense subset of (2) implies that each mapping f from to (n 2) preserving unit distance preserves all distances, if f is continuous with respect to the product topologies on and