On the Enumeration of Labeled Series-Parallel $$k $$ -Cyclic $$2 $$ -Connected Graphs

Journal of Applied and Industrial Mathematics - We deduce an explicit formula for the number of labeled series-parallel $$k $$ -cyclic $$n $$ -vertex $$2 $$ -connected graphs and find the...     

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...     

Ramanujan-type $$1/\pi $$ -series from bimodular forms

The Ramanujan Journal - We develop an approach to establish $$1/\pi $$ -series from bimodular forms. Utilizing this approach, we obtain new families of 2-variable $$1/\pi $$ -series associated to...     

$$\tilde{A}$$ 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...     

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...     

Actions of the groups $${\mathbb C}$$ and $${\mathbb C^*}$$ on Stein varieties

In this paper we present recent results concerning global aspects of and -actions on Stein surfaces. Our approach is based on a byproduct of techniques from Geometric Theory of Foliations (holonomy, stability), Potential theory (parabolic Riemann surfaces, Riemann-Koebe Uniformization theorem) and Several Complex Variables (Hartogs’ extension theorems, Theory of Stein spaces). Our main motivation comes from the original works of M. Suzuki and Orlik-Wagreich. Some of their results are extended to a more general framework. In particular, we prove some linearization theorems for holomorphic actions of and on normal Stein analytic spaces of dimension two. We also add a list of questions and open problems in the subject. The underlying idea is to present the state of the art of this research field.      

$$\Gamma $$ 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...     

$${\cal K}$$-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.     

Characterizing cryptogroups with a finite number of $${\mathcal{H}}$$ -classes in each $${\mathcal{D}}$$ -class by their subsemigroups

We construct a family of completely regular semigroups with the property that each completely regular semigroup S with a finite number of -classes in each -class is non-cryptic if and only if S contains an isomorphic image of a member of . Each member F of is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F. Here with I and Λ finite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to where is the natural partial order and a if and only if a ² = ab = ba. Hence the above result can be formulated in terms of and .      

Pro- $$\mathcal {C}$$ C congruence properties for groups of rooted tree automorphisms

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro- $$\mathcal {C}$$ completions of the group, where $$\mathcal {C}$$ is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the $$\mathcal {C}$$ -congruence subgroup property ( $$\mathcal {C}$$ -CSP) if its pro- $$\mathcal {C}$$ completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the $$\mathcal {C}$$ -CSP. In the case where $$\mathcal {C}$$ is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.     

Construction of $${\text {MDS}}$$ MDS matrices from generalized Feistel structures

Designs, Codes and Cryptography - This paper investigates the construction of $${\text {MDS}}$$ matrices with generalized Feistel structures ( $${\text {GFS}}$$ ). The approach developed by this...     

Domain decomposition based $${\mathcal H}$$ -LU preconditioning

Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an -matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In this paper, we develop a new approach to construct the necessary partition based on domain decomposition. Compared to standard geometric bisection based -matrices, this new approach yields -LU factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements. These rigorously proven and numerically verified improvements result from an -matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an LU factorization. We provide numerical results in which a domain decomposition based -LU factorization is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation. This work was supported in part by the US Department of Energy under Grant No. DE-FG02-04ER25649 and by the National Science Foundation under grant No. DMS-0408950.     

The completeness characterization of $$C(\mathcal {L})$$ C ( L ) , $$\mathcal {L}$$ L a locale

Positivity - The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb...     

Automorphisms of a Distance Regular Graph with Intersection Array $$\{21,18,12,4;1,1,6,21\}$$

Mathematical Notes - A. A. Makhnev and M. S. Nirova found the intersection arrays of distance regular graphs with $$\lambda=2$$ and at most 4096 vertices. For graphs of diameter $$4$$ , of most...     

A Fast Computation of the Best $${k}$$ -Digit Rational Approximation to a Real Number

Mediterranean Journal of Mathematics - Given a real number $${\alpha}$$ , we aim at computing the best rational approximation with at most $${k}$$ digits and with exactly $${k}$$ digits at the...     

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:

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...     

$${\mathcal{C}}_{0}$$ ( X)-algebras,stability and strongly self-absorbing $${\mathcal{C}}^{*}$$ -algebras

We study permanence properties of the classes of stable and so-called -stable -algebras, respectively. More precisely, we show that a (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for -algebras absorbing the Jiang–Su algebra tensorially). Furthermore, we prove that if is a K ₁-injective strongly self-absorbing -algebra, then A absorbs tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a -algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of -absorbing -algebras. Research supported by: Deutsche Forschungsgemeinschaft (through the SFB 478), by the EU-Network Quantum Spaces - Noncommutative Geometry (Contract No. HPRN-CT-2002-00280), and by the Center for Advanced Studies in Mathematics at Ben-Gurion University     

Tropical Duality in $$(d+2)$$ ( d + 2 ) -Angulated Categories

Applied Categorical Structures - Let $$\mathscr {C}$$ be a 2-Calabi–Yau triangulated category with two cluster tilting subcategories $$\mathscr {T}$$ and $$\mathscr {U}$$ . A result from...     

$$\aleph _0$$ -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...