Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in $$\mathbf{R}^\mathbf{4}$$

In this paper, we prove that if a symmetric compact star-shaped hypersuface in \(\mathbf{R}^4\) carries exactly two geometrically distinct closed characteristics, then both of them must be irrationally elliptic.     

Actions of $$\mathbf {SAut}\varvec{(F_n)}$$

We study actions of SAut\((F_n)\), the unique subgroup of index two in the automorphism group of a free group of rank n, and obtain rigidity results for its representations. In particular, we show that every smooth action of SAut\((F_n)\) on a low dimensional torus is trivial.     

2-Dimensional complete self-shrinkers in $$\mathbf {R}^3$$

It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for \(\mathcal {L}\)-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \(\mathbb R^3\). Ding and Xin (Trans Am Math Soc 366:5067–5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.     

ACCR ring of the forms $$\mathcal {A}[X]$$ and $$\mathcal {A}[[X]]$$A[[X]]

Let \(\mathcal {A}=(A_n)_{n\in \mathbb {N}}\) be an ascending chain of commutative rings with identity and let \(\mathcal {A}[X]\) (respectively, \(\mathcal {A}[[X]]\)) be the ring of polynomials (respectively, power series) with coefficient of degree n in \(A_n\) for each \(n\in \mathbb {N}\) (Hamed and Hizem in Commun Algebra 43:3848–3856, 2015; Haouat in Thèse de doctorat. Faculté des Sciences de Tunis, 1988). An A-module M is said to satisfy ACCR if the ascending chain of residuals of the form \(N:B\subseteq N:B^2\subseteq N:B^3\subseteq \cdots \) terminates for every submodule N of M and for every finitely generated ideal B of A (Lu in Proc Am Math Soc 117:5–10, 1993). We give necessary and sufficient condition for the ring \(\mathcal {A}[X]\) (respectively, \(\mathcal {A}[[X]]\)) to satisfy ACCR.     

Ergodicity of non-homogeneous $$\mathbf {p}$$ p -majorizing quadratic stochastic operators

Positivity - In this paper, we study the strong ergodicity of non-homogeneous $$\mathbf {p}$$ -majorizing quadratic stochastic operators acting on the finite dimension simplex. We first provide a...     

The Cocompleteness of the Category $$\mathbf{Tych}^G$$

Mathematical Notes - The cocompleteness of the category $$\mathbf{Tych}^G$$ is proved.     

Essential conformal actions of $${{\mathrm{PSL}}}(2,\mathbf {R})$$ on real-analytic compact Lorentz manifolds

The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least three admitting a conformal essential action of a Lie group locally isomorphic to \({{\mathrm{PSL}}}(2,\mathbf {R})\). It is established by using a general result on local isometries of real-analytic rigid geometric structures. As corollary, we deduce the same conclusion for conformal essential actions of connected semi-simple Lie groups on real-analytic compact Lorentz manifolds. This work is a contribution to the understanding of the Lorentzian version of a question asked by A. Lichnerowicz.     

Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$

We introduce a new notion of modular independence to define bases and the generator matrices for the codes over the ring of integers of general modulus m. We define standard forms for such generator matrices, and discuss how to find such forms and the parity check matrices.      

Type $${{\varvec{D}}}_{{\varvec{n}}}^\mathbf{(1)}$$ rigged configuration bijection

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type \(D^{(1)}_n\) in full generality. We prove the invariance of rigged configurations under the action of the combinatorial R-matrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type \(D_n^{(1)}\). In addition, we establish that the bijection is a classical crystal isomorphism.     

Geometric Optimization Problems Likely Not Contained in $$\mathbb{A}\mathbb{P}\mathbb{X}$$

   Abstract. Maximizing geometric functionals such as the classical l _p -norms over polytopes plays an important role in many applications, hence it is desirable to know how efficiently the solutions can be computed or at least approximated. While the maximum of the l _∞ -norm over polytopes can be computed in polynomial time, for 2≤ p < ∞ the l _p -norm-maxima cannot be computed in polynomial time within a factor of 1.090 , unless P=NP. This result holds even if the polytopes are centrally symmetric parallelotopes. Quadratic Programming is a problem closely related to norm-maximization, in that in addition to a polytope P ⊂ R ⁿ , numbers c _ij , 1≤ i≤ j≤ n , are given and the goal is to maximize Σ _{1≤ i≤ j≤ n} c _ij x _i x _j over P . It is known that Quadratic Programming does not admit polynomial-time approximation within a constant factor, unless P=NP. Using the observation that the latter result remains true even if the existence of an integral optimal point is guaranteed, in this paper it is proved that analogous inapproximability results hold for computing the l _p -norm-maximum and various l _p -radii of centrally symmetric polytopes for 2≤ p < ∞.     

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...     

Ideals of some configurations of lines in $${\mathbb{P}^n_\mathbf{K}}$$ : generators and macaulayness

We consider ideals arising from the intersection of hyperplanes of the projective space \mathbbPⁿ{\mathbb{P}^n} belonging to a partition. We determinate their generators and we prove that they are Cohen-Macaulay.     

Some infinite families of Ramsey ($${\varvec{P}}_\mathbf{3},{\varvec{P}}_{{\varvec{n}}}$$)-minimal trees

For any given two graphs G and H, the notation \(F\rightarrow \) (G, H) means that for any red–blue coloring of all the edges of F will create either a red subgraph isomorphic to G or a blue subgraph isomorphic to H. A graph F is a Ramsey (G, H)-minimal graph if \(F\rightarrow \) (G, H) but \(F-e\nrightarrow (G,H)\), for every \(e \in E(F)\). The class of all Ramsey (G, H)-minimal graphs is denoted by \(\mathcal {R}(G,H)\). In this paper, we construct some infinite families of trees belonging to \(\mathcal {R}(P_3,P_n)\), for \(n=8\) and 9. In particular, we give an algorithm to obtain an infinite family of trees belonging to \(\mathcal {R}(P_3,P_n)\), for \(n\ge 10\).     

Recognition of PSL($$\mathbf {2, 2}^{{\varvec{a}}}$$) by the orders of vanishing elements

Here, we show that the simple groups PSL\((2, 2^a)\), \(a\ge 2\), are characterized by the orders of vanishing elements.     

On a Solution of the Quaternion Matrix Equation X - A X B = C and Its Application

This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X B = C, characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - AXB =C.     

On the Biharmonic Curves in the Special Linear Group $${{\mathbf{SL}}{\bf (2},{\mathbb{R}}{\bf )}}$$

Mediterranean Journal of Mathematics - We characterize the biharmonic curves in the special linear group $${\mathrm{SL}(2,{\mathbb{R}})}$$ . In particular, we show that all proper biharmonic curves...     

$${\mathcal{C}}_{0}$$ ( 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     

A Characterisation of Some $$\mathbf {}$$-Like Logics

In Béziau (Log Log Philos 15:99–111, 2006) a logic \(\mathbf {Z}\) was defined with the help of the modal logic \(\mathbf {S5}\). In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \(\mathbf {Z}\) with respect to a version of Kripke semantics was also given there. Following the formulation of \(\mathbf {Z}\) we can talk about \(\mathbf {Z}\)-like logics or Beziau-style logics if we consider other modal logics instead of \(\mathbf {S5}\)—such a possibility has been mentioned in [1]. The correspondence result between modal logics and respective Beziau-style logics has been generalised for the case of normal logics naturally leading to soundness–completeness results [see Marcos (Log Anal 48(189–192):279–300, 2005) and Mruczek-Nasieniewska and Nasieniewski (Bull Sect Log 34(4):229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski (Bull Sect Log 37(3–4):185–196, 2008), (Bull Sect Log 38(3–4):189–203, 2009) some partial results for non-normal cases are given. In the present paper we try to give similar but more general correspondence results for the non-normal-worlds case. To achieve this aim we have to enrich original Beziau’s language with an additional negation operator understood as ‘it is necessary that not’.