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1. CMB Online first

Kalaj, David; Vujadinović, Djordjije
 Gradient of solution of the Poisson equation in the unit ball and related operators In this paper we determine the $L^1\to L^1$ and $L^{\infty}\to L^\infty$ norms of an integral operator $\mathcal{N}$ related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions. Keywords:MÃ¶bius transformation, Poisson equation, Newtonian potential, Cauchy transform, Bessel functionCategories:35J05, 47G10

2. CMB Online first

Zhang, Guo-Bao; Tian, Ge
 Stability of Traveling Wavefronts for a Two-Component Lattice Dynamical System Arising in Competition Models In this paper, we study a two-component Lotka-Volterra competition system on an one-dimensional spatial lattice. By the method of the comparison principle together with the weighted energy, we prove that the traveling wavefronts with large speed are exponentially asymptotically stable, when the initial perturbation around the traveling wavefronts decays exponentially as $j+ct \rightarrow -\infty$, where $j\in\mathbb{Z}$, $t\gt 0$, but the initial perturbation can be arbitrarily large on other locations. This partially answers an open problem by J.-S. Guo and C.-H. Wu. Keywords:lattice dynamical system, competition model, traveling wavefront, stabilityCategories:34A33, 34K20, 92D25

3. CMB Online first

Koşan, Tamer; Sahinkaya, Serap; Zhou, Yiqiang
 Additive maps on units of rings Let $R$ be a ring. A map $f: R\rightarrow R$ is additive if $f(a+b)=f(a)+f(b)$ for all elements $a$ and $b$ of $R$. Here a map $f: R\rightarrow R$ is called unit-additive if $f(u+v)=f(u)+f(v)$ for all units $u$ and $v$ of $R$. Motivated by a recent result of Xu, Pei and Yi showing that, for any field $F$, every unit-additive map of ${\mathbb M}_n(F)$ is additive for all $n\ge 2$, this paper is about the question when every unit-additive map of a ring is additive. It is proved that every unit-additive map of a semilocal ring $R$ is additive if and only if either $R$ has no homomorphic image isomorphic to $\mathbb Z_2$ or $R/J(R)\cong \mathbb Z_2$ with $2=0$ in $R$. Consequently, for any semilocal ring $R$, every unit-additive map of ${\mathbb M}_n(R)$ is additive for all $n\ge 2$. These results are further extended to rings $R$ such that $R/J(R)$ is a direct product of exchange rings with primitive factors Artinian. A unit-additive map $f$ of a ring $R$ is called unit-homomorphic if $f(uv)=f(u)f(v)$ for all units $u,v$ of $R$. As an application, the question of when every unit-homomorphic map of a ring is an endomorphism is addressed. Keywords:additive map, unit, 2-sum property, semilocal ring, exchange ring with primitive factors ArtinianCategories:15A99, 16U60, 16L30

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Li, Bao Qin
 An Equivalent Form of Picard's Theorem and Beyond This paper gives an equivalent form of Picard's theorem via entire solutions of the functional equation $f^2+g^2=1$, and then its improvements and applications to certain nonlinear (ordinary and partial) differential equations. Keywords:entire function, Picard's Theorem, functional equation, partial differential equationCategories:30D20, 32A15, 35F20

5. CMB Online first

Huang, Yanhe; Sottile, Frank; Zelenko, Igor
 Injectivity of generalized Wronski maps We study linear projections on PlÃ¼cker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of $m$-dimensional linear subspaces in a symplectic vector space of dimension $2m$, and the linear map is the Lagrangian involution. The Wronski map for a self-adjoint linear differential operator and pole placement map for symmetric linear systems are natural examples. Keywords:Wronski map, PlÃ¼cker embedding, curves in Lagrangian Grassmannian, self-adjoint linear differential operator, symmetric linear control system, pole placement mapCategories:14M15, 34A30, 93B55

6. CMB Online first

Tang, Xianhua
 New super-quadratic conditions for asymptotically periodic SchrÃ¶dinger equation This paper is dedicated to studying the semilinear SchrÃ¶dinger equation $$\left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbf{R}}^{N}, \\ u\in H^{1}({\mathbf{R}}^{N}), \end{array} \right.$$ where $f$ is a superlinear, subcritical nonlinearity. It focuses on the case where $V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbf{R}^N)$, $V_0(x)$ is 1-periodic in each of $x_1, x_2, \ldots, x_N$ and $\sup[\sigma(-\triangle +V_0)\cap (-\infty, 0)]\lt 0\lt \inf[\sigma(-\triangle +V_0)\cap (0, \infty)]$, $V_1\in C(\mathbf{R}^N)$ and $\lim_{|x|\to\infty}V_1(x)=0$. A new super-quadratic condition is obtained, which is weaker than some well known results. Keywords:SchrÃ¶dinger equation, superlinear, asymptotically periodic, ground state solutions of Nehari-Pankov typeCategories:35J20, 35J60

7. CMB Online first

Ha, Pham Hoang; Kawakami, Yu
 A note on a unicity theorem for the Gauss maps of complete minimal surfaces in Euclidean four-space The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness theorem for the Gauss maps of complete minimal surfaces in Euclidean four-space. Keywords:minimal surface, Gauss map, unicity theoremCategories:53A10, 30D35, 53C42

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Bu, Shangquan; Cai, Gang
 HÃ¶lder continuous solutions of degenerate differential equations with finite delay Using known operator-valued Fourier multiplier results on vector-valued HÃ¶lder continuous function spaces $C^\alpha (\mathbb R; X)$, we completely characterize the $C^\alpha$-well-posedness of the first order degenerate differential equations with finite delay $(Mu)'(t) = Au(t) + Fu_t + f(t)$ for $t\in\mathbb R$ by the boundedness of the $(M, F)$-resolvent of $A$ under suitable assumption on the delay operator $F$, where $A, M$ are closed linear operators on a Banach space $X$ satisfying $D(A)\cap D(M) \not=\{0\}$, the delay operator $F$ is a bounded linear operator from $C([-r, 0]; X)$ to $X$ and $r \gt 0$ is fixed. Keywords:well-posedness, degenerate differential equation, $\dot{C}^\alpha$-multiplier, HÃ¶lder continuous function spaceCategories:34N05, 34G10, 47D06, 47A10, 34K30

9. CMB Online first

Bao, Guanlong; Göğüş, Nıhat Gökhan; Pouliasis, Stamatis
 $\mathcal{Q}_p$ spaces and Dirichlet type spaces In this paper, we show that the MÃ¶bius invariant function space $\mathcal {Q}_p$ can be generated by variant Dirichlet type spaces $\mathcal{D}_{\mu, p}$ induced by finite positive Borel measures $\mu$ on the open unit disk. A criterion for the equality between the space $\mathcal{D}_{\mu, p}$ and the usual Dirichlet type space $\mathcal {D}_p$ is given. We obtain a sufficient condition to construct different $\mathcal{D}_{\mu, p}$ spaces and we provide examples. We establish decomposition theorems for $\mathcal{D}_{\mu, p}$ spaces, and prove that the non-Hilbert space $\mathcal {Q}_p$ is equal to the intersection of Hilbert spaces $\mathcal{D}_{\mu, p}$. As an application of the relation between $\mathcal {Q}_p$ and $\mathcal{D}_{\mu, p}$ spaces, we also obtain that there exist different $\mathcal{D}_{\mu, p}$ spaces; this is a trick to prove the existence without constructing examples. Keywords:$\mathcal {Q}_p$ space, Dirichlet type space, MÃ¶bius invariant function spaceCategories:30H25, 31C25, 46E15

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Moslehian, Mohammad Sal; Zamani, Ali
 Characterizations of operator Birkhoff--James orthogonality In this paper, we obtain some characterizations of the (strong) Birkhoff--James orthogonality for elements of Hilbert $C^*$-modules and certain elements of $\mathbb{B}(\mathscr{H})$. Moreover, we obtain a kind of Pythagorean relation for bounded linear operators. In addition, for $T\in \mathbb{B}(\mathscr{H})$ we prove that if the norm attaining set $\mathbb{M}_T$ is a unit sphere of some finite dimensional subspace $\mathscr{H}_0$ of $\mathscr{H}$ and $\|T\|_{{{\mathscr{H}}_0}^\perp} \lt \|T\|$, then for every $S\in\mathbb{B}(\mathscr{H})$, $T$ is the strong Birkhoff--James orthogonal to $S$ if and only if there exists a unit vector $\xi\in {\mathscr{H}}_0$ such that $\|T\|\xi = |T|\xi$ and $S^*T\xi = 0$. Finally, we introduce a new type of approximate orthogonality and investigate this notion in the setting of inner product $C^*$-modules. Keywords:Hilbert $C^*$-module, Birkhoff--James orthogonality, strong Birkhoff--James orthogonality, approximate orthogonalityCategories:46L05, 46L08, 46B20

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Motegi, Kimihiko; Teragaito, Masakazu
 Generalized torsion elements and bi-orderability of 3-manifold groups It is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of $3$-manifolds, and verify the conjecture for non-hyperbolic, geometric $3$-manifolds. We also confirm the conjecture for some infinite families of closed hyperbolic $3$-manifolds. In the course of the proof, we prove that each standard generator of the Fibonacci group $F(2, m)$ ($m \gt 2$) is a generalized torsion element. Keywords:generalized torsion element, bi-ordering, 3-manifold groupCategories:57M25, 57M05, 06F15, 20F05

12. CMB Online first

Chen, Bin; Zhao, Lili
 On a Yamabe type problem in Finsler geometry In this paper, a new notion of scalar curvature for a Finsler metric $F$ is introduced, and two conformal invariants $Y(M,F)$ and $C(M,F)$ are defined. We prove that there exists a Finsler metric with constant scalar curvature in the conformal class of $F$ if the Cartan torsion of $F$ is sufficiently small and $Y(M,F)C(M,F)\lt Y(\mathbb{S}^n)$ where $Y(\mathbb{S}^n)$ is the Yamabe constant of the standard sphere. Keywords:Finsler metric, scalar curvature, Yamabe problemCategories:53C60, 58B20

13. CMB Online first

Liu, Li; Weng, Peixuan
 Globally asymptotic stability of a delayed integro-differential equation with nonlocal diffusion We study a population model with nonlocal diffusion, which is a delayed integro-differential equation with double nonlinearity and two integrable kernels. By comparison method and analytical technique, we obtain globally asymptotic stability of the zero solution and the positive equilibrium. The results obtained reveal that the globally asymptotic stability only depends on the property of nonlinearity. As application, an example for a population model with age structure is discussed at the end of the article. Keywords:integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structureCategories:45J05, 35K57, 92D25

14. CMB Online first

Friedl, Stefan; Vidussi, Stefano
 Twisted Alexander invariants detect trivial links It follows from earlier work of Silver--Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexander modules detect trivial links. We use this result to provide algorithms for detecting whether a link is the unlink, whether it is split and whether it is totally split. Keywords:twisted Alexander polynomial, virtual fibering theorem, unlink detectionCategory:57M27

15. CMB Online first

Bhuniya, Anjan Kumar; Hansda, Kalyan
 On radicals of Green's relations in ordered semigroups In this paper, we give a new definition of radicals of Green's relations in an ordered semigroup and characterize left regular (right regular), intra regular ordered semigroups by radicals of Green's relations. Also we characterize the ordered semigroups which are unions and complete semilattices of t-simple ordered semigroups. Keywords:radical of Green's relation, intra regular ordered semigroup, left regular, t-simple ordered semigroupCategory:06F05

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Ding, Fan; Geiges, Hansjörg; Zhang, Guangjian
 On subcritically Stein fillable 5-manifolds We make some elementary observations concerning subcritically Stein fillable contact structures on $5$-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case the fundamental group is finite cyclic, and we show that on the $5$-sphere the standard contact structure is the unique subcritically fillable one. More generally, it is shown that subcritically fillable contact structures on simply connected $5$-manifolds are determined by their underlying almost contact structure. Along the way, we discuss the homotopy classification of almost contact structures. Keywords:subcritically Stein fillable, 5-manifold, almost contact structure, thickeningCategories:53D35, 32Q28, 57M20, 57Q10, 57R17

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Buijs, Urtzi; Félix, Yves; Murillo, Aniceto; Tanré, Daniel
 Maurer-Cartan elements in the Lie models of finite simplicial complexes In a previous work, we have associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we have also a realization functor from the category of complete differential graded Lie algebras to the category of simplicial sets. We have already interpreted the homology of a Lie algebra in terms of homotopy groups of its realization. In this paper, we begin a dictionary between models and simplicial complexes by establishing a correspondence between the Deligne groupoid of the model and the connected components of the finite simplicial complex. Keywords:complete differential graded Lie algebra, Maurer-Cartan element, rational homotopy theoryCategory:16E45

18. CMB Online first

Rousseau, C.
 The Bifurcation Diagram of Cubic Polynomial Vector Fields on $\mathbb C\mathbb P^1$ In this paper we give the bifurcation diagram of the family of cubic vector fields $\dot z=z^3+ \epsilon_1z+\epsilon_0$ for $z\in \mathbb{C}\mathbb{P}^1$, depending on the values of $\epsilon_1,\epsilon_0\in\mathbb{C}$. The bifurcation diagram is in $\mathbb{R}^4$, but its conic structure allows describing it for parameter values in $\mathbb{S}^3$. There are two open simply connected regions of structurally stable vector fields separated by surfaces corresponding to bifurcations of homoclinic connections between two separatrices of the pole at infinity. These branch from the codimension 2 curve of double singular points. We also explain the bifurcation of homoclinic connection in terms of the description of Douady and Sentenac of polynomial vector fields. Keywords:complex polynomial vector field, bifurcation diagram, Douady-Sentenac invariantCategories:34M45, 32G34

19. CMB Online first

Bahmanpour, Kamal; Naghipour, Reza
 Faltings' finiteness dimension of local cohomology modules over local Cohen-Macaulay rings Let $(R, \frak m)$ denote a local Cohen-Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings' finiteness dimension $f_I(R)$ and equidimensionalness of certain homomorphic image of $R$. As a consequence we deduce that $f_I(R)=\operatorname{max}\{1, \operatorname{ht} I\}$ and if $\operatorname{mAss}_R(R/I)$ is contained in $\operatorname{Ass}_R(R)$, then the ring $R/ I+\cup_{n\geq 1}(0:_RI^n)$ is equidimensional of dimension $\dim R-1$. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module $H^{\operatorname{ht} I}_I(R)$, in the case $(R, \frak m)$ is a complete equidimensional local ring. Keywords:Cohen Macaulay ring, equidimensional ring, finiteness dimension, local cohomologyCategories:13D45, 14B15

20. CMB Online first

Miranda-Neto, Cleto Brasileiro
 A module-theoretic characterization of algebraic hypersurfaces In this note we prove the following surprising characterization: if $X\subset {\mathbb A}^n$ is an (embedded, non-empty, proper) algebraic variety defined over a field $k$ of characteristic zero, then $X$ is a hypersurface if and only if the module $T_{{\mathcal O}_{{\mathbb A}^n}/k}(X)$ of logarithmic vector fields of $X$ is a reflexive ${\mathcal O}_{{\mathbb A}^n}$-module. As a consequence of this result, we derive that if $T_{{\mathcal O}_{{\mathbb A}^n}/k}(X)$ is a free ${\mathcal O}_{{\mathbb A}^n}$-module, which is shown to be equivalent to the freeness of the $t$th exterior power of $T_{{\mathcal O}_{{\mathbb A}^n}/k}(X)$ for some (in fact, any) $t\leq n$, then necessarily $X$ is a Saito free divisor. Keywords:hypersurface, logarithmic vector field, logarithmic derivation, free divisorCategories:14J70, 13N15, 32S22, 13C05, 13C10, 14N20, , , , , 14C20, 32M25

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Basu, Samik; Subhash, B
 Topology of certain quotient spaces of Stiefel manifolds We compute the cohomology of the right generalised projective Stiefel manifolds. Following this, we discuss some easy applications of the computations to the ranks of complementary bundles, and bounds on the span and immersibility. Keywords:projective Stiefel manifold, span, spectral sequenceCategories:55R20, 55R25, 57R20

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Gilligan, Bruce
 Levi's problem for pseudoconvex homogeneous manifolds Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup. Then there exists a closed complex subgroup $J$ of $G$ containing $H$ such that the fibration $\pi:G/H \to G/J$ is the holomorphic reduction of $G/H$, i.e., $G/J$ is holomorphically separable and ${\mathcal O}(G/H) \cong \pi^*{\mathcal O}(G/J)$. In this paper we prove that if $G/H$ is pseudoconvex, i.e., if $G/H$ admits a continuous plurisubharmonic exhaustion function, then $G/J$ is Stein and $J/H$ has no non--constant holomorphic functions. Keywords:complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilatorCategories:32M10, 32U10, 32A10, 32Q28

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Lee, Tsiu-Kwen
 Ad-nilpotent elements of semiprime rings with involution Let $R$ be an $n!$-torsion free semiprime ring with involution $*$ and with extended centroid $C$, where $n\gt 1$ is a positive integer. We characterize $a\in K$, the Lie algebra of skew elements in $R$, satisfying $(\operatorname{ad}_a)^n=0$ on $K$. This generalizes both Martindale and Miers' theorem and the theorem of Brox et al. To prove it we first prove that if $a, b\in R$ satisfy $(\operatorname{ad}_a)^n=\operatorname{ad}_b$ on $R$, where either $n$ is even or $b=0$, then $\big(a-\lambda\big)^{[\frac{n+1}{2}]}=0$ for some $\lambda\in C$. Keywords:Semiprime ring, Lie algebra, Jordan algebra, faithful $f$-free, involution, skew (symmetric) element, ad-nilpotent element, Jordan elementCategories:16N60, 16W10, 17B60

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Le Fourn, Samuel
 Nonvanishing of central values of $L$-functions of newforms in $S_2 (\Gamma_0 (dp^2))$ twisted by quadratic characters We prove that for $d \in \{ 2,3,5,7,13 \}$ and $K$ a quadratic (or rational) field of discriminant $D$ and Dirichlet character $\chi$, if a prime $p$ is large enough compared to $D$, there is a newform $f \in S_2(\Gamma_0(dp^2))$ with sign $(+1)$ with respect to the Atkin-Lehner involution $w_{p^2}$ such that $L(f \otimes \chi,1) \neq 0$. This result is obtained through an estimate of a weighted sum of twists of $L$-functions which generalises a result of Ellenberg. It relies on the approximate functional equation for the $L$-functions $L(f \otimes \chi, \cdot)$ and a Petersson trace formula restricted to Atkin-Lehner eigenspaces. An application of this nonvanishing theorem will be given in terms of existence of rank zero quotients of some twisted jacobians, which generalises a result of Darmon and Merel. Keywords:nonvanishing of $L$-functions of modular forms, Petersson trace formula, rank zero quotients of jacobiansCategories:14J15, 11F67

25. CMB Online first

Liu, Zhongyun; Qin, Xiaorong; Wu, Nianci; Zhang, Yulin
 The shifted classical circulant and skew circulant splitting iterative methods for Toeplitz matrices It is known that every Toeplitz matrix $T$ enjoys a circulant and skew circulant splitting (denoted by CSCS) i.e., $T=C-S$ with $C$ a circulant matrix and $S$ a skew circulant matrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss-Seidel (GS) iterative methods if the CSCS is convergent, and that there is always a constant $\alpha$ such that the shifted CSCS iteration converges much faster than the Gauss-Seidel iteration, no matter whether the CSCS itself is convergent or not. Keywords:Hermitian positive definite, CSCS splitting, Gauss-Seidel splitting, iterative method, Toeplitz matrixCategories:15A23, 65F10, 65F15
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