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We investigate the Chow groups of projective determinantal varieties and those of their strata of matrices of fixed rank, using Chern class computations (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We give an example of an affinoid curve without analytic continuation. We use this to produce an example of an affinoid morphism that cannot be flattened by a finite sequence of local blow-ups. Thus the global rigid analogue of Hironaka's complex analytic flattening theorem given by T. Gardener and H. Schoutens, in Theorem 2.3 of ?Flattening and subanalytic sets in rigid analytic geometry?, Proc. London Math. Soc (3) 83 (2001) 681?707, is not true. Since this is a key step in the proof of the affinoid elimination theorem (loc. cit. Theorem 3.12), that proof contains a serious gap. We also give an example of an affinoid subset of the plane that is not the image under a proper rigid analytic map of a set that is globally semianalytic in the domain of that map. This clarifies the relationship among several natural categories of rigid subanalytic sets.

In a preceding paper of Jin and Wang the authors describe computations concerning differential systems of the form x=y, y=-x+a 1 x 2 +a 2 xy+a 3 y 2 +a 4 x x3 +a 5 x 2 y+a 6 xy 2 +a 7 y 3 . We give proofs of the results suggested by these computations and provide a full description of the bifurcation of small-amplitude limit cycles in a subclass of these systemes

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In this short paper, we study $n$-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all $n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any $\ell>0$, twisted $\frac{n(\ell-1)}{\ell}$-Calabi-Yau algebras of global dimension at most $n$ are $n$-representation-finite. As an application, we give a construction of $n$-representation-finite algebras using the tensor product., 15 pages, more detailed proofs and examples are added

Let $\Omega\subset\mathbb R^n$ be a $C^1$ domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In this paper it is shown that if $u$ is a function harmonic in $\Omega$ and continuous in $\overline \Omega$ which vanishes in a relatively open subset $\Sigma\subset\partial\Omega$ and moreover the normal derivative $\partial_\nu u$ vanishes in a subset of $\Sigma$ with positive surface measure, then $u$ is identically $0$., Comment: More detailed explanation in some argument involving integration by parts and in Remark 3.3. An additional appendix with a self-contained proof of Lemma 4.3, whose proof was not included in the paper previously

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order 𝛼(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and 𝜆(x) of the Morrey space. Assumptions on the exponents were different depending on whether 𝛼(x)p(x)−n+𝜆(x) p(x) takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range 0 ⩽ 𝛼(x)p(x)−n+𝜆(x) p(x) ⩽ 1. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper. info:eu-repo/semantics/publishedVersion

Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves in the isogeny class, with the degree recorded as a label of the edge. In this paper, we define an isogeny‐torsion graph to be an isogeny graph where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over Q of the corresponding elliptic curve. Then, the main result of the paper is a classification of all the possible isogeny‐torsion graphs that occur for Q‐isogeny classes of elliptic curves defined over the rationals.

We establish a theory of $Q$-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\mathrm{mod}(p)$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension., 37 pages. First part of a two-papers work aimed at establishing a first general partial regularity theory for area minimizing currents modulo p, for any p and in any dimension and codimension. v3 is the final version, to appear on Comm. Pure Appl. Math

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three frameworks, a generic homogeneous observable of a generic random model is mod-Gaussian under an appropriate renormalisation. This implies a central limit theorem with an extended zone of normality, a moderate deviation principle, an estimate of the speed of convergence, a local limit theorem and a concentration inequality. The universal asymptotic behavior of the observables of these models gives rise to a notion of mod-Gaussian moduli space., Comment: New version: the paper has been slightly shortened, and a few references were added. 52 pages, 13 figures

As is well-know, on an Arens regular Banach algebra all continuous functionals are weakly almost periodic. In this paper we show that $\ell^1$-bases which approximate upper and lower triangles of products of elements in the algebra produce large sets of functionals that are not weakly almost periodic. This leads to criteria for extreme non-Arens regularity of Banach algebras in the sense of Granirer. We find in particular that bounded approximate identities (bai's) and bounded nets converging to invariance (TI-nets) both fall into this approach, suggesting that this is indeed the main tool behind most known constructions of non-Arens regular algebras. These criteria can be applied to the main algebras in harmonic analysis such as the group algebra, the measure algebra, the semigroup algebra (with certain weights) and the Fourier algebra. In this paper, we apply our criteria to the Lebesgue-Fourier algebra, the 1-Segal Fourier algebra and the Fig\`a-Talamanca Herz algebra., Comment: 23 pages. Third version. The proof of Theorem 5.5 had to be corrected to include locally compact groups that are not unimodular. Definition 3.1 had to adapted to match its use in Theorem 3.9

Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this question and gives several answers. In particular, a complete answer is given in the case where R is local: it is proved in this paper that every ideal of R is isomorphic to a trace ideal if and only if R is an artinian Gorenstein ring, or a 1-dimensional hypersurface with multiplicity at most 2, or a unique factorization domain.

The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities for the functions whose derivatives in absolute value are convex. Finally, we show that our main inequalities reduce to Ostrowski type inequalities, Simpson type inequalities and trapezoid type inequalities which are proved in earlier published papers. WOS:000655362700001 2-s2.0-85106753378

The paper deals with boundedness problems of integral operators in weighted grand Bochner-Lebesgue spaces. We will treat both cases: when a weight function appears as a multiplier in the definition of the norm, or when it defines the absolute continuous measure of integration. Along with the diagonal case we deal with the off-diagonal case. To get the appropriate result for the Hardy-Littlewood maximal operator we rely on the reasonable bound of the sharp constant in the Buckley type theorem which is also derived in the paper.

The purpose of this document is to connect two maps related to certain graphs embedded in the disc. The first is Postnikov's boundary measurement map, which combines partition functions of matchings in the graph into a map from an algebraic torus to an open positroid variety in a Grassmannian. The second is a rational map from the open positroid variety to an algebraic torus, given by certain Plucker coordinates which are expected to be a cluster in a cluster structure. This paper clarifies the relationship between these two maps, which has been ambiguous since they were introduced by Postnikov in 2001. The missing ingredient supplied by this paper is a twist automorphism of the open positroid variety, which takes the target of the boundary measurement map to the domain of the (conjectural) cluster. Among other applications, this provides an inverse to the boundary measurement map, as well as Laurent formulas for twists of Plucker coordinates.

In this paper we prove a sharp distortion property of the Cassinian metric under Mobius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in proper subdomains of Rn. Inclusion properties of the Cassinian metric balls with other hyperbolic-type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.

Dunkl operators may be regarded as differential-difference operators parameterized by finite reflection groups and multiplicity functions. In this paper, the Littlewood--Paley square function for Dunkl heat flows in $\mathbb{R}^d$ is introduced by employing the full "gradient" induced by the corresponding carr\'{e} du champ operator and then the $L^p$ boundedness is studied for all $p\in(1,\infty)$. For $p\in(1,2]$, we successfully adapt Stein's heat flows approach to overcome the difficulty caused by the difference part of the Dunkl operator and establish the $L^p$ boundedness, while for $p\in[2,\infty)$, we restrict to a particular case when the corresponding Weyl group is isomorphic to $\mathbb{Z}_2^d$ and apply a probabilistic method to prove the $L^p$ boundedness. In the latter case, the curvature-dimension inequality for Dunkl operators in the sense of Bakry--Emery, which may be of independent interest, plays a crucial role. The results are dimension-free., Comment: Comments welcome!

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo-Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo-Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light-like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light-like homogeneous geodesic.

We study in this paper the Q-symmetry and conditional Q-symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd.

A major questions in the theory of p-local finite groups was whether any saturated fusion system over a finite p-group admits an associated centric linking system, and when it does, whether it is unique. Both questions were answered in the affirmative by A. Chermak, using the theory of partial groups and localities he developed. Using Chermak’s ideas combined with the techniques of obstruction theory, Bob Oliver gave a different proof of Chermak’s theorem. In this paper we generalise Oliver’s proof to the context of fusion systems over discrete p-toral groups, thus positively resolving the analogous questions in p-local compact group theory. A p-local compact group is an algebraic object designed to encode in an algebraic setup the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups, as well as some other families of a similar nature [BLO3]. The theory of p-local compact groups includes, and in many aspects generalises, the earlier theory of p-local finite groups [BLO2]. A p-local compact group is thus a triple (S,F ,L), where S is a discrete p-toral group (Definition 1.1(c)), F is a saturated fusion system over S (Definition 1.4), and L is a centric linking system associated to F [BLO3, Definition 4.1]. In [Ch] A. Chermak showed that for any saturated fusion system F over a finite p-group S, there exists an associated centric linking system, which is unique up to isomorphism. To do so he used the theory of partial groups and localities, which he developed in order to provide an alternative, more group theoretic approach, to p-local group theory. Armed with Chermak’s ideas and techniques of obstruction theory, B. Oliver [O, Theorem 3.4] proved that the obstructions to the existence and uniqueness of a centric linking system associated to a saturated fusion system all vanish. In particular, this implies Chermak’s theorem. For a fusion system F over a discrete p-toral group S, let O(F) denote the associated orbit category of all F-centric subgroup P ≤ S, and let Z : O(F) → Ab denote the functor which associates with a subgroup its centre, [BLO3, Section 7]. Throughout this paper we will write H∗(C;F ) for lim ←− ∗ C F where F : C → Ab is a functor from a small category C. The main result of this paper is the following generalisation of [O, Theorem 3.4] to saturated fusion systems over discrete p-toral groups. Theorem A. Let F be a saturated fusion system over a discrete p-toral group S. Then H(O(F),Z) = 0 for all i > 0 if p is odd, and for all i > 1 if p = 2. The following result (cf. [Ch], and [O, Theorem A]) now follows from Proposition 1.7 below. Theorem B. Let F be a saturated fusion system over a discrete p-toral group. Then there exists a centric linking system associated to F which is unique up to isomorphism. 2000 Mathematics Subject Classification 55R35 (primary), 20J05, 20N99, 20D20 (secondary).. Page 2 of 24 RAN LEVI AND ASSAF LIBMAN The proof of Theorem A follows very closely Oliver’s argument in [O], adapting his methods to the infinite case. The main new input in this paper is the re-definition of best offenders in the context of discrete p-toral groups (Definition 2.2). Chermak, in his original solution of the existence-uniqueness problem, relies on a paper by Meierfrankenfeld and Stellmacher [MS], which in turn depends on the classification theorem of finite simple groups. Oliver’s interpretation of Chermak’s work, and as a consequence our result, remain dependent on the classification theorem. The paper is organised as follows. In Section 1 we collect the definitions, notation and background material needed throughout the paper. Section 2 introduces the Thompson subgroups and offenders in the context of discrete p-toral groups, and analyses the properties of these objects along the lines of [O]. Finally in Section 3 we prove Theorem A, which will be restated there as Theorem 3.6. In Section 4 we give an outline of Oliver’s proof and highlight the changes necessary to adapt it to the infinite case we deal with. Readers who are familiar with [O] may find it useful to read this section first. The crucial observations that led to Definition 2.2, without which this paper could not have been written, were made by Andy Chermak, and we are deeply indebted to him for his interest in these results.

This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations apply. We start by reducing the inequality to a much simpler dual variational problem using mass transportation theory. Our second main result is devoted to the construction of a Lyapunov functional associated with a nonlinear diffusion equation, that provides an alternative proof of the inequality. The key observation is that the inequality on the line is equivalent to Sobolev's inequality on the sphere, at least when the dimension is an integer, or to the critical interpolation inequality for the ultraspherical operator in the general case. The time derivative of the functional along the flow is itself very interesting. It explains the machinery of some rigidity estimates for nonlinear elliptic equations and shows how eigenvalues of a linearized problem enter in the computations. Notions of gradient flows are then discussed for various notions of distances. Throughout this paper we shall deal with two classes of inequalities corresponding either to p>2 or to p

This paper revisits and complement in different directions the classical work by W. T. Reid on symmetrizable completely continuous transformations in Hilbert spaces and a more recent paper by one of the authors. More precisely, we deal with spectral properties of % non-compact operators G on a complex Hilbert space H such that SG is self-adjoint where S is a (not necessarily injective) nonnegative operator. We study the isolated eigenvalues of G outside its essential spectral interval and provide variational characterization of them as well as stability estimates. We compare them also to spectral objects of SG. Finally, we characterize the Schechter essential spectrum of strongly symmetrizable operators in terms singular Weyl sequences; in particular, we complement J. I. Nieto's paper on the essential spectrum of symmetrizable. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems (FHS) where α ∈ (1 ∕ 2,1), , , is a symmetric and positive definite matrix for all , , and ∇ W is the gradient of W at u. The novelty of this paper is that, assuming L is bounded in the sense that there are constants 0

In this paper, we study the minimal free resolution of a nondegenerate projective variety when X is contained in a variety Y of minimal degree as a divisor. Such a variety is of interest because of its extremal behavior with respect to various properties. The graded Betti diagram of X has been completely known only when X is arithmetically Cohen-Macaulay. Our main result in the present paper provides a detailed description of the graded Betti diagram of X for the case where X is not arithmetically Cohen-Macaulay.

Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A^{0}(\Gamma _{2})$ denote the ring of scalar-valued Siegel modular forms of degree two, level $1$ and even weights. In this paper, we prove the determinant of a basis of the module of vector-valued Siegel modular forms $\bigoplus _{k \equiv \epsilon \ {\rm mod}\ {2}}A_{\det ^{k}\otimes \mathrm{Sym}(j)}(\Gamma _{2})$ over $A^{0}(\Gamma _{2})$ is equal to a power of the cusp form of degree two and weight $35$ up to a constant. Here $j = 4, 6$ and $\epsilon = 0, 1$. The main result in this paper was conjectured by Ibukiyama (Comment. Math. Univ. St. Pauli 61 (2012) 51–75).

In this paper, we obtain difference analogues of the second main theorem for meromorphic functions in several complex variables from which difference analogues of Picard-type theorems are also obtained. Our results are improvements or extensions of some recent results of papers [Proc. Royal Soc. Edinburgh Section A Math. 137, 457–474 (2007); Comput. Meth. Funct. Theor. 12, No. 1, 343–361 (2012)]. The method we used is very different from theirs.

In this paper, we investigate the existence of infinitely many solutions for the following fractional Hamiltonian systems: (FHS) where α ∈ (1 ∕ 2,1), , , and are symmetric and positive definite matrices for all , , and ∇ W is the gradient of W at u. The novelty of this paper is that, assuming L is coercive at infinity, and W is of subquadratic growth as | u | + ∞ , we show that (FHS) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.

We discuss the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. This category allows for the simultaneous presence of conical singularities and of non-compact, asymptotically conical, ends. Our main theorem is the natural next step in the chain of results initiated by McLean and continued by the author and by Joyce. We emphasize a unifying framework for studying the various cases and discuss analogies and differences between them. This paper also lays down the geometric foundations for our paper "Special Lagrangian conifolds, II" concerning gluing constructions for SL conifolds in C^m., This is the final version, to appear in Proc. LMS. I have also posted on arXiv an "extended version" of this paper, including many additional details of possible interest

This paper deals with the quasilinear ‘degenerate’ Keller–Segel system of parabolic–parabolic type under the super-critical condition. In the ‘non-degenerate’ case, Winkler (Math. Methods Appl. Sci. 2010; 33:12–24) constructed the initial data such that the solution blows up in either finite or infinite time. However, the blow-up under the super-critical condition is left as an open question in the ‘degenerate’ case. In this paper, we try to give an answer to the question under assuming the existence of local solutions. Copyright © 2012 John Wiley & Sons, Ltd.

Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class , which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.

We give a possible generalization of Lutz twist to all dimensions. This reproves the fact that every contact manifold can be given a non-fillable contact structure and also shows great flexibility in the manifolds that can be realized as cores of overtwisted families. We moreover show that $R^{2n+1}$ has at least three distinct contact structures. This version of the paper contains both the texts of the published version of the paper together with an Erratum to the published version appended to the end., Comment: 19 pages, 2 figures, and erratum to the published version of the paper