Authors:Marian Aprodu; Edoardo Sernesi Pages: 1 - 7 Abstract: We extend a result of W. Fulton, J. Harris and R. Lazarsfeld [6] to secant loci in symmetric products of curves. We compare three secant loci and prove that the dimensions of bigger loci can not be excessively larger than the dimension of smaller loci. PubDate: 2017-01-01 DOI: 10.1007/s13348-016-0166-2 Issue No:Vol. 68, No. 1 (2017)

Authors:Abel Castorena; Gian Pietro Pirola Pages: 9 - 20 Abstract: Let E be a vector bundle on a smooth complex projective variety X. We study the family of sections \(s_t\in H^0(E\otimes L_t)\) where \(L_t\in Pic^0(X)\) is a family of topologically trivial line bundle and \(L_0={\mathcal {O}}_X,\) that is, we study deformations of \(s=s_0\) . By applying the approximation theorem of Artin (Invent Math 5:277–291, 1968) we give a transversality condition that generalizes the semi-regularity of an effective Cartier divisor. Moreover, we obtain another proof of the Severi–Kodaira–Spencer theorem (Bloch In Invent Math 17:51–66, 1972). We apply our results to give a lower bound to the continuous rank of a vector bundle as defined by Miguel Barja (Duke Math J 164(3):541–568, 2015) and a proof of a piece of the generic vanishing theorems (Green and Lazarsfeld, Invent Math 90:389–407, 1987) and (Green and Lazarsfeld, J Am Math Soc 4:87–103, 1991) for the canonical bundle. We extend also to higher dimension a result given in (Mendes-Lopes et al. In Geo Topol 17:1205:1223, 2013) on the base locus of the paracanonical base locus for surfaces. PubDate: 2017-01-01 DOI: 10.1007/s13348-016-0169-z Issue No:Vol. 68, No. 1 (2017)

Authors:Martin Křepela Pages: 21 - 50 Abstract: We characterize the validity of the weighted inequality $$\begin{aligned} \left( \int _0^\infty \Big [ \sup _{s\in [t,\infty )} u(s) \int _s^\infty g(x)\,\mathrm {d}x\Big ]^q w(t)\,\mathrm {d}t\right) ^\frac{1}{q} \le C \left( \int _0^\infty g^p(t) v(t)\,\mathrm {d}t\right) ^\frac{1}{p} \end{aligned}$$ for all nonnegative functions g on \((0,\infty )\) , with exponents in the range \(1\le p<\infty \) and \(0<q<\infty \) . Moreover, we give an integral characterization of the inequality $$\begin{aligned} \left( \int _0^\infty \Big [ \sup _{s\in [t,\infty )} u(s) f(s) \Big ]^q w(t)\,\mathrm {d}t\right) ^\frac{1}{q} \le C \left( \int _0^\infty f^p(t) v(t)\,\mathrm {d}t\right) ^\frac{1}{p} \end{aligned}$$ being satisfied for all nonnegative nonincreasing functions f on \((0,\infty )\) in the case \(0<q<p<\infty \) , for which an integral condition was previously unknown. PubDate: 2017-01-01 DOI: 10.1007/s13348-016-0170-6 Issue No:Vol. 68, No. 1 (2017)

Authors:Giovanni Calvaruso; Amirhesam Zaeim Pages: 51 - 67 Abstract: We consider the four-dimensional oscillator group, equipped with a well known one-parameter family of left-invariant Lorentzian metrics. We obtain a full classification of its Ricci (curvature, Weyl) collineations and matter collineations, and also point out the left-invariant collineations. PubDate: 2017-01-01 DOI: 10.1007/s13348-016-0173-3 Issue No:Vol. 68, No. 1 (2017)

Authors:Neil Epstein; Yongwei Yao Pages: 69 - 85 Abstract: Let R be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do not assume that their quotient has finite length. In this paper, we develop various sufficient numerical criteria for when the tight closures of these ideals (or submodules) match. For some of the criteria we only prove sufficiency, while some are shown to be equivalent to the tight closures matching. We compare the various numerical measures (in some cases demonstrating that the different measures give truly different numerical results) and explore special cases where equivalence with matching tight closure can be shown. All of our measures derive ultimately from Hilbert–Kunz multiplicity. PubDate: 2017-01-01 DOI: 10.1007/s13348-016-0174-2 Issue No:Vol. 68, No. 1 (2017)

Authors:José Ángel Peláez; Daniel Seco Abstract: Let \(\mathcal {D}_v\) denote the Dirichlet type space in the unit disc induced by a radial weight v for which \(\widehat{v}(r)=\int _r^1 v(s)\,\text {d}s\) satisfies the doubling property \(\int _r^1 v(s)\,\text {d}s\le C \int _{\frac{1+r}{2}}^1 v(s)\,\text {d}s.\) In this paper, we characterize the Schatten classes \(S_p(\mathcal {D}_v)\) of the generalized Hilbert operators $$\begin{aligned} \mathcal {H}_g(f)(z)=\int _0^1f(t)g'(tz)\,\text {d}t \end{aligned}$$ acting on \(\mathcal {D}_v\) , where v satisfies certain Muckenhoupt type conditions. For \(p\ge 1\) , it is proved that \(\mathcal {H}_{g}\in S_p(\mathcal {D}_v)\) if and only if $$\begin{aligned} \int _0^1 \left( (1-r)\int _{-\pi }^\pi g'(r\text {e}^{i\theta }) ^2\,\text {d}\theta \right) ^{\frac{p}{2}}\frac{{\text {d}}r}{1-r} <\infty . \end{aligned}$$ . PubDate: 2017-03-21 DOI: 10.1007/s13348-017-0195-5

Authors:J. J. Nuño-Ballesteros; B. Oréfice-Okamoto; J. N. Tomazella Abstract: Let (X, 0) be an ICIS of dimension 2 and let \(f:(X,0)\rightarrow (\mathbb C^2,0)\) be a map germ with an isolated instability. We look at the invariants that appear when \(X_s\) is a smoothing of (X, 0) and \(f_s:X_s\rightarrow B_\epsilon \) is a stabilization of f. We find relations between these invariants and also give necessary and sufficient conditions for a 1-parameter family to be Whitney equisingular. As an application, we show that a family \((X_t,0)\) is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant with respect to t. PubDate: 2017-03-20 DOI: 10.1007/s13348-017-0194-6

Authors:Shohei Nakamura; Yoshihiro Sawano Abstract: In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the \(A_q\) -theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated. PubDate: 2017-02-23 DOI: 10.1007/s13348-017-0193-7

Authors:Serge Nicaise Abstract: We perform some hierarchical analyses of dissipative systems. For that purpose, we first propose a general abstract setting, prove a convergence result and discuss some stability properties. This abstract setting is then illustrated by significant examples of damped (acoustic) wave equations for which we characterize the family of reduced problems. For each concrete problems the decay of the energy is discussed and the density assumption is proved. PubDate: 2017-02-08 DOI: 10.1007/s13348-017-0192-8

Authors:Alessandra Bernardi; Joachim Jelisiejew; Pedro Macias Marques; Kristian Ranestad Abstract: Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur. PubDate: 2017-01-11 DOI: 10.1007/s13348-016-0190-2

Authors:Hara Charalambous; Apostolos Thoma; Marius Vladoiu Abstract: Let \(L\subset \mathbb {Z}^n\) be a lattice and \(I_L=\langle x^{\mathbf {u}}-x^{\mathbf {v}}:\ {\mathbf {u}}-{\mathbf {v}}\in L\rangle \) be the corresponding lattice ideal in \(\Bbbk [x_1,\ldots , x_n]\) , where \(\Bbbk \) is a field. In this paper we describe minimal binomial generating sets of \(I_L\) and their invariants. We use as a main tool a graph construction on equivalence classes of fibers of \(I_L\) . As one application of the theory developed we characterize binomial complete intersection lattice ideals, a longstanding open problem in the case of non-positive lattices. PubDate: 2017-01-10 DOI: 10.1007/s13348-017-0191-9

Authors:A. Bravo; S. Encinas; B. Pascual-Escudero Abstract: The Nash multiplicity sequence was defined by Lejeune-Jalabert as a non-increasing sequence of integers attached to a germ of a curve inside a germ of a hypersurface. Hickel generalized this notion and described a sequence of blow ups which allows us to compute it and study its behavior. In this paper, we show how this sequence can be used to compute some invariants that appear in algorithmic resolution of singularities. Moreover, this indicates that these invariants from constructive resolution are intrinsic to the variety since they can be read in terms of its space of arcs. This result is a first step connecting explicitly arc spaces and algorithmic resolution of singularities. PubDate: 2017-01-04 DOI: 10.1007/s13348-016-0188-9

Authors:Ganga Ram Gautam; Jaydev Dabas Abstract: In this research article, we establish the existence results of mild solutions for semi-linear impulsive neutral fractional order integro-differential equations with state dependent delay subject to nonlocal initial condition by applying well known classical fixed point theorems. At last, we present an example of partial derivative to illuminate the results. PubDate: 2017-01-03 DOI: 10.1007/s13348-016-0189-8

Authors:E. M. Bonotto Abstract: In this work, we introduce the concept of monotone impulsive dynamical systems. We exhibit sufficient conditions for a set to be Zhukovskij quasi stable in dissipative monotone impulsive systems. Also, some recursive properties as minimality and recurrence are related with monotone impulsive systems. PubDate: 2016-12-05 DOI: 10.1007/s13348-016-0186-y

Authors:M. Emilia Alonso; Henri Lombardi Abstract: In this paper we prove what we call Local Bézout Theorem (Theorem 3.7). It is a formal abstract algebraic version, in the frame of Henselian rings and \(\mathfrak {m}\) -adic topology, of a well known theorem in the analytic complex case. This classical theorem says that, given an isolated point of multiplicity r as a zero of a local complete intersection, after deforming the coefficients of these equations we find in a sufficiently small neighborhood of this point exactly r isolated zeroes counted with multiplicities. Our main tools are, first the border bases [11], which turned out to be an efficient computational tool to deal with deformations of algebras. Second we use an important result of de Smit and Lenstra [7], for which there exists a constructive proof in [13]. Using these tools we find a very simple proof of our theorem, which seems new in the classical literature. PubDate: 2016-11-17 DOI: 10.1007/s13348-016-0184-0

Authors:Alexander V. Abanin; Pham Trong Tien Abstract: Motivated by some recent results on the boundedness and dynamical properties of the differentiation and integration operators in weighted Banach spaces of holomorphic functions, we study conditions on weights that guarantee the compactness of these two operators in the corresponding weighted spaces. PubDate: 2016-11-11 DOI: 10.1007/s13348-016-0185-z

Authors:Joachim Jelisiejew Abstract: The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our technique to analyse when an algebra is isomorphic to its associated graded algebra. We classify algebras with Hilbert function (1, 3, 3, 3, 1), obtaining finitely many isomorphism types, and those with Hilbert function (1, 2, 2, 2, 1, 1, 1). We consider fields of arbitrary, large enough, characteristic. PubDate: 2016-10-18 DOI: 10.1007/s13348-016-0183-1

Authors:O. Blasco Abstract: Following the scalar-valued case considered by Djakow and Ramanujan (A remark on Bohr’s theorem and its generalizations 14:175–178, 2000) we introduce, for each complex Banach space X and each \(1\le p<\infty \) , the p-Bohr radius of X as the value $$\begin{aligned} r_p(X)= \sup \bigg \{r\ge 0: \sum _{n=0}^\infty \Vert x_n\Vert ^pr^{np}\le \sup _{ z <1} \Vert f(z)\Vert ^p\bigg \} \end{aligned}$$ where \(x_n\in X\) for each \(n\in \mathbb {N}\cup \{0\}\) and \(f(z)=\sum _{n=0}^\infty x_nz^n\in H^\infty (\mathbb {D},X)\) . We show that a complex (possibly infinite dimensional) Banach space X is p-uniformly \(\mathbb {C}\) -convex for \(p\ge 2\) if and only if \(r_{p}(X)>0\) . We study the p-Bohr radius of the Lebesgue spaces \(L^q(\mu )\) for different values of p and q. In particular we show that \(r_p(L^q(\mu ))=0\) whenever \(p<2\) and \(dim(L^q(\mu ))\ge 2\) and \(r_p(L^q(\mu ))=1\) whenever \(p\ge 2\) and \(p'\le q\le p\) . We also provide some lower estimates for \(r_2(L^q(\mu ))\) for the values \(1\le q<2\) . PubDate: 2016-09-20 DOI: 10.1007/s13348-016-0181-3

Authors:Kangwei Li Abstract: Let \(1\le p_0<p,q <q_0\le \infty \) . Given a pair of weights \((w,\sigma )\) and a sparse family \({\mathcal {S}}\) , we study the two weight inequality for the following bi-sublinear form $$\begin{aligned} B(f, g)= \sum _{Q\in {\mathcal {S}}}\langle f ^{p_0}\rangle _Q^{\frac{1}{p_0}} \langle g ^{q_0'}\rangle _Q^{\frac{1}{q_0'}}\lambda _Q\le \mathcal N\Vert f\Vert _{L^{p}(w)}\Vert g\Vert _{L^{q'}(\sigma )}. \end{aligned}$$ When \(\lambda _Q= Q \) and \(p=q\) , Bernicot, Frey and Petermichl showed that B(f, g) dominates \(\langle Tf, g\rangle \) for a large class of singular non-kernel operators. We give a characterization for the above inequality and then obtain the mixed \(A_p-A_\infty \) estimates and the corresponding entropy bounds when \(\lambda _Q= Q \) and \(p=q\) . We also propose a new conjecture which implies both the one supremum conjecture and the separated bump conjecture. PubDate: 2016-09-16 DOI: 10.1007/s13348-016-0182-2

Authors:Shapour Heidarkhani; Giuseppe Caristi; Amjad Salari Abstract: The present paper is an attempt to the study of multiplicity results of solutions for a class of perturbed p-Laplacian discrete problems of Kirchhoff-type. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for the problems. Moreover, assuming sign conditions on the nonlinear terms, we will prove that the solutions are non-negative. Finally, by presenting two examples, we will ensure the applicability of our results. PubDate: 2016-09-15 DOI: 10.1007/s13348-016-0180-4