Authors:Henrique F. de Lima; Eraldo Lima; Adriano Medeiros; Márcio S. Santos Pages: 43 - 55 Abstract: We establish Liouville type results concerning two-sided hypersurfaces immersed in a weighted Killing warped product, under suitable constraints either on the Bakry-Émery-Ricci tensor of the base of the ambient space or on the height function of the hypersurface. PubDate: 2018-03-01 DOI: 10.1007/s00574-017-0043-y Issue No:Vol. 49, No. 1 (2018)

Authors:Yin Chen Pages: 57 - 72 Abstract: We study modular invariants of finite affine linear groups over a finite field \(\mathbb {F}_{q}\) under affine actions and linear actions. We generalize a result of Chuai (J Algebra 318:710–722, 2007, Theorem 4.2) to any m-folds affine actions. Suppose \(G\leqslant \mathrm{GL}(n,\mathbb {F}_{q})\) is a subgroup and W denotes the canonical module of \(\mathrm{GL}(n,\mathbb {F}_{q})\) . We denote by \(\mathbb {F}_{q}[W]^{G}\) the invariant ring of G acting linearly on W and denote by \(\mathbb {F}_{q}[W_{n+1}]^{AG(W^{*})}\) the invariant ring of the affine group \(AG(W^{*})\) of G acting canonically on \(W_{n+1}:=W\oplus \mathbb {F}_{q}\) . We show that if \(\mathbb {F}_{q}[W]^{G}=\mathbb {F}_{q}[f_{1},f_{2},\ldots ,f_{s}]\) , then \(\mathbb {F}_{q}[W_{n+1}]^{AG(W^{*})}=\mathbb {F}_{q}[f_{1},f_{2},\ldots ,f_{s},h_{n+1}]\) , where \(h_{n+1}\) denotes the \((n+1)\) -th Mui’s invariant of degree \(q^{n}\) . Let \(\mathrm{AGL}_{1}(\mathbb {F}_{p})\) be the 1-dimensional affine general linear groups over the prime field \(\mathbb {F}_{p}\) . We find a generating set for the ring of vector invariants \(\mathbb {F}_{p}[mW_{2}]^{\mathrm{AGL}_{1}(\mathbb {F}_{p})}\) and determine the Noether’s number \(\upbeta _{mW_{2}}(\mathrm{AGL}_{1}(\mathbb {F}_{p}))\) for any \(m\in \mathbb {N}^{+}\) . PubDate: 2018-03-01 DOI: 10.1007/s00574-017-0050-z Issue No:Vol. 49, No. 1 (2018)

Authors:Thaís Maria Dalbelo; Marcelo Messias; Alisson C. Reinol Pages: 137 - 157 Abstract: In this paper we give the normal form of all polynomial differential systems in \(\mathbb {R}^3\) having a weighted homogeneous surface \(f=0\) as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when \(f=0\) is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface. PubDate: 2018-03-01 DOI: 10.1007/s00574-017-0045-9 Issue No:Vol. 49, No. 1 (2018)

Authors:Talat Körpinar; Rıdvan Cem Demirkol Pages: 159 - 177 Abstract: In this work, we firstly describe conditions for being elastica for a moving particle corresponding to different type of space curves in Minkowski space \(\mathsf{E}_2^4\) . Then, we investigate the energy on the elastic curves corresponding to a particular particle in the space and we also exploit its relationship with energy on the same particle in the Frenet vector fields. Finally, we characterize non-elastic curves in \(\mathsf{E}_2^4\) and we compute their energy to see the distinction between energies for the curves of elastic and non-elastic case in Minkowski space \(\mathsf{E}_2^4\) . PubDate: 2018-03-01 DOI: 10.1007/s00574-017-0047-7 Issue No:Vol. 49, No. 1 (2018)

Authors:E. Fernández-Cara; F. Hernández; J. Límaco Abstract: The purpose of this article is to give a new proof of a null controllability result for a 1D free-boundary problem of the Stefan kind for a heat PDE. We introduce a method based on local inversion that, in contrast with other previous arguments, does not rely on any compactness property and can be generalized to higher dimensions. PubDate: 2018-05-24 DOI: 10.1007/s00574-018-0093-9

Authors:Khaista Rahman; Saleem Abdullah; Asad Ali; Fazli Amin Abstract: For the multi-attribute group decision-making problems where attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on induced Einstein averaging aggregation operators are developed. Firstly, induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator and induced interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging (I-IVPFEHWA) aggregation operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for multi-attribute group decision-making problems based on these operators was developed, and the operational progressions were explained in detail. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in daily life problems. At the end of the paper the proposed operators have been applied to decision making problems to show the weight, practicality and effectiveness of the new approach. PubDate: 2018-05-16 DOI: 10.1007/s00574-018-0091-y

Authors:Andrés Chirre Abstract: In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire L-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet L-functions \(L(s,\chi )\) for primitive characters \(\chi \) . PubDate: 2018-05-12 DOI: 10.1007/s00574-018-0092-x

Authors:Fernando Abadie; Alcides Buss; Damián Ferraro Abstract: We introduce notions of weak and strong equivalence for non-saturated Fell bundles over locally compact groups and show that every Fell bundle is strongly (resp. weakly) equivalent to a semidirect product Fell bundle for a partial (resp. global) action. Equivalences preserve cross-sectional \({\mathrm {C}}^*\) -algebras and amenability. We use this to show that previous results on crossed products and amenability of group actions carry over to Fell bundles. PubDate: 2018-05-09 DOI: 10.1007/s00574-018-0088-6

Authors:Tomonori Fukunaga; Masatomo Takahashi Abstract: A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities. We treat smooth surfaces with singular points, that is, singular surfaces more directly. By using the moving frame, the basic invariants and curvatures of the framed surface are introduced. Then we show that the existence and uniqueness for the basic invariants of the framed surfaces. We give properties of framed surfaces and typical examples. Moreover, we construct framed surfaces as one-parameter families of Legendre curves along framed curves. We give a criteria for singularities of framed surfaces by using the curvature of Legendre curves and framed curves. PubDate: 2018-05-03 DOI: 10.1007/s00574-018-0090-z

Authors:Daniyal M. Israfilov; Elife Gursel; Esra Aydin Abstract: The maximal convergence properties of the partial sums of the Faber series in the variable exponent Smirnov classes are investigated. PubDate: 2018-05-02 DOI: 10.1007/s00574-018-0086-8

Authors:Ahmed Mostafa Khalil; Sheng-Gang Li; Fei You; Sheng-Quan Ma Abstract: In this paper, we present and study the concepts of fuzzifying pre- \(\theta \) -neighborhood system of a point, fuzzifying pre- \(\theta \) -closure of a set, fuzzifying pre- \(\theta \) -interior of a set, fuzzifying pre- \(\theta \) -open sets and fuzzifying pre- \(\theta \) -closed sets in fuzzifying topological spaces. The basic properties of these concepts are investigated. Two types of functions in a fuzzifying topological spaces called fuzzifying strongly pre-irresolute and fuzzifying weakly pre-irresolute functions are introduced. Then the interrelations of these functions with the parallel existing allied concepts are established. Finally, several characterizations of these functions along with different conditions for their existence are obtained. PubDate: 2018-04-28 DOI: 10.1007/s00574-018-0089-5

Authors:Sorina Barza; Anca N. Marcoci; Liviu G. Marcoci Abstract: We present factorizations of weighted Lebesgue, Cesàro and Copson spaces, for weights satisfying the conditions which assure the boundedness of the Hardy’s integral operator between weighted Lebesgue spaces. Our results enhance, among other, the best known forms of weighted Hardy inequalities. PubDate: 2018-04-28 DOI: 10.1007/s00574-018-0087-7

Authors:Jihua Yang Abstract: The sixteen generators of Abelian integral \(I(h)=\oint _{\Gamma _h}g(x,y)dx-f(x,y)dy\) , which satisfy eight different Picard–Fuchs equations respectively, are obtained, where \(\Gamma _h\) is a family of closed orbits defined by \(H(x,y)=ax^4+by^4+cx^8=h\) , \(h\in \Sigma \) , \(\Sigma \) is the open intervals on which \(\Gamma _h\) is defined, and f(x, y) and g(x, y) are real polynomials in x and y of degree n. Moreover, an upper bound of the number of zeros of I(h) is obtained for a special case $$\begin{aligned} f(x,y)=\sum \limits _{0\le i\le 4k+1=n}a_ix^{4k+1-i}y^i,\ \ \ g(x,y)=\sum \limits _{0\le i\le 4k+1=n}b_ix^{4k+1-i}y^i. \end{aligned}$$ PubDate: 2018-04-23 DOI: 10.1007/s00574-018-0085-9

Authors:M. A. Bronzi; J. G. Oler Abstract: Let \(L:[0,1]{\setminus }\{d\}\rightarrow [0,1]\) be a one-dimensional Lorenz-like expanding map (d is the point of discontinuity), \(\mathcal {P}=\{ (0,d),(d,1) \}\) and \(C^{\alpha }([0,1],{\mathcal {P}})\) the set of piecewise Hölder-continuous potentials of [0, 1] with the usual \(\mathcal {C}^0\) topology. In this context, applying a criteria by Buzzi and Sarig (Ergod Theory Dyn Syst 23(5):1383–1400, 2003, Th. 1.3), we prove that there exists an open and dense subset \(\mathcal {H}\) of \(C^{\alpha }([0,1],{\mathcal {P}})\) , such that each \(\phi \in \mathcal {H}\) admits exactly one equilibrium state. PubDate: 2018-04-06 DOI: 10.1007/s00574-018-0084-x

Authors:Besma Amri Abstract: We define wavelets and wavelet transforms associated with spherical mean operator. We establish a Plancherel theorem, orthogonality property and inversion formula for the wavelet transform. Next, we define the Toeplitz operators \(\mathfrak {T}_{\varphi ,\psi }(\sigma )\) associated with two wavelets \(\varphi ,\psi \) and with symbol \(\sigma .\) We establish the boundedness and compactness of these operators. Last, we define the Schatten-von Neumann class \(S^p\ ;\ p\in \ [1,+\infty ],\) and we show that the Toeplitz operators belong to the class \(S^p\) and we prove a formula of trace. PubDate: 2018-03-23 DOI: 10.1007/s00574-018-0083-y

Authors:J. P. O. Santos; M. L. Matte Abstract: In this work we define a new set of integer partition, based on a lattice path in \({\mathbb {Z}}^2\) connecting the line \(x+y=n\) to the origin, which is determined by the two-line matrix representation given for different sets of partitions of n. The new partitions have only distinct odd parts with some particular restrictions. This process of getting new partitions, which has been called the Path Procedure, is applied to unrestricted partitions, partitions counted by the 1st and 2nd Rogers–Ramanujan Identities, and those generated by the Mock Theta Function \(T_1^*(q)=\sum _{n=0}^{\infty }\dfrac{q^{n(n+1)}(-q^2,q^2)_n}{(q,q^2)_{n+1}}\) . PubDate: 2018-03-16 DOI: 10.1007/s00574-018-0082-z

Authors:A. Hefez; J. H. O. Rodrigues; R. Salomão Abstract: The Milnor number of an isolated hypersurface singularity, defined as the codimension \(\mu (f)\) of the ideal generated by the partial derivatives of a power series f that represents locally the hypersurface, is an important topological invariant of the singularity over the complex numbers. However it may loose its significance when the base field is arbitrary. It turns out that if the ground field is of positive characteristic, this number depends upon the equation f representing the hypersurface, hence it is not an invariant of the hypersurface. For a plane branch represented by an irreducible convergent power series f in two indeterminates over the complex numbers, it was shown by Milnor that \(\mu (f)\) always coincides with the conductor c(f) of the semigroup of values S(f) of the branch. This is not true anymore if the characteristic of the ground field is positive. In this paper we show that, over algebraically closed fields of arbitrary characteristic, this is true, provided that the semigroup S(f) is tame, that is, the characteristic of the field does not divide any of its minimal generators. PubDate: 2018-03-14 DOI: 10.1007/s00574-018-0080-1

Authors:Katsuei Kenmotsu Abstract: The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: when the curvature of the ambient space is positive, there exists a unique such surface up to rigid motions of the target space. On the other hand, when the curvature of the ambient space is negative, there are ‘non-trivial’ complete parallel mean curvature surfaces generated by Jacobi elliptic functions and they exhaust such surfaces. PubDate: 2018-03-13 DOI: 10.1007/s00574-018-0081-0

Authors:Jenő Szirmai Abstract: In this paper we study the interior angle sums of geodesic triangles in \(\mathbf {Nil}\) geometry and prove that these can be larger, equal or less than \(\pi \) . We use for the computations the projective model of \(\mathbf {Nil}\) introduced by Molnár (Beitr. Algebra Geom. 38(2):261–288, 1997). PubDate: 2018-03-03 DOI: 10.1007/s00574-018-0077-9

Authors:Grzegorz Oleksik; Adam Różycki Abstract: Let f be a real polynomial, non-negative at infinity with non-compact zero-set. Suppose that f is non-degenerate in the Kushnirenko sense at infinity. In this paper we give a formula for the Łojasiewicz exponent at infinity of f and a formula for the exponent of growth of f in terms of its Newton polyhedron. PubDate: 2018-03-02 DOI: 10.1007/s00574-018-0078-8