Revista de la
Unión Matemática Argentina

Volumen 55, número 1 (2014)

Published online: June 23, 2014
A new family of parametric isoperimetric inequalities. Xiang Gao, Jin-Mu Song, and Hai-Yong Li
In this paper, we deal with isoperimetric-type inequalities for the closed convex curve in the Euclidean plane $\mathbb{R}^2$. In fact we establish a family of parametric inequalities involving some geometric functionals associated to the given closed convex curve with a simple Fourier series proof. Furthermore, we investigate some stability properties of such inequalities.
Posinormal factorable matrices with a constant main diagonal. H. C. Rhaly Jr. and B. E. Rhoades
Sufficient conditions are found for a posinormal factorable matrix with a constant main diagonal to be hyponormal. Those conditions are satisfied by some Toeplitz matrices, and a non-Toeplitz example is also presented. Along the way, a more general result is also obtained.
Vector valued T(1) Theorem and Littlewood-Paley theory on spaces of homogeneous type. Pablo Sebastián Viola
Singular integral operators associated to kernels valued on Hilbert spaces are studied in the setting of spaces of homogeneous type. By following the work of David and Journé (Ann. of Math. (2) 120 (1984), no. 2, 371-397), a T1-Theorem is obtained in this context. This result is applied to prove a Littlewood-Paley estimate.
A geometric inequality for warped product semi-slant submanifolds of nearly cosymplectic manifolds. Siraj Uddin, Abdulqader Mustafa, Bernardine Renaldo Wong, and Cenap Ozel
Recently, we have shown that there do not exist warped product semi-slant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55-65]. The nearly cosymplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian setting. It is interesting that the warped product semi-slant submanifolds exist in the nearly cosymplectic case while in the cosymplectic case they do not. In the beginning, we prove some preparatory results and finally we obtain an inequality such as $\|h\|^2 \geq 4q\csc^2\theta\{1+\frac{1}{9}\cos^2\theta\}\|\nabla \ln f\|^2$ in terms of intrinsic and extrinsic invariants. The equality case is also considered.
Laplace transform using the Henstock-Kurzweil integral. Salvador Sánchez-Perales and Jesús F. Tenorio
We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.
The Brauer-Picard group of the representation category of finite supergroup algebras. Martín Mombelli
We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173-192), to study bimodule categories over the representation categories of arbitrary finite-dimensional Hopf algebras. We compute the Brauer-Picard group of equivalence classes of exact invertible bimodule categories over the representation categories of a certain large family of pointed non-semisimple Hopf algebras, the so called supergroup algebras (N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49 (2001), 277-298). To obtain this result we first give a classification of equivalence classes of exact indecomposable bimodule categories over such Hopf algebras.
A classification of solvable quadratic and odd quadratic Lie superalgebras in low dimensions. Minh Thanh Duong
We give an expansion of two notions of double extension and $T^*$-extension for quadratic and odd quadratic Lie superalgebras. Also, we provide a classification of quadratic and odd quadratic Lie superalgebras up to dimension 6. This classification is considered up to isometric isomorphism, mainly in the solvable case, and the obtained Lie superalgebras are indecomposable.
Projective spaces in the algebraic sets of planar normal sections of homogeneous isoparametric submanifolds. Ana M. Giunta and Cristián U. Sánchez
The present paper is devoted to studying the algebraic sets of planar normal sections of homogeneous isoparametric submanifolds. The main objective is to describe the presence of real projective spaces in these algebraic sets. This indicates an important connection between homogeneous isoparametric submanifolds and the family of symmetric spaces of the corresponding group.

Volumen 55, número 2 (2014)

Published online: December 3, 2014
Accurate approximation of a generalized Mathieu series. Vito Lampret
New, accurate lower and upper bounds for the sum of the generalized Mathieu series \[ \sum\limits_{k=1}^{\infty}\frac{2k}{\left( k^2 + x^2\right)^{p+1}},\quad p > 0, \] are obtained.
Hopf-Galois objects and cogroupoids. Julien Bichon
We survey some aspects of the theory of Hopf-Galois objects that may be studied advantageously by using the language of cogroupoids. These are the notes for a series of lectures given at Universidad Nacional de Córdoba, May 2010. The lectures are part of the course “Hopf-Galois theory” by Sonia Natale.
Semi-convergence of the generalized local HSS method for singular saddle point problems. Shu-Xin Miao and Yang Cao
Recently, Zhu [Appl. Math. Comput., 218 (2012), 8816-8824] considered the generalized local HSS (GLHSS) method for solving nonsingular saddle point problems and studied its convergence. In this paper, we prove the semi-convergence of the GLHSS method when it is applied to solve the singular saddle point problems.
On slant curves in trans-Sasakian manifolds. Şaban Güvenç and Cihan Özgür
We find the characterizations of the curvatures of slant curves in trans-Sasakian manifolds with $C$-parallel and $C$-proper mean curvature vector field in the tangent and normal bundles.
On minimal non-$\mathscr{B}$-groups. Huaguo Shi and Zhangjia Han
A finite group $G$ is called a $\mathscr{B}$-group if every proper subgroup of $G$ is either normal or abnormal in $G$. In this paper the authors classify the non-$\mathscr{B}$-groups whose proper subgroups are all $\mathscr{B}$-groups.
Planar normal sections on isoparametric hypersurfaces and the infinity Laplacian. Julio C. Barros and Cristián U. Sánchez
We present a new characterization of Cartan isoparametric hypersurfaces in terms of properties of the polynomial that determines the algebraic set of planar normal sections on the homogeneous isoparametric hypersurfaces in spheres. We show that Cartan isoparametric hypersurfaces are the only homogeneous isoparametric hypersurfaces in spheres for which the infinity Laplacian of the polynomial that defines the algebraic set of planar normal sections is the polynomial multiplied by the squared norm of the tangent vector. Since it is required for our work, we also give these polynomials for all homogeneous isoparametric hypersurfaces in spheres.
On the rate of convergence for modified gamma operators. Grażyna Krech
We give direct approximation theorems for some linear operators in certain weighted spaces. The results are given in terms of some Ditzian-Totik moduli of smoothness.