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19521968 Revista de la Unión Matemática Argentina y de la Asociación Física Argentina
19441951 Revista de la Unión Matemática Argentina; órgano de la Asociación Física Argentina
19361944

Volumen 55, número 1 (2014)
Published online: June 23, 2014
A new family of parametric isoperimetric inequalities.
Xiang Gao, JinMu Song, and HaiYong Li
PDF
In this paper, we deal with isoperimetrictype 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.

118 
Posinormal factorable matrices with a constant main diagonal.
H. C. Rhaly Jr. and B. E. Rhoades
PDF
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 nonToeplitz example is also
presented. Along the way, a more general result is also obtained.

1924 
Vector valued T(1) Theorem and LittlewoodPaley
theory on spaces of homogeneous type.
Pablo Sebastián Viola
PDF
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,
371397), a T1Theorem is obtained in this context. This result is
applied to prove a LittlewoodPaley estimate.

2553 
A geometric inequality for warped product semislant
submanifolds of nearly cosymplectic manifolds.
Siraj Uddin, Abdulqader Mustafa, Bernardine Renaldo Wong, and Cenap Ozel
PDF
Recently, we have shown that there do not exist warped product semislant
submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj
Uddin, Balkan J. Geom. Appl. 13 (2008), 5565].
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 semislant 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.

5569 
Laplace transform using the HenstockKurzweil integral.
Salvador SánchezPerales and Jesús F. Tenorio
PDF
We consider the Laplace transform as a
HenstockKurzweil integral. We give conditions for the existence,
continuity and differentiability of the Laplace transform. A
RiemannLebesgue Lemma is given, and it is proved that the Laplace
transform of a convolution is the pointwise product of Laplace
transforms.

7181 
The BrauerPicard group of the representation category of finite supergroup algebras.
Martín Mombelli
PDF
We develop further the techniques presented in a previous
article
(M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173192),
to study bimodule categories over the representation categories of
arbitrary finitedimensional Hopf algebras. We compute the
BrauerPicard group of equivalence classes of exact invertible bimodule
categories over the representation categories of a certain large family of
pointed nonsemisimple Hopf algebras, the so called supergroup
algebras
(N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49
(2001), 277298).
To obtain this result we first give a classification of equivalence classes
of exact indecomposable bimodule categories over such Hopf algebras.

83117 
A classification of solvable quadratic and odd
quadratic Lie superalgebras in low dimensions.
Minh Thanh Duong
PDF
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.

119138 
Projective spaces in the algebraic sets of planar normal sections of
homogeneous isoparametric submanifolds.
Ana M. Giunta and Cristián U. Sánchez
PDF
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.

139154 
Volumen 55, número 2 (2014)
Published online: December 3, 2014
Accurate approximation of a generalized Mathieu series.
Vito Lampret
PDF
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.

110 
HopfGalois objects and cogroupoids.
Julien Bichon
PDF
We survey some aspects of the theory of HopfGalois 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 “HopfGalois theory” by Sonia Natale.

1169 
Semiconvergence of the generalized
local HSS method for singular saddle point problems.
ShuXin Miao and Yang Cao
PDF
Recently, Zhu [Appl. Math. Comput., 218 (2012),
88168824] considered the generalized local HSS (GLHSS) method for
solving nonsingular saddle point problems and studied its convergence. In
this paper, we prove the semiconvergence of the GLHSS method when it is
applied to solve the singular saddle point problems.

7180 
On slant curves in transSasakian manifolds.
Şaban Güvenç and Cihan Özgür
PDF
We find the characterizations of the curvatures of slant
curves in transSasakian manifolds with $C$parallel and $C$proper mean
curvature vector field in the tangent and normal bundles.

81100 
On minimal non$\mathscr{B}$groups.
Huaguo Shi and Zhangjia Han
PDF
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.

101106 
Planar normal sections on isoparametric hypersurfaces and the
infinity Laplacian.
Julio C. Barros and Cristián U. Sánchez
PDF
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.

107121 
On the rate of convergence for modified gamma operators.
Grażyna Krech
PDF
We give direct approximation theorems for some linear operators
in certain weighted spaces. The results are given in terms of some DitzianTotik
moduli of smoothness.

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