Serdica Mathematical Journal
Volume 45, Number 3, 2019
C O N T E N T S
·
Ali, E., A. Hassoon.
CI-property for cyclotomic S-rings over (ℤp)2×ℤq×ℤr
(pp. 189−196)
·
Urure, R. I. Q.
*-polynomial identities for the block upper triangular matrix algebra UT2(UT2(F)) with the transpose-like involution
(pp. 197−216)
·
Mittal, G.
On unit group of group algebra of Pauli's group over any finite field of odd characteristics
(pp. 217−224)
·
Kostov, V. P.
On the zero set of the partial theta function
(pp. 225−258)
·
Reyes, E. O. S., C. M. C. Riveros.
Weingarten hypersurfaces of the spherical type in space forms
(pp. 259−288)
A B S T R A C T S
CI-PROPERTY FOR CYCLOTOMIC S-RINGS OVER (ℤp)2×ℤq×ℤr
Eskander Ali,
Pr.Eskander.Ali@gmail.com,
Ahed Hassoon
Ahed100@gmail.com
2010 Mathematics Subject Classification:
05C25, 05C60.
Key words:
CI-groups, Schur ring, wreath product.
An S-ring 𝒜 over a group H is called cyclotomic if it is a transitive module of a group K≤ Aut(H). In this paper we prove that every cyclotomic S-ring over (ℤp)2×ℤq×ℤr is a CI-S-ring where p, q, r are pairwise different primes.
*-POLYNOMIAL IDENTITIES FOR THE BLOCK UPPER TRIANGULAR MATRIX ALGEBRA UT2(UT2(F)) WITH THE TRANSPOSE-LIKE INVOLUTION
Ronald Ismael Quispe Urure
urure6@dm.ufscar.br
2010 Mathematics Subject Classification:
16R10, 16R50, 16W10.
Key words:
upper triangular matrix algebra, transpose-like involution, identities with involution.
Let UT4(F) be 4 × 4 upper triangular matrix algebra over F a field of characteristic zero and let 𝒜 be the subalgebra of UT4(F) linearly generated by {eij : 1 ≤ i ≤ j ≤ 4 } \ e23, where eij, 1 ≤ i ≤ j ≤ 4 is the standard basis of UT4(F). We describe the set of all *-polynomial identities for 𝒜 with the transpose-like involution.
ON UNIT GROUP OF GROUP ALGEBRA OF PAULI'S GROUP OVER ANY FINITE FIELD OF ODD CHARACTERISTICS
Gaurav Mittal
gmittal@ma.iitr.ac.in
2010 Mathematics Subject Classification:
16U60, 20C05.
Key words:
unit group, finite field, Wedderburn decomposition.
In this article, we characterize the unit group of the group algebra 𝔽qG where 𝔽q is a finite field with q = pk elements for prime p > 2 and G is the Pauli group of order 16.
ON THE ZERO SET OF THE PARTIAL THETA FUNCTION
Vladimir Petrov Kostov
vladimir.kostov@unice.fr
2010 Mathematics Subject Classification:
26A06.
Key words:
partial theta function, Jacobi theta function,
Jacobi triple product.
We consider the partial theta function
θ(q,x) := ∑j=0∞ qj(j+1)/2xj, where
q ∈ (−1, 0) ∪ (0, 1) and either x ∈ ℝ or x ∈ ℂ. We prove that for x ∈ ℝ, in each of the
two cases q ∈ (−1, 0) and q ∈ (0, 1), its zero set consists of countably-many smooth curves in the (q,x)-plane each of which
(with the exception of one curve for q ∈ (−1, 0)) has a single point with a tangent line parallel to the x-axis. These points define double zeros of the function θ(q, ⋅); their x-coordinates belong to the interval [−38.83...,−e1.4 = 4.05...) for q ∈ (0, 1) and to the interval (−13.29, 23.65) for q ∈ (−1, 0). For q ∈ (0, 1), infinitely-many of the complex conjugate pairs of zeros to which the double zeros give rise cross the imaginary axis and then remain in the half-disk {|x| < 18, Re x > 0}. For q ∈ (−1, 0), complex conjugate pairs do not cross the imaginary axis.
WEINGARTEN HYPERSURFACES OF THE SPHERICAL TYPE IN SPACE FORMS
Edwin O. S. Reyes
edwin.reyes@ufob.edu.br,
Carlos M. C. Riveros
carlos@mat.unb.br
2010 Mathematics Subject Classification:
53C42, 53A35.
Key words:
Ribaucour transformations, lines of curvature, Rotation spherical hypersurface, Weingarten hypersurfaces.
In this paper, we generalize the parametrization obtained by Machado in [13] (Hipersuperfícies Weingarten de tipo esférico. Thesis,
Universidade de Brasíla, 2018) in the n-dimensional Euclidean space for hypersurfaces Σ in space forms M̅n+1(c), c = 0, ± 1. Using this parametrization we study the class of Weingarten hypersurfaces of the spherical type in M̅n+1(c), n ≥ 2, this class of hypersurfaces includes the surfaces of the spherical type (Laguerre minimal surfaces).
We generalize the results and definitions of Weingarten hypersurfaces of the spherical type and we classify the Weingarten hypersurfaces of the spherical type of rotation in forms space.
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