274 research outputs found
Infinite Log-Concavity and r-Factor
D. Uminsky and K. Yeats [6] studied the properties of the log- operator L on
the subset of the finite symmetric sequences and prove the existence of an
infinite region R, bounded by parametrically de- fined hypersurfaces such that
any sequence corresponding a point of R is infinitely log concave. We study the
properties of a new operator L_r and redefine the hypersurfaces which
generalizes the one defined by Uminsky and Yeats [6]. We show that any sequence
corresponding a point of the region R, bounded by the new generalized
parametrically defined r-factor hypersurfaces, is Generalized r-factor
infinitely log concave. We also give an improved value of r_0 found by McNamara
and Sagan [4] as the log-concavity criterion using the new log-operator
-constacyclic codes over
Let be a finite field and be an indeterminate. This
article studies -constacyclic codes over the ring
where . We illustrate the generator polynomials and investigate the
structural properties of these codes via decomposition theorem
Gravitational Dust Collapse in Gravity
This paper is devoted to investigate gravitational collapse of dust in metric
gravity. We take FRW metric for the interior region while the
Schwarzchild spacetime is considered for the exterior region of a star. The
junction conditions have been derived to match interior and exterior
spacetimes. The assumption of constant scalar curvature is used to find a
solution of field equations. Gravitational mass is found by using the junction
conditions. It is concluded that the constant curvature term plays the
role of the cosmological constant involved in the field equations of general
relativity.Comment: 17 Page
Admissible local systems for a class of line arrangements
A rank one local system \LL on a smooth complex algebraic variety is
admissible roughly speaking if the dimension of the cohomology groups
H^m(M,\LL) can be computed directly from the cohomology algebra H^*(M,\C).
We say that a line arrangement \A is of type \CC_k if is the
minimal number of lines in \A containing all the points of multiplicity at
least 3. We show that if \A is a line arrangement in the classes \CC_k for
, then any rank one local system \LL on the line arrangement
complement is admissible. Partial results are obtained for the class
\CC_3.Comment: 9 pages, 2figure
On the Structure of Involutions and Symmetric Spaces of Quasi Dihedral Group
Let be the quasi-dihedral group of order and be an
automorphism of of finite order. The fixed-point set of
is defined as and
generalized symmetric space of given by Q_{\theta}=\{g\in G \mid
g=x\theta(x)^{-1}~\mbox{for some}~x\in G\}.
The characteristics of the sets and have been calculated. It is shown
that for any and the -orbits on are obtained
under different conditions. Moreover, the formula to find the order of -th
root of unity in for has been calculated. The
criteria to find the number of equivalence classes denoted by of the
involution automorphism has also been constructed. Finally, the set of twisted
involutions has been explored.Comment: major revisio
Solution of Certain Pell Equations
Let be any positive integers such that and is a
square free positive integer of the form where
and The main focus of this paper to find the fundamental
solution of the equation with the help of the continued
fraction of We also obtain all the positive solutions of the
equations and by means of the
Fibonacci and Lucas sequences.
Furthermore, in this work, we derive some algebraic relations on the Pell
form including cycle, proper cycle,
reduction and proper automorphism of it. We also determine the integer
solutions of the Pell equation in terms of
$d_i^\pm.
We generalized all the results of the papers [2], [9], [26], and [37].Comment: 16 page
Cylindrically Symmetric Solutions in Gravity
The main purpose of this paper is to investigate the exact solutions of
cylindrically symmetric spacetime in the context of gravity [1], where
is an arbitrary function of Ricci scalar and trace of the energy
momentum tensor . We explore the exact solutions for two different classes
of models. The first class yields a solution which
corresponds to an exterior metric of cosmic string while the second class
provides an additional solution representing a non-null
electromagnetic field. The energy densities and corresponding functions for
models are evaluated in each case.Comment: 18 Pages. arXiv admin note: text overlap with arXiv:1506.0869
Algebraic characterization of the SSC
In this paper, we characterize the set of spanning trees of
(a simple connected graph consisting of edges,
containing exactly one -edge-connected chain of cycles
and is a forest). We compute the
Hilbert series of the face ring for the
spanning simplicial complex . Also, we
characterize associated primes of the facet ideal . Furthermore, we prove that the face ring
is Cohen-Macaulay.Comment: 12 page
Counting Of Binary Matrices Avoiding Some 2 Γ 2 Matrices
The number of matrices avoiding certain types of matrices is NP-hard in general. In this paper the binary matrices are considered. In particular, the problem of finding the total number of special binary matrices avoiding some types of 2 Γ 2 matrices is the main objective of this paper. The solution of the problem is given under some constraints as well as under general situation. The formula for the special binary matrices is obtained for total count of matrices of order n Γ k and also obtained the formula for special binary matrices avoiding some matrices of order 2 Γ 2. The formula is obtained in terms of the Catalan numbers
On Algebraic Characterization of SSC of the Jahangir's Graph
In this paper, some algebraic and combinatorial characterizations of the
spanning simplicial complex of the Jahangir's
graph are explored. We show that
is pure, present the formula for -vectors
associated to it and hence deduce a recipe for computing the Hilbert series of
the Face ring . Finaly, we show that the face
ring of is Cohen-Macaulay and give some open
scopes of the current work.Comment: arXiv admin note: text overlap with arXiv:1509.0430
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