The main aim of this paper is to extend the results of Nguyen
Van Luong and Nguyen Xuan Thuan [4] on xed point theory. Incidently, we
observed some inconsistencies in their proof and example. We extended their
results and exhibited a supporting example.
The concept of -reflexive semigroups is due to Chacron and
Thierrin in 1972. In the present paper we discuss -reflexive semigroups with
apartness. We prove some fundamental properties of these semigroups.
In this paper using Simpson's quadrature formula for convex func-
tion, the inequality involving ratio of means for four positive arguments proved
by Rooin and Hassni (2007) is re ned.
Let G = (V;E) be a graph, D ⊆ V and u be any vertex in D.
Then the out degree of u with respect to D denoted by odD(u), is de ned as
odD(u) = |N(u) ∩ (V − D)|. A subset D ⊆ V (G) is called a near equitable
dominating set of G if for every v ∈ V − D there exists a vertex u ∈ D
such that u is adjacent to v and |odD(u) − odV
The average lower domination number
av(G) is defined as
1
jV (G)jΣv2V (G)
v(G)
where
v(G) is the minimum cardinality of a maximal dominating set that
contains v. In this paper, the average lower domination number of complete
k-ary tree and Bn tree are calculated. Moreover we obtain the
av(G) for
thorn graph G. Finally we compute the
av(G1 + G2) of G1 and G2
The rst Zagreb index M1 of a graph G is equal to the sum of
squares of the vertex degrees of G. In a recent work [Goubko, MATCH Com-
mun. Math. Comput. Chem. 71 (2014), 33{46], it was shown that for a tree
with n1 pendent vertices, the inequality M1 > 9 n1
We describe a family of posets with positive
ag h-vectors that do
not admit an R-labeling. This family contains the example of R. Ehrenborg
and M. Readdy presented in [4]. Furthermore, for a poset that has an R-
labeling, we consider the complex of all rising chains. We show that the
f-vector and homotopy type of this complex do not depend of a concrete
labeling.
1.
In this paper, we define the equitable associate signed graph E(Σ)
of a given signed graph Σ and offer a structural characterization of equitable
associate signed graphs. In the sequel, we also obtained switching equivalence
characterization: E(Σ) E(Σ), where E(Σ) are E(Σ) are complementary
equitable associate signed graph and equitable associate signed graph of complementary
signed graph of Σ respectively.
Let G = (V;E) be a simple graph. A subset S of V is called
an equitable vertex covering of G if for every equitable edge e = uv, either
u 2 S or v 2 S. The minimum cardinality of an equitable vertex cover of G
ia called the euitable covering number of G and is denoted by e
o(G).In this
paper results involving in this new parameter are found. Also we introduced
the Equitable Packing and Equitable Full sets.
In a former article, the rst author introduces and analyzes quasi-
conjugative relations. In this paper, following Jiang Guanghao and Xu Lu-
oshan's concepts of nitely conjugative and nitely dual normal relations on
sets, the concept of nitely quasi-conjugative relations is introduced. A char-
acterization of nitely quasi-conjugative relations is obtained. Particulary we
show when the anti-order relation
is nitely quasi-conjugative.
A steady three-dimensional Magnetohydrodynamic (MHD) boundary
layer viscous flow and heat transfer due to a permeable stretching sheet
with prescribed surface heat flux is studied in presence of a uniform applied
magnetic field transverse to the flow. Using the implicit finite-difference
scheme, known as the Keller-box method, the nonlinear ordinary differential
equations are solved. The velocity and temperature profiles, skin friction coefficient
and wall temperature are discussed for various parameters.
Inequalities involving two Seiffert means, logarithmic
mean, and the Neuman-S´andor mean are established. Those results
are utilized to obtain four inequalities which have structure
of the Wilker and Huygens inequalities for the trigonometric and
hyperbolic functions.
The energy of a digraph D with eigenvalues z1; z2; : : : ; zn is defined
as E(D) =
nΣ
j=1
|ℜzj |, where ℜzj is the real part of the complex number
zj . In this paper, we characterize some positive reals that cannot be the
energy of a digraph. We also obtain a sharp lower bound for the energy of
strongly connected digraphs.
The concept of complementary tree vertex edge dominating set
(ctved-set) of a nite, connected graph G is introduced and characterization
result for a non empty proper subset of the vertex set V of G to be a ctved-set
is obtained. The minimum cardinality of a ctved-set is denoted by
ctve(G)
and is called as ctved number of G. Bounds for this parameter as well, are
obtained. Further, the graphs of order n for which the ctved numbers are
1; 2; n
In this paper, we are concerned with the existence of at least two
symmetric positive solutions for the even order boundary value problems on
time scales satisfying Sturm-Liouville two-point boundary conditions by using
Avery–Henderson fixed point theorem. We also establish the existence of at
least 2m symmetric positive solutions to the boundary value problem for an
arbitrary positive integer m
In 1998, V.R.Kulli and B.Janakiram posed three problems in
Graph Theory Notes of New York, XXXIV. Among the three, solution to one
problem is published in Graph Theory Notes of New York LIII, 37-38(2007).
In this paper the remaining two problems are solved.
Laplace decomposition method is based on Laplace transform
method and Adomian decomposition method. In this paper we show that
the method is applicable to certain successive interval valued linear as well as
nonlinear differential-difference equations of order (1, 2), that means the differential
is of order one and the difference is of order two. It is also shown that
the method gives exact solution for linear problems and suitable approximate
solution for nonlinear problems. Three problems are selected to illustrate the
applicability of the method.
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