# Volume 6 (2014), Number 1

## A Differential Sandwich-type Result Using an Extended Generalized Sălăgean Operator and Extended Ruscheweyh Operator

### Author(s): LORIANA ANDREI

**Abstract:** The purpose of this paper is to introduce sufficient conditions
for strong differential subordination and superordination involving the extended
derivative operator $D{R}_{\lambda}^{m,n}$ and also to obtain
sandwich-type result.

## Mathematical Models Regarding the Basic Informative Elements for the Classical Computers and the Quantum Computers Respectively

### Author(s): MALVINA BAICA and MIRCEA CARDU

**Abstract:** In this paper we use the results obtained in a previous paper [1]
regarding the pairs of the DUAL roots (+1 OR -1) and respectively BIPOLAR roots
(+1 AND -1) of a couple of equations “seen in the mirror”
(${y}^{2}\pm 1=0$) and with the help of a mathematical
artifice we arrive to the basic informative elements characteristic to the Classical Computers
(1 OR 0) and respectively to the Quantum Computers (1 AND 0). In this way we also prove that
the two categories of the basic informative elements have a joint origin in the couple of
the equations mentioned above.

## Starlikeness of Libera Operator on Certain Concave Univalent Functions

### Author(s): IBTISAM AL-DAWISH and MASLINA DARUS

**Abstract:** Let ${C}_{0}\left(\alpha \right)$ denote the class of concave
univalent functions deﬁned in the open unit disk
$\mathbb{D}$.
Each function $f\in {C}_{0}\left(\alpha \right)$ maps the unit disk
$\mathbb{D}$
onto the complement of an unbounded convex set. In this paper, we shall prove that
the Libera operator $F\left(z\right)=\frac{2}{z}{\int}_{0}^{z}f\left(t\right)dt$ is starlike
by ﬁnding certain conditions on $Re\phantom{\rule{0.3em}{0ex}}2{f}^{\prime}$.

## A New Approach to One-Dimensional Oscillators in Relativistic Quantum Mechanics

### Author(s): LAUREAN HOMORODEAN

**Abstract:** A new approach to the one-dimensional oscillatory motion of a
relativistic quantum particle with the spin $\frac{1}{2}$ is presented. It is based on a modiﬁed form of the Hamilton operator of
the particle. As particular cases, the one-dimensional Dirac oscillator and the
one-dimensional oscillator with equidistant energy levels are discussed. In this context,
the ﬁrst oscillator appears as an ancient representative, while the second oscillator
is a new representative of an entire class of relativistic quantum one-dimensional oscillators.

## On the Maximum Term and Lower Order of Entire Monogenic Functions

### Author(s): SUSHEEL KUMAR and G.S. SRIVASTAVA

**Abstract:** In the present paper, we study the growth properties of entire monogenic
functions. The characterizations of lower order of entire monogenic functions have been
obtained in terms of their Taylor’s series coeﬃcients. Also we have obtained some
inequalities between order, type, maximum term and central index of entire monogenic functions.

## A Note to Geometry of Cosserat Media and Deformation Bundles

### Author(s): MIROSLAV KUREŠ

**Abstract:** We study Cosserat media from the geometric point of view;
in particular, we present a construction of Cosserat deformation bundles and demonstrate
the role of the velocities bundles.

## On the Convergence of Modiﬁed Noor Iteration Method for Nearly Lipschitzian Mappings in Arbitrary Real Banach Spaces

### Author(s): ADESANMI ALAO MOGBADEMU

**Abstract:** In this present paper, we employed a modiﬁed Noor iteration method
introduced by Raﬁq [9]. Some strong convergence theorems of this iteration scheme are
established for three nearly uniformly Lipschitzian mappings if at least one of these
maps is uniformly Lipschitzian mapping. Our results extend and improve the recent ones
proved by Chang et al., Kim et al., Olaleru and Mogbademu, Ofoedu and many others.

## State Space Approach for Solving Transient Queuing Systems

### Author(s): T.S.L. RADHIKA and B.L.R. DEEPIKA

**Abstract:** In the present paper, we consider a transient queuing system and
ﬁnd its solution using the state space approach. For this, the given interval of study
[0,T] is sub divided into small sub intervals, where it is reasonable to assume that
the instantaneous arrival and service rates are constants. The system of equations
together with the initial conditions is solved for an analytical expression for
${P}_{n}$s’ in each interval. The solution
obtained at the right end point of the previous sub interval is taken as the initial
condition in the sub sequent interval. The developed method is illustrated for an
(M/M/1):(FCFS/m/∞) system.

## On the Natural ${q}^{2}$-analogue of the Generalized Gegenbauer Form

### Author(s): I. BEN SALAH and L. KHÉRIJI

**Abstract:** The aim of this paper is to highlight a
${q}^{2}$-analogue of the generalized Gegenbauer polynomials
orthogonal with respect to the form $\mathcal{\mathcal{G}}\left(\alpha ,\beta ,{q}^{2}\right)$. Integral representation and discrete measure of
$\mathcal{\mathcal{G}}\left(\alpha ,\beta ,{q}^{2}\right)$ are given for some
values of parameters.

## Positive Solutions for Second Order Impulsive Differential Equations with Integral Boundary Conditions on Time Scales

### Author(s): WENGUI YANG

**Abstract:** In this paper, a class of second order impulsive differential equations
with integral boundary conditions on time scales are considered. Under diﬀerent combinations
of superlineary and sublinearity of nonlinear term and the impulses, some existence,
multiplicity, and nonexistence criteria of positive solutions are established based on
Guo-Krasnosel’skii ﬁxed point theorem, which are new and complement previously
known results.