Approximate Controllability of Fractional Semilinear Stochastic System of Order <Emphasis Type="Italic">α</Emphasis>∈ (1,2]

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L _p spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.     

Approximate Controllability of Impulsive Neutral Stochastic Differential Equations Driven by Poisson Jumps

This work studies the approximate controllability of a class of impulsive neutral stochastic differential equations with infinite delay and Poisson jumps involving generalized Caputo fractional derivative under the condition that the corresponding linear system is approximately controllable. Utilizing the fixed point theory and sectorial operator theory, the existence of the mild solution of the impulsive neutral stochastic equation is established imposing weaker regularity on nonlinear terms. A set of sufficient conditions establishing controllability results is derived with the help of stochastic analysis and fractional calculus. Finally, an example is provided to illustrate the obtained abstract result.     

Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, α-norm, fractional calculus, and Krasnoselskii’s fixed point theorem. An example is provided to illustrate the applicability of the main results.     

Hierarchical Control for the One-dimensional Plate Equation with a Moving Boundary

In this paper, we investigate the controllability for the one-dimensional plate equation in intervals with a moving boundary. This equation models the vertical displacement of a point x at time t in a bar with uniform cross section. We assume the ends of the bar with small and uniform variations. More precisely, we have introduced functions α(t) and β(t) modeling the motion of these ends. We present the following results: the existence and uniqueness of Nash equilibrium, the approximate controllability with respect to the leader control, and the optimality system for the leader control.     

Adjoint Orbits of <Emphasis Type="Italic">sl</Emphasis>(2, ℝ) on Real Simple Lie Algebras and Controllability

This paper shows that for any Lie group G whose Lie algebra L is the split real form of a complex simple Lie algebra, and for any arbitrary root α, there exists a Cartan decomposition of L, related to α, which characterizes some controllability properties by using the adjoint orbits of sl(2, ?). For a class of invariant control systems evolving on G, it is proved that the necessary full rank condition for controllability is also sufficient.     

Attractor for the nonlinear Schr?dinger equation with a nonlocal nonlinear term

In this paper, we consider the long-time behavior of solutions of the dissipative 1D nonlinear Schrödinger (NLS) equation with nonlocal integral term and with periodic boundary conditions. We prove the existence of the global attractor \( \mathcal{A} \) for the nonlocal equation in the strong topology of H ¹(Ω). We also prove that the global attractor is regular, i.e., \( \mathcal{A} \subset {H^2}\left( \Omega \right) \), assuming that f(x) is of class C ². Furthermore, we estimate the number of the determining modes for this equation.     

When a Minimal Map Is Totally Transitive on a <Emphasis Type="Italic">G</Emphasis>-Space

In this paper, we introduce the notion of G-regular periodic decomposition (GRPD) for maps on G-spaces and investigate its relation with G-transitivity. It is shown that if a pseudoequivariant, G-transitive map on a G-space has a GRPD of some length n, then its nth iterate is not G-transitive. On the other hand, if a pseudoequivariant, G-transitive map on a G-space has a non-G-transitive nth iterate, then it admits a GRPD of length p for some prime p dividing n. Using the notion of GRPD, it is obtained that a pseudoequivariant, G-minimal map is totally G-transitive on a connected G-space.     

Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.     

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number 40≤ Re ≤200 and various rotation rate θ_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method(FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow.The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases,the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution forθ_iθ_(crit), It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.     

General Expansiveness for Diffeomorphisms from the Robust and Generic Properties

Let f:M → M be a diffeomorphism on a closed smooth d(d ≥ 2)-dimensional manifold. For each \(n\in \mathbb N\), if f belongs to C ¹-interior of the set of the n-expansive diffeomorphisms, then f satisfies quasi-Anosov. For C ¹-generic f, if f is n-expansive then f satisfies both Axiom A and the no-cycle condition.     

Distributionally <Emphasis Type="Italic">n</Emphasis>-Scrambled Set for Weighted Shift Operators

The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ? 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained.     

On High Dimensional Schrödinger Equation with Quasi-Periodic Potentials

In this paper, we consider the high dimensional Schrödinger equation \( -\frac {d^{2}y}{dt^{2}} + u(t)y= Ey, y\in \mathbb {R}^{n}, \) where u(t) is a real analytic quasi-periodic symmetric matrix, \(E= \text {diag}({\lambda _{1}^{2}}, \ldots , {\lambda _{n}^{2}})\) is a diagonal matrix with λ _j >0,j=1,…,n, being regarded as parameters, and prove that if the basic frequencies of u satisfy a Bruno-Rüssmann’s non-resonant condition, then for most of sufficiently large λ _j ,j=1,…,n, there exist n pairs of conjugate quasi-periodic solutions.     

Does oil price affect the value of firms? Evidence from Tunisian listed firms

A new debate on the potential impact of oil price changes on the value of firms was initiated in this paper. Using a stochastic frontier approach, an attempt was made to derive the optimal value Q* of firms and calculate the Q value observed. Then the shortfall (Q*–Q) which represents the inefficiency term was explained. Starting from 19 industrial Tunisian firms listed on the Tunis Stock Exchange between 2007 and 2011, the fact that variation of oil prices can largely explain distortions in the value of firms was empirically demonstrated.     

Influence of composition and heat treatment in CdCl<Subscript>2</Subscript> solution on intrinsic point defects in CdTe films

CdTe films of different compositions were grown by the chemical molecular-beam deposition method. The activation energy and the nature of deep levels in relation with the composition of films based on the temperature dependence of electroconductivity are defined, and the influence on these levels of heat treatment process in CdCl₂ solution has been studied. Deep levels with the following activation energies are defined: E_v +0.31 eV; E_v + 0.42 ± 0.03 eV; E_c–0.44 ± 0.01 eV; E_c–0.28 eV; E_v + 0.24 ± 0.01 eV.     

On Symmetries in Time Optimal Control,Sub-Riemannian Geometries,and the <Emphasis Type="Italic">K</Emphasis>−<Emphasis Type="Italic">P</Emphasis> Problem

The goal of this paper is to describe a method to solve a class of time optimal control problems which are equivalent to finding the sub-Riemannian minimizing geodesics on a manifold M. In particular, we assume that the manifold M is acted upon by a group G which is a symmetry group for the dynamics. The action of G on M is proper but not necessarily free. As a consequence, the orbit space M/G is not necessarily a manifold but it presents the more general structure of a stratified space. The main ingredients of the method are a reduction of the problem to the orbit space M/G and an analysis of the reachable sets on this space. We give general results relating the stratified structure of the orbit space, and its decomposition into orbit types, with the optimal synthesis. We consider in more detail the case of the so-called K?P problem where the manifold M is itself a Lie group and the group G is determined by a Cartan decomposition of M. In this case, the geodesics can be explicitly calculated and are analytic. As an illustration, we apply our method and results to the complete optimal synthesis on S O(3).     

Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

Gauss-Bonnet Theorem in Sub-Riemannian Heisenberg Space $\mathbb H^{1}$

We prove a version of the Gauss-Bonnet theorem in sub-Riemannian Heisenberg space \(\mathbb H^{1}\). The sub-Riemannian distance makes \(\mathbb H^{1}\) a metric space that consequently has a spherical Hausdorff measure. Using this measure, we define a Gaussian curvature at points of a surface S where the sub-Riemannian distribution is transverse to the tangent space of S. If all points of S have this property, we prove a Gauss-Bonnet formula and, for compact surfaces (which are topologically a torus), we obtain \({\int }_{S}K=0\).     

Semi-Analytical Simulation and Optimization of AlGaAs/GaAs <Emphasis Type="Italic">p-i-n</Emphasis> Quantum Well Solar Cell

This paper deals with a AlGaAs/GaAs p-i-n quantum well solar cell. The doped region are based on AlGaAs semiconductor while the intrinsic region “I” contain multi quantum well (MQW) system AlGaAs/GaAs. A semi-analytical model in the intrinsic region and numerical drift-diffusion model in doped regions are combined to extract the total current density of the cell versus voltage. The current-voltage (J-V) characteristics are generated for the AM1.5 solar spectrum. The effect of the Aluminum molar fraction x (Al_xGa_1–xAs), the number, the width, the depth of the wells and barriers in the “i” layer and the doping densities on the electrical outputs of the solar cell are also presented. The optimized solar cell reached a conversion efficiency of 28.72% with a short circuit current density of 36.9 mA/cm² and an open circuit voltage of 0.97 V.     

Analysis of turbulence and surface growth models on the estimation of soot level in ethylene non-premixed flames

Soot prediction in a combustion system has become a subject of attention, as many factors influence its accuracy. An accurate temperature prediction will likely yield better soot predictions, since the inception, growth and destruction of the soot are affected by the temperature. This paper reported the study on the influences of turbulence closure and surface growth models on the prediction of soot levels in turbulent flames. The results demonstrated that a substantial distinction was observed in terms of temperature predictions derived using the k-ε and the Reynolds stress models, for the two ethylene flames studied here amongst the four types of surface growth rate model investigated, the assumption of the soot surface growth rate proportional to the particle number density, but independent on the surface area of soot particles, f(A_s) = ρN_s, yields in closest agreement with the radial data. Without any adjustment to the constants in the surface growth term, other approaches where the surface growth directly proportional to the surface area and square root of surface area, f(A_s) = A_s and f(A_s) = √A_s, result in an under-prediction of soot volume fraction. These results suggest that predictions of soot volume fraction are sensitive to the modelling of surface growth.     

Harmonic Analysis of Finite Lamplighter Random Walks

Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular, in the case where the underlying graph is the infinite path \( \mathbb{Z} \). In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C ₂-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. If the graph has a transitive isometry group G, we also describe the spectral analysis in terms of the representation theory of the wreath product C ₂?G. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples have already been studied by Häggström and Jonasson by probabilistic methods.