Studying the interaction of 10-keV electrons with a dielectric surface

The grazing incidence interaction of a 10-keV electron beam with a planar surface of plexiglass is studied experimentally. Moreover, the electron passage through flat channels formed by such surfaces is investigated. The experiments reveal the presence of a guiding effect of the electron passage as in the case of a glass surface. However, there are some features, such as the existence of an initial elevation angle for the case of negative inclination angles of the plate. The formation of self-consistent charge on the surface of the plexiglass and its drain when the current is turned off occur more slowly than on the glass surface. This fact points to the difference in the surface conductivity of insulators.     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.     

Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control

Using the direct scheme method, we construct an asymptotic expansion for the solution of a singularly perturbed optimal problem in critical case with cheap control and two fixed end-points. The asymptotic solution contains the outer series and two boundary-layer series in the vicinities of the two end-points. The error estimates for state and control variables and the functional are obtained. It is shown that the value of minimized functional does not increase when a higher-order approximation to the optimal control is used. An illustrative example is given.     

On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f ^nm (z)f ^nd (qz + c))^(k) for meromorphic functions in a non-Archimedean field.     

Density functional theory study on sensing properties of g-C3N4 sheet to atmospheric gasses: Role of zigzag and armchair edges

The ability of the polymer-based graphitic carbon nitride (g-C₃N₄) as a gas sensor toward NO, NO₂, CO, CO₂, SO₂, SO₃, and O₂ gasses is assessed using density functional theory (DFT) calculations in terms of energetic and electronic transport characteristics. In particular, this study is aimed to explore the role of zigzag and armchair edges of the g-C₃N₄ sheet on sensing performances. The electronic properties of adsorption systems, such as Bader charge analysis, band gaps, work function, and density of states (DOS), are used to understand the interaction between the adsorbed gas molecules and the g-C₃N₄ sheet. Our calculated results indicate that SOx (SO₃ and SO₂) gasses have higher adsorption energies on the g-C₃N₄ sheet than other gasses. Furthermore, the transport properties, such as current–voltage (I-V) and resistance-voltage (R-V) curves along the zigzag and armchair directions are calculated using the non-equilibrium Green's function (NEGF) method to understand the performance of the g-C₃N₄ sheet as a prominent conductive/resistive sensor. The I-V/R-V results indicate that the zigzag g-C₃N₄ sheet has excellent sensing ability toward SOx gasses at low applied voltages. However, the presence of H₂O degrades the sensing performance of the armchair g-C₃N₄ sheet. Theoretical recovery time has also been calculated to evaluate the reusability of g-C₃N₄ sheet-based gas sensors. Our results reveal that the zigzag g-C₃N₄ sheet-based sensing device has a remarkably high sensitivity (>300%) and selectivity toward SOx gasses and has the potential to work in a complex environment.     

The challenge in managing new financial risks: adopting an heuristic or theoretical approach

The financial crisis began with the collapse of Lehman Brothers and the subprime asset backed securities debacle. Credit risk was turned into liquidity risk, resulting in a lack of confidence among financial institutions. In this article, we will propose a way to model liquidity risk and the credit risk in best practices. We will show that liquidity risk is a new type of risk and the current way to deal with it is based solely on observed variables without any theoretical link. We propose an heuristic approach to combine the numerous liquidity risk indicators with a logistic regression for the first time. In regards to credit risk, several articles prove that the best practice is to use an option model to appreciate this risk. We will present our methodology using stochastic diffusion for the interest rate because currently the yield curves aren’t liquid. This approach is more relevant because the basis model in prior publications has a constant interest rate or a forward rate. Both models allow a better understanding of liquidity and credit risks and the further development of research deals with the link between these two financial risks.     

Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches

In this paper, we consider a task allocation model that consists of assigning a set of m unmanned aerial vehicles (UAVs) to a set of n tasks in an optimal way. The optimality is quantified by target scores. The mission is to maximize the target score while satisfying capacity constraints of both the UAVs and the tasks. This problem is known to be NP-hard. Existing algorithms are not suitable for the large scale setting. Scalability and robustness are recognized as two main issues. We deal with these issues by two optimization approaches. The first approach is the Cross-Entropy (CE) method, a generic and practical tool of stochastic optimization for solving NP-hard problem. The second one is Branch and Bound algorithm, an efficient classical tool of global deterministic optimization. The numerical results show the efficiency of our approaches, in particular the CE method for very large scale setting.     

Perfect impedance-matched left-handed behavior in combined metamaterial

Matching the impedance of a medium to free space, which is usually not available in natural materials, is an important advance in metamaterials. In this paper, we present a simple mechanism for a perfect impedance-matched left-handed metamaterials, that reveals a nearly zero reflection over operating frequency. This finding is based on the independent manipulation of the electric response without any effect on the magnetic one.