Multi-variable Hermite matrix polynomials: Properties and applications

In this paper, the multi-variable Hermite matrix polynomials are introduced by algebraic decomposition of exponential operators. Their properties are established using operational methods. The matrix forms of the Chebyshev and truncated polynomials of two variable are also introduced, which are further used to derive certain operational representations and expansion formulae.     

Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur.     

On the Possible Automorphism Groups of a Steiner Quintuple System of Order 21

A Steiner system is called a Steiner quintuple systems of order v. The smallest order for which the existence, or otherwise, of a Steiner quintuple system is unknown is 21. In this article, we prove that, if an S(4, 5, 21) exists, the order of its full automorphism group is 1, 2, 3, 4, 5, 6, 7, or 10.     

Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups

In this paper, we propose a new general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the generalized mixed equilibrium problem and the set of all common fixed points of a finite family of nonexpansive semigroups. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality that is the optimality condition for the minimization problem. Our results extend and improve some recent results of Cianciaruso et al. (J. Optim. Theory Appl. 146:491–509, 2010), Kamraksa and Wangkeeree (J. Glob. Optim. 51:689–714, 2011), and many others.     

On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）

In this paper,we consider the family of generalized Petersen graphs P(n,4).We prove that the metric dimension of P(n,4) is 3 when n ≡ 0(mod 4),and is 4 when n = 4k + 3(k is even).For n ≡ 1,2(mod 4) and n = 4k + 3(k is odd),we prove that the metric dimension of P(n,4) is bounded above by 4.This shows that each graph of the family of generalized Petersen graphs P(n,4)has constant metric dimension.     

Numerical Simulation of a Turbulent FSI Benchmark Case

In an effort to expand the capabilities of a validated simulation environment for fluid-structure interaction to turbulent flows, we present the simulation of a turbulent FSI benchmark case with large displacements in a simplified two-dimensional unsteady RANS setup. We find a fair agreement to experimental data that encourages further refinement of our approach and future three-dimensional simulations with eddy-resolving schemes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On managerial risk-taking incentives when compensation may be hedged against

We consider a continuous time principal-agent model where the principal/firm compensates an agent/manager who controls the output’s exposure to risk and its expected return. Both the firm and the manager have exponential utility and can trade in a frictionless market. When the firm observes the manager’s choice of effort and volatility, there is an optimal contract that induces the manager to not hedge. In a two factor specification of the model where an index and a bond are traded, the optimal contract is linear in output and the log return of the index. We also consider a manager who receives exogenous share or option compensation and illustrate how risk taking depends on the relative size of the systematic and firm-specific risk premia of the output and index. Whilst in most cases, options induce greater risk taking than shares, we find that there are also situations under which the hedging manager may take less risk than the non-hedging manager.     

Chemical vapor functionalization: a continuous production process for functionalized ZnO nanoparticles

The continuous functionalization of nanoparticles in the gas-phase directly after their generation, chemical vapor functionalization, is studied with ZnO and 1-hexanol as a model system using two reactors in series. In the first reactor ZnO nanoparticles are synthesized in the gas-phase from diethylzinc and oxygen at 1,073 K with grain sizes of 13 nm as determined by Rietveld refinement of X-ray diffractograms. The second reactor, connected at the exit of the first reactor and kept at lower temperatures (573, 673, and 773 K), is used as a functionalization chamber. At the connection point of the two reactors, the vapor of 1-hexanol is injected to react with the surface of ZnO nanoparticles in the gas phase. The process has been analyzed by quadrupole mass spectrometry to obtain information about optimal conditions for functionalization. Dynamic light scattering data show that the functionalized particles have substantially improved colloidal dispersibility with hydrodynamic diameters of 60 nm. Diffuse reflectance fourier transform infrared spectra and ¹H nuclear magnetic resonance spectra are consistent with 1-hexanol adsorbed at the particle surface acting as a functionalizing agent. The agglomerate size is substantially reduced owing to chemical vapor functionalization.