Positive solutions of non‐positone Dirichlet boundary value problems with singularities in the phase variables

The paper presents existence results for positive solutions of the differential equations x ″ + μh (x) = 0 and x ″ + μf (t, x) = 0 satisfying the Dirichlet boundary conditions. Here μ is a positive parameter and h and f are singular functions of non‐positone type. Examples are given to illustrate the main results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence principles for higher-order nonlocal boundary-value problems and their applications to singular Sturm-Liouville problems

We present existence principles for the nonlocal boundary-value problem (φ(u^(p−1)))′=g(t,u,...,u^(p−1), α_k(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α _k: C ^p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)ⁿ(φ(u⁽²ⁿ⁻⁾))′=f(t,u,...,u⁽²ⁿ⁻¹⁾), u^(2k)(0)=0, α_ku^(2k)(T)+b_ku^(2k=1)(T)=0, 0≤k≤n−1, is given. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008.     

Jamming communication networks under complete uncertainty

This paper describes a problem of interdicting/jamming wireless communication networks in uncertain environments. Jamming communication networks is an important problem with many applications, but has received relatively little attention in the literature. Most of the work on network interdiction is focused on preventing jamming and analyzing network vulnerabilities. Here, we consider the case where there is no information about the network to be jammed. Thus, the problem is reduced to jamming all points in the area of interest. The optimal solution will determine the locations of the minimum number of jamming devices required to suppress the network. We consider a subproblem which places jamming devices on the nodes of a uniform grid over the area of interest. The objective here is to determine the maximum grid step size. We derive upper and lower bounds for this problem and provide a convergence result. Further, we prove that due to the cumulative effect of the jamming devices, the proposed method produces better solutions than the classical technique of covering the region with uniform circles.     

Mechatronic Design of the 2 DOF PRRRP Parallel Robot

Mechatronics consists in integration of three fields in engineering: mechanics, electronics and information technology. The paradigm of mechatronics is the integration concept, being the first step in the design of complex mechatronic systems. The need for an integrated approach to the design of complex engineering system involving electronic engineering, mechanical engineering and computing has led to the growth of the concept of mechatronics. The paper presents details regarding the integration process for the kinematic axis in mechatronic. The example of the positioning system based on dc motor and screw–nut transmission is analysed. This actuator is further used for driving a 2 DOF PRRRP parallel robot. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oscillatory behaviour in the energy and nonlinear optical rectification spectra of elliptic quantum rings under electric field: influence of impurity and eccentricity

We have theoretically investigated the electronic properties and nonlinear optical rectification spectra of GaAs/AlGaAs anisotropic quantum ring, modelled by an outer ellipsis and an inner circle, in connection to the presence of a donor off-centre impurity, structural distortions and in-plane electric field. The one-electron energy spectrum and wave functions are found using the adiabatic approximation and the finite element method within the effective-mass model. The energy spectrum of concentric ring reveals an anomalous oscillatory behaviour in the region of relatively small values of the electric field (< 12?kV/cm) followed by linear Stark effect at higher field values. We showed that this unusual behaviour is strongly affected by the ratio of the outer/inner ring radii, the displacement of the inner circle (eccentricity) along the x or y axis and the impurity presence. The related nonlinear optical rectification spectra present maxima whose positions mirror this oscillatory behaviour and consequently can be used as an excellent tool to distinguish the presence of an impurity or the direction of the eccentricity.     

A Model Predictive Control Algorithm Applied To Non-Linear Processes

Model predictive control (MPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. In most of nonlinear strategies, the controllers are based on linear models with fixed parameters so that the vast body of linear control theory can be applied. Other solutions include the use of a nonlinear analytical model, combinations of linear empirical models, etc. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gas-chromatographic determination of the enantiomeric composition of optically active alcohols and amines using achiral bifunctional reagents

A technique for determining the enantiomeric composition of 2-octanol and -phenylethylamine with the use of gas chromatography on optically inactive stationary phases is proposed. The technique is based on the formation of symmetrical diastereomeric derivatives upon the interaction of enantiomers with bifunctional achiral reagents: dimethyldichlorosilane, bromochloromethane, and dibromoethane. The reagents were chosen from the viewpoint of the synthesis of diastereomers with a minimum distance between the chiral centers. This minimum distance is responsible for a difference in the energies of interaction of the derivatives with the stationary liquid phase, which is sufficient for the separation of these derivatives.Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 3, 2005, pp. 297–306.Original Russian Text Copyright © 2005 by Stankov, Sitnikov, Sadovnikov, Sergeeva, Derevyagina, Morozova, Mylova, Kuzmina, Gurenko.     

Electronic structure,chemical bond,and optical spectra of metal bis(porphyrin) complexes: a DFT/TDDFT study of the bis(porphyrin)M(IV) (M = Zr,Ce, Th) series

The electronic absorption spectra of the bis(porphyrin) sandwich complexes of the metals Zr, Ce, and Th are studied with time-dependent density functional theory (TDDFT). A ground-state electronic structure analysis reveals that the highest occupied one-electron levels are, as expected, composed of the porphyrin a(1u) and a(2u) highest occupied orbitals (the Gouterman orbitals), but the level pattern is not simply a pair of low-lying nearly degenerate in-phase combinations and a pair of high-lying approximately degenerate antibonding combinations. Instead, the a(1u) split strongly and the a(2u) do not. Since the calculated spectrum agrees very well with experiment, the assignment leaves little doubt that although the experimental spectrum has porphyrin-like features, such as the well-known Q and B bands, the actual composition of the states is rather different from that in porphyrin. In particular the strong mixing of a(1u) --> e(g) and a(2u) --> e(g) is absent, there is mixing with excitations of non-Gouterman type, and, in Ce, ring to metal charge-transfer transitions play an important role. The composition of the states as calculated in this work does not lead to a classification of the excitations as purely "excitonic" or "charge-resonance".