Electron paramagnetic resonance and optical absorption spectra of Cr ions in cadmium phosphate glass

EPR and optical absorption investigations of chromium doped cadmium phosphate glass are carried out. Crystal field, spin-Hamiltonian and bonding parameters are evaluated. From the results and analyses of the EPR and optical studies, the site symmetry of Cr³⁺ ion in the glass is ascribed to a distorted octahedron. The bonding parameters suggest the ionic nature of Cr³⁺ ion with the ligands.     

Nanometric Antimony Powder Synthesis by Activated Alkaline Hydride Reduction of Antimony Pentachloride

A novel chemical reduction method using an activated alkaline hydride (LiH or NaH-t-BuONa) in tetrahydrofuran solvent has been applied to antimony salt reduction. X-ray diffraction and transmission electron microscopy studies have been carried out to characterize the morphology and structure of the materials. Alkali hydride nature influence has been proved. In both cases the process allows to prepare antimony particles in nanometer range from few nanometers to about 20nm which could be used as anodic materials for lithium–ion batteries. With lithium hydride well-crystallized particles inclined to agglomeration were observed whereas finely dispersed amorphous particles were pointing out after activated sodium hydride reduction.     

Isotopic production cross sections of residues in reactions induced by relativistic heavy ions with protons and deuterons

The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets.     

Generalized optical logic elements - GOLEs

A Generalized Optical Logic Element or GOLE is device that performs any of the 16 Boolean logic operations on signals in an optical beam with very fast switching among functions. The advantages of a generalized or universal gate in manufacturing are obvious. Extremely flexible functioning becomes possible if the GOLE functionality is switched in response to earlier computations. Likewise Field Programmable Gate Arrays or FPGAs can be used to fix the GOLE functions, making one of the most powerful and flexible processor units ever designed - called a Field GOLE. Such systems can be made in bulk optics to utilize Spatial Light Modulator or SLM capabilities, but integrated optics on silicon will be the choice for most applications. GOLEs can be generalized in several ways to become Fredkin gates and generalized Fredkin gates. They can also be cascaded similarly to electronic gates.     

Studies on the curing kinetics of epoxy resins using mixture of nadic/or maleic anhydride and 4,4′-diaminodiphenyl sulfone

Curing kinetics of diglycidyl ether of bisphenol-A (DGEBA) in the presence of maleic anhydride (MA)/or nadic anhydride (NA) or mixture of MA/NA: 4,4′-diaminodiphenyl sulfone (DDS) in varying molar ratios were investigated using differential scanning calorimetry. Curing behaviour of DGEBA in the presence of varying amounts of DDS:MA/NA was evaluated by recording DSC scans at heating rates of 5, 10, 15 and 20°C min⁻¹. The peak exotherm temperature depends on the heating rate, structure of the anhydride as well as on the ratio of anhydride: DDS. Thermal stability of the isothermally cured resins was evaluated by thermogravimetry. The char yield was highest in case of resins cured using mixture of DDS:MA (0.75:0.25; sample EM-1) and DDS:NA (0.75:0.25, sample EN-1).     

Two-dimensional phased arrays for surgical applications: Multiple focus generation and scanning

A numerical simulation and a comparative analysis of the acoustic fields produced by two-dimensional phased arrays intended for ultrasonic surgery are performed for the case of a multiple focus (in particular, 25 foci) generation. The calculations were conducted for arrays (with an operating frequency of 1.5 MHz) consisting of 256 elements 5 mm in diameter, which were positioned on the array surface both regularly and randomly. The array foci can be formed simultaneously, but, in this case, the intensity levels of the secondary peaks in the ultrasonic field can exceed the values that guarantee the safe application of this method in surgery. A much safer way is to synthesize many foci with the use of several configurations, each of which contains a smaller number of foci. The number of foci in individual configurations must be approximately the same. It is demonstrated that randomization of the element distribution over the array surface provides an opportunity to improve the array performance, to reduce the intensity levels of secondary peaks in the acoustic field, and to increase the array capability for multiple focus scanning off the array axis.     

Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.     

Dupin hypersurfaces with four principal Curvatures,II

If M is an isoparametric hypersurface in a sphere S ⁿ with four distinct principal curvatures, then the principal curvatures κ₁, . . . , κ₄ can be ordered so that their multiplicities satisfy m ₁ = m ₂ and m ₃ = m ₄, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R ⁿ (or S ⁿ ) with four distinct principal curvatures with multiplicities m ₁ = m ₂ ≥ 1 and m ₃ = m ₄ = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.      

Robust Dynamics and Control of a Partially Observed Markov Chain

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721–734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear). Clark’s method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.