Mathematical model and efficient algorithms for object packing problem

The article is devoted to mathematical models and practical algorithms for solving the cutting and packing (C&P) problem. We review and further enhance the main tool of our studies – phi-functions. Those are constructed here for 2D and 3D objects (unlike other standard tools, such as No-Fit Polygons, which are restricted to the 2D geometry). We also demonstrate that in many realistic cases the phi-functions can be described by quite simple formulas without radicals and other complications. Lastly, a general solution strategy using the phi-functions is outlined and illustrated by several 2D and 3D examples.     

Electrical and electroluminescent properties of InAsSb-Based LEDs (λ = 3.85–3.95 μm) in the temperature interval 20–200°C

The temperature dependences of the electrical and electroluminescent properties of InAsSbP/InAsSb/InAsSbP heterostructure LEDs (λ ≈ 3.8−4.0 μm) are studied in the temperature interval 20–200°C. It is shown that the radiation power decreases with increasing temperature in a superexponential manner and that this decrease is associated primarily with a rise in the rate of Auger recombination. The position of the maximum in the radiation spectrum varies with temperature nonmonotonically, since radiative recombination is observed both in the active region and in the wide-gap layer. At room temperature, current through the heterostructure is tunneling current irrespective of the applied voltage polarity. As the temperature rises, either the thermal emission of charge carriers appears (direct bias) or the diffusion current becomes significant (reverse bias).     

A magnetostatic-coupling based remote query sensor for environmental monitoring

A new type of in situ, remotely monitored magnetism-based sensor is presented that is comprised of an array of magnetically soft, magnetostatically-coupled ferromagnetic thin-film elements or particles combined with a chemically responsive material that swells or shrinks in response to the analyte of interest. As the chemically responsive material changes size the distance between the ferromagnetic elements changes, altering the inter-element magnetostatic coupling. This in turn changes the coercive force of the sensor, the amplitude of the voltage spikes detected in nearby pick-up coils upon magnetization reversal and the number of higher-order harmonics generated by the flux reversal. Since the sensor is monitored through changes in magnetic flux, no physical connections such as wires or cables are needed to obtain sensor information, nor is line of sight alignment required as with laser telemetry; the sensors can be detected from within sealed, opaque or thin metallic enclosures.     

Vibrations of mechanical systems in the presence of uncertainty

The minimax state estimation problem is solved for a linear mechanical system with a finite number of degrees of freedom. The proposed procedure is extended to distributed-parameter systems. As an example, we consider an elastic rod that executes small longitudinal oscillations under uncertainty in the initial-boundary conditions.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 95–100, 1986.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). VIII. General principles for computer implementation

The computer implementation of the HOC procedures presented in Parts I, II and III of this series is based on the module principle. It contains a main program and seventeen subroutines in Fortran IV. The system is able to provide unique atom numbering and code for all kinds of chemical compounds in their tremendous variety of structures.     

On the free scalar massless field in two-dimensional space-time

In the present paper the solutions of the quantum field problem for the free scalar massless field in two-dimensional space time are constructed. It is shown that the fields obtained cannot vanish at space-like infinity. The latter fact implies the existence of two conserved charge operators. The transformation properties of these solutions under the two-dimensional Lorentz group are examined.     

$\Phi $-functions for complex 2D-objects

Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of -functions has been proven to be very helpful for several solution approaches. In order to construct such -functions a previous work, in which so-called primary objects are considered, is continued. Now -functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer     

Spin-dependent electron-hole capture kinetics in luminescent conjugated polymers

The recombination of electron-hole pairs injected in extended conjugated systems is modeled as a multistep interconversion relaxation in monoexcited electronic state space, mediated by electron-phonon coupling. The computed ratio of triplet-to-singlet exciton formation times r=tau(T)/tau(S) increases from 0.9 for a model dimer to 2.5 for a 32-unit chain, in good agreement with recent experiments. We rationalize the conjugation-length dependence of r in terms of spin-specific energetics and mutual vibronic coupling of the excited states.     

On the Existence of a Generalized Solution to a Three-Dimensional Elliptic Equation with Radiation Boundary Condition

For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent q which is greater than for the fourth power law.