Solution of a Multidimensional Tropical Optimization Problem Using Matrix Sparsification

A complete solution is proposed for the problem of minimizing a function defined on vectors with elements in a tropical (idempotent) semifield. The tropical optimization problem under consideration arises, for example, when we need to find the best (in the sense of the Chebyshev metric) approximate solution to tropical vector equations and occurs in various applications, including scheduling, location, and decision-making problems. To solve the problem, the minimum value of the objective function is determined, the set of solutions is described by a system of inequalities, and one of the solutions is obtained. Thereafter, an extended set of solutions is constructed using the sparsification of the matrix of the problem, and then a complete solution in the form of a family of subsets is derived. Procedures that make it possible to reduce the number of subsets to be examined when constructing the complete solution are described. It is shown how the complete solution can be represented parametrically in a compact vector form. The solution obtained in this study generalizes known results, which are commonly reduced to deriving one solution and do not allow us to find the entire solution set. To illustrate the main results of the work, an example of numerically solving the problem in the set of three-dimensional vectors is given.     

Pseudoisocyanine J-aggregate to optical waveguiding crystallite transition: microscopic and microspectroscopic exploration

Using fluorescent microscopy and microspectroscopy, optical properties and morphology transformations in individual pseudoisocyanine (PIC) J-aggregates in aqueous electrolyte solutions have been explored. A stringlike structure of J-aggregates with a string diameter much less than 1 microm has been observed. Photodestruction of the strings under short-wavelength excitation has been revealed. Rodlike PIC crystallites, about 1 microm in diameter, have been observed with time. The fluorescence spectrum of rodlike crystallites has been found to differ from that of stringlike J-aggregate and from PIC crystal powder spectra. The crystallites are very stable, and their photodestruction has not been observed under any excitation conditions. It has been found that rodlike crystallites in contrast to stringlike J-aggregates possess optical waveguide properties. The luminescence of crystallites can be observed only at the excitation spot and at butt ends located up to hundreds of micrometers from the excitation spot.     

Laguerre projection method for finite Hankel transform of arbitrary order

We propose a modification of the projection method for the problem of inverting finite Hankel transform of arbitrary order. In expanding the solution of an integral equation of the first kind, eigenfunctions corresponding to eigenvalues close to the multiple are replaced with Laguerre functions. These functions are eigenfunctions of Hankel transform on the half-line. Our test calculations demonstrated the effectiveness of the elaborated method.     

Growth and defect structure of CdF2 crystal and nonstoichiometric Cd1−x R x F2+x phases (R are rare earth elements and in): 6. Growth and ionic conductivity of Cd0.904In0.096F2.096 single crystal

Cd_0.904In_0.096F_2.096 crystals with fluorite-type defect structures have been grown from melt in a fluorinating atmosphere by the Bridgman method, and their ionic conductivity is investigated. The fluorine-ion transport activation enthalpy in Cd_0.904In_0.096F_2.096 (ΔH = 0.68 eV) is much smaller than the corresponding characteristic of the crystals belonging to the isoconcentration series Cd_0.9 R _0.1F_2.1, R = La-Lu, Y (ΔH = 0.8–0.9 eV). The ionic conductivity of Cd_0.904In_0.096F_2.096 is σ = 2 × 10^?4 S/cm (at 467 K); this value exceeds the conductivity of the CdF₂ crystal matrix and the highest conductivity Cd_0.9 R _0.1F_2.1 crystals with rare earth elements by factors of 3 × 10³ and ～10, respectively. Nonstoichiometric crystals of solid electrolyte Cd_{1 ? x} In _x F_{2 + x} have the highest conductivity out of all studied electrolytes based on the CdF₂ matrix.     

Anisotropy of the ionic conductivity of CsCu2Cl3 single crystals

The conductivity of CsCu₂Cl₃ single crystals (orthorhombic system, sp. gr. Cmcm) has been investigated for different electric-field directions, perpendicular to the crystallographic c axis and along it, in the temperature range 390–530 K. The increase in conductivity with temperature is due to the ion-carrier transport with activation energies E _a = 0.65 and 0.80 eV for the directions perpendicular to and along the crystallographic axis, respectively. The anisotropy of the crystal ionic conductivity is found to be σ_⊥c /σ_∥c ≈ 40 at 435 K. The thermally activated contribution to the conductivity in the CsCu₂Cl₃ structure is determined by the transport of Cu⁺ ions.     

Topology design for on-demand dual-path routing in wireless networks

One way to achieve reliability with low-latency is through multi-path routing and transport protocols that build redundant delivery channels (or data paths) to reduce end-to-end packet losses and retransmissions. However, the applicability and effectiveness of such protocols are limited by the topological constraints of the underlying communication infrastructure. Multiple data delivery paths can only be constructed over networks that are capable of supporting multiple paths. In mission-critical wireless networks, the underlying network topology is directly affected by the terrain, location and environmental interferences, however the settings of the wireless radios at each node can be properly configured to compensate for these effects for multi-path support. In this work we investigate optimization models for topology designs that enable end-to-end dual-path support on a distributed wireless sensor network. We consider the case of a fixed sensor network with isotropic antennas, where the control variable for topology management is the transmission power on network nodes. For optimization modeling, the network metrics of relevance are coverage, robustness and power utilization. The optimization models proposed in this work eliminate some of the typical assumptions made in the pertinent network design literature that are too strong in this application context.     

The effect of phase noise of bichromatic radiation upon resonances of coherent population trapping

We consider the effect of the noise difference phase of a bichromatic field upon coherent population trapping resonances in the simplest three-level system in Λ configuration. The quasi-stationary solution of Bloch optical equations, which was found with some assumptions, shows that the presence of exciting short-correlated fluctuations of the phase of radiation reduces the contrast of the resonance line without affecting its spectral width. For the Gaussian phase noise the contrast suppression factor is χ = exp[?? _rms ² ], where ? _rms ² is phase dispersion. The experimental results obtained earlier by our group are analyzed.     

Hydrophobicity effect on interactions between organic molecules in nanocages of surfactant micelle

Interactions between the cationic polymethine dyes 3,3′-diethyloxacarbocyanaine iodide (DiOC₂), 3,3′-dioctadecyloxacarbocyanine iodide (DiOC₁₈), and 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine perchlorate (DiI) in the nano-scale volume of anionic sodium dodecylsulfate (SDS) micelles have been studied using optical spectroscopy techniques. The solubilization of pairs of dye molecules (DiOC₁₈/DiI or DiOC₂/DiI) within SDS micelles was monitored by Forster resonance energy transfer (FRET) between the dyes in each pair. The influence of the hydrophobicity of the dyes DiOC₂ and DiOC₁₈ on the efficiency of their binding to SDS micelles and, consequently, on the efficiency of FRET between DiOC₁₈ and DiI or DiOC₂ and DiI fluorophors has been analyzed. It has been shown that hydrophobic interactions in addition to electrostatic interactions are of key importance for the binding between the positively charged dyes and negatively charged surfactant micelles. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 646–652, September–October, 2008.     

Manifestation of intramolecular and intermolecular interactions in infrared absorption spectra of biologically active aminophenols

FTIR methods were used to study intramolecular and intermolecular interactions in solutions and the solid state of the biologically active aminophenols 2-anilino-4,6-di-tert-butylphenol, N-(3,5-di-tert-butyl-2-methoxyphenyl)aniline, and 2,4-di-tert-butyl-10H-1-phenothiazinol. An analysis of the IR spectra has shown that intramolecular interactions between the OH and NH groups occur in solutions of 2-anilino-4,6-di-tertbutylphenol in CCl₄ to form O-H⋯N hydrogen bonds. The NH groups in solutions of N-(3,5-di-tert-butyl-2-methoxyphenyl)aniline in CCl₄ are present in the non-associated state because of the absence of hydroxyl groups in the molecular structure. The OH and NH groups in solutions of 2,4-di-tert-butyl-10H-1-phenothiazinol in CCl₄ do not interact within the molecule due to a decrease in the conformational mobility of the molecular fragments due to the presence of the rigid C_Ar-S-C_Ar molecular bond in this compound. Intermolecular interactions involving the NH groups occur in the solid state of these compounds. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 68–73, January–February, 2008.     

Influence of initial conditions at the nozzle exit on the structure of round jet

Experimental data concerning the influence of initial conditions at the nozzle exit on the structure and development characteristics of round jets are reported. Features in the development of laminar and turbulent round jets emanating from variously elongated nozzles at identical Reynolds numbers are revealed. Smoke visualization pictures obtained for jets formed under different initial conditions (with different distributions of mean and pulsating flow velocities at the nozzle exit) are discussed. It is shown possible to make the zone of laminar flow in the jet stream more extended, and to delay the jet turbulization process in space, by making the flow-velocity profile more parabolic at the exit of elongated nozzle. Features in the development of vortical structures in a jet under an acoustic action are identified. It is shown that, for a turbulent round jet to be produced right at the nozzle exit, the nozzle length must be increased in excess of a certain value so that to provide for spatial growth of turbulent boundary layer thickness, finally ending in the formation of a fully turbulent flow velocity profile across the channel. This work was supported by the Russian Foundation for Basic Research (Grant No. 08-01-00027), the Ministry of Education and Science of the Russian Federation (project RNP 2.1.2.3370), and by the grants of President of the Russian Federation (NSH-454.2008.1 and. MK-420.2008.1).