Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated. AMS Subject Classifications Primary 60K25 · 60K20     

Study of the dielectric properties of water in the frequency range 75–120 GHz

We study experimentally the frequency dependences of the refractive index n and the absorption coefficient k of distilled, sea, and river water. The measurements were performed using a quasioptical device with a backward-wave oscillator as the radiation source and OAP-7 optical-acoustic receivers at a water temperature of 27°C in the cell. The quantities n and k were determined from the measured transmission and reflection coefficients of the cell with water by means of joint numerical solution of the equations for these quantities. For distilled water in the frequency range f = 75–120 GHz, we obtained n = 6.142–3.926 · 10–2f[GHz] + 1.307 · 10–4(f[GHz])² and k = 3.607–2.101 · 10⁻² f[GHz] + 5.252 · 10–5(f[GHz])². On the whole, these data are in good agreement with the measurement results obtained by other authors at several frequencies of the indicated range and coincide with the calculation data based on the models by Meissner and Wentz and by Liebe et al. within the limits of the rms determination errors 0.05 and 0.02 for the parameters n and k, respectively. The values of n and k for different seawater samples and river water containing insoluble admixtures coincide with the values of these quantities for distilled water within the limits of the experimental measurement errors 3–5% and 1–2%, respectively. The dependences n(f) and k(f) obtained experimentally for seawater are compared with those calculated on the basis of the developed models. Measurements of the transmission spectrum of a cell with double distilled water were performed for low power density of radiation (less than μW/cm²) to reproduce the effect of water resonant transparency reported many times in the literature. Our measurements did not reveal any resonant features in the spectral behavior of the refractive index n and the absorption coefficient k of water and gave the same result as for a power density exceeding the threshold of appearance of this effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 489–501, June 2006.     

Supersonic Flow Past a Bent Delta Wing and Its Aerodynamic Characteristics

The supersonic flow past a bent delta wing and its aerodynamic characteristics, both local and integral, are studied using approximate analytic estimates and numerical calculations. The flow regimes with the shock attached to the leading edges are considered. It is established that at M = 4–6 and angles of attack as high as 6° the lift-drag ratio of the wing can be increased by 10% by deflecting the wing nose downwards. This is confirmed by the results obtained earlier in the hypersonic thin-shock-layer approximation. The effect is also obtained in calculations made within the framework of the Navier-Stokes equations.     

High-pressure alkylation of bis(benzylidene)phenylenediamines

The reactions of alkyl chlorides with bisanils (obtained from o-, m-, and p-phenylenediamines) under high pressure (10 kbar) were studied. Depending on the structure of the starting diamines and the solvent nature, hydrolysis of the reaction mixtures gave pure N-monoalkyl- or N,N"-dialkylphenylenediamines in high yields. The effect of the phase transition of the solvent on the direction of alkylation is discussed.     

Formal intramolecular [5 + 2] photocycloaddition reactions of maleimides: a novel approach to the CDE ring skeleton of (-)-cephalotaxine

A concise approach to the cephalotaxine CDE ring skeleton based on the intramolecular formal [5 + 2] photocycloaddition of cyclopentenyl-substituted maleimides is described. An investigation of the diastereoselectivity afforded by various protected alkoxy groups demonstrated that the best selectivity (3.5:1) was afforded by the free hydroxyl group, strongly suggesting a hydrogen-bonded excited state. Reaction: see text.     

Measurement of dense plasma temperature of the shock-compressed silicon

Measurements of the brightness temperature and compressibility of a dense silicon plasma formed by powerful shock waves (SWs) passing through a single-crystal sample have been carried out. Plane SWs were created using an explosive technique: the traditional plane acceleration of a steel driver plate made it possible to obtain pressures in silicon up to 133 GPa, and the use of “Mach” cumulative generators realized the pressures up to 510 GPa. The shock Hugoniot of silicon was determined by the impedance matching with α-quartz as the reference. The intensity of emitted thermal radiation was measured in the infrared range λ ∼ 1.5 μm, where silicon is optically transparent, and in the visible range of the spectrum. A significant (up to five times) understatement of the measured values of the brightness temperature in comparison with the values calculated by the equation of state was found. Taking into account the reflective properties of the SW in silicon does not lead to an agreement with the experiment. The estimates of relaxation processes behind the shock front suggest the presence of a zone of the establishment of ionization equilibrium with a width of ∼10 μm.     

BMAP|SM⥻1 model with Markov modulated retrials

This paper deals with the single server queueing system with a Batch Markovian Arrival Process (BMAP), the semi-Markovian (SM) service process, and the retrial process of a MMPP (Markov Modulated Poisson Process) type. The stationary distribution of orbit size at the embedded and arbitrary epochs is the subject of research. We appreciate the INTAS program for the financial support of this research via project #96-828.     

Visualizing zeptomole (electro)catalysis at single nanoparticles within an ensemble

The relationship between the structural properties, such as the size and the shape, of a catalytic nanoparticle and its reactivity is a key concept in (electro)catalysis. Current understanding of this relationship is mainly derived from studies involving large ensembles of nanoparticles (NPs). However, the results necessarily reflect the average catalytic behavior of an ensemble, even though the properties of individual particles may vary widely. Here, we demonstrate a novel approach using scanning electrochemical cell microscopy (SECCM) to locate and map the reactivity of individual NPs within an electrocatalytic ensemble, consisting of platinum NPs supported on a single carbon nanotube. Significantly, our studies show that subtle variations in the morphology of NPs lead to dramatic changes in (potential-dependent) reactivity, which has important implications for the design and assessment of NP catalysts. The instrumental approach described is general and opens up new avenues of research in functional imaging, nanoscale electron transfer, and catalysis.     

Law of transverse sections for the three-dimensional boundary layer on a thin wing in a hypersonic stream

The investigation of three-dimensional flows in boundary layers is important to determine the aerodynamic characteristics of wings such as the heat fluxes and friction drag. However, the circumstance that interaction of the boundary layer and the wake with an inviscid stream can play a governing role for the formation of the flow diagram as a whole is more important. The three-dimensional flow on a thin delta wing in a hypersonic stream is investigated in this paper. An important singularity of hypersonic flow is the low value of the gas density in the boundary layer as compared with the density on its outer boundary. It is shown that in the general case when the pressure in the wing span direction varies mainly by an order, high transverse velocities originate because of the smallness of the density within the boundary layer. This circumstance permits expansion of the solution for smallspan wings in a series in an appropriate small parameter. The equations in each approximation depend on two variables, while the third—longitudinal—variable enters as a parameter. The zero approximation can be considered as the formulation of the law of transverse plane sections for a three-dimensional boundary layer. As a comparison with the exact solutions calculated for delta wings with power-law distributions of the wing thickness has shown, the first approximation yields a very good approximation. Furthermore, flow modes with a different direction of parabolicity on the whole wing, as well as zones in which interaction with the external stream should absolutely be taken into account, are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–84, March–April, 1976.