Space-time processing for «range – azimuth – elevation» measurements in non-cooperative systems of radars with phased array antennas

The methods of measuring the three coordinates of an aircraft in the takeoff and landing mode on the runway of airfields based on the use of non - cooperative two-and three-position systems of radars with phased array antennas are considered. For these variants, general analytical expressions are obtained for the complex generalized correlation integral of space – time processing in the function of spatial coordinates, taking into account the individual directional pattern of phased array antennas. On the basis of two – dimensional profiles of the correlation integral modules «range – elevation» and «azimuth – elevation», examples of comparing particular variants of two-position and three-position systems of radars with their location on one straight line parallel runway are given. In conditions of large signal-to-noise ratios, power-law nonlinear transformations of the correlation integral correlation integral module are applied to reduce the level of side lobes in the two – dimensional sections «range – elevation» and «azimuth – elevation». The following results are obtained using examples. Two-dimensional diagrams of the correlation integral module «range – elevation» do not depend on the azimuth of the aircraft in the range of azimuth values β=0…10 ̊ and correctly display the angle of elevation and the range of the aircraft when 2…3 radars of a non-cooperative system are located on the straight line parallel runway. The two-dimensional diagrams of the correlation integral module «azimuth – elevation angle» have an interference structure, and the number and level of their side lobes increase with increasing azimuth of the aircraft. With azimuth β≥10 ̊, this can lead to ambiguity in the measurement of the azimuth and uncertainty in the elevation angle . One of the measures to reduce the side level of the diagrams of the correlation integral module can be the use of a power-law transformation of normalized diagrams exponentiation of degree 3...4. An increase in the number of radars from two to three when they are located on one straight line parallel to the runway led to a decrease in the side lobes level of the «range – elevation angle» and «azimuth – elevation angle» diagrams. In this case, it may be advisable to solve the problem of optimal choice of the position of the intermediate radar on the same straight line. Calculations were also carried out for an additional example of the location of the intermediate radar of a 3-position system with its removal from the base line. At the same time, there was an increase of the side lobes level in the «azimuth – elevation angle» sections, which in the future may require additional research in terms of optimizing the placement of the radars in horizontal plane for such a radar systems.

Mathematical model of gas hydrate formation of sulfur dioxide by injecting liquid sulfur dioxide into a layer saturated with methane and water

This paper presents the results of a theoretical study for the gas hydrate formation of sulfur dioxide by injecting liquid sulfur dioxide into a layer saturated with water and methane. Self-similar solutions of a straight-line parallel problem are constructed. The dependences of the temperature and the coordinates of the formation front of sulfur dioxide gas hydrate on the layer permeability are explored. It is established that, as the layer permeability increases, the temperature of the phase transition increases on the surface. As a result, at sufficiently large values of layer permeability, the temperature at the hydrate formation border may exceed the equilibrium decomposition temperature of sulfur dioxide gas hydrate, which will correspond to the appearance of an intermediate region saturated with a mixture of water, sulfur dioxide and its gas hydrate in a state of thermodynamic equilibrium. It is established that at sufficiently high values of injection pressure and permeability, the gas hydrate formation of sulfur dioxide will occur in the extended region.

Longitudinal vibrations in electrodynamics suspension system

A system of electrodynamics suspension (EDS) in which the primary source of the field (electromagnet) is moving in a straight line parallel to the surface of the track and his speed makes small oscillations around a mean value is considered. The approximation of an infinitely wide track is allowed, the primary source of the electromagnetic field acts as a so-called periodic source. This problem is a special case of the general problem of the rate of the transients in the EDS, caused by uneven movement. Named speed determines the amount of time constants that make sense, and in contrast to the simplest case of a one-dimensional linear oscillator system EDS characterizes not by a single time constant, but by infinite set of values. The method of calculation of levitation and braking forces acting in this oscillatory motion on carriage electromagnet is worked out and simple explicit formulas to calculate these forces are got. On the basis of the calculation of time constants the rate of the transients in the EDS, caused by uneven movement is assessed. The calculations of levitation and braking forces according to the developed technique are made. The results obtained allow to delimit the applicability of the so-called quasi-static approach which consists in that the irregularly moving of electromagnet replaced by concurrent, i.e., the same electromagnet, similarly disposed and uniformly moving with a speed coinciding with the instantaneous value of the actual longitudinal speed of the electromagnet. In the quasi-static approximation, fluctuations of levitation and braking forces are in phase with oscillations of speed and amplitude of the forces oscillations do not depends on the frequency of the speed oscillation. The calculations show that in reality there is phase shift between the forces oscillations and speed oscillations depending on the frequency. Amplitudes of levitation and braking forces oscillations also depend on the oscillation frequency, and for each speed value a resonance frequency exists at which they reach the maximum value.

Extensible-Link Kinematic Model for Determining Motion Characteristics of Compliant Mechanisms

We present an extensible-link kinematic model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. This is accomplished by creating an analogous kinematic model consisting of links that change length over the course of actuation to represent elastic deformation of the compliant mechanism. Within the model, the motion trajectory is represented as an analytical function. By Taylor series expansion, the trajectory is expressed in a parametric formulation composed of load-independent and load-dependent terms. Here, the load-independent terms are entirely defined by the shape of the undeformed compliant mechanism topology, and all load-geometry interdependencies are captured by the load-dependent terms. This formulation adds insight to the process for designing compliant mechanisms for high accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications for improving the accuracy of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components of the motion trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. We develop the generalized model framework, and then demonstrate its utility by designing a compliant micro-gripper with straight-line parallel jaw motion. We use the model to analytically determine all topology modifications for optimizing the jaw trajectory, and to predict the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized by iterative finite elements (FE) simulation until the polynomial order of the uncorrectable trajectory component becomes apparent.

Growth of CuO and CuGaO2 Thin Films by Spin-coating Method

ABSTRACTCuO and CuGaO2 thin films have been grown on Si (100) substrates using a sol-gel spincoating method. CuO films were successfully fabricated by the annealing around 700°C. At higher temperatures (>800°C), pyramidal CuO islands with 1~2μm in width and 0.4~0.8μm in height were observed. They arranged structures as a straight line parallel to the <110> and <010> directions, which suggests the self-organized growth of CuO pyramidal islands. Delafossite CuGaO2 films were fabricated as well, using Cu-Ga-O mixed solutions with Ga/(Cu+Ga) atomic ratio of 0.5. These results indicate that Cu-based compounds were fabricated by the sol-gel spincoating method.

A remark on the resonance set for a semilinear elliptic equation

We study the resonance set ∑ of pairs (α,β) ∊ ℝ2 for which the problem ∆u + αu+ − βu− = 0 has a nontrivial solution . We show that if λ0, is an eigenvalue of multiplicity two of −Δ, then has measure zero, where are the neighbouring eigenvalues of λ0. Moreover, we have that, if the operator Δ + αIu<0 + βIu < 0 has a kernel of dimension one for(α, β) ∊ ∑ and u ≠ 0 such that Δu + αu+ − βu− = 0, then (α, β) is an isolated point on ∑ ∩ L, where L is the straight line parallel to the diagonal of ℝ+ × ℝ+ through (α, β).

3D Reconstruction of Single Particles by Quasi-Conical Tilting from Micrographs Recorded with Dynamic Focusing

The method of quasi-conical tilting for the 3D reconstruction of single macromolecules utilizes the fact that particles tend to adsorb to the supporting film in a few preferred orientations, though with arbitrary azimuthal angles. Therefore, a single electron micrograph of a tilted specimen containing a large number of particle projections provides the data of a conical tilt series with projection directions distributed randomly on a cone. For the selection of particles of equal orientation with respect to the supporting film and for the determination of their azimuth angles, a zero tilt image taken after the minimum dose “tilt image” is utilized.A disadvantage of the method is the large focal range of the tilt image, which e.g. at 30,000× magnification exceeds 5 μm. This, however, can be overcome by small-spot illumination in conjunction with dynamic focusing. For this, the illuminating beam is reduced to a diameter of 50-200 nm, and shifted stepwise or continuously over the object; for each spot position the focus is properly adjusted. Thus the focus range of the whole image is restricted to that of a single spot. Another way to realize dynamic focusing of a tilted object is the use of a narrow slit aperture in the condenser C2, thus illuminating a straight line parallel to the tilt axis.

Dose, Response, and Survival in Metastatic Mammary Cancer

To the Editor: Congratulations to Hryniuk and Bush in their effort to make sense out of many different chemotherapy regimens. However, in my opinion, I think they interpret their results too narrowly. For example, in Fig 2 and especially Fig 4, a straight line parallel to the ordinate at 0.6 fits the data as well as a line with a slope. In Fig 5, I am led by the discussion to accept a line from a median survival time (MST) of 10 months to an MST of 20 months, as the CR plus PR percent is increased from 20% to 80%. A line parallel to the abscissa at an MST of 15 months fits the data as well. If the lines drawn through the data have slopes, then the authors are correct in postulating increased dose intensity from 0.6 to 1.0+ indicates increased responses and increased survival. On the other hand, parallel lines drawn through the data give an alternate conclusion, namely that a threshold must be reached to achieve maximum benefit and doses above the threshold dose achieve very little. Accepting the data points by Hryniuk and Bush without criticism, how do we know what line best fits their compilation of data, a straight line or a line with a slope?