20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.     

Interference inspection of the aspherical components of an objective for nanolithography

Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved.     

Calculation of the Radiating Characteristics of a Thermodynamically Nonuniform Gas Medium

Passive methods of remote analysis of waste gases of industrial enterprises and aircrafts engines and gases ejected in eruptions of volcanos, in fires, and in other processes disturbing the atmosphere are now of limited utility because of the lack of well-developed mathematical techniques for solving the inverse problems of gas analysis. However, the advantage of these methods is obvious, since the equipment is limited to a receiving device and the gas medium serves as a radiator. At the same time, in modern techniques, the interpretation of measurements of emissivities of gases is performed using a phenomenological approach such that experimental data on radiation characteristics of various objects are approximated by simple polynomial relations whose coefficients are determined by minimization methods. This approach does not allow one to investigate the mechanism of the processes occurring in a radiating medium and gives no way of solving the inverse problem of monitoring the composition and thermodynamic parameters of a medium which disturbs the atmosphere by thermal effects. In elaborating theoretical methods of gas analysis, the elaboration of the direct problem of calculation of radiating characteristics of gases is of importance, since it is not clear how the emissivity of a gas medium depends on its thermodynamic parameters. This paper is devoted to the above problem. Here, the error is estimated that arises in modeling a nonuniform gas medium with an actual temperature distribution, which linearly depends on coordinate, by a uniform gas layer. It is shown that the difference between the radiation intensities calculated for uniform and nonuniform media can be significant in the practically important case where the recording device is in a zone of normal temperatures. This implies that the error of reconstruction of the spectroscopic and molecular parameters of gaseous compounds from high-temperature measurements of the radiating and absorbing characteristics should take into account the thermodynamic nonuniformity of the medium.     

A rapid and sensitive extractive spectrophotometric determination of copper(II) in pharmaceutical and environmental samples using benzildithiosemicarbazone.

Benzildithiosemicarbazone (BDTSC) is proposed as a sensitive and selective analytical reagent for the extractive spectrophotometric determination of copper(II). BDTSC reacts with copper(II) in the pH range 1.0-7.0 to form a yellowish complex. Beer's law is obeyed in the concentration range 0.5-0.4 microg cm(-3). The yellowish Cu(II)-BDTSC complex in chloroform shows a maximum absorbance at 380 nm, with molar absorptivity and Sandell's sensitivity values of 1.63 x 10(4) dm3 mol(-1) cm(-1) and 0.00389 microg cm(-2), respectively. A repetition of the method is checked by finding the relative standard deviation (RSD) (n = 10), which is 0.6%. The composition of the Cu(II)-BDTSC complex is established as 1:1 by slope analysis, molar ratio and Asmus' methods. An excellent linearity with a correlation coefficient value of 0.98 is obtained for the Cu(II)-BDTSC complex. The instability constant of the complex calculated from Edmond and Birnbaum's method is 7.70 x 10(-4) and that of Asmus' method is 7.66 x 10(-4), at room temperature. The method is successfully employed for the determination copper(II) in pharmaceutical and environmental samples. The reliability of the method is assured by analyzing the standard alloys (BCS 5g, 10g, 19e, 78, 32a, 207 and 179) and by inter-comparison of experimental values, using an atomic absorption spectrometer.     

Sound propagation in an unstable atmospheric layer

The equation of sound propagation in an unstable medium produced by the presence of supersaturated water vapor in it, which can appear in a hurricane area, is derived. This equation takes into account the effects of sound velocity dispersion, amplification, damping, and nonlinear effects. Some solutions to this equation are presented, illustrating the specific features of sound propagation in an unstable medium. Published in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 3, pp. 477–480.     

Time-resolved fluorescence study of the single tryptophan in thiocyanate and azide derivatives of horseradish peroxidase: Implication for a p H-induced conformational change in the heme cavity

Detailed pH-dependent steady state and picosecond time-resolved tryptophan fluorescence studies on thiocyanate and azide complexes of horseradish peroxidase have been carried out. The fluorescence decay of the single tryptophan in these species was fitted to a discrete three exponential model. Maximum entropy method analysis also gave three distinct regions of lifetime distributions. The fast subnanosecond lifetime component was found to have > 97% amplitude contribution while other two longer lifetime components have small contributions. Small contributions from the nanosecond lifetime components possibly arise from apoprotein impurity or some small amount of disordered heme conformer of the protein. pH dependence of the fast picosecond lifetime components was found to show a systematic behavior which has been interpreted in the light of obligatory conformation change associated with activation of the enzyme at low pH.     

Theoretical and experimental investigation of the linear optical response of YBa2Cu4O8 The relevance of LDA calculations

We report results of ellipsometric measurements of the dielectric tensor of YBa₂Cu₄O₈ as well as calculations employing density functional theory in the local density approximation (LDA). For the computation of the one-electron eigenvalues and states the linear-muffin-tin-orbital method (LMTO) was used. Measured and calculated results show good agreement. In particular, the calculation predicts different band structures for YBa₂Cu₃O₇ and YBa₂Cu₄O₈ in the vicinity of the Fermi energy which lead to significant differences in the optical spectra. One such difference is a region of small ε₂ in the near infrared which is a fingerprint of the high (relative to the top of the highest fully occupied band) Fermi energy as compared to the situation in YBa₂Cu₃O₇. Our experimental results confirm the theoretical findings.     

Influence of layer and anisotropic fluctuations of the refractive index on the beyond-the-horizon SHF propagation in the troposphere over the sea when there is an evaporation duct

On the basis of the invariant imbedding method the disturbance theory for complex constants of propagation is proposed. This approach allows us to consider the influence of layer and anisotropic fluctuations of refractive index on the beyond-the-horizon propagation in the adiabatic approximation with the existence of an evaporation duct. Finally, the authors consider some examples of the calculations and investigate stochastic effects connected with the interaction between fluctuating and regular waveguides.