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Speaking about the oblique Talbot effect, one usually assumes the case when the diffraction grating is illuminated by a plane wave at an angle, while the screen for observing the diffraction pattern is located parallel to the plane of the diffraction grating. At the same time, as the presented consideration shows, if the grating is illuminated at an angle, then in order to observe the Talbot effect, the observation screen must be tilted as well. In the present work, we considered the inclined Talbot effect for a grating with a finite number of slits, when the observation of the diffraction pattern and the illumination of the grating are performed at an angle. The dependence of the Talbot length on the angles of observation and illumination is determined. It is shown that the effect of self-reproduction can be observed only at certain values of these angles. It is proved that the value of the Talbot length does not depend on the parity of the number of lattice slits. At the same time, the number of slits determines the character of the distribution of maximums on the screen. Thus, in the case of a diffraction grating with an even number of slits, a maximum is observed in the center of the screen. In the case of a grating with an odd number of slits, the pattern of maximums is shifted by half the period of the grating compared to the pattern of maximums in the case of gratings with an even number of slits. [ABSTRACT FROM AUTHOR]

An interval t -coloring of a multigraph G is a proper edge coloring with colors 1 , … , t such that the colors of the edges incident with every vertex of G are colored by consecutive colors. A cyclic interval t -coloring of a multigraph G is a proper edge coloring with colors 1 , … , t such that the colors of the edges incident with every vertex of G are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t . Denote by w ( G ) ( w c ( G ) ) and W ( G ) ( W c ( G ) ) the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph G , respectively. We present some new sharp bounds on w ( G ) and W ( G ) for multigraphs G satisfying various conditions. In particular, we show that if G is a 2 -connected multigraph with an interval coloring, then W ( G ) ≤ 1 + | V ( G ) | 2 ( Δ ( G ) − 1 ) . We also give several results towards the general conjecture that W c ( G ) ≤ | V ( G ) | for any triangle-free graph G with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most 4 . [ABSTRACT FROM AUTHOR]

In this work thermochemistry of solvation of mono-, di-, tri- and tetra-substituted benzenes in 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF 4 ]) ionic liquid was studied. Enthalpies of solution at infinite dilution of 34 substituted benzenes in [BMIM][BF 4 ] were measured at 298.15 K using solution calorimetry technique. Based on the experimental and literature data enthalpies of solvation of 36 substituted benzenes in [BMIM][BF 4 ] were calculated. It was shown that enthalpies of solvation of substituted benzenes in [BMIM][BF 4 ] are independent on the mutual position of subtituents and dipole moment of molecules. Group contribution scheme for prediction of enthalpies of solvation of substituted benzenes was applied. Values of methyl- (CH 3 ), tert -butyl- ( tert -C 4 H 9 ), bromo- (Br), iodo- (I), amino- (NH 2 ), methoxy- (OCH 3 ), dimethylamino- (N(CH 3 ) 2 ), methylcarboxylate- (COOCH 3 ) group contributions to the enthalpies of solvation in [BMIM][BF 4 ] were derived and compared with molecular solvents. Solvation enthalpies of substituted benzenes in [BMIM][BF 4 ] calculated through group contribution scheme were in good agreement with experimental data. [ABSTRACT FROM AUTHOR]

An edge-coloring of a graph G with colors 1 , 2 , … , t is an interval t -coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t -coloring for some positive integer t . For an interval colorable graph G , W ( G ) denotes the greatest value of t for which G has an interval t -coloring. It is known that the complete graph is interval colorable if and only if the number of its vertices is even. However, the exact value of W ( K 2 n ) is known only for n ≤ 4 . The second author showed that if n = p 2 q , where p is odd and q is nonnegative, then W ( K 2 n ) ≥ 4 n − 2 − p − q . Later, he conjectured that if n ∈ N , then W ( K 2 n ) = 4 n − 2 − ⌊ log 2 n ⌋ − ‖ n 2 ‖ , where ‖ n 2 ‖ is the number of 1’s in the binary representation of n . In this paper we introduce a new technique to construct interval colorings of complete graphs based on their 1-factorizations, which is used to disprove the conjecture, improve lower and upper bounds on W ( K 2 n ) and determine its exact values for n ≤ 12 . [ABSTRACT FROM AUTHOR]

The description of the superposition field generated by a system of wave source points with coherent emission is discussed in this paper. The conditions for the problem parameters are identified in a general form, which enable satisfactory description of wave field within the framework of Fresnel and Fraunhofer approximations, respectively. In the presented approach a number of known results of the wave theory are reproduced, which are used for directional amplification. These results are summarized for the Fresnel diffraction case. The possibility to obtain a superposition field with point amplification is considered. [ABSTRACT FROM AUTHOR]

The problem of a wave field description for a harmonic in time plane wave propagating through arbitrary one dimensional absorbing media is considered. The analysis is performed in the framework of the so-called approach of counter-propagating waves developed for a case of the normal incidence, so that the results given in this work can be considered in many respects as a generalization on this approach. The suggested approach is also applied for calculations of a space distribution of a wave field both inside and outside of different layered structures. [ABSTRACT FROM AUTHOR]

In the paper the character of the phase relationships between oscillations at different points of the wave field generated by two coherent point sources is discussed. It is shown that on the surfaces of the maxima and minima of the amplitude, the in-phase or anti-phase of the oscillations is determined by the multiplicity of the path sum to the wavelength. The locations of the phase points in the interference pattern were defined. [ABSTRACT FROM AUTHOR]

Abstract: The dynamics of the S(1D)+CD4→SD+CD3 reaction has been studied in a photolysis-probe experiment. S(1D) reagent was prepared by laser photolysis of CS2, and the SD(X2Π) product was detected by laser fluorescence excitation. The nascent rotational/fine-structure state distribution of the SD(X2Π) product was determined. The experimentally determined rotational state distribution within each fine-structure manifold agrees well with the predictions of a statistical ‘prior’ distribution, while the F1 to F2 fine-structure branching ratio is higher than predicted statistically. The product state distribution is consistent with reaction through the formation and decay of an energized CD3SD complex. [Copyright &y& Elsevier]

A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the electron transmission and reflection amplitudes corresponding to the part of potential inside the well. The results are applied to three difference test problems. [Copyright &y& Elsevier]