Self-similarity in diffraction by a self-similar fractal screen

Using the Sierpinski gasket as an example, it has been shown here that the paraxial Fraunhoffer-zone diffracted field of a self-similar fractal screen also exhibits self-similarity. This also establishes that fractal structures can be used with great profit in problems involving array syntheses. Recently, it has been shown that the Sierpinski gasket is itself a member of a much wider class of gaskets, and the potential for the use of fractal structures in electromagnetic (EM) problems may be vast indeed.     

Convergence of genetic algorithms

The mean convergence of various versions of a genetic algorithm are considered. A number of convergence statements are formulated and relevant estimates are obtained. A hypothesis concerning the form of these estimates under variation of the structure of a genetic algorithm is put forward. Roman Riviyanovich Sharapov. Born 1981. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: genetic algorithms, neural networks, and financial mathematics. Aleksandr Vyacheslavovich Lapshin. Born 1980. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: financial mathematics, genetic algorithms, and neural networks.     

Incremental transmission loss allocation under pool dispatch

Incremental transmission loss analysis has been used for decades, but recent interest in its application to loss allocation calls for new in-depth results. This paper demonstrates that, for incremental methods to be applied correctly in loss allocation, it is first necessary to specify the load distribution and loss supply strategies. Incremental loss allocation among bus power injections is shown to be arbitrary and, therefore, open to challenge as discriminatory. Loss allocation is possible among incremental loads and/or generators, but the proportion of the total losses assigned to either one is arbitrary. Unique, nonarbitrary incremental loss allocations are however possible among the "equivalent" incremental bilateral exchanges between generators and loads. From these basic components it is possible then to calculate the allocation among generators or loads in any specified proportion. The main results, although developed initially for small increments, are extended to large variations. Finally, a general incremental loss allocation algorithm is developed and tested     

Modern Aluminum and Magnesium Alloys and Composite Materials Based on Them

Aluminum and magnesium alloys are the base structural materials in aircraft and spacecraft engineering. The main stages of the development and introduction of light alloys are described.     

The Onsager relations analyzed using an ellipsoidal statistical equation

Validity on the well-known Onsager reciprocal relations L ₁₂=L ₂₁ is verified in the kinetic theory of gases taking into account mass and heat transfer near the surface. Using an analytical solution to the ellipsoidal statistical equation (providing for the true Prandtl number), it is demonstrated that the Onsager relations are obeyed, at least to within exponential corrections of the type exp(−1/Kn) in the Knudsen number.     

Influence of Edible Films upon the Moisture Loss and Microstructure of Dietetic Sucrose-Free Sponge Cakes during Storage

The kinetics of changes in the bound water content in dietetic sucrose-free sponge cakes (DC) during storage was investigated. The effect of edible films of polymyxan, pectin, xanthan, and carboxymethylcellulose upon this kinetics was also investigated. The quantitative changes in both states of water (slightly bound water and strongly bound water) were registered by combined dynamic analysis (thermogravimetry analysis, TGA, and differential thermal analysis, DTA). The moisture changes in DC crumb were analyzed by drying out to constant mass. The rate constants were determined according the equation q = q_oe^-kt. The values of rate constants 'k', in day^-1, concerning the different edible films were as follows: for crumb moisture is (8.00 ≤ k ≤ 12.47) × 10^-3, for bound water is (3.07 ≤ k_w ≤ 6.26) × 10^-2, for slightly bound water is (4.22 ≤ k₁ ≤ 8.49) × 10^-2 and for strongly bound water is (2.02 ≤ k₂ ≤ 5.62) × 10^-2 as compared to 18.53 × 10^-3, 7.16 × 10^-2, 9.04 × 10^-2, and 5.36 × 10^-2 in the uncovered DC, respectively. The best water-retaining effect in respect to crumb moisture during storage was ascertained in the use of polymyxan and xanthan films. The lowest rate constant values for bound water and its two states were measured for DC covered with pectin. The relation between the kinetics of both bound water states during storage and ageing of the crumb of DC covered with different edible films and the crumb microstructure was represented. By means of scanning electron microscope was read the smallest change in crumb microstructure of pectin-covered DC on the sixth day of storage.     

Structure and composition of guanidine acrylate, guanidine methacrylate, their homopolymers, and copolymers with diallyldimethylammonium chloride

Structures and compositions of the monomers guanidine acrylate and guanidine methacrylate, their homopolymers, and copolymers with diallyldimethylammonium chloride enriched in acrylate comonomer units were determined. It was shown that ampholytic copolymers, owing to their ionic nature, contained comonomeric guanidine acrylate or methacrylate units and diallyldimethylammonium chloride units, as well as the acrylate comonomer with the diallyl counterion and polymeric acrylate and diallyl ion pairs. It follows from IR and ¹H NMR data that guanidine methacrylate has the same structure (with two hydrogen bonds) in the solid state and in solutions. Guanidine acrylate structures in the solid state and in dimethylsulfoxide are identical and analogous to guanidine methacrylate structure in this solvent. In water, the guanidine acrylate structure has another type of hydrogen bonding (with one hydrogen bond, where the proton is shifted toward the guanidine group). These features of hydrogen bonding of guanidine acrylate and guanidine methacrylate are also retained in their homopolymers and copolymers with diallyldimethylammonium chloride. It was shown that the thermal stability of the copolymers was higher than that of their homopolymers, confirming the formation of intramolecular ion pairs of oppositely charged units of ampholytic copolymers. Moreover, the thermal stability of guanidine methacrylate-diallyldimethylammonium chloride copolymers is higher than that of guanidine acrylate-diallyldimethylammonium chloride copolymers.