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11.
Nikolay K. Vitanov Zlatinka I. Dimitrova Kaloyan N. Vitanov 《Entropy (Basel, Switzerland)》2021,23(1)
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of to solution for arbitrary finite values of . Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM. 相似文献
12.
Anna Kasikova 《Journal of Combinatorial Theory, Series A》2011,118(2):641-671
For a class of parapolar spaces that includes the geometries E6,4, E7,7, and E8,1 with lines of size at least three, the metasymplectic spaces with lines of size at least four, and the polar line Grassmannians with lines of size at least four except D4,2(3), we show that the subgraph of the point-collinearity graph induced on the complement of a hyperplane is simply connected. We also show that these parapolar spaces have Veldkamp lines. 相似文献
13.
《Tetrahedron》2014,70(21):3447-3451
Copper(II) catalyzed cross-dehydrogenative coupling of cyclic benzylic ethers with a variety of simple carbonyl compounds mediated by Na2S2O8 is developed. The scope of carbonyl components is broad, including simple aldehydes as well as ketones. The use of Na2S2O8 as the oxidant for the CDC reaction is attractive based on economical and environmental factors. 相似文献
14.
Rebecca Wiesner Christin Scheller Finja Krebs Hermann Wätzig Imke Oltmann-Norden 《Electrophoresis》2021,42(3):206-218
The development of capillary electrophoresis, especially CE-SDS devices, has led CE-SDS to become an established tool in a wide range of applications in the analysis of biopharmaceuticals and is increasingly replacing its method of origin, SDS-PAGE. The goal of this study was to evaluate the comparability of molecular weight (MW) determination especially by CE-SDS and SDS-PAGE. For ensuring comparability, model proteins that have little or no posttranslational modifications and an IgG antibody were used. Only a minor influence of sample preparation conditions, including sample buffer, temperature conditions, and different reducing agents on the MW determination were found. In contrast, the selection of the MW marker plays a decisive role in determining the accurate apparent MW of a protein. When using different MW markers, the deviation in MW determination can exceed 10%. Interestingly, CE-SDS and 10% SDS-PAGE hardly differ in their trueness of MW determination. The trueness in relation to the reference MW for each protein was calculated. Although the trueness values for the model proteins considered range between 1.00 and 1.11 using CE-SDS, they range between 0.93 and 1.03 on SDS-PAGE, depending on the experimental conditions chosen. 相似文献
15.
Co3xNi3−3x(PO4)2·8H2O (x = 1, 0.8, 0.6, 0.4, 0.2, and 0) were synthesized via simple wet chemical reaction and energy saving route method. The final decomposition products of hydrates are corresponding anhydrous tri(cobalt nickel) diphosphates. The metal and water contents of the synthesized hydrates were confirmed by AAS and TG/DTG/DTA techniques, respectively. The observed metal and water contents agree well with the formula of the title compounds. The crystal structures and lattice parameters as well as crystallite sizes of the studied compounds were determined using XRD data. The results from XRD and TG/DTG/DTA techniques confirmed that Co3xNi3−3x(PO4)2·8H2O at all ratios were the single phase. The FTIR spectra of studied compounds were recorded and assigned. The thermal behaviours of single and binary tri(cobalt nickel) diphosphate octahydrates were studied for the first time. The morphologies of the studied compounds were investigated by using the SEM technique. The micrographs of all studied compounds exhibited the thin plated morphology. The surface area and the pore size data of anhydrous forms were measured by N2 adsorption at −190 °C according to the BET method. The anhydrous forms of binary metal phosphate at x = 0.8, Co2.4Ni0.6(PO4)2, exhibits the highest surface area and expects to improve the catalytic activity. 相似文献
16.
Let G be a simple Lie group of real rank one, with Iwasawa decomposition and Bruhat big cell . Then the space may be (almost) identified with N and with K/M, and these identifications induce the (generalised) Cayley transform . We show that is a conformal map of Carnot-Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplication by appropriate powers of the Jacobian, induces isomorphisms of Sobolev spaces and . We use this to construct uniformly bounded and slowly growing representations of G. 相似文献
17.
The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated
on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations
have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the
phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from
other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at
d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior. 相似文献
18.
L.Yu. Kolotilina 《Linear algebra and its applications》2008,429(10):2521-2539
The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern. 相似文献
19.
Qiaohua Yang 《Journal of Mathematical Analysis and Applications》2008,341(2):998-1006
Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. We prove a refined version of the Sobolev inequality on N in presence of symmetry. 相似文献
20.
Maarten H. van der Vlerk 《Mathematical Methods of Operations Research》2005,62(2):225-242
We consider multiple simple recourse (MSR) models, both continuous and integer versions, which generalize the corresponding
simple recourse (SR) models by allowing for a refined penalty cost structure for individual shortages and surpluses. It will
be shown that (convex approximations of) such MSR models can be represented as explicitly specified continuous SR models,
and thus can be solved efficiently by existing algorithms.
This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. 相似文献