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71.
A new method for exact solutions of variant types of time‐fractional Korteweg‐de Vries equations in shallow water waves
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The current article devoted on the new method for finding the exact solutions of some time‐fractional Korteweg–de Vries (KdV) type equations appearing in shallow water waves. We employ the new method here for time‐fractional equations viz. time‐fractional KdV‐Burgers and KdV‐mKdV equations for finding the exact solutions. We use here the fractional complex transform accompanied by properties of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results are demonstrated by graphs for the new solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
72.
Bikash KarmakarJulie Banerji 《Tetrahedron letters》2011,52(38):4957-4960
A simple, efficient, and eco-friendly method for the synthesis of 1-(α-aminoalkyl) naphthols, the Betti bases, has been carried out over a basic nanocrystalline MgO catalyst in aqueous condition. The method has been applied for the synthesis of a range of compounds with variable functionalities in excellent yield and selectivity. 相似文献
73.
The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin. 相似文献
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The reaction of [Cp*MoCl(4)] with an excess of LiBH(4), followed by thermolysis with tellurium powder in toluene, afforded a tricapped cubane cluster, [(Cp*Mo)(4)B(4)H(4)(μ(4)-BH)(3)] (1), which represents an unprecedented metal-rich metallaborane cluster with a cubane core containing 58 cluster valence electrons (cve) and three metal-metal bonds. 相似文献
77.
Bose SK Geetharani K Sahoo S Reddy KH Varghese B Jemmis ED Ghosh S 《Inorganic chemistry》2011,50(19):9414-9422
The reaction of [Cp*TaCl(4)], 1 (Cp* = η(5)-C(5)Me(5)), with [LiBH(4)·THF] at -78 °C, followed by thermolysis in the presence of excess [BH(3)·THF], results in the formation of the oxatantalaborane cluster [(Cp*Ta)(2)B(4)H(10)O], 2 in moderate yield. Compound 2 is a notable example of an oxatantalaborane cluster where oxygen is contiguously bound to both the metal and boron. Upon availability of 2, a room temperature reaction was performed with [Fe(2)(CO)(9)], which led to the isolation of [(Cp*Ta)(2)B(2)H(4)O{H(2)Fe(2)(CO)(6)BH}], 3. Compound 3 is an unusual heterometallic boride cluster in which the [Ta(2)Fe(2)] atoms define a butterfly framework with one boron atom lying in a semi-interstitial position. Likewise, the diselenamolybdaborane, [(Cp*Mo)(2)B(4)H(4)Se(2)], 4 was treated with an excess of [Fe(2)(CO)(9)] to afford the heterometallic boride cluster [(Cp*MoSe)(2)Fe(6)(CO)(13)B(2)(BH)(2)], 5. The cluster core of 5 consists of a cubane [Mo(2)Se(2)Fe(2)B(2)] and a tricapped trigonal prism [Fe(6)B(3)] fused together with four atoms held in common between the two subclusters. In the tricapped trigonal prism subunit, one of the boron atoms is completely encapsulated and bonded to six iron and two boron atoms. Compounds 2, 3, and 5 have been characterized by mass spectrometry, IR, (1)H, (11)B, (13)C NMR spectroscopy, and the geometric structures were unequivocally established by crystallographic analysis. The density functional theory calculations yielded geometries that are in close agreement with the observed structures. Furthermore, the calculated (11)B NMR chemical shifts also support the structural characterization of the compounds. Natural bond order analysis and Wiberg bond indices are used to gain insight into the bonding patterns of the observed geometries of 2, 3, and 5. 相似文献
78.
Sahoo T Sardar S Mondal P Sarkar B Adhikari S 《The journal of physical chemistry. A》2011,115(21):5256-5273
We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D?2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D?2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D). 相似文献
79.
Jena BK Sahu SC Satpati B Sahu RK Behera D Mohanty S 《Chemical communications (Cambridge, England)》2011,47(13):3796-3798
A facile approach has been developed for synthesis of highly-structured, anisotropic Pd nanostructures. The dendritic Pd nanostructures show superior performance toward oxidation of formic acid and methanol for fuel cell application. 相似文献
80.