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991.
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
992.
Joseph F. Grcar 《Historia Mathematica》2011,38(2):163-218
Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — which Euler did not recommend, which Legendre called “ordinary,” and which Gauss called “common” — is now named after Gauss: “Gaussian” elimination. Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least-squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices. 相似文献
993.
Joseph W. Jerome 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7486-7498
The initial-boundary value problem for the Poisson–Nernst–Planck/Navier–Stokes model was investigated in [J.W. Jerome, R. Sacco, Global weak solutions for an incompressible charged fluid with multi-scale couplings: initial-boundary-value problem, Nonlinear Anal. 71 (2009) e2487–e2497], where an existence theory was demonstrated, based upon Rothe’s method of horizontal lines. In this article, the steady case is considered, and the existence of a weak solution is established for the boundary-value problem. This solution satisfies a weak maximum principle for the concentrations relative to the boundary values. As noted in the above-mentioned citation, the model assumes significance because of its connection to the electrophysiology of the cell, including neuronal cell monitoring and microfluidic devices in biochip technology. The model has also been used in other applications, including electro-osmosis. The steady model is especially important in ion channel modeling, because the channel remains open for milliseconds, and the transients appear to decay on the scale of tens of nanoseconds. 相似文献
994.
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional
parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal unitary extensions
of a partially defined isometry constructed explicitly from the problem data. A special role is played by a particular unitary
extension, called the central or universal unitary extension. The coefficient matrix for the Redheffer linear-fractional map has a simple expression in terms of the universal unitary
extension. The universal unitary extension can be seen as a unitary coupling of four unitary operators (two bilateral shift
operators together with two unitary operators coming from the problem data) which has special geometric structure. We use
this special geometric structure to obtain an inverse theorem (Theorem 8.4) which characterizes the coefficient matrices for
a Redheffer linear-fractional map arising in this way from a lifting problem. The main tool is the formalism of unitary scattering
systems developed in Boiko et al. (Operator theory, system theory and related topics (Beer-Sheva/Rehovot 1997), pp. 89–138,
2001) and Kheifets (Interpolation theory, systems theory and related topics, pp. 287–317, 2002) 相似文献
995.
Erik D. Demaine Martin L. Demaine Vi Hart John Iacono Stefan Langerman Joseph O��Rourke 《Graphs and Combinatorics》2011,27(3):363-376
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming. 相似文献
996.
Convex and concave relaxations are used extensively in global optimization algorithms. Among the various techniques available
for generating relaxations of a given function, McCormick’s relaxations are attractive due to the recursive nature of their
definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically
stronger than those resulting from convexification or linearization procedures. This article leverages the recursive nature
of McCormick’s relaxations to define a generalized form which both affords a new framework within which to analyze the properties
of McCormick’s relaxations, and extends the applicability of McCormick’s technique to challenging open problems in global
optimization. Specifically, relaxations of the parametric solutions of ordinary differential equations are considered in detail,
and prospects for relaxations of the parametric solutions of nonlinear algebraic equations are discussed. For the case of
ODEs, a complete computational procedure for evaluating convex and concave relaxations of the parametric solutions is described.
Through McCormick’s composition rule, these relaxations may be used to construct relaxations for very general optimal control
problems. 相似文献
997.
A robust route to 2,4-disubstituted pyrrole heterocycles relying upon a cascade reaction is reported. The reaction benefits from operational simplicity: it is air and moisture tolerant and is performed at ambient temperature. Control over the reaction conditions provides ready access to isopyrroles, 2,3,4-trisubstituted pyrroles, and 3-substituted pyrollidin-2-ones. 相似文献
998.
Salandria KJ Arico JW Calhoun AK McLaughlin LW 《Journal of the American Chemical Society》2011,133(6):1766-1768
We describe here the synthesis and properties of A-T rich DNA containing covalently bound water mimics located in the DNA minor groove. 相似文献
999.
Kumarasamy E Jesuraj JL Omlid JN Ugrinov A Sivaguru J 《Journal of the American Chemical Society》2011,133(43):17106-17109
Nonbiaryl axially chiral 2-pyridones were synthesized and employed for light-induced electrocyclic 4π ring closure leading to bicyclo-β-lactam photoproducts in solution. The enantioselectivity in the photoproducts varied from 22 to 95% depending on the reaction temperature and the ability of the axially chiral chromophore to form intramolecular and/or intermolecular H-bonds with the solvent. On the basis of the differential activation parameters, entropic control of the enantiospecificity was observed for 2-pyridones lacking the ability to form H-bonds. Conversely, enthalpy played a significant role for 2-pyridones having the ability to form H-bonds. 相似文献
1000.
The Ph(4)P(+) salt of the tetrahedral complex [Co(SPh)(4)](2-), possessing an S = (3)/(2) ground state with an axial zero-field splitting of D = -70 cm(-1), displays single-molecule magnet behavior in the absence of an applied magnetic field. At very low temperatures, ac magnetic susceptibility data show the magnetic relaxation time, τ, to be temperature-independent, while above 2.5 K thermally activated Arrhenius behavior is apparent with U(eff) = 21(1) cm(-1) and τ(0) = 1.0(3) × 10(-7) s. Under an applied field of 1 kOe, τ more closely approximates Arrhenius behavior over the entire temperature range. Upon dilution of the complex within a matrix of the isomorphous compound (Ph(4)P)(2)[Zn(SPh)(4)], ac susceptibility data reveal the molecular nature of the slow magnetic relaxation and indicate that the quantum tunneling pathway observed at low temperatures is likely mediated by intermolecular dipolar interactions. 相似文献