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281.
Patricio Felmer Salomé Martínez 《Calculus of Variations and Partial Differential Equations》2008,31(2):231-261
This article is devoted to the study of radially symmetric solutions to the nonlinear Schrödinger equation where B is a ball in \({\mathbb{R}}^N\) , 1 < p < (N + 2)/(N ? 2), N ≥ 3 and the potential V is radially symmetric. We construct positive clustering solutions in an annulus having O(1/?) critical points, as well as sign changing solutions with O(1/?) zeroes concentrating near zero.
相似文献
$\varepsilon^2 \Delta u - V(r)u + |u|^{p-1}u = 0\, {\rm in} B,\quad \frac{\partial u}{\partial n} = 0\, {\rm on}\,{\partial}B,$
282.
283.
Rodrigo?M.?GesterEmail author Herbert?C.?Georg Tertius?L.?Fonseca Patricio?F.?Provasi Sylvio?CanutoEmail author 《Theoretical chemistry accounts》2012,131(5):1220
Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect
the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use
of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a
model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on
the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the 15N magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization
of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry
relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding
constant is calculated as −58.7 ppm, in good agreement with the experimental value of −56.3 ppm. The explicit inclusion of
hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of
−61.8 ppm. 相似文献
284.
Gloriana González Patricio G. Herbst 《International Journal of Computers for Mathematical Learning》2009,14(2):153-182
This paper describes students’ interactions with dynamic diagrams in the context of an American geometry class. Students used
the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK¢ model
of conceptions, suggests that incorporating technology in mathematics classrooms enabled a measure-preserving conception of
congruency with which students’ could shift focus from shapes to properties. Students also interacted with dynamic diagrams
in a novel way, which we call the functional mode of interaction with diagrams, relating outputs and inputs that result when dragging a figure. Students’ participation
in classroom interactions through discourse and through actions on diagrams provided evidence of learning using tools within
dynamic geometry software. 相似文献
285.
This paper studies new inversion methods for the Laplace transform of vector-valued functions arising from a combination of A-stable rational approximation schemes to the exponential and the shift operator semigroup. Each inversion method is provided in the form of a (finite) linear combination of the Laplace transform of the function and a finite amount of its derivatives. Seven explicit methods arising from A-stable schemes are provided, such as the Backward Euler, RadauIIA, Crank-Nicolson, and Calahan scheme. The main result shows that, if a function has an analytic extension to a sector containing the nonnegative real line, then the error estimate for each method is uniform in time. 相似文献
286.
Manuel Abad Juan Manuel Cornejo Patricio Díaz Varela 《Mathematical Logic Quarterly》2012,58(3):168-176
In this paper we prove that the free algebras in a subvariety $\mathcal V$ of the variety $\mathcal {SH}$ of semi‐Heyting algebras are directly decomposable if and only if $\mathcal V$ satisfies the Stone identity. 相似文献