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61.
We compute analytically the full distribution of Andreev conductance G(NS) of a metal-superconductor interface with a large number N(c) of transverse modes, using a random matrix approach. The probability distribution P(G(NS),N(c) in the limit of large N(c) displays a Gaussian behavior near the average value =(2-√2)N(c) and asymmetric power-law tails in the two limits of very small and very large G(NS). In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power-law tail for large G(NS). Weakly nonanalytic points separate these four regimes-these are shown to be consequences of three phase transitions in an associated Coulomb gas problem. 相似文献
62.
Pierpaolo Soravia 《偏微分方程通讯》2013,38(9-10):1493-1514
We introduce a new formulation of Dirichlet problem for a class of first order, nonlinear equations containing the minimum time problem, whose solution is expected to be discontinuous. We prove existence, uniqueness and representation formulas for the solution in the sense of viscosity solutions. Our method relies on a new way of prescribing the boundary condition, the use of recent ideas of Barron-Jensen [8] and Barles [5] , and the derivation of a "backwards" dynamic programming principle. We use the same ideas to prove uniqueness for the usual Dicchlet type formulation, following Ishii [13] and Bales-Perthame [6], under additional regularity conditions on the domain. 相似文献
63.
Density functional theory (DFT) has become ubiquitous for chemical applications in research and in education. The exact functional at the foundation of DFT is unfortunately unknown, and issues arise when choosing an approximation for a specific application. With this tutorial review, we tackle the selection problem and many related ones, such as the choices of a basis set and of an integration grid, that are often overlooked by occasional practitioners and by more experienced users as well. We offer a practical approach in the form of a commented notebook containing 12 experiences that can be run on a simple computer in just a few hours. We propose this review as a primary source for those who are willing to include DFT in their everyday research or teaching activities in a way that reflects the research advances of the field in the last couple of decades. 相似文献
64.
Given an undirected graph and a collection of vertex subsets with suitable costs, we consider the problem of partitioning the graph into subgraphs of limited cost, splitting as little as possible the given subsets among different subgraphs. This problem originates from the organization of a region (the graph) including several towns (the vertices) into administrative areas (the subgraphs). The officers assigned to each area take care of activities which involve several towns at a time (the subsets). An activity involving towns from more areas engages the officers of all those areas, leading to redundancies which must be minimized. 相似文献
65.
66.
Valeria Gallo Pierpaolo Tomai Valerio Di Lisio Chiara Dal Bosco Paola DAngelo Chiara Fanali Giovanni DOrazio Ilaria Silvestro Yolanda Pic Alessandra Gentili 《Molecules (Basel, Switzerland)》2021,26(17)
The use of psychoactive substances is a serious problem in today’s society and reliable methods of analysis are necessary to confirm their occurrence in biological matrices. In this work, a green sample preparation technique prior to HPLC-MS analysis was successfully applied to the extraction of 14 illicit drugs from urine samples. The isolation procedure was a dispersive liquid–liquid microextraction based on the use of a low transition temperature mixture (LTTM), composed of choline chloride and sesamol in a molar ratio 1:3 as the extracting solvent. This mixture was classified as LTTM after a thorough investigation carried out by FTIR and DSC, which recorded a glass transition temperature at −71 °C. The extraction procedure was optimized and validated according to the main Food and Drug Administration (FDA) guidelines for bioanalytical methods, obtaining good figures of merit for all parameters: the estimated lower limit of quantitation (LLOQ) values were between 0.01 µg L−1 (bk-MMBDB) and 0.37 µg L−1 (PMA); recoveries, evaluated at very low spike levels (in the ng-µg L−1 range), spanned from 55% (MBDB) to 100% (bk-MMBDB and MDPV); finally, both within-run and between-run precisions were lower than 20% (LLOQ) and 15% (10xLLOQ). 相似文献
67.
Pierpaolo Soravia 《Applied Mathematics and Optimization》2009,59(2):175-201
When Hamiltonians are nonsmooth, we define viscosity solutions of the Aronsson equation and prove that value functions of
the corresponding deterministic optimal control problems are solutions if they are bilateral viscosity solutions of the Hamilton-Jacobi-Bellman
equation. We characterize such a property in several ways, in particular it follows that a value function which is an absolute
minimizer is a bilateral viscosity solution of the HJB equation and these two properties are often equivalent. We also determine
that bilateral solutions of HJB equations are unique among absolute minimizers with prescribed boundary conditions.
This research was partially supported by MIUR-Prin project “Metodi di viscosità, metrici e di teoria del controllo in equazioni
alle derivate parziali nonlineari”. 相似文献
68.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
69.
G. Baldini Huang Fu-Hua G. Varani L. Cordone S. L. Fornili G. Onori 《Il Nuovo Cimento D》1985,6(6):618-630
Summary The isothermal denaturation of calf thymus DNA, induced by the presence of some monohydric alcohols in the solution, was investigated.
Measurements were performed at a temperature (67.2°C) at which the denaturation, in the absence of alcohols, is about 20%
and melting profiles at varying temperatures were also recorded. Results show that with increasing alcohol concentration and
alkyl group size DNA denaturation first reaches a maximum and then falls back. This behaviour, ascribed to ?unusual? water
properties as inferred also from compressibility measurements, indicates that hydrophobic and electrostatic effects are connected
in a complex way.
Partially supported by Consiglio Nazionale delle Ricerche, Italy. 相似文献
70.