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1.
2.
For ν≥0 let cνk be the k-th positive zero of the cylinder functionC v(t)=J v(t)cosα-Y v(t)sinα, 0≤α>π whereJ ν(t) andY ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC v,k 1+H(x) is convex as a function of ν, ifc νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1. 相似文献
3.
A mathematical analysis of the Bjerrum function is carried out. This function arises from the Stepwise Equilibrium Model, which is used to describe successive complex formation in systems consisting of free metal ion, free ligand, and all theML
i
complexes that can form in solution. The appropriate root of the Bjerrum polynomial allows the determination of the concentrations of all species present in solution, given the initial concentrations of metal and of ligand, and the equilibrium constants governing the system. It is proved that there is only one positive root of the Bjerrum polynomial, and thus that only a single equilibrium state can exist. It is also shown that the positive root of the Bjerrum polynomial can be reliably obtained by Newton's method, but only if the initialization point is properly chosen, and that the initial concentrationL of ligand is the optimum such point. Finding this root is a calculation that typically must be carried out at each iteration in nonlinear least squares procedures for determining equilibrium constants. Finally, the necessary mathematical analysis is carried out to determine the optimum initial concentrations of metal and lgand which maximize the resulting concentration of a particularML
i
complex. 相似文献
4.
5.
P. Valtazanos S. T. Elbert S. Xantheas K. Ruedenberg 《Theoretical chemistry accounts》1991,78(5-6):287-326
Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH2 groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH2 groups rotate in a disrotatory manner, maintainingC
s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH
2
groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences 相似文献
6.
Hedstrom JA Toney MF Huang E Kim HC Volksen W Magbitang T Miller RD 《Langmuir : the ACS journal of surfaces and colloids》2004,20(5):1535-1538
Materials with nanometer size heterogeneities are commonplace in the chemical and biological sciences (e.g, polymer blends, microemulsions, gels) and often exhibit complex morphologies. Although this morphology has a dramatic effect on the materials' properties, it is often difficult to accurately characterize. We describe a method, using small-angle X-ray scattering data, of generating representative three-dimensional morphologies of isotropic two-phase materials where the morphology is disordered, and we apply this to thin films containing nanometer sized pores with a range of porosities (4-44%). These representations provide a visualization of the pore morphology, give the pore size scale and extent of interconnection, and permit the determination of the transitions from closed pore to interconnected pores to bicontinuous morphology. 相似文献
7.
Stephen R. Langhoff Stephen T. Elbert Ernest R. Davidson 《International journal of quantum chemistry》1973,7(5):999-1019
The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the 3A2 (n → π*) and 3A1 (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm?1 and E = 0.031 cm?1 were obtained for the 3A2(n → π*) state and D = ?0.588 cm?1 and E = 0.058 cm?1 were obtained for the 3A1 (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the 3A2 (n n → π*) state of formaldehyde and the 3B1 ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF ) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the 1A1 ground state gave an energy of ?114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C+O?) in good agreement with the experimental value of 2.33 ± 0.02 Debye. 相似文献
8.
9.
We present a review of photoexcited quasiparticle dynamics of cuprate and pnictide high‐temperature superconductors in regimes (temperature, doping) where different phases such as superconductivity, spin‐density‐wave (SDW) and pseudogap phases coexist or compete with one another. We start with the overdoped cuprate superconductor Y1–xCax Ba2Cu3O7–δ, where the superconducting gap and pseudogap coexist in the superconducting state. In another cuprate Tl2Ba2Ca2Cu3Oy, we ob‐ serve a competition between SDW and superconducting orders deep in the superconducting state. Finally, in the underdoped iron pnictide superconductor (Ba,K)Fe2As2, SDW order forms at 85 K, followed by superconductivity at 28 K. We also find the emergence of a normal‐state order that suppresses SDW at a temperature T * ~ 60 K and argue that this normal‐state order is a precursor to superconductivity. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Chia EE Zhu JX Talbayev D Averitt RD Taylor AJ Oh KH Jo IS Lee SI 《Physical review letters》2007,99(14):147008
We present studies of the photoexcited quasiparticle dynamics in Tl(2)Ba(2)Ca(2)Cu(3)O(y) (Tl-2223) using femtosecond optical techniques. Deep into the superconducting state (below 40 K), a dramatic change occurs in the temporal dynamics associated with photoexcited quasiparticles rejoining the condensate. This is suggestive of entry into a coexistence phase which, as our analysis reveals, opens a gap in the density of states (in addition to the superconducting gap), and furthermore, competes with superconductivity resulting in a depression of the superconducting gap. 相似文献