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91.
O.V. Bychuk B. O'Shaughnessy N.J. Turro 《The European physical journal. E, Soft matter》2001,4(3):281-291
We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute
solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially
highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions.
In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved.
This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t
- (1 + g/3) is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ,
- ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t
1/2 and S(t) ∼ 1/x
3(t). At the shortest times ( t
10-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited
by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d
3(t)/d (for randomly distributed ends) is replaced by ∼d2x
3(t)/d
2 for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions.
Received 18 May 2000 相似文献
92.
We study the generic linearly normal special scroll of genus g in P N . Moreover, we give a complete classification of the linearly normal scrolls in P 3 of genus 2 and 3. 相似文献
93.
Yu. A. Brychkov 《Applied mathematics and computation》2011,218(3):689-692
A method is proposed for evaluation of some definite integrals and infinite sums containing products of Bessel, Struve and other special functions. 相似文献
94.
ICP-MS测定饮用水源中的钼、钴、铍、锑、镍、钡、钒、钛和铊等9种特定项目 总被引:2,自引:0,他引:2
采用电感耦合等离子体-质谱法(ICP-M S)测定水中的钼、钴、铍、锑、镍、钡、钒、钛、铊等9种元素。结果表明,各元素检出限0.005—0.07μg.L^-1,满足饮用水源分析要求;空白加标回收率94.2%—106.0%,相对标准偏差RSD〈4.0%,n=9)。样品加标回收率93.8%—110.0%,该方法高效、简便、线性范围宽,适用于饮用水源水质分析。 相似文献
95.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(11):4037-4041
It is known that the simplest equation method is applied for finding exact solutions of autonomous nonlinear differential equations. In this paper we extend this method for finding exact solutions of non-autonomous nonlinear differential equations (DEs). We applied the generalized approach to look for exact special solutions of three Painlevé equations. As ODE of lower order than Painlevé equations the Riccati equation is taken. The obtained exact special solutions are expressed in terms of the special functions defined by linear ODEs of the second order. 相似文献
96.
We study the degrees of special cubic divisors on moduli space of cubic fourfolds with at worst ADE singularities. In this paper, we show that the generating series of the degrees of such divisors is a level three modular form. 相似文献
97.
This paper studies the possibility to calculate efficiently compounds of real matrices which have a special form or structure.
The usefulness of such an effort lies in the fact that the computation of compound matrices, which is generally noneffective
due to its high complexity, is encountered in several applications. A new approach for computing the Singular Value Decompositions
(SVD’s) of the compounds of a matrix is proposed by establishing the equality (up to a permutation) between the compounds
of the SVD of a matrix and the SVD’s of the compounds of the matrix. The superiority of the new idea over the standard method
is demonstrated. Similar approaches with some limitations can be adopted for other matrix factorizations, too. Furthermore,
formulas for the n − 1 compounds of Hadamard matrices are derived, which dodge the strenuous computations of the respective numerous large determinants.
Finally, a combinatorial counting technique for finding the compounds of diagonal matrices is illustrated.
相似文献
98.
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This
is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension. Moreover, the
spectrum is then typically quasi-periodic, but non-periodic, i.e., the spectrum is a “small perturbation” of a lattice. Due
to earlier research on IFSs, there are known results on certain classes of spectral duality-pairs, also called spectral pairs
or spectral measures. It is known that some duality pairs are associated with complex Hadamard matrices. However, not all
IFSs X admit spectral duality. When X is given, we identify geometric conditions on X for the existence of a Fourier spectrum, serving as the second part in a spectral pair. We show how these spectral pairs
compose, and we characterize the decompositions in terms of atoms. The decompositions refer to tensor product factorizations
for associated complex Hadamard matrices.
Research supported in part by a grant from the National Science Foundation DMS-0704191. 相似文献
99.
Richard M. Slevinsky Hassan Safouhi 《Journal of Computational and Applied Mathematics》2009,233(2):405-419
We present new formulae (the Slevinsky–Safouhi formulae I and II) for the analytical development of higher order derivatives. These formulae, which are analytic and exact, represent the kth derivative as a discrete sum of only k+1 terms. Involved in the expression for the kth derivative are coefficients of the terms in the summation. These coefficients can be computed recursively and they are not subject to any computational instability. As examples of applications, we develop higher order derivatives of Legendre functions, Chebyshev polynomials of the first kind, Hermite functions and Bessel functions. We also show the general classes of functions to which our new formula is applicable and show how our formula can be applied to certain classes of differential equations. We also presented an application of the formulae of higher order derivatives combined with extrapolation methods in the numerical integration of spherical Bessel integral functions. 相似文献
100.
We consider a collection of heterogeneous assets which exhibit independent stochastic behavior, but are economically interdependent due to resource constraints on management decisions. We represent the collection of assets as a network of nonhomogeneous Markov decision processes linked by side constraints. To facilitate a procedure for obtaining nonrandomized decision policies, we express the resource limitations as integrated chance constraints and relax them into the objective function within a Lagrangian penalty term. We utilize subgradient optimization to establish upper bounds and a greedy randomized Lagrangian repair heuristic to obtain feasible solutions. We empirically validate the tightness of these a posteriori upper and lower bounds with computational experiments on a pair of applications. For pavement maintenance, we examine the effect that the reward structure of each constituent MDP has on the maintenance policy in the presence of budget constraints. For equipment replacement, we consider constraints on two resource types. 相似文献