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1.
2.
In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point. 相似文献
3.
José L. Ló pez Nico M. Temme 《Transactions of the American Mathematical Society》2004,356(11):4323-4342
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in several points as well as Taylor-Laurent expansions.
4.
In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms. 相似文献
5.
We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property. 相似文献
6.
This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works. 相似文献
7.
R. Srinivasan 《Pramana》2006,66(1):3-30
Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly
interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity.
Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of
a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature,
(d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped
and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction
of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically
expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect
ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex
and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures,
nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation
takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular
right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few
hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature;
(d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent
on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations
(Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed. 相似文献
8.
本文研究了混合范数空间H(p,q,a)中解析函数f的Taylor系数,对0<p≤2,0<q<∞,a>0和2≤p<∞,0<q<∞,a>0两种情形,分别给出了f属于H(p,q,a)的必要条件和充分条件。用上述结果我们还得到了几个关于混合范数空间的乘子定理,这些结果也推广了Hardy和Littlewood关于H^p空间的相应结论。 相似文献
9.
纯生跳跃扩散型交换期权定价公式 总被引:1,自引:0,他引:1
在假定标的资产价格服从纯生跳跃过程的条件下,研究一类多资产期权——资产权重不同的交换期权,并在风险中性的条件下建立相应的定价方程,运用条件期望等相关知识得出交换期权的解析公式。文中最后列出一些特殊纯生跳跃扩散型交换期权的定价的例子. 相似文献
10.
Higher-order implicit strong numerical schemes for stochastic differential equations 总被引:2,自引:0,他引:2
Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined. 相似文献