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101.
ABSTRACTIn this paper, we introduce a discrete convolution involving both the Fourier sine and cosine series. We study Young's type inequality and a discrete transform related to this convolution and solve in closed form a class of discrete Toeplitz plus Hankel equations. 相似文献
102.
103.
We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201–236,
2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance
and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost
of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance.
In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context. 相似文献
104.
We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs
and apply, in Sect. 2, to two situations. First, let W\mathcal{W} be a wedge of ℂ
n
with C
ω
, generic edge ℰ: a holomorphic function f on W\mathcal{W} has always a generalized (hyperfunction) boundary value bv(f) on ℰ, and this coincides with the collection of the boundary values along the discs which have C
ω
transversal intersection with ℰ. Thus Sect. 1 can be applied and yields the uniform continuity at ℰ of f when bv(f) is (separately) continuous. When W\mathcal{W} is only smooth, an additional property, the temperateness of f at ℰ, characterizes the existence of boundary value bv(f) as a distribution on ℰ. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again
the uniform continuity at ℰ of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63–72, 1986), in whose original proof the method of “slicing” by discs is not used. 相似文献
105.
106.
107.
Dang Huyen Vu Xuan Dang Hanh Vu Bich Doan Huu Dung Nguyen Tan Phong 《Research on Chemical Intermediates》2022,48(3):1311-1311
Research on Chemical Intermediates - 相似文献
108.
Nguyen H. N. Vu M. A. Hy D. M. Ta N. A. Do A. T. 《Journal of Applied and Industrial Mathematics》2021,15(2):315-325
Journal of Applied and Industrial Mathematics - In this paper, we introduce a nonlinear Lanchester-type model involving supply units. The model describes a battle where the Blue party consisting of... 相似文献
109.
Pham Loi Vu 《Acta Appl Math》2014,129(1):41-59
We consider the initial-boundary value problem (IBVP) for the Korteweg–de Vries equation with zero boundary conditions at x=0 and arbitrary smooth decreasing initial data. We prove that the solution of this IBVP can be found by solving two linear inverse scattering problems (SPs) on two different spectral planes. The first SP is associated with the KdV equation. The second SP is self-conjugate and its scattering function is found in terms of entries of the scattering matrix s(k) for the first SP. Knowing the scattering function, we solve the second inverse SP for finding the potential self-conjugate matrix. Consequently, the unknown object entering coefficients in the system of evolution equations for s(k,t) is found. Then, the time-dependent scattering matrix s(k,t) is expressed in terms of s(k)=s(k,0) and of solutions of the self-conjugate SP. Knowing s(k,t), we find the solution of the IBVP in terms of the solution of the Gelfand–Levitan–Marchenko equation in the first inverse SP. 相似文献
110.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献