Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case

Time-independent nonlinear Schrödinger-type (NLS) formulation of FRW cosmology with canonical scalar field is considered in the case of two barotropic fluids. We derived Friedmann formulation variables in terms of NLS variables. Seven exact solutions found by D’Ambroise [Ph.D. thesis, arXiv:1005.1410 ] and one new found solution are explored and tested in cosmology. The result suggests that time-independent NLS formulation of cosmology case should be upgraded to the time-dependent case.

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MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513500619 ◽

2013 ◽

Vol 24 (03) ◽

pp. 599-626 ◽

Cited By ~ 2

Author(s):

HICHEM HAJAIEJ ◽

PETER A. MARKOWICH ◽

SABER TRABELSI

Keyword(s):

Molecular Dynamics ◽

Initial Data ◽

Neutron Stars ◽

Time Dependent ◽

System Of Equations ◽

Critical Number ◽

Dependent Case ◽

Hartree Fock ◽

The Third ◽

Time Solution

In [Setting and analysis of the multi-configuration time-dependent Hartree–Fock equations, Arch. Ration. Mech. Anal.198 (2010) 273–330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree–Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr .

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The Bloch wave operator: generalizations and applications: II. The time-dependent case

Journal of Physics A General Physics ◽

10.1088/0305-4470/36/40/r01 ◽

2003 ◽

Vol 36 (40) ◽

pp. R411-R473 ◽

Cited By ~ 27

Author(s):

Georges Jolicard ◽

John P Killingbeck

Keyword(s):

Wave Operator ◽

Bloch Wave ◽

Time Dependent ◽

Dependent Case

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ANALYTIC–NUMERICAL SOLUTIONS WITH A PRIORI BOUNDS FOR MATRIX–VECTOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s001309150000033x ◽

2002 ◽

Vol 45 (1) ◽

pp. 5-25 ◽

Cited By ~ 1

Author(s):

Lucas Jódar ◽

Marco Marletta

Keyword(s):

Numerical Solutions ◽

A Priori ◽

Approximate Solutions ◽

Time Dependent ◽

Vector System ◽

Approximation Procedure ◽

Time Step ◽

Dependent Case ◽

Independent Case ◽

Matrix Vector

AbstractWe consider a parabolic matrix–vector system in which the diffusion matrix may be time dependent. For the time-independent case we construct approximate solutions with guaranteed error bounds using spectral information from certain matrix–vector Sturm–Liouville problems. For the time-dependent case we employ an approximation procedure which reduces the problem, on each time-step, to the time-independent case. We give an algorithm which may be used a priori at each time-step in the time-dependent case to guarantee accuracy to a specified tolerance.AMS 2000 Mathematics subject classification: Primary 35C10; 35M10. Secondary 15A

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The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025714500301 ◽

2014 ◽

Vol 17 (04) ◽

pp. 1450030 ◽

Cited By ~ 4

Author(s):

Litan Yan ◽

Junfeng Liu ◽

Chao Chen

Keyword(s):

Banach Space ◽

Brownian Motion ◽

Fractional Brownian Motion ◽

Local Time ◽

Borel Function ◽

Time Dependent ◽

Hurst Index ◽

Dependent Case ◽

Measurable Functions ◽

Quadratic Covariation

In this paper, we study the generalized quadratic covariation of f(BH) and BH defined by [Formula: see text] in probability, where f is a Borel function and BH is a fractional Brownian motion with Hurst index 0 < H < 1/2. We construct a Banach space [Formula: see text] of measurable functions such that the generalized quadratic covariation exists in L2(Ω) and the Bouleau–Yor identity takes the form [Formula: see text] provided [Formula: see text], where [Formula: see text] is the weighted local time of BH. These are also extended to the time-dependent case, and as an application we give the identity between the generalized quadratic covariation and the 4-covariation [g(BH), BH, BH, BH] when [Formula: see text].

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