Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Table Of Integrals Series And Products

Ordinary differential equations Constant coefficient linear dispersive equations Semilinear dispersive equations The Korteweg de Vries equation Energy-critical semilinear dispersive equations Wave maps Tools from harmonic analysis Construction of ground states Bibliography.

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Nonlinear dispersive equations : local and global analysis

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Methods Of Modern Mathematical Physics

Conditioned place preference (CPP) continues to be one of the most popular models to study the motivational effects of drugs and non-drug treatments in experimental animals. This is obvious from a steady year-to-year increase in the number of publications reporting the use this model. Since the compilation of the preceding review in 1998, more than 1000 new studies using place conditioning have been published, and the aim of the present review is to provide an overview of these recent publications. There are a number of trends and developments that are obvious in the literature of the last decade. First, as more and more knockout and transgenic animals become available, place conditioning is increasingly used to assess the motivational effects of drugs or non-drug rewards in genetically modified animals. Second, there is a still small but growing literature on the use of place conditioning to study the motivational aspects of pain, a field of pre-clinical research that has so far received little attention, because of the lack of appropriate animal models. Third, place conditioning continues to be widely used to study tolerance and sensitization to the rewarding effects of drugs induced by pre-treatment regimens. Fourth, extinction/reinstatement procedures in place conditioning are becoming increasingly popular. This interesting approach is thought to model certain aspects of relapse to addictive behavior and has previously almost exclusively been studied in drug self-administration paradigms. It has now also become established in the place conditioning literature and provides an additional and technically easy approach to this important phenomenon. The enormous number of studies to be covered in this review prevented in-depth discussion of many methodological, pharmacological or neurobiological aspects; to a large extent, the presentation of data had to be limited to a short and condensed summary of the most relevant findings.

Measuring reward with the conditioned place preference (CPP) paradigm: update of the last decade.

We consider the scattering problem for the nonlinear Schrodinger equation in 1+1 dimensions:
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where ∂ = ∂/∂x,λ∈R∖{0},μ∈R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL2(R) or in the Sobolev spaceH1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

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Long range scattering for nonlinear Schrödinger equations in one space dimension

On Critical Cases of Sobolev′s Inequalities

On the derivative nonlinear Schro¨dinger equation

We consider the scattering problem for the non-linear Schrodinger (NLS) equation with a power interaction with critical powerp=1+2/n in space dimensionsn=2 and 3 and for the Hartree equation with potential |x|−1 in space dimensionn≥2. We prove the existence of modified wave operators in theL2 sense on a dense set of small and sufficiently regular asymptotic states.

/pdf/long-range-scattering-for-non-linear-schrodinger-and-hartree-svd9w8u82c.pdf

Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schrodinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in \(L^2\).

Tohru Ozawa

Papers

Long range scattering for nonlinear Schrödinger equations in one space dimension

On Critical Cases of Sobolev′s Inequalities

On the derivative nonlinear Schro¨dinger equation

Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations