Search results for "Partial"
showing 10 items of 1477 documents
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
2001
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
2021
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…
ADI schemes for valuing European options under the Bates model
2018
Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.
Calcification is not the Achilles'heel of cold-water corals in an acidifying ocean
2015
Ocean acidification is thought to be a major threat to coral reefs: laboratory evidence and CO2 seep research has shown adverse effects on many coral species, although a few are resilient. There are concerns that cold-water corals are even more vulnerable as they live in areas where aragonite saturation (Omega ara) is lower than in the tropics and is falling rapidly due to CO2 emissions. Here, we provide laboratory evidence that net (gross calcification minus dissolution) and gross calcification rates of three common cold-water corals, Caryophyllia smithii, Dendrophyllia cornigera, and Desmophyllum dianthus, are not affected by pCO2 levels expected for 2100 (pCO2 1058 µatm, Omega ara 1.29),…
Mappings of finite distortion: The Rickman-Picard theorem for mappings of finite lower order
2004
We show that an entire mappingf of finite distortion with finite lower order can omit at most finitely many points when the distortion function off is suitably controlled. The proof uses the recently established modulus inequalities for mappings of finite distortion [15] and comparison inequalities for the averages of the counting function. A similar technique also gives growth estimates for mappings having asymptotic values.
Quasiconformal distortion on arcs
1994
Optimal Shape Design in Contact Problems
1989
From the mathematical point of view, optimal shape design (or optimum design, optimization of the domain, structural optimization) is a branch of the calculus of variations and especially of optimal control where study is devoted to the problem of finding the optimal shape for an object. In an optimal shape design process the objective is to optimize certain criteria involving the solution of a partial differential equation with respect to its domain of definition, [2, 3, 5].
Assessing fat-tailed sequential forecast distributions for the Dow-Jones index with logarithmic scoring rules
2007
We use the logarithmic scoring rule for distributions to assess a variety of fat-tailed sequential forecasting distributions for the Dow-Jones industrial stock index from 1980 to the present. The methodology applies Bruno de Finetti''s contributions to understanding how to compare the quality of different coherent forecasting distributions for the same sequence of observations, using proper scoring rules. Four different forms of forecasting distributions are compared: a mixture Normal, a mixture of convex combinations of three Normal distributions, a mixture exponential power distribution, and a mixture of a convex combination of three exponential power distributions. The mixture linear com…
Therapeutic Monitoring of Aripiprazole by HPLC with Column-Switching and Spectrophotometric Detection
2005
Aripiprazole is a novel atypical antipsychotic drug for the treatment of schizophrenia and schizoaffective disorders (1)(2)(3). The drug is metabolized by the cytochrome P450 isoenzymes 3A4 and 2D6 (4). Because of high interindividual variability in the expression of these enzymes, the aripiprazole concentration varies among healthy individuals after administration of the drug (5). In patients, insufficient response or side effects, such as somnolence, akathisia, or nausea, may result from too low or too high drug concentrations. Therapeutic drug monitoring (TDM), which is established practice for many antipsychotic drugs (6)(7), may be helpful for patients treated with aripiprazole. We mea…
Analysis of the Effects of Modifying Agents on Six Different Phenotypes in Preneoplastic Foci in the Liver in Medium-Term Bioassay Model in Rats
1988
Recently a great deal of interest has been expressed in characterizing the altered enzyme phenotype of putative preneoplastic rat liver lesions. In particular, attention has been given to the changes in drug metabolizing potential, conferring physiological advantage to initiated cells, and their usefulness as marker lesions for the analysis of the development of neoplasia1–2.