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Analytic and Experimental Studies of the Errors in Numerical Methods for the Valuation of Options

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Numerical Mathematics(Theory,Methods and Applications) 2008年第2期1卷 150-164页

作者： P.Lin J.J.H.Miller g.i.shishkin Department of Mathematics National University of Singapore Department of Mathematics Trinity College Dublin institute for Mathematics and Mechanics Russian Academy of Science Ekaterinburg

The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary *** transform the problem to an initial boundary value problem in dimensionless *** are two parameters in the coefficients of the resulting linear parabolic partial differential *** a range of values of these parameters,the solution of the problem has a boundary or an initial *** initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior *** construct analytically the asymptotic solution of the equation in a finite *** on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the ***,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are *** present numerical computations,which determine experimentally the parameter-uniform rates of *** note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.

关键词： Options singularities finite difference methods monotone robust method

A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

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Numerical Mathematics(Theory,Methods and Applications) 2008年第2期1卷 214-234页

作者： grigory i.shishkin institute of Mathematics and Mechanics Ural Branch of Russian Academy of Sciences

A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori （sequentially） adapted meshes and study its convergence. The scheme on α priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find α priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in χ, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for improving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical solution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N^-1 = o （ε^v）, where N denotes the number of nodes in the spatial mesh, and the value v = v（K） can be chosen arbitrarily small for suitable K.

关键词： Singular perturbations convection-diffusion problem piecewise-uniform mesh α priori adapted mesh almost ε-uniform convergence

Arctic sea-ice extent: No record minimum in 2023 or recent years

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Atmospheric and Oceanic Science Letters 2025年第1期18卷 52-55页

作者： Ola M.Johannessen Tor i.Olaussen Nansen Scientific Society BergenNorway Nansen Environmental and Remote Sensing Center BergenNorway

Arctic sea-ice extent reaches its minimum each year in September. On 11 September 2023 the minimum was 4.969 million square kilometers(***^(2)). This was not a record low, which occurred in 2012, when the minimum was 4.175 ***^(2), 0.794 ***^(2) less than the minimum in 2023. However, the ice extent had decreased by 0.432 ***^(2) compared with 2022. Nevertheless, the summer melting in 2023 was remarkably less than expected when considering the strong heat waves in the atmosphere and ocean, with record temperatures set around the world. in general, there is a high correlation between the long-term decrease in sea-ice extent and the increasing CO_(2) in the atmosphere, where the increase of CO_(2) in recent decades explains about 80% of the decrease in sea ice in September, while the remainder is caused by natural variability.

关键词： Sea ice Arctic Minimum ice Climate

Stepping up after spinal cord injury:negotiating an obstacle during walking

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Neural Regeneration Research 2025年第7期20卷 1919-1929页

作者： Alain Frigon Charly g.Lecomte Department of Pharmacology-Physiology Faculty of Medicine and Health SciencesUniversitéde SherbrookeCentre de recherche du Centre Hospitalier Universitaire de SherbrookeSherbrookeQCCanada

Every day walking consists of frequent voluntary modifications in the gait pattern to negotiate *** spinal cord injury,stepping over an obstacle becomes *** over an obstacle requires sensorimotor transformations in several structures of the brain,including the parietal cortex,premotor cortex,and motor *** information and planning are transformed into motor commands,which are sent from the motor cortex to spinal neuronal circuits to alter limb trajectory,coordinate the limbs,and maintain *** spinal cord injury,bidirectional communication between the brain and spinal cord is disrupted and animals,including humans,fail to voluntarily modify limb trajectory to step over an ***,in this review,we discuss the neuromechanical control of stepping over an obstacle,why it fails after spinal cord injury,and how it recovers to a certain extent.

关键词： biomechanics locomotion neurophysiology obstacle negotiation spinal cord injury

An SPH Framework for Earthquake-induced Liquefaction Hazard Assessment of geotechnical Structures

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 251-277页

作者： Sourabh Mhaski g.V.Ramana Department of Civil Engineering Indian Institute of Technology DelhiNew Delhi110016India

Earthquake-induced soil liquefaction poses significant risks to the stability of geotechnical structures *** understanding of the liquefaction triggering,and the post-failure large deformation behaviour is essential for designing resilient *** present study develops a Smoothed Particle Hydrodynamics(SPH)framework for earthquake-induced liquefaction hazard assessment of geotechnical *** coupled flowdeformation behaviour of soils subjected to cyclic loading is described using the PM4Sand model implemented in a three-phase,single-layer SPH framework.A staggered discretisation scheme based on the stress particle SPH approach is adopted to minimise numerical inaccuracies caused by zero-energy modes and tensile ***,non-reflecting boundary conditions for seismic analysis of semi-infinite soil domains using the SPH method are *** numerical framework is employed for the analysis of cyclic direct simple shear test,seismic analysis of a level ground site,and liquefaction-induced failure of the Lower San Fernando *** agreement for liquefaction triggering and post-failure behaviour demonstrates that the SPH framework can be utilised to assess the effect of seismic loading on field-scale geotechnical *** present study also serves as the basis for future advancements of the SPH method for applications related to earthquake geotechnical engineering.

关键词： Earthquake seismic liquefaction stress particle PM4Sand smoothed particle hydrodynamics(SPH)

Coarse to Fine: The Role of Severe Plastic Deformation in Advancing Titanium-Based Medical implants - A Comprehensive Review

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Journal of Wuhan University of Technology(Materials Science) 2025年第1期40卷 295-306页

作者： Dragana R Mihajlović Bojan i Međo ivana Lj Cvijović-Alagić Veljko R Djokić Faculty of Technology and Metallurgy University of BelgradeKarnegijeva 411120 BelgradeSerbia Vinča institute of Nuclear Sci-ences-National institute of the Republic of Serbia University of Belgrade11001BeogradSerbia innovation Centre of the Faculty of Technology and Metallurgy Karnegijeva 411120 BelgradeSerbia

This paper describes severe plastic deformation(SPD)procedures,which are utilized to form an ultrafine-grained structure in metallic *** the SPD process,a solid material sample is subjected to very high loads without a significant change in sample *** the present work,the high-pressure torsion(HPT)process,as one of the SPD techniques,which achieves a high degree of deformation and ensures refinement of the microstructure,will be discussed in more *** that grain size control is accepted as a method to obtain materials with desired characteristics,an overview of the properties of ultrafine-grained titanium-based biomaterials to be used in medicine is ***,particular attention is dedicated to the influences of HPT process parameters,primarily hydrostatic pressure,and number of revolutions during torsion,on the grain size and physical and mechanical characteristics(modulus of elasticity,microhardness,and tensile properties),corrosion resistance,and biocompatibility of the titanium-based biomaterials.A review of the literature indicates that titanium-based materials obtained by the SPD process show improved mechanical and physical properties without losing biocompatibility and corrosion resistance,which suggests that these methods of obtaining implants are something that should be further developed in the future.

关键词： high-pressure torsion process ultrafine-grained titanium-based materials electrochemical anodization physical properties mechanical properties

Bioelectronic medicine in modulation of cortical spreading depolarization and beyond

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Neural Regeneration Research 2025年第2期20卷 481-482页

作者： Khaled Alok Timothy g.White Chunyan Li Department of Neurosurgery Donald and Barbara Zucker School of Medicine at Hofstra/NorthwellHempsteadNYUSA Translational Brain Research Laboratory The Feinstein Institutes for Medical ResearchManhassetNYUSA

Bioelectronic interventions,specifically trigeminal nerve st imulat ion(TNS),have attracted considerable attention in conditions where cortical spreading depolarizations(CSDs)accompanied by compromised cerebral perfusion may exacerbate neurological *** pharmacological interventions have demonstrated initial potential in addressing CSDs,a standardized treatment approach has not yet been *** objective of this perspective is to explore emerging bioelectronic methodologies for addressing CSDs,particularly emphasizing TNS,and to underscore TNS’s capacity to enhance neurovascular coupling and cerebral perfusion.

关键词： cerebral perfusion electronic

Plasmon-assisted optical trapping and anti-trapping

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Light(Science & Applications) 2016年第1期5卷 52-57页

作者： Aliaksandra ivinskaya Mihail i Petrov Andrey A Bogdanov ivan shishkin Pavel ginzburg Alexander S Shalin Department of Nanophotonics and Metamaterials ITMO UniversityBirzhevaja Line14199034 St PetersburgRussia School of Electrical Engineering Tel Aviv UniversityRamat AvivTel Aviv 69978Israel Kotel’nikov institute of Radio Engineering and Electronics of Russian Academy of Sciences(Ulyanovsk branch) Goncharova Street 48/2432071 UlyanovskRussia Ulyanovsk State University Lev Tolstoy Street 42432017 UlyanovskRussia

The ability to manipulate small objects with focused laser beams has opened a venue for investigating dynamical phenomena relevant to both fundamental and applied *** and plasmonic structures enable superior performance in optical trapping via highly confined *** this case,the interplay between the excitation field,re-scattered fields and the eigenmodes of a structure can lead to remarkable effects;one such effect,as reported here,is particle trapping by laser light in a vicinity of metal *** plasmon excitation at the metal substrate plays a key role in tailoring the optical forces acting on a nearby *** on whether the illuminating gaussian beam is focused above or below the metal-dielectric interface,an order-of-magnitude enhancement or reduction of the trap stiffness is achieved compared with that of standard glass ***,a novel plasmon-assisted anti-trapping effect(particle repulsion from the beam axis)is predicted and studied.A highly accurate particle sorting scheme based on the new anti-trapping effect is *** ability to distinguish and configure various electromagnetic channels through the developed analytical theory provides guidelines for designing auxiliary nanostructures and achieving ultimate control over mechanical motion at the microand nano-scales.

关键词： gaussian beam green’s function optical forces optical tweezers surface plasmon

impact of Zika virus non-structural protein mutations on hippocampal damage

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Neural Regeneration Research 2025年第8期20卷 2307-2308页

作者： Larissa M.g.Cassiano Roney S.Coimbra Neurogenômica/imunopatologia Instituto RenéRachouFiocruzBelo HorizonteBrazil Departamento de Bioquímica e imunologia Instituto de Ciências BiológicasUniversidade Federal de Minas GeraisBelo HorizonteBrazil

The Zika virus(ZiKV),a member of the Flaviviridae family,attracted worldwide attention for its connection to severe neurological effects,notably microcephaly in newborns,first reported during the 2015 epidemic in ***,its impact goes beyond fetal and neonatal abnormalities,also affecting the central nervous system(CNS)in both children and adults,leading to enduring cognitive and behavioral impairments.

关键词： damage fetal neonatal