In this paper the linear viscous stability theory for stably stratified parallel shear flow is reviewed and some new results are presented. Attention is focused on recent work on unbounded flows with emphasis placed o...
A method is described for the calculation of the eigenvalues of general integral operators. Several classical results from functions of a complex variable and the theory of integral equations are combined with a recen...
The method used by Drazin to investigate the stability of unbounded, viscous, homogeneous, parallel shear flow to small wavenumber disturbances is extended to study the effect of thermal stratification on the stabilit...
The method used by Drazin to investigate the stability of unbounded, viscous, homogeneous, parallel shear flow to small wavenumber disturbances is extended to study the effect of thermal stratification on the stability of unbounded jets and shear layers. By this method the stability characteristics of continuous profiles are inferred from the stability characteristics of discontinuous profiles. The characteristic value problem for discontinuous jet and shear layers is posed by the requirement that the solutions of the governing differential equation satisfy the matching conditions and boundedness conditions for layers that extend to infinity. The analysis leads to a characteristic determinant which is required to vanish for the characteristic values of the parameters: the Reynolds number, the wavenumber, and the wave speed. The stabilizing effect of the thermal stratification as parameterized by the Richardson number was found to be most stabilizing for small wavenumber (large‐scale) disturbances.
Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different acc...
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ISBN:
(数字)9783319564364
ISBN:
(纸本)9783319564357;9783030132590
Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
The flow of water over a regular array of hills in a rotating laboratory experiment is studied as an analogue of planetary boundary layers. Gaussian-shaped hills of height h = 1 cm and h = 1/3 cm covered the floor of ...
Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resol...
Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.
The Athens Conference on applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes.;includes papers on applied probability in Honor of J...
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ISBN:
(数字)9781461207498
ISBN:
(纸本)9780387947884
The Athens Conference on applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes.;includes papers on applied probability in Honor of J.M. Gani. The topics include probability and probabilistic methods in recursive algorithms and stochastic models, Markov and other stochastic models such as Markov chains, branching processes and semi-Markov systems, biomathematical and genetic models, epidemilogical models including S-I-R (Susceptible-Infective-Removal), household and AIDS epidemics, financial models for option pricing and optimization problems, random walks, queues and their waiting times, and spatial models for earthquakes and inference on spatial models.
This volume contains the papers selected for presentation at IPCO 2002, the NinthInternationalConferenceonIntegerprogrammingandCombinatorial- timization, Cambridge, MA (USA), May 27–29, 2002. The IPCO series of c- fe...
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ISBN:
(数字)9783540478676
ISBN:
(纸本)9783540436768
This volume contains the papers selected for presentation at IPCO 2002, the NinthInternationalConferenceonIntegerprogrammingandCombinatorial- timization, Cambridge, MA (USA), May 27–29, 2002. The IPCO series of c- ferences highlights recent developments in theory, computation, and application of integer programming and combinatorial optimization. IPCO was established in 1988 when the ?rst IPCO program committee was formed. IPCO is held every year in which no International Symposium on Ma- ematical programming (ISMP) takes places. The ISMP is triennial, so IPCO conferences are held twice in every three-year period. The eight previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995, Vancouver (Canada) 1996, Houston (USA) 1998, Graz (Austria) 1999, and Utrecht (The Netherlands) 2001. In response to the call for papers for IPCO 2002, the program committee received 110 submissions, a record number for IPCO. The program committee met on January 7 and 8, 2002, in Aussois (France), and selected 33 papers for inclusion in the scienti?c program of IPCO 2002. The selection was based on originality and quality, and re?ects many of the current directions in integer programming and combinatorial optimization research.
Targeted therapies, immunotherapies, and improved chemotherapies are being developed to reduce the suffering and mortality that come from human cancer. Although these approaches, and in particular combinations of them...
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Targeted therapies, immunotherapies, and improved chemotherapies are being developed to reduce the suffering and mortality that come from human cancer. Although these approaches, and in particular combinations of them, are expected to succeed eventually to a large degree, they all suffer one obstacle: Populations of replicating cells move away—typically in a high-dimensional space—from any opposing selection pressure they encounter. They evolve resistance. It is possible, however, to develop a precise mathematical understanding of the problem and to design treatment strategies that prevent resistance if possible or manage resistance otherwise. In this article, we present the fundamental equations that characterize the evolution of resistance. We provide formulas for the probability that resistant cells exist at the start of therapy, for the average number and sizes of resistant clones, and for the probability of successful combination treatment. We also demonstrate that developing new therapies that only maximize the killing rate of cancer cells may not be optimal, and that instead the parameters determining the fraction of resistant cells and their growth rate have a larger effect on the long-term control of cancer. These mathematical tools inform the search process for optimal therapies that aim to cure cancer.
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