To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Given a partial action
of a group on a set with an algebraic structure, we construct a reflector of
in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if
is a partial action on an algebra from a variety
, then we show that the problem reduces to the embeddability of a certain generalized amalgam of
-algebras associated with
. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.
We present a complex analytic proof of the Pila–Wilkie theorem for subanalytic sets. In particular, we replace the use of
-smooth parametrizations by a variant of Weierstrass division. As a consequence we are able to apply the Bombieri–Pila determinant method directly to analytic families without limiting the order of smoothness by a
parametrization. This technique provides the key inductive step for our recent proof (in a closely related preprint) of the Wilkie conjecture for sets definable using restricted elementary functions. As an illustration of our approach we prove that the rational points of height
in a compact piece of a complex-analytic set of dimension
are contained in
complex-algebraic hypersurfaces of degree
. This is a complex-analytic analog of a recent result of Cluckers, Pila, and Wilkie for real subanalytic sets.
The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.
We characterize those partially ordered sets I for which the canonical maps Mi → colim Mj into colimits of abstract sets are always injective, provided that the transition maps are injective. We also obtain some consequences for colimits of vector spaces.
We consider an optimal stopping problem for a general discrete-time process X1, X2, …, Xn, … on a common measurable space. Stopping at time n (n = 1, 2, …) yields a reward Rn(X1, …, Xn) ≥ 0, while if we do not stop, we pay cn(X1, …, Xn) ≥ 0 and keep observing the process. The problem is to characterize all the optimal stopping times τ, i.e., such that maximize the mean net gain:
The irradiation of thin films by intensive subpicosecond laser pulses with nanosecond prepulse is accompanied by a number of various physical processes. The laser beam transmissions through the film as well as the re-emission flux on both sides of the film plasma have been evaluated by simulation for Al and CH2 materials. It has been demonstrated that the thickness of the film can be chosen to cut off the long nanosecond prepulse whereas the main pulse is transmitted through the plasma. Thus, thin films can be useful for the laser contrast improvement in experiments with different targets.
Nevertheless, the laser energy transformation into the soft X-ray radiation on the back side of the shielding film plasma can reach up to 7% of the incident intensity for the Al film and result in strong preheating of the target. At the same time the re-emission flux produced by a CH2 film is an order lower than that in the case of Al film. The shielding of an Ag bulk target by Al and CH2 films is simulated and discussed.
Results of investigation of X-ray sensors on the basis of GaAs compensated with chromium (HR GaAs) are presented in this work. HR GaAs material is shown to have the following physical parameters: the resistivity about 1GOhm*cm, the nonequilibrium charge carrier lifetime – hundreds of nanoseconds. Prototypes of microstrip and array HR GaAs sensors have been manufactured and tested. It is demonstrated that the sensors provide spatial resolution according to the pixel pitch and allow obtaining high quality X-ray images.
In this chapter we explain how to construct a discrete network for nonlinear high-contrast densely-packed composites. We use this presentation to demonstrate the so-called perforated medium technique in the analysis of high-contrast composites. We also use this investigation to demonstrate how the discrete network approximation arises from the interplay between geometry and asymptotic analysis. More specifically, the key mathematical feature of partial differential equations that describe high-contrast densely-packed composites is that their solutions exhibit asymptotically singular behavior, when particles are close to touching (high concentration). The singularities of the solutions occur exactly in the necks between almost touching particles. The location of these singularities can be characterized naturally by the geometric patterns of the distribution of the particles in the materials. Thus a geometric construction of a network is completely natural. As it is illustrated in this book, a rigorous mathematical justification is based on geometric and asymptotic arguments. These two arguments are coupled together. As a result, most of the constructions of asymptotic discrete network approximations for high-contrast composites are complicated, thus they are not attractive for practitioners. It is possible, however, to separate the geometric and the asymptotic arguments. It makes the construction of the network more transparent, and allows us to strengthen some of the previous results. In particular, it turns out that the validity of discrete network approximations could be verified for a class of composites, which is larger than the one that satisfies the δ-N close-packing condition.
In recent years the traditional subject of continuum mechanics has grown rapidly and many new techniques have emerged. This text provides a rigorous, yet accessible introduction to the basic concepts of the network approximation method and provides a unified approach for solving a wide variety of applied problems. As a unifying theme, the authors discuss in detail the transport problem in a system of bodies. They solve the problem of closely placed bodies using the new method of network approximation for PDE with discontinuous coefficients, developed in the 2000s by applied mathematicians in the USA and Russia. Intended for graduate students in applied mathematics and related fields such as physics, chemistry and engineering, the book is also a useful overview of the topic for researchers in these areas.
In this chapter we review several ways of applying network models to inhomogeneous continuum media and systems of inclusions.
Discrete networks have been used as analogs of continuum problems in various areas of physics and engineering for a long time (see, e.g., Acrivos and Chang (1986); Ambegaokar et al. (1971); Bergman et al. (1990); Curtin and Scher (1990b); Koplik (1982); Newman (2003); Schwartz et al. (1984)). However, as demonstrated in Kolpakov (2006a), such analogs may or may not provide a correct approximation. In recent decades, the problem of the development of network models as rigorous approximations of continuum models was posed and solved for certain physical problems.
The objectives of our book are two-fold. First, we will develop an approach that allows us to derive network models by structural discretization (structural approximation). The key feature of this approach is that it is based on a rigorous asymptotic analysis with controlled error estimates, and thus we obtain the limits of validity for the network approximation. Secondly, we show that our network models are efficient tools in the study and prediction of properties of disordered particle-filled composites of various kinds.
Examples of real-world problems leading to discrete network models
Our interest is motivated by real-word problems and we next present three examples of highly packed composites which can be modeled by networks.