Search results for "Differentia"
showing 10 items of 8428 documents
Mappings of finite distortion: Reverse inequalities for the Jacobian
2007
Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Holder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f.
Distribution of Large Eigenvalues for Elliptic Operators
2019
In this chapter we consider elliptic differential operators on a compact manifold and rather than taking the semi-classical limit (h →), we let h = 1 and study the distribution of large eigenvalues. Bordeaux Montrieux (Loi de Weyl presque sure et resolvante pour des operateurs differentiels non-autoadjoints, these, CMLS, Ecole Polytechnique, 2008. https://pastel.archives-ouvertes.fr/pastel-00005367, Ann Henri Poincare 12:173–204, 2011) studied elliptic systems of differential operators on S1 with random perturbations of the coefficients, and under some additional assumptions, he showed that the large eigenvalues obey the Weyl law almost surely. His analysis was based on a reduction to the s…
Stochastic linearization for the response of MDOF systems subjected to external and parametric Gaussian excitations
1991
The stochastic linearization approach is examined for the most general case of non zero-mean response of non-linear MDOF systems subjected to parametric and external Gaussian white excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. Moreover, an extension of the Atalik-Utku approach to non zero-mean response systems allows to obtain simple formulations for the linearized drift coefficients. Some applications show the good accuracy of the method.
Optimal control of the Schrödinger equation with two or three levels
2007
In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.
Absolute quantification of noncoding RNA by microscale thermophoresis
2019
Abstract Accurate quantification of the copy numbers of noncoding RNA has recently emerged as an urgent problem, with impact on fields such as RNA modification research, tissue differentiation, and others. Herein, we present a hybridization‐based approach that uses microscale thermophoresis (MST) as a very fast and highly precise readout to quantify, for example, single tRNA species with a turnaround time of about one hour. We developed MST to quantify the effect of tRNA toxins and of heat stress and RNA modification on single tRNA species. A comparative analysis also revealed significant differences to RNA‐Seq‐based quantification approaches, strongly suggesting a bias due to tRNA modifica…
On shape differentiation of discretized electric field integral equation
2013
Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Ensemble strategies in Compact Differential Evolution
2011
Differential Evolution is a population based stochastic algorithm with less number of parameters to tune. However, the performance of DE is sensitive to the mutation and crossover strategies and their associated parameters. To obtain optimal performance, DE requires time consuming trial and error parameter tuning. To overcome the computationally expensive parameter tuning different adaptive/self-adaptive techniques have been proposed. Recently the idea of ensemble strategies in DE has been proposed and favorably compared with some of the state-of-the-art self-adaptive techniques. Compact Differential Evolution (cDE) is modified version of DE algorithm which can be effectively used to solve …
Super-fit and population size reduction in compact Differential Evolution
2011
Although Differential Evolution is an efficient and versatile optimizer, it has a wide margin of improvement. During the latest years much effort of computer scientists studying Differential Evolution has been oriented towards the improvement of the algorithmic paradigm by adding and modifying components. In particular, two modifications lead to important improvements to the original algorithmic performance. The first is the super-fit mechanism, that is the injection at the beginning of the optimization process of a solution previously improved by another algorithm. The second is the progressive reduction of the population size during the evolution of the population. Recently, the algorithm…