Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings

The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider several aspects of these groups: First, their systematic construction from associative algebras, secondly, their suitability for the characterization of wavefront sets, and finally, the question of constructing embeddings into the symplectic group in a way that intertwines the quasi-regular representation with the metaplectic one. For all questions, it is possible to treat the full class of generalized shearlet groups in a comprehensive and unified way, thus generalizing known results to an infinity of new cases. Our presentation emphasizes the interplay between the algebraic structure underlying the construction of the shearlet dilation groups, the geometric properties of the dual action, and the analytic properties of the associated shearlet transforms.Comment: 28 page

Экономическая целесообразность прогнозирования брака по параметру биения

Для выбора экономически целесообразного применения технологий обработки и сборки предлагается учитывать величину прогнозированного брака по параметру биения.For the choice economic expedient application of technologies of treatment and assembling the method of prognostication of marriage is offered on the parameter of beating

A Probabilistic proof of the breakdown of Besov regularity in LL-shaped domains

{We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in $L$-shaped domains. In particular, we obtain (probabilistic) integral representations for the solution. We also recover Grisvard's classic result on the angle-dependent breakdown of the regularity of the solution measured in a Besov scale

Value and Use of Artificial Insemination by Beef Producers

Artificial insemination and estrous synchronization remain underutilized by U.S. beef producers. The most recent National Animal Health Monitoring Survey (NAHMS 2007–08) reported that 7.6% of producers used artificial insemination and 7.9% used estrous synchronization. The most common reason cited for not using these reproductive technologies was time and labor, followed by cost and difficulty. Little information is available on actual management practices used by producers who do use these technologies and their value to such operations

Distillation column dynamics and control

A pilot plant scale, atmospheric pressure, sieve plate distillation column was constructed and fully instrumented. Novel speed controllable pumps were used to control liquid flows. A microcomputer was constructed to provide local and hierarchical control of the column. The microcomputer included an operator console, a 16 channel data acquisition unit, a 4 channel control output unit, and a hardware arithmetic processor. A software development system was assembled by linking the microcomputer to a minicomputer. Software written for the development system included a cross-assembler, a transfer program, and a microcomputer control program. A binary steady state distillation column model was developed, solved on a digital computer, and verified against experimental data using a binary mixture of methanol and water. Two control schemes were investigated using only the microcomputer resources. A multi-loop system using digital PI controllers was found to give excellent control within the accuracy of the instrumentation. An adaptive feedforward controller was proposed and verified using a steady state model, and experiments. The results were good, but because of the relatively simple dynamics of the experimental column, the feedforward controller was no better than the feedback controllers. A microcomputer control system has been shown to be an effective replacement for conventional analog control on a distillation column. The computing power of the microcomputer has enabled a sophisticated control scheme to be implemented at low cost

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

Induced Crystallization of Polyelectrolyte-Surfactant Complexes at the Gas-Water Interface

Synchrotron-X-ray and surface tension studies of a strong polyelectrolyte (PE) in the semi-dilute regime (~ 0.1M monomer-charges) with varying surfactant concentrations show that minute surfactant concentrations induce the formation of a PE-surfactant complex at the gas/solution interface. X-ray reflectivity and grazing angle X-ray diffraction (GIXD) provide detailed information of the top most layer, where it is found that the surfactant forms a two-dimensional liquid-like monolayer, with a noticeable disruption of the structure of water at the interface. With the addition of salt (NaCl) columnar-crystals with distorted-hexagonal symmetry are formed.Comment: 4 pages, 5 eps figure

A wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141