ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

Measurement of drop size in horizontal annular flow with the immersion method

A modified version of the oil immersion sampling system developed by Okada was exploited to obtain measurements of drop diameter in a horizontal annular flow of air and water in a 9.53-cm pipe. Drop samples were captured in a high-viscosity oil and photographic images of the samples were used to measure the distribution of diameters. Advantages of the immersion method are that the drops are spherical when photographed and that the measurement does not require removal of the film from the wall. Drop size distributions are found to be similar to distributions measured using a photographic technique for vertical annular flow in a 4.2-cm pipe. Drop size distributions show some differences from measurements that used a laser diffraction system in the same horizontal pipeline. In particular, the diffraction method indicates the existence of larger maximal drop sizes than are determined with the immersion technique.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.     

Computing isogeny covariant differential modular forms

We present the computation modulo and explicit formulas for the unique isogeny covariant differential modular form of order one and weight called , an isogeny covariant differential modular form of order two and weight denoted by , and an isogeny covariant differential modular form of order two and weight .

     

Isogeny Covariant Differential Modular Forms Modulo p

An interesting theory arises when the classical theory of modular forms is expanded to include differential analogs of modular forms. One of the main motivations for expanding the theory of modular forms is the existence of differential modular forms with a remarkable property, called isogeny covariance, that classical modular forms cannot possess. Among isogeny covariant differential modular forms there exists a particular modular form that plays a central role in the theory. The main result presented in the article will be the explicit computation modulo p of this fundamental isogeny covariant differential modular form.     

Optical measurement of liquid film thickness and wave velocity in liquid film flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The first technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photo sensors, spaced a fixed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.The authors appreciate the support of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign under project 45.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part I: Methods and data

Most approaches to the modeling of annular flow require information regarding the thin liquid film surrounding the central gas core. This film is hypothesized to present a rough surface to the gas core, enhancing interfacial shear and pressure loss, with the roughness closely linked to the height of the film. This height is typically obtained from conductance probe measurements. The present work used planar laser-induced fluorescence to provide direct visualization of the liquid film in upward vertical air–water annular flow. Images were processed to produce the distribution of film heights. The standard deviation and average film thickness are found to be an increasing function of liquid flow and a decreasing function of gas flow, with the standard deviation approaching 0.4 times the average at sufficient liquid flow.     

Structural and functional alterations in major peanut allergens caused by thermal processing

The majority of foods that we eat are subjected to some type of processing either at home or by the manufacturer. The biochemical reactions that occur in foods as a result of thermal processing can be both beneficial and harmful. Here, we briefly review the effects of thermal processing and some of the effects of the Maillard reaction on the allergenicity of food proteins. Specifically, we focus on the known effects of roasting on the allergenic properties of peanut proteins and the contribution of Maillard reaction products or advanced glycation end products to these observed effects. The most thorough understanding of the effects of thermal processing on allergenicity involves the peanut proteins. Thermal processing alters specific biophysical and immunological properties of peanut proteins, such as structure, function, solubility, digestibility, immunoglobulin E (IgE) binding, and T-cell responses. A better understanding of the effects of thermal processing-induced biochemical and immunological alterations is of utmost importance for proper risk assessment of existing and newly introduced proteins in the food source, as well as development of effective diagnostic tools and therapeutic treatments for food allergy.     

ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nαθ(p)-summability. Furthermore, some relations between the spaces Nαθ(p) and Sαθare examined.