Connectivity patterns of ecological elements are often the core concern of ecologists working at multiple levels of organization (e.g., populations, communities, ecosystems, and landscapes) because these patterns often reflect the forces shaping the system’s development as well as constraining their operation. One reason these patterns of direct connections are critical is that they establish t...

We review recent results on the homogenization in Sobolev spaces with variable exponents. In particular, we are dealing with the Γ-convergence of variational functionals with rapidly oscillating coefficients, the homogenization of the Dirichlet and Neumann variational problems in strongly perforated domains, as well as double porosity type problems.The growth functions also depend on the small ...

We study the homogenization of Lagrangian functionals of Hamilton-Jacobi equations (HJ) with quadratic nonlinearity and unbounded stationary ergodic random potential in R, d≥1. We show that homogenization holds if and only if the potential is bounded from above. When the potential is unbounded from above, homogenization breaks down, due to the almost sure growth of the running maxima of the ran...

atorvastatin calcium, the lipid lowering agent, is taken as a model drug characterized by poor water solubility and bioavailability. in this study an attempt was made for preparation of nanocrystals using high pressure homogenization. a number of stabilizers were included as well as polymers at different concentrations, and the formulations were homogenized for ten cycles at a pressure of 1000 ...

Imaging and simulation methods are typically constrained to resolutions much coarser than the scale of physical micro-structures present in body tissues or geological features. Mathematical and numerical homogenization address this practical issue by identifying and computing appropriate spatial averages that result in accuracy and consistency between the macro-scales we observe and the underly...

This study demonstrated that homogenization did not increase the activity of lipoprotein lipase (LPL) in spite of a fast accumulation of free fatty acids (FFA). Two homogenization pressures (100 and 170 bar) and two temperatures (40 ̊C and 50 ̊C) were examined. The activity of LPL was analyzed and the formation of FFA was measured with two different methods, the B.D.I.-method and a nonesterified ...

Protein hydrolysate is highly regarded as a source of naturally occurring antioxidant peptides. The purpose of this study was to investigate the effect of Ultrasonic (Frequency, 20 KHz; Amplitude, 50%; Time, 30 min) and high-pressure homogenization (Power, 1500 bar; Rated flow, 10 dm/h) pretreatmenton the enzymatic hydrolysis and antioxidant properties of yeast protein hydrolysate obtained from...

Biotic homogenization, the process of gradual replacement of native biotas by nonindigeous and locally expanding nonnative species, is rapidly diminishing the regional distinctiveness of global terrestrial and aquatic ecosystems. Although the empirical study of biotic homogenization is substantial and growing, the mechanisms underlying its dynamics remain poorly understood. We recently develope...

This lecture is devoted to a brief introduction to the mathematical theory of homogenization. For a more advanced presentation of homogenization, the reader is referred to the books [2], [5], [6], [11], [12], [21], [27], [32] and [33]. Roughly speaking, homogenization is a rigorous version of what is known as averaging. In other words, homogenization extracts homogeneous effective parameters fr...