Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten

Updates on understanding of probiotic lactic acid bacteria responses to environmental stresses and highlights on proteomic analyses

Probiotics are defined as live microorganisms that improve the health of the host when administered in adequate quantities. Nonetheless, probiotics encounter extreme environmental conditions during food processing or along the gastrointestinal tract. This review discusses different environmental stresses that affect probiotics during food preparation, storage, and along the alimentary canal, including high temperature, low temperature, low and alkaline pH, oxidative stress, high hydrostatic pressure, osmotic pressure, and starvation. The understanding of how probiotics deal with environmental stress and thrive provides useful information to guide the selection of the strains with enhanced performance in specific situations, in food processing or during gastrointestinal transit. In most cases, multiple biological functions are affected upon exposure of the cell to environmental stress. Sensing of sublethal environmental stress can allow for adaptation processes to occur, which can include alterations in the expression of specific proteins

Relationship between tensile and shear strengths of the mushy zone in solidifying aluminum alloys

Strength development in the mushy zone during solidification of three aluminum alloys (Al-4 wt pct Cu, Al-7 wt pct Si-1 wt pct Cu, and Al-7 wt pct Si-4 wt pct Cu) has been measured with two different techniques - horizontal tensile testing and direct shear cell testing. The strength results from the two methods correspond with one another to a much higher degree than suggested by the results presented in the literature. Tensile strength starts to develop at the maximum packing solid fraction, confirmed by the shear strength measurements. The maximum packing fraction represents the point where the internal network structure of the mushy zone is established and ligaments of the network must be broken to rearrange the dendrites. The data indicate a converging trend of the shear and tensile strength at high solid fractions, therefore indicating that the deformation mechanisms are also becoming similar. The results presented in this article suggest that it is possible to develop constitutive equations for the mechanical properties of the mushy zone over the entire solid fraction regime, i.e., from coherency to complete solidification. These equations could be used for the prediction of stress development as well as defect formation