The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions

In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green's function for a free particle in the general case, for an arbitrary order of the derivative index.Comment: 32 pages. No figure

Fractional Generalization of Kac Integral

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.Comment: 16 pages, LaTe

Space science/space station attached payload pointing accommodation study: Technology assessment white paper

Technology assessment is performed for pointing systems that accommodate payloads of large mass and large dimensions. Related technology areas are also examined. These related areas include active thermal lines or power cables across gimbals, new materials for increased passive damping, tethered pointing, and inertially reacting pointing systems. Conclusions, issues and concerns, and recommendations regarding the status and development of large pointing systems for space applications are made based on the performed assessments

Dynamics with Low-Level Fractionality

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order $\alpha<2$ is dissipation. In systems with many spacially coupled elements (oscillators) the fractional derivative, along the space coordinate, corresponds to a long range interaction. We discuss a method of constructing a solution using an expansion in $\epsilon=n-\alpha$ with small $\epsilon$ and positive integer $n$. The method is applied to the fractional linear and nonlinear oscillators and to fractional Ginzburg-Landau or parabolic equations.Comment: LaTeX, 24 pages, to be published in Physica

Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure

Fractional dynamics of systems with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power wise interaction defined by a term proportional to 1/|n-m|^{\alpha+1}. Continuous medium equation for this system can be obtained in the so-called infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of motion of the particles into a partial differential equation with the Riesz fractional derivative of order \alpha, when 0<\alpha<2. Few models of coupled oscillators are considered and their synchronized states and localized structures are discussed in details. Particularly, we discuss some solutions of time-dependent fractional Ginzburg-Landau (or nonlinear Schrodinger) equation.Comment: arXiv admin note: substantial overlap with arXiv:nlin/051201

Mechanisms Mediating the Biologic Activity of Synthetic Proline, Glycine, and Hydroxyproline Polypeptides in Human Neutrophils

The accumulation of neutrophils at sites of tissue injury or infection is mediated by chemotactic factors released as part of the inflammatory process. Some of these factors are generated as a direct consequence of tissue injury or infection, including degradation fragments of connective tissue collagen and bacterial- or viral-derived peptides containing collagen-related structural motifs. In these studies, we examined biochemical mechanisms mediating the biologic activity of synthetic polypeptides consisting of repeated units of proline (Pro), glycine (Gly), and hydroxyproline (Hyp), major amino acids found within mammalian and bacterial collagens. We found that the peptides were chemoattractants for neutrophils. Moreover, their chemotactic potency was directly related to their size and composition. Thus, the pentameric peptides (Pro-Pro-Gly)(5) and (Pro-Hyp-Gly)(5) were more active in inducing chemotaxis than the corresponding decameric peptides (Pro-Pro-Gly)(10) and (Pro-Hyp-Gly)(10). In addition, the presence of Hyp in peptides reduced chemotactic activity. The synthetic peptides were also found to reduce neutrophil apoptosis. In contrast to chemotaxis, this activity was independent of peptide size or composition. The effects of the peptides on both chemotaxis and apoptosis were blocked by inhibitors of phosphatidylinositol 3-kinase (PI3-K) and p38 mitogen-activated protein (MAP) kinase. However, only (Pro-Pro-Gly)(5) and (Pro-Pro-Gly)(10) induced expression of PI3-K and phosphorylation of p38 MAP kinase, suggesting a potential mechanism underlying reduced chemotactic activity of Hyp-containing peptides. Although none of the synthetic peptides tested had any effect on intracellular calcium mobilization, each induced nuclear binding activity of the transcription factor NF-κB. These findings indicate that polymeric polypeptides containing Gly-X-Y collagen-related structural motifs promote inflammation by inducing chemotaxis and blocking apoptosis. However, distinct calcium-independent signaling pathways appear to be involved in these activities

Mechanisms of Oxidant Generation by Catalase

The enzyme catalase converts solar radiation into reactive oxidant species (ROS). In this study, we report that several bacterial catalases (hydroperoxidases, HP), including Escherichia coli HP-I and HP-II also generate reactive oxidants in response to ultraviolet B light (UVB). HP-I and HP-II are identical except for the presence of NADPH. We found that only one of the catalases, HPI, produces oxidants in response to UVB light, indicating a potential role for the nucleotide in ROS production. This prompts us to speculate that NADPH may act as a cofactor regulating ROS generation by mammalian catalases. Structural analysis of the NADPH domains of several mammalian catalases revealed that the nucleotide is bound in a constrained conformation and that UVB irradiation induces NADPH oxidation and positional changes. Biochemical and kinetic analysis indicate that ROS formation by the enzyme is enhanced by oxidation of the cofactor. Conformational changes following absorption of UVB light by catalase NADPH have the potential to facilitate ROS production by the enzyme