Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schr\"odinger Equations

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions.Comment: 46 pages, 2 figure

Cosmology and thermodynamics of FRW universe with bulk viscous stiff fluid

We consider a cosmological model dominated by stiff fluid with a constant bulk viscosity. We classify all the possible cases of the universe predicted by the model and analyzing the scale factor, density as well as the curvature scalar. We find that when the dimensionless constant bulk viscous parameter is in the range $0 < \bar\zeta <6$ the model began with a Big Bang, and make a transition form the decelerating expansion epoch to an accelerating epoch, then tends to the de Sitter phase as $t\to \infty$. The transition into the accelerating epoch would be in the recent past, when $4<\bar\zeta<6.$ For $\bar\zeta>6$ the model doesn't have a Big Bang and suffered an increase in the fluid density and scalar curvature as the universe expands, which are eventually saturates as the scale factor $a \to \infty$ in the future. We have analyzed the model with statefinder diagnostics and find that the model is different from $\Lambda$CDM model but approaches $\Lambda$CDM point as $a \to \infty.$ We have also analyzed the status of the generalized second law of thermodynamics with apparent horizon as the boundary of the universe and found that the law is generally satisfied when $0 \leq \bar\zeta <6$ and for $\bar\zeta >6$ the law is satisfied when the scale factor is larger than a minimum value

User Attitudes on E-Books Collection in Mahatma Gandhi University Library: A Case Study

A study on the user’s attitudes, interest and understanding of e-book collections. The sample taken for the study is the E-book collection developed at the Mahatma Gandhi University Library and its users. The survey assessed the impact of the e-books on teaching learning and research. The problems associated with the use of e-books aware also identified. The inference of the study are that the user’s require an orientation on different types of collections, and also extended facilities for access which is possible in this format

The induced path function, monotonicity and betweenness

The induced path function $J(u, v)$ of a graph consists of the set of all vertices lying on the induced paths between vertices $u$ and $v$. This function is a special instance of a transit function. The function $J$ satisfies betweenness if $w \\in J(u, v)$ implies $u \\notin J(w, v)$ and $x \\in J(u, v)$ implies $J(u, x \\subseteq J(u, v)$, and it is monotone if $x, y \\in J(u, v)$ implies $J(x, y) \\subseteq J(u, v)$. The induced path function of aconnected graph satisfying the betweenness and monotone axioms are characterized by transit axioms.betweenness;induced path;transit function;monotone;house domino;long cycle;p-graph

Micro-abrasion-corrosion interactions of Ni-Cr/WC based coatings : approaches to construction of tribo-corrosion maps for the abrasion-corrosion synergism

The process of micro-abrasion-corrosion has been the subject of much research in recent years due to the fact that the action of micron sized particles, typically less than 10 um in diameter, can cause significant degradation of materials in many diverse environments involving aqueous corrosion. Cermet based coatings are often used to combat micro-abrasion-corrosion, but has been little work carried out to characterize the performance of such coatings exposed to micro-abrasion-corrosion or to provide a basis for coating optimisation. In addition, a basis for defining the various micro-abrasion-corrosion interactions has not been suggested to date. In this study the micro-abrasion-corrosion performance of a Ni-Cr/WC coating was assessed and compared to the performance of the steel substrate. The results were used to identify regimes of micro-abrasion as a function of applied load and pH of the solution. In addition, micro-abrasion-corrosion maps were constructed based on the results, showing the variation between micro-abrasion-corrosion regimes, as a function of applied load and pH of the solution

Strategic Management and HRM

[Excerpt] The purpose of this chapter is to discuss this intersection between Strategic Management and HRM, what we know, and future directions for SHRM research. We will begin by briefly discussing the concept of strategy and the popularization of the resource-based view (RBV) of the firm. Next we will address its role in creating the link between HRM and Strategic Management including key questions that the RBV has raised in relation to SHRM. We will then examine the current state of affairs in SHRM; the progress made, and key questions and concerns occupying the attention of SHRM researchers. Finally, we will conclude with our views on future directions for SHRM research