Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities, they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold ?cr such that minimizers for this variational problem exist if their power is bigger than ?cr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of [15] and [16].Comment: 49 pages, no figure

Moderating Effects of Relationship Length and Contact Frequency on Customer Citizenship Behaviors

Studies show that contact frequency and relationship length impact co-creative and in-role behaviors with service providers. However, their influence on extra-role or customer citizenship behaviors (CCBs) remains unexplored. This study delves into the moderating role of relationship length and contact frequency within the CCB model. Utilizing an online survey (n = 665), the study unveils that perceived justice’s impact on affective commitment is not moderated by contact frequency, whereas the impact is stronger in short-term than in longer-term relationships. The perceived support-affective commitment-CCBs relationship is stronger in high contact than in low contact group. Similarly, the relationship is stronger for customers in long-term interaction with service providers. CCBs more strongly influence continuous relationship intention for low contact customers, but there is no difference in the association across the relationship length. This study contributes an original viewpoint by investigating the intervening effects of contact frequency and relationship length in the CCB model

Discrete diffraction managed solitons: threshold phenomena and rapid decay for general nonlinearities

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities, they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions\u27 concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of [15] and [16]

Well-posedness of dispersion managed nonlinear Schr\"odinger equations

We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schr\"odinger equation with a large class of nonlinearities and arbitrary average dispersion on $L^2(\mathbb{R})$ and $H^1(\mathbb{R})$. Moreover, when the average dispersion is non-negative, we show that the set of nonlinear ground states is orbitally stable.Comment: 29 page

Existence of dispersion management solitons for general nonlinearities

We give a proof of existence of solitary solutions of the dispersion management equation for positive and zero average dispersion for a large class of nonlinearities. These solutions are found as minimizers of nonlinear and nonlocal variational problems which are invariant under a large non compact group. Our proof of existence of minimizers is rather direct and avoids the use of Lions\u27 concentration compactness argument. The existence of dispersion managed solitons is shown under very mild conditions on the dispersion profile and the nonlinear polarization of optical active medium, which cover all physically relevant cases for the dispersion profile and a large class of nonlinear polarizations

Human β-galactoside α-2,3-sialyltransferase (ST3Gal III) attenuated Taxol-induced apoptosis in ovarian cancer cells by downregulating caspase-8 activity

Taxol triggers apoptosis in a variety of cancer cells, but it also upregulates cytoprotective proteins and/or pathways that compromise its therapeutic efficacy. In this report, we found that Taxol treatment resulted in caspase-8-dependent apoptosis in SKOV3 human ovarian cancer cells. Moreover, Taxol-induced apoptosis was associated with caspase-3 activation. Interestingly, Taxol treatment upregulated α-2,3-sialyltransferase (ST3Gal III) expression and forced expression of ST3Gal III attenuated Taxol-induced apoptosis. Furthermore, ST3Gal III overexpression inhibited Taxol-ttiggered caspase-8 activation, indicating that ST3Gal III upregulation produces cellular resistance to Taxol and hence reduces the efficacy of Taxol therapy

One-Step Synthesis of Pd-M/ZnO (M=Ag, Cu, and Ni) Catalysts by γ

ZnO-supported Pd, Pd-Ag, Pd-Cu, and Pd-Ni catalysts (Pd-M/ZnO) were prepared in MeOH/H2O mixture (4/1, v/v-%) by γ-irradiation at room temperature. Small mono- and bimetallic nanoparticles were loaded on the surface of ZnO nanopowder as confirmed with TEM, TEM-EDXS, XRD, and ICP-AES data. The catalytic efficiency against Pd-M/ZnO was determined in hydrogenation and Suzuki reaction and compared with the commercial Pd/C catalyst. The Pd-Ag/ZnO showed the highest catalytic efficiency in the Suzuki reaction