Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

ESSenTIAL : EPIXfab services specifically targeting (SME) industrial takeup of advanced silicon photonics

ePIXfab brings silicon photonics within reach of European small and medium sized enterprises, thereby building on its track record and its integration into Europractice. To this end, ePIXfab offers affordable access to standardized active and passive silicon photonic IC and packaging technology, a path from design to manufacturing and hands-on training. Based on a consortium of major research institutes with silicon photonics expertise, ePIXfab reaches out to European industry and supports them to evaluate silicon photonics in the context of concrete applications and markets. In order to ensure low-cost, quick access and scalability to manufacturing, the maturity of silicon photonic IC technology is enhanced by setting up a library of generic devices, a level of process and device benchmarking and a well maintained design flow. For the first time, devices in a standard package are offered to facilitate measurements. Training programs on the IC and packaging services are also offered, including hands-on training in making designs. Maturity, standardization and sustainability are driven by a steadily growing worldwide user base

Characteristics of PEO Incorporated with CaTiO3 Nanoparticles: Structural and Optical Properties

In this research, direct band gap polymer composites with amorphous phase, which are imperative for optoelectronic devices applications were synthesized. The solution cast technique was used to produce polyethylene oxide (PEO)/calcium titanate (CaTiO3) nanocomposite (NC) films. The X-ray diffraction (XRD) confirms the growth of amorphous nature within PEO with CaTiO3 addition. The optical band gaps of pure PEO and PEO/CaTiO3 NC films were calculated using analysis of ultraviolet–visible (UV-Vis) spectra. The change in absorption edge toward lower photon energy is evidence of polymer modification. The dispersion behavior of the refractive index of PEO was manipulated to a higher wavelength upon doping with CaTiO3. Upon adding CaTiO3 to the pure PEO polymer, the dielectric constant and refractive index were considerably modified. The band gap shifts from 4.90 eV to 4.19 eV for the PEO incorporated with an optimum portion of 8 wt. % of CaTiO3. The types of the electronic transition in composite samples were specified, based on the Taucs model and the optical dielectric loss. The alteration of UV/Vis absorption spectra of the NC film was considered a suitable candidate to be applied in nanotechnology-based devices. The spherulites ascribed to the crystalline phase were distinguished through the optical microscopy (OM) study