Restricted Modules and Conjectures for Modules of Constant Jordan Type

We introduce the class of restricted k[A]-modules and p ^t -Jordan types for a finite abelian p-group A of exponent at least p ^t and a field k of characteristic p. For these modules, we generalize several theorems by Benson, verify a generalization of conjectures stated by Suslin and Rickard giving constraints on Jordan types for modules of constant Jordan type when t is 1. We state conjectures giving constraints on p ^t -Jordan types and show that many p ^t -Jordan types are realizable.     

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed ‘splitting.’ We discuss far-field ‘splitting’ in the full field and near-horizon ‘splitting’ in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the ‘splitting’ behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field ‘splitting’ is explained by competition between projected modes. The near-horizon ‘splitting’ is due to excitation of lower multipole modes that back excite the multipole mode for which ‘splitting’ is observed. In both cases ‘splitting’ is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter-mode excitation effect that we study.     

New relationship of displacement signal at quadrant photodiode: Control signal analysis and simulation of a laser tracker

New relationship of displacement signal using opposite sectors on a quadrant photodiode is derived. Standard and new displacement signals are analyzed in details. Through MATLAB^® laser tracking simulation models, based on common and suggested approaches, detailed analysis is performed, and it is shown that better results for the new relationship signal processing are obtained. Within new relationship of displacement signal, the sensitivity of the system to the displacement of the spot increases and, hence, provides better accuracy in positioning up to 30%.     

Dithienoindophenines: p‐Type Semiconductors Designed by Quinoid Stabilization for Solar‐Cell Applications

Compared with the dominant aromatic conjugated materials, photovoltaic applications of their quinoidal counterparts featuring rigid and planar molecular structures have long been unexplored despite their narrow optical bandgaps, large absorption coefficients, and excellent charge‐transport properties. The design and synthesis of dithienoindophenine derivatives (DTIPs) by stabilizing the quinoidal resonance of the parent indophenine framework is reported here. Compared with the ambipolar indophenine derivatives, DTIPs with the fixed molecular configuration are found to be p‐type semiconductors exhibiting excellent unipolar hole mobilities up to 0.22 cm² V^?1 s^?1, which is one order of magnitude higher than that of the parent IP‐O and is even comparable to that of QQT(CN)4‐based single‐crystal field‐effect transistors (FET). DTIPs exhibit better photovoltaic performance than their aromatic bithieno[3,4‐b]thiophene (BTT) counterparts with an optimal power‐conversion efficiency (PCE) of 4.07 %.     

A DFT Study on Estrone – TNT Interaction

Trinitrotoluene, known as TNT, is a widely used powerful explosive. It is a poisonous material, which injures almost all cells, especially those of liver, bone marrow, and kidney. Estrone is a sex hormone having an electron rich aromatic (phenolic) ring that is capable of forming a π complex with molecules containing an electron deficient π system. This study has focused on investigating the tendency of the complex formation of TNT with estrone. It has been thought that the formation of estrone‐TNT π complex might take place in a human body exposed to acute or prolong period of this hazardous chemical and consequently estrone activities might be impaired. The complex formation reaction was investigated mainly using DFT method with B3LYP/6‐31G(d, p) basis set in gas phase. The existence of π interaction between estrone and TNT was demonstrated by computational spectroscopic analyses (UV/Vis, IR, and ¹H NMR techniques). The frontier molecular orbital (HOMO and LUMO) analyses have shown that the considered π complex is very resistant to oxidation with respect to its components, estrone and TNT.     

Single- and multi-shot laser-induced damages of Ta_2O_5/SiO_2 dielectric mirrors at 1064 nm

Ta2O5/SiO2 dielectric mirrors deposited by ion beam sputtering (IBS) are studied. The multi-shot laserinduced damage threshold (LIDT) and its dependence on the number of shots are investigated, after which we find that the multi-shot LIDT is lower than that of single-shot. The accumulation effects of defects play an important role in the multi-shot laser damage. A simple model, which includes the conduction band electron production vsa multiphoton and impact ionizations, is presented to explain the experimental phenomena.