Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

Summierbarkeit der geometrischen Reihe auf vorgeschriebenen Mengen

In this paper we are concerned with the summability of the geometric series by matrix methods. We prove the following theorem: Suppose M_o:={z:|z|<1}, M₁, M₂, is a collection of countably many Lebesgue measureable, disjoint sets. For k=1,2, let f_k be a prescribed function, analytic on . Then there exists a triangular matrix , such that the V-transform {_n(z)} of the geometric series has the following properties: {_n(z)} converges compactly to on M_o; for k=1,2, there are sets B_k, such that has Lebesgue-measure zero and _n(z)f_k(z) for zB_k; if there is a set B^*, such that B^*M^* has Lebesgue-measure zero and {_n(z)} diverges for zB^*.     

Scheduling of a machining center

A machining center is an advanced NC (Numerical Control) machine that has the capability to perform a variety of operations on a part by automatically changing the cutting tools. Because of its versatile processing capabilities, a machining center is often a production bottleneck, and effective scheduling can result in significant improvement of system performance. The problem, however, is very difficult since many factors such as machine setups, pallets, tool magazine, and possible tool overlapping among different part types, etc., have to be considered. This paper presents an optimization-based approach for the scheduling of a machining center with two pallets. A novel “separable” problem formulation that considers the above mentioned factors is presented. Lagrangian relaxation is applied to decompose the problem into simple subproblems, which are efficiently solved without encountering complexity difficulties. The subgradient method is then used to update the multipliers. Testing results indicate that the approach is effective, and the algorithm provides a valuable tool for solving stand-alone machining center problems. The approach also points out a direction on how to consider machining centers within a job shop environment.     

NaK 22Σ+ → 11Σ+ band optically pumped laser near 1.02 μm

Optically pumped laser emission has been observed on the NaK 2(A)¹⁺ 1(X)¹⁺ electronic state transition. The emission occurs between 1.015 and 1.035 m when a sodium-potassium heat-pipe oven is pumped with 695–745 nm pulsed dye laser radiation. The laser emission occurs on many ro-vibrational transitions without the use of cavity mirrors. However, the addition of a simple cavity increases both the number of observed lasing transitions and the amplitude of the emission on each line. We report our results for the dependence of the emission intensity on pump laser power, oven temperature, and buffer gas pressure.     

Transition from disorder to order in thin metallic films studied with angle-resolved photoelectron spectroscopy

The transition from disorder to order in Ag film grown on Au(111) was investigated by monitoring the quantum well states using angle-resolved photoelectron spectroscopy. Our results show that the binding energies do not alter, but the in-plane dispersion alters from flat to parabolic when the film is annealed. We suggest that there are isolated and ordered patches scattered across the film at an early stage of the transition and that atoms inside the patches are fully ordered along the surface normal. These ordered patches grow and merge together as the annealing temperature increases.     

Piper betle (L): Recent Review of Antibacterial and Antifungal Properties,Safety Profiles,and Commercial Applications

Piper betle (L) is a popular medicinal plant in Asia. Plant leaves have been used as a traditional medicine to treat various health conditions. It is highly abundant and inexpensive, therefore promoting further research and industrialization development, including in the food and pharmaceutical industries. Articles published from 2010 to 2020 were reviewed in detail to show recent updates on the antibacterial and antifungal properties of betel leaves. This current review showed that betel leaves extract, essential oil, preparations, and isolates could inhibit microbial growth and kill various Gram-negative and Gram-positive bacteria as well as fungal species, including those that are multidrug-resistant and cause serious infectious diseases. P. betle leaves displayed high efficiency on Gram-negative bacteria such as Escherichia coli and Pseudomonas aeruginosa, Gram-positive bacteria such as Staphylococcus aureus, and Candida albicans. The ratio of MBC/MIC indicated bactericidal and bacteriostatic effects of P. betle leaves, while MFC/MIC values showed fungicidal and fungistatic effects. This review also provides a list of phytochemical compounds in betel leaves extracts and essential oils, safety profiles, and value-added products of betel leaves. Some studies also showed that the combination of betel leaves extract and essential oil with antibiotics (streptomycin, chloramphenicol and gentamicin) could provide potentiating antibacterial properties. Moreover, this review delivers a scientific resume for researchers in respected areas and manufacturers who want to develop betel leaves-based products.     

Synthesis and photophysical studies of siloxane-tethered cyclophanes

Novel siloxane tethered para divinylarene cyclophanes, containing phenyl, biphenyl and naphthalene rings as the aromatic nuclei, were prepared by the hydrolytic condensation of the corresponding bis{[dimethyl(i-propoxy)silyl]vinyl}arenes under basic conditions.The photophysics of the cyclophanes were investigated using UV and fluorescence spectroscopy.     

Folding of alternating dialkylsilylene-spaced donor-acceptor copolymers: the oligomer approach

A series of oligmers with donor-acceptor pairs separated by diisopropylsilylene (iPr(2)Si) spacers, composed of monomer 4b, dimer 5, trimer 6, and tetramer 7, were synthesized to scrutinize the folding behavior. Monomer 4a with a dimethylsilylene (Me(2)Si) spacer was also prepared for comparison. The 4-aminostyrene moiety was used as the donor and the stilbene moiety as the acceptor. Both steady-state and time-resolved fluorescence spectroscopic measurement were made. Regardless of the substituents on the silicon atom, the emission spectra of 4a and 4b exhibit both local excited (LE) emission of the acceptor chromophore and emission from the charge-separated state (CT emission), which are similar to that of the corresponding Me(2)Si-spaced copolymer 2a with the same donor and acceptor chromophores, but different from that of the copolymer with the iPr(2)Si spacer 2b. Dimer 5 behaves like 4 and 2a. As the chain length of the oligomers increases, the emission properties of the higher homologues become prone to that of 2b. Thus, tetramer 7 exhibits emission from the charge-transfer complex, which is essentially same as that of 2b. Moreover, charge-transfer absorptions emerge in 6 and 7. These results suggest that the folding nature of oligomers approaches that of the corresponding polymer, as the degree of oligomerization increases, and the electronic interactions between adjacent donor-acceptor pairs are controlled by the steric effect of the substituents on the silicon atoms and concomitant amplification of the stabilizing energy by extending the distance of the folding structure.