Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

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.     

Efficient light harvesting and energy transfer in organic-inorganic hybrid multichromophoric materials

Thin films of silica hybrid materials consisting of two to three covalently bound organic chromophores at different ratios were conveniently synthesized and fabricated. The photophysical properties of these materials have been studied. The fluorescence spectra reveal complete fluorescence resonance energy transfer (FRET) from donor to acceptor, and the light-harvesting ability of these hybrid materials increases with increasing the molar fraction of donor chromophore. In a three-chromophore system, the energy is transferred from 300 to 530 nm successfully. Time-resolved fluorescence experiments are employed to elucidate the average rates and efficiencies (84-97%) of energy transfer in these organic/inorganic hybrid systems. The hybrid materials have been shown to provide antenna effect to facilitate energy transfer and light harvesting.     

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^*.     

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.     

New Bundle Methods for Solving Lagrangian Relaxation Dual Problems

Bundle methods have been used frequently to solve nonsmooth optimization problems. In these methods, subgradient directions from past iterations are accumulated in a bundle, and a trial direction is obtained by performing quadratic programming based on the information contained in the bundle. A line search is then performed along the trial direction, generating a serious step if the function value is improved by or a null step otherwise. Bundle methods have been used to maximize the nonsmooth dual function in Lagrangian relaxation for integer optimization problems, where the subgradients are obtained by minimizing the performance index of the relaxed problem. This paper improves bundle methods by making good use of near-minimum solutions that are obtained while solving the relaxed problem. The bundle information is thus enriched, leading to better search directions and less number of null steps. Furthermore, a simplified bundle method is developed, where a fuzzy rule is used to combine linearly directions from near-minimum solutions, replacing quadratic programming and line search. When the simplified bundle method is specialized to an important class of problems where the relaxed problem can be solved by using dynamic programming, fuzzy dynamic programming is developed to obtain efficiently near-optimal solutions and their weights for the linear combination. This method is then applied to job shop scheduling problems, leading to better performance than previously reported in the literature.     

Combining furan annulation,heck reaction,and Sonogashira coupling for the synthesis of oligoaryls

[structure: see text] A variety of benzene-furan-alkene/alkyne conjugated oligomers of precise length and constitution were synthesized iteratively by combining furan annulation, Heck reaction, and Sonogashira coupling.     

Theoretical infrared transition matrix elements for the water molecule

Using the Hartree-Fock-Roothaan method, symmetric potential energy and dipole moment functions have been obtained for the ground state of the water molecule. These functions were transformed and analyzed in terms of the normal symmetric stretching (v₁) and bending (v₂) coordinates for the calculation of i.r. transition matrix elements. There is satisfactory agreement between this work and the experimental values for the transition matrix element of the v₂ fundamental. However, a discrepancy of a factor of 2.5 is observed between calculated and experimental matrix elements for the v₁ fundamental.     

Über die Nörlund-Summierbarkeit von Potenzreihen

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