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961.
ABSTRACTNonlinear optical materials (NLO) have been garnering attention due to their role in optical data storage, optical communication and laser technology. Organic crystals have emerged as an extremely important class of NLO materials, since their NLO properties compare very well with traditional inorganic NLO materials like KCl, LiNbO3, KDP (potassium dihydrogen phosphate), etc. They offer the additional advantage that they can be grown relatively inexpensively from solution close to room temperature, unlike the inorganic NLO materials which are grown from high temperature melts. In the present work, organic transparent single crystals of methyl para-hydroxy benzoate (MHB) were grown by slow evaporation solution growth technique (SEST) from aqueous solution at room temperature. The changes in structural, electrical and optical properties of gamma irradiated MHB single crystals were studied using X-ray diffraction (XRD), UV–Visible absorption spectroscopy, Photo-luminescence (PL), Fourier transform infrared (FTIR) spectroscopy and AC conductivity measurements at room temperature. The polished MHB single crystals were irradiated with gamma rays of doses 10 and 15 kilogray (kGy). From the XRD analysis, it was observed that gamma irradiation for these doses drastically decreases the crystallinity. The optical absorption constants were examined by UV-Visible absorption spectroscopy, measured over the wavelength range of 200–800?nm, at normal incidence. The optical band gap as estimated from the Tauc plot ((αhν)2 vs hν) was found to be reduced with increasing gamma irradiation doses. PL spectra showed emission at wavelengths of 361?nm (3.43?eV) and 452?nm (2.74?eV), with enhanced intensities for the irradiated crystals. FTIR spectroscopy was utilised to identify the functional groups of MHB and indicated the rupture of specific types of bonds with gamma irradiation. Apart from that, the enhancement of AC conductivity with gamma irradiation was also observed for the gamma irradiated crystals. 相似文献
962.
963.
A.S. Mohamed 《Applicable analysis》2013,92(3-4):179-184
In this paper, we study conditions under which Schrodinger type operators with a matrix potential is separated and Schrodinger equation has a unique solution in the weighted space L2,k(Rn)l, where l is any natural number and k ε C1(Rn) is a positive function 相似文献
964.
965.
A brief historical introduction to Euler's formula for polyhedra,topology, graph theory and networks
Lokenath Debnath 《International Journal of Mathematical Education in Science & Technology》2013,44(6):769-785
This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included. 相似文献
966.
T. Stevens X. Liu Z. Aguirre-Munoz 《International Journal of Mathematical Education in Science & Technology》2013,44(7):984-995
In this paper, we explore a novel approach for assessing the impact of a professional development programme on classroom practice of in-service middle school mathematics teachers. The particular focus of this study is the assessment of the impact on teachers’ employment of strategies used in the classroom to foster the mathematical habits of mind and mathematical self-efficacy of their students. We describe the creation and testing of a student survey designed to assess teacher classroom practice based primarily on students’ ratings of teacher practices. 相似文献
967.
Miguel Vivas-Cortez Muhammad Aamir Ali Hüseyin Budak Humaira Kalsoom Praveen Agarwal 《Entropy (Basel, Switzerland)》2021,23(7)
In this investigation, for convex functions, some new –Hermite–Hadamard-type inequalities using the notions of derivative and integral are obtained. Furthermore, for -differentiable convex functions, some new () estimates for midpoint and trapezoidal-type inequalities using the notions of integral are offered. It is also shown that the newly proved results for and can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities. 相似文献
968.
Manuela Royer 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(4):281-307
In this paper, we study one-dimensional backward stochastic differential equations (BSDE) with a random terminal time driven by a monotone generator, and their links with elliptic partial differential equations. Firstly, we present the case of BSDEs driven by a strictly monotone generator, and next we consider BSDEs driven by a monotone generator. 相似文献
969.
In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given. 相似文献
970.
This article introduces a graphical goodness-of-fit test for copulas in more than two dimensions. The test is based on pairs of variables and can thus be interpreted as a first-order approximation of the underlying dependence structure. The idea is to first transform pairs of data columns with the Rosenblatt transform to bivariate standard uniform distributions under the null hypothesis. This hypothesis can be graphically tested with a matrix of bivariate scatterplots, Q-Q plots, or other transformations. Furthermore, additional information can be encoded as background color, such as measures of association or (approximate) p-values of tests of independence. The proposed goodness-of-fit test is designed as a basic graphical tool for detecting deviations from a postulated, possibly high-dimensional, dependence model. Various examples are given and the methodology is applied to a financial dataset. An implementation is provided by the R package copula. Supplementary material for this article is available online, which provides the R package copula and reproduces all the graphical results of this article. 相似文献