Fundamental equations of certain electromagnetic-acoustic discontinuous fields in variational form

We present, in the first part of the paper, the well-known fundamental electromagnetic-acoustic equations, that is, the coupled Maxwells and Newtons equations for an elastic dielectric continuum in differential form, and we also discuss the uniqueness of their linear solutions. In the second part, from a general principle of physics, we deduce a three-field variational principle that operates on the mechanical displacements, the electric potential, and the electromagnetic vector potential of the dielectric continuum. Then, we extend it through an involutory (or Friedrichss) transformation in deriving a nine-field unified variational principle that operates on the mechanical, electrical, and magnetic continuous linear fields under the infinitesimal strains. This variational principle generates Maxwells and Newtons equations, the coupled linear constitutive relations, and the associated natural boundary conditions for the regular region of the dielectric continuum as its Euler-Lagrange equations. In the third part, we further generalise the unified variational principle so as to incorporate the jump conditions across a surface of discontinuity within the dielectric region. We also show that the integral and differential types of variational principles that apply to the linear motions of the elastic dielectric region with a fixed internal surface of discontinuity are in agreement with and recover, as special cases, some of the earlier variational principles. Further, the variational principles may be directly used in linear electromagnetic and/or acoustic field computations and in consistently establishing the lower order one- or two-dimensional equations of the elastic dielectric continuum.Received: 9 January 2002, Accepted: 26 May 2003, Published online: 5 December 2003PACS: 03.40, 41.10, 77.60 Correspondence to: G.A. Altay     

On Cesàro summability of vector valued multiplier spaces and operator valued series

In this paper, we introduce and study vector valued multiplier spaces with the help of the sequence of continuous linear operators between normed spaces and Cesàro convergence. Also, we obtain a new version of the Orlicz–Pettis Theorem by means of Cesàro summability.     

Alternative,High‐Yield Synthesis of (E)‐4‐Oxonon‐2‐enoic Acid from 2‐Methoxyfuran

Alkylation of 2‐methoxyfuran, followed by in situ TPP‐sensitized photooxygenation of 2‐methoxy‐5‐pentylfuran in the presence of Me₂S, gave methyl (Z)‐4‐oxonon‐2‐enoate. Hydrolysis of methyl (Z)‐4‐oxonon‐2‐enoate afforded (E)‐4‐oxonon‐2‐enoic acid in three steps and in 79% overall yield.     

Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness

The spaces and introduced by Ayd?n and Ba?ar [C. Ayd?n, F. Ba?ar, Some new difference sequence spaces, Appl. Math. Comput. 157 (3) (2004) 677-693] can be considered as the matrix domains of a triangle in the sets of all sequences that are summable to zero, summable, and bounded by the Cesàro method of order 1. Here we define the sets of sequences which are the matrix domains of that triangle in the sets of all sequences that are summable, summable to zero, or bounded by the strong Cesàro method of order 1 with index p?1. We determine the β-duals of the new spaces and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.     

A comparison of iterative Fourier transform algorithms for image quality estimation

A comparison was established between two iterative Fourier transform algorithms (IFTAs), such as the original Gerchberg–Saxton (GS) and the mixed-region amplitude freedom (MRAF) algorithms, for the hologram reconstruction of different target images through the full reference image quality estimation (IQE) and pixel homogeneity in the Fourier plane presented theoretically and experimentally. The comparison was applied depending upon both algorithms based on a computer-generated hologram (CGH) implemented utilizing a reflective phase-modulated liquid-crystal spatial light modulator (LC-SLM) to obtain the digital kinoform holograms of the desired intensity distributions. These digital holograms were applied to reconstruct the intensity patterns for 852 nm, which represents a laser beam source. The theoretical and experimental results of the reconstructed patterns obtained using the MRAF algorithm were found to be smoother and better than the patterns obtained using the GS algorithm. Unmodulated light beam (dc term) is removed from the reconstructed patterns attributed to digital kinoform holograms of MRAF algorithm as an alternative to the theoretical and experimental results without using any additional optic equipment at the light path. Moreover, this paper discussed the full reference objective quality estimations, such as mean square error (MSE), peak signal-to-noise ratio (PSNR), structural content (SC), normalized absolute error (NAE), normalized cross correlation (NK), and homogeneity of pixels, through the contrast (Cont) and inverse difference moment (IDM) for numerical and experimental results. According to the two desired intensity distributions processed theoretically and experimentally, the results of MRAF algorithm were found to be in the highly accurate recovered phase, the quality of image was enhanced, and the dc term was decreased. Image quality estimation of full reference objective relay on the feedback algorithms experimental attestation has not been implemented yet.     

N-picolinamides as ligands for Ullmann-type homocoupling reactions

The use of N-phenylpicolinamide (NPPA) as a ligand in Ullmann-type homocoupling reactions of aryl iodides and bromides in common solvents, such as DMF and MeCN has been successfully demonstrated at room temperature. In addition, this work provided the first example of the homocoupling of an aryl chloride at 82 °C, which is a relatively low temperature when compared to regular Ullmann reaction temperatures. Also, NPPA was successfully employed in base—and heat free Suzuki reactions, including electron rich and poor aryl halides with heteroarylboronic acids in moderate yields.     

Crystallization of CaAl4O7 and CaAl12O19 powders

Calcium is always present in alumina systems as an unintentional (or intentional) dopant, and yet the fundamental effect of its incorporation into the aluminas is not well understood, and is further complicated by the presence of Si. The synthesis of powders of two calcium aluminate phases (CaAl₄O₇, which is also known as CaO · 2Al₂O₃ or CA₂, and CaAl₁₂O₁₉, which is also known as CaO · 6Al₂O₃ or CA₆) has been investigated using low-temperature chemical-processing techniques. The crystallization of these powders from the amorphous precursor has been examined using various characterization techniques. The precursors for the powders were prepared by mixing stoichiometric proportions of the nitrate salts into a 5 wt% aqueous solution of poly(vinyl alcohol). Conversion of the amorphous precursors to crystalline powders and the subsequent phase transitions were monitored using differential thermal analysis (DTA), thermogravimetric analysis (TGA) and powder X-ray diffractometry (XRD). While powders with CA₂ stoichiometry crystallized directly at 883°C, amorphous powders with CA₆ stoichiometry first crystallized into an intermediate structure without partitioning and then transformed into CA₆ at 1175°C. Fully and partially crystallized powders were analyzed using transmission electron microscopy and electron energy-loss spectroscopy (EELS). Measured near-edge structures (Al–L_2,3, Ca–L_2,3 and O–K) are presented for the CA₂, γ-Al₂O₃ and CA₆ phases. The intermediate phase, identified as γ-Al₂O₃, was found to accommodate a significant concentration of Ca.