The main aim of this paper is to develop the generalized Bessel matrix polynomials. We derive the various families of the generating matrix functions for the generalized hypergeometric matrix function. Some new, known and unknown generating matrix functions involving the generalized Bessel matrix polynomials are obtained by using the hypergeometric matrix function as applications of the main results. We give connections between generalized Bessel and Jacobi matrix polynomials. An expansion formula of these matrix polynomials is given. We get some generating matrix functions for the generalized Bessel matrix polynomials, involving the Horn’s and hypergeometric matrix functions. The results obtained here include a number of linear, bilinear and bilateral generating matrix functions for the generalized Bessel matrix polynomials which further leads to certain recent generalizations of the known and unknown bilinear and bilateral generating matrix functions and give some applications of the obtained results.

The classical Hermite-Hermite matrix polynomials for commutative matrices were rst studied by Metwally et al.[M. S. Metwally, M. T. Mohamed and A. Shehata: On Hermite-Hermite matrix polynomials. Math. Bohemica 133 (2008), 421-434]. Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula for the Hermite-Hermite matrix polynomials has also been investigated. Furthermore, we have dened a new polynomial associated with the Hermite-Hermite matrix polynomials and have established the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, general families and several new results of generalized Hermite-Hermite matrix polynomials have been established.

The aim of the present work is to develop a pair of Lommel matrix functions of two variables suggested by the Bessel matrix functions and some of their properties are studied to be special cases of our results.

Pyrolysis of hydrazines and their derivatives often results in homolytic cleavage of the N N bonds, but molecular rearrangements and eliminations are also observed in many cases. Thermal reactions in solution, in the solid state, and in the gas phase under static, flow, and flash vacuum pyrolysis conditions are considered in this review. Arrhenius or Eyring activation parameters are reported whenever available, but the original literature should always be consulted, as these parameters are often derived under widely different experimental conditions. The compound classes investigated include open-chain and cyclic hydrazine derivatives and their relationship with azomethine imines, N-amino-heterocycles, Nisocyanoamines and N-isocyanatoamines, N-aminocarbodiimides, azines, hydrazones, semicarbazides and semicarbazones, hydrazides, aminimides, amidrazones, azimines, triazenes, tetrazadienes, pentazadienes and hexazatrienes, and triazines. Understanding of reaction mechanisms is emphasized whenever possible. Reactive intermediates involved in these pyrolysis reactions include ketenes, ketenimines and other cumulenes, free radicals and diradicals, zwitterions, carbenes, nitrenes, nitrile ylides, nitrile imines, arynes and azetes.

Abstract The weed flora of the reclaimed desert lands in the eastern and western stretches of Qena Governorate along the Nile Valley was investigated. This study attempted to identify the vegetation groups (communities) prevailing in common winter and summer crops, to recognise the crop–weed relationships, and to assess the role of different soil factors on the distribution and composition of the weed flora in each season. Three major crops were selected: alfa–alfa (winter and summer seasons), wheat (winter season) and millet (summer season). Altogether, 146 studied fields (stands) were monitored, and distributed as follows: 49 in the wheat fields, 38 in alfa– alfa (summer season), 24 in alfa–alfa (winter season), and 35 in millet fields. Frequency (f %) of weed species within the different crop farmlands was used as measure of ecological success. The total number of species varied among the studied crops: the highest was 131 species in alfa–alfa (the perennial crop), followed by 111 species in wheat (the winter crop), and the lowest (29 species) was in millet (the summer crop). The relationships between the recorded species and crops were discussed. TWINSPAN as a classification method and DCA as an ordination methods were used to assess differences in floristic composition in different seasons. The resulted TWINSPAN vegetation groups from winter and summer seasons were clearly separated along the first 2 axes of DCA. Canonical correspondence analysis was used to evaluate the relationships between the examined soil factors and the floristic presence/absence data sets in each season.

Abstract The weed flora of the reclaimed desert lands in the eastern and western stretches of Qena Governorate along the Nile Valley was investigated. This study attempted to identify the vegetation groups (communities) prevailing in common winter and summer crops, to recognise the crop–weed relationships, and to assess the role of different soil factors on the distribution and composition of the weed flora in each season. Three major crops were selected: alfa–alfa (winter and summer seasons), wheat (winter season) and millet (summer season). Altogether, 146 studied fields (stands) were monitored, and distributed as follows: 49 in the wheat fields, 38 in alfa– alfa (summer season), 24 in alfa–alfa (winter season), and 35 in millet fields. Frequency (f %) of weed species within the different crop farmlands was used as measure of ecological success. The total number of species varied among the studied crops: the highest was 131 species in alfa–alfa (the perennial crop), followed by 111 species in wheat (the winter crop), and the lowest (29 species) was in millet (the summer crop). The relationships between the recorded species and crops were discussed. TWINSPAN as a classification method and DCA as an ordination methods were used to assess differences in floristic composition in different seasons. The resulted TWINSPAN vegetation groups from winter and summer seasons were clearly separated along the first 2 axes of DCA. Canonical correspondence analysis was used to evaluate the relationships between the examined soil factors and the floristic presence/absence data sets in each season.

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In this work, a variety of hyperbranched polymers (HBPs), such as hyperbranched polycarbonates, polyesters, polyurethanes and polyacetals, was successfully synthesized from castor oil and soybean oil based monomers via a A21B3 polycondensation. First, B3 monomer triols (TriOL), trialdehydes (TriAD), and tricarboxylic acids (TriAC) were obtained by ozonolysis of castor oil and soybean oil with following reductive or oxidative treatment. Their structures were characterized by 1H NMR and ATR-FTIR spectroscopy as well as electrospray ionization-Time of Flight-mass spectrometry. These trifunctional B3 monomers were applied in the preparation of HBPs. The resulting HBPs had number averaged molar mass (Mn) up to 9400 g/mol and weight averaged molar mass (Mw) up to 40,000 g/mol. Through adjusting the initial molar ratio of A2 to B3 monomers, hydroxyl terminated (from TriOL monomers) or carboxylic acid (from TriAC monomers) terminated HBPs could be obtained. All the HBPs were characterized by 1H NMR, size exclusion chromatography, and DSC. These HBPs are potential candidates for the synthesis of cross-linked polymeric materials or in biomedical applications.

Optical constants of vacuum evaporated thin films in the Se90-xTe10Snx (x = 0, 2.5, 5 and 7.5 at %) system were calculated from reflectance and transmittance data in the wavelength range of 300-2500 nm using Murmann's equations. The maximum value of refractive index increased and suffered a shift towards the short wavelength as the Sn content increases this behavior can be attributed to increasing the values of cross-linking chains density and decrease tailing. The variations in the real and the imaginary parts of the dielectric constant, the dissipation factor tan(), the optical conductivity, the volume, and surface energy loss functions with photon energy have also been reported. The normal dispersion of the refractive index is discussed regarding the single oscillator Wemple-DiDomenico model from which the dispersion parameters were determined. The single oscillator energy, the dispersion energy, the high-frequency dielectric constant, the ratio of free charge carrier concentration to the effective mass, plasma frequency, single oscillator strength and its position are then estimated as a function of alloy composition. It is interesting to note that the increase of Sn content on the parent Se90Te10 is connected to the decreasing covalent nature of the structure. Besides, the presence of such a sharp absorption edge in transmission spectra recommends Se90-xTe10Snx thin films as a good optical filter material.