Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces.We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.     

Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength r_s≈24 from the paramagnetic to the fully spin-polarized fluid.     

t-Extending Modules and t-Baer Modules

We introduce the notions of “t-extending modules,” and “t-Baer modules,” which are generalizations of extending modules. The second notion is also a generalization of nonsingular Baer modules. We show that a homomorphic image (hence a direct summand) of a t-extending module and a direct summand of a t-Baer module inherits the property. It is shown that a module M is t-extending if and only if M is t-Baer and t-cononsingular. The rings for which every free right module is t-extending are called right Σ-t-extending. The class of right Σ-t-extending rings properly contains the class of right Σ-extending rings. Among other equivalent conditions for such rings, it is shown that a ring R is right Σ-t-extending, if and only if, every right R-module is t-extending, if and only if, every right R-module is t-Baer, if and only if, every nonsingular right R-module is projective. Moreover, it is proved that for a ring R, every free right R-module is t-Baer if and only if Z ₂(R _R ) is a direct summand of R and every submodule of a direct product of nonsingular projective R-modules is projective.     

Preparation and characterization of new photosensitive and optically active poly(amide-imide)s from N-trimellitylimido-L-amino acid and dibenzalacetone moiety in the main chain

Six new photosensitive and optically active poly(amide-imide)s 8a–8f with good inherent viscosities based on dibenzalacetone moiety were synthesized from the direct polycondensation reaction of N-Trimellitylimido-L-amino acids 3a–3f with 2,5-bis(4-aminobenzylidene)cyclopentanone 7 by two different methods such as direct polycondensation in a medium consisting of N-methyl-2-pyrrolidone/triphenyl phosphite/calcium chloride/pyridine and direct polycondensation in a tosyl chloride/pyridine (py)/N,N-dimethylformamide system. Diamine 7 was synthesized by using a two-step reaction. At first 2,5-bis(4-nitrobenzylidene)cyclopentanone 6 was prepared from the reaction of two equimolars 4-nitrobenzaldehyde 5 and one equimolar cyclopentanone 4 and dinitro compound 6 was reduced by using Na2S. Also N-trimellitylimido-L-amino acids 3a–3f were synthesized by the condensation reaction of trimellitic anhydride 1 with two equimolars of various L-amino acids 2a–2f in an acetic acid solution. The polymerization reactions produced a series of photosensitive and optically active poly(amide-imide)s with high yield and good inherent viscosity. The resulted polymers were fully characterized by means of FTIR and ¹H-NMR spectroscopy, elemental analyses, inherent viscosity, specific rotation, solubility tests, UV-VIS spectroscopy, differential scanning calorimeter, thermogravimetric analysis, and derivative of thermogravimetric. These macromolecules exhibited maximum UV-VIS absorption at around 395 and 265 nm in a N,N-dimethylformamide solution.     

Design of ionic liquid 3-methyl-1-sulfonic acid imidazolium nitrate as reagent for the nitration of aromatic compounds by in situ generation of NO(2) in acidic media

3-Methyl-1-sulfonic acid imidazolium nitrate ([Msim]NO(3)) as a new Br?nsted acidic ionic liquid and nitrating agent was prepared and used for the efficient nitration of aromatic compounds (even aniline derivatives). The dramatic effect of this reagent by in situ generation of nitrogen dioxide as a radical on aromatic compounds to give nitroarenes has been studied.     

Trityl Chloride (TrCl): Efficient and Homogeneous Organocatalyst for the Solvent‐Free Synthesis of 14‐Aryl‐14H‐dibenzo[a,j]xanthenes by in situ Formation of Carbocationic System

Trityl chloride (triphenylmethyl chloride, TrCl, Ph₃CCl) is utilized as an efficient and homogeneous organocatalyst for the synthesis of 14‐aryl‐14H‐dibenzo[a,j]xanthenes from β‐naphthol and arylaldehydes under solvent‐free conditions. Moreover, a plausible mechanism is suggested based on the literature and on in situ formation of trityl carbocation with inherent instability during the reaction.     

New characterizations of fusion frames (frames of subspaces)

In this article, we give new characterizations of fusion frames, on the properties of their synthesis operators, on the behavior of fusion frames under bounded operators with closed range, and on erasures of subspaces of fusion frames. Furthermore we show that every fusion frame is the image of an orthonormal fusion basis under a bounded surjective operator.