Relative T -Injective Modules and Relative T -Flat Modules

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ _T ¹ (N, M) = 0 (resp. Γ₁ ^T (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I _n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.     

Solving the generalized regularized long wave equation on the basis of a reproducing kernel space

On the basis of a reproducing kernel space, an iterative algorithm for solving the generalized regularized long wave equation is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u_n is constructed by truncating the series to n terms. The convergence of u_n to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations.     

Applications of Nano-Baskets of Calixarenes in Chromatography

Nano-baskets of calixarenes have been subject to extensive research in the construction of liquid chromatographic phases, extractants, transporters, electrode ionophores, and optical and electrochemical sensors over the past 4 decades. There has long been interest in calixarene-based liquid chromatographic phases. Owing to the recent rapid growth in the number of publications on calixarene-based liquid chromatographic phases, this review paper focuses on their different applications in the main fields of molecular and ionic species as well as liquid chromatographic mobile and stationary phases. Although the recent reports have focused on the optimization and application of one kind or a unique group of calixarenic mobile or stationary phases, this review is a collection and comparison of a variety of research data dealing with the synthesis, preparation and behavior of calixarene-based liquid chromatographic phases.     

Synthesis of Dialkyl 2‐(Alkylamino)‐4,9‐dihydro‐9‐oxocyclohepta[b]pyran‐3,4‐dicarboxylates

Dialkyl 2‐(alkylamino)‐4,9‐dihydro‐9‐oxocyclohepta[b]pyran‐3,4‐dicarboxylates are prepared in a one‐pot three‐component reaction of alkyl isocyanide, dialkyl acetylenedicarboxylate, and α‐tropolone (=2‐hydroxycyclohepta‐2,4,6‐trienone). The reaction proceeds smoothly at room temperature and under neutral conditions to afford tropolone derivatives in high yield.     

Synthesis, spectral and electrochemical studies of Cu(II) and Ni(II) complexes with new N2O2 ligands: a new precursor capable of depositing copper nanoparticles using thermal reduction

Cu(II) and Ni(II) complexes of the general type [M(N2O2)] are described. The N2O2 ligands used are [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,3-diamine] (HOMeSalpn) and [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,2-diamine (HOMeSalpr). These complexes have been characterized by IR, UV-vis, CV, TG-DTA and 1H NMR spectroscopy. The electrochemical behavior of these complexes at a glassy carbon electrode in acetonitrile solution indicates that the first reduction process corresponding to Cu(II)-Cu(I) and Ni(II)-Ni(I) is electrochemically irreversible. The new copper complexes have been applied for the preparation of copper nanoparticles using non-ionic surfactant (Triton X-100) by thermal reduction. The copper nanoparticles with average size of 48nm were formed by thermal reduction of [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,3-diamine]copper(II) in the presence of triphenylphosphine thus releasing the reduced copper and affording the high-purity copper nanoparticles.     

Two phase mixed convection Al2O3–water nanofluid flow in an annulus

Heat transfer enhancement of a mixed convection laminar Al₂O₃–water nanofluid flow in an annulus with constant heat flux boundary condition has been studied employing two phase mixture model and effective expressions of nanofluid properties. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq’s hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. The Brownian motions of nanoparticles have been considered to determine the effective thermal conductivity and the effective dynamic viscosity of Al₂O₃–water nanofluid, which depend on temperature. Three-dimensional Navier–Stokes, energy and volume fraction equations have been discretized using the finite volume method while the SIMPELC algorithm has been introduced to couple the velocity–pressure. Numerical simulations have been presented for the nanoparticles volume fraction (?) between 0 and 0.05 and different values of the Grashof and Reynolds numbers. The calculated results show that at a given Re and Gr, increasing nanoparticles volume fraction increases the Nusselt number at the inner and outer walls while it does not have any significant effect on the friction factor. Both the Nusselt number and the friction coefficient at the inner wall are more than their corresponding values at the outer wall.     

Nonlinear vibration mitigation of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc

Nonlinear Dynamics - This study is dedicated to investigate the nonlinear dynamics of a system composed of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc. The...     

Binomial Sums and Functions of Exponential Type

Let (a_n)_n0 be a sequence of complex numbers, and, for n0, let A number of results are proved relating the growth of the sequences(b_n) and (c_n) to that of (a_n). For example, given p0, if b_n= O(n^p and for all > 0,then a_n=0 for all n > p. Also, given 0 < p < 1, then for all > 0 if and onlyif . It is further shown that, given rß > 1, if b_n,c_n=O(rßⁿ), then a_n=O(ⁿ),where , thereby proving a conjecture of Chalendar, Kellay and Ransford. The principal ingredientsof the proogs are a Phragmén-Lindelöf theorem forentire functions of exponential type zero, and an estimate forthe expected value of e^(X), where X is a Poisson random variable.2000 Mathematics Subject Classification 05A10 (primary), 30D15,46H05, 60E15 (secondary).     

A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.