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.     

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.     

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...     

Sorption and immobilization of cellulase on silicate clay minerals

The interaction of organic molecules with mineral surfaces is a subject of interest in a variety of disciplines. Enzymes are able to be sorbed and immobilized by clay minerals and humic colloids in soil environment. The present study was done to elucidate some aspects of sorption and immobilization of cellulase on soil components by analysis of the sorption, and immobilization of cellulase on Avicel, a soil sample, illite, kaolinite, montmorillonite, and palygorskite. Palygorskite displayed the highest sorption capacity. Sorbents coated with hydroxyaluminum displayed significantly higher capacity than uncoated sorbents. The positive effects of Al(OH)(x) coating on sorption capacities of the different sorbents were not equal. The effect decreased in the order soil > palygorskite > kaolinite > Avicel > montmorillonite > illite. The amount of sorbed cellulase desorbed from external surfaces of soil was quite low (about 16%), especially in coated samples (about 6%). X-ray diffraction analysis of K-montmorillonite and Ca-montmorillonite showed that Al(OH)(x) was intercalated between the montmorillonite layers. Immobilization of cellulase on the sorbents did not result in expansion of their crystal structures. Therefore, it may be concluded that the amount of cellulase immobilized on internal surfaces of the sorbents was negligible.     

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.     

Forcing strong convergence of Korpelevich’s method in Banach spaces with its applications in game theory

We develop a variant of Korpelevich’s method for solving variational inequality problems with pseudomonotone operators in Banach spaces. We establish the strong convergence of the sequence generated by the method under reasonable assumptions on the problem data. Finally, we justify the motivation of our theory by including compelling examples of infinite dimensional variational inequality problems for which our method is applicable.     

Algorithms for solutions of extended general mixed variational inequalities and fixed points

In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S, we construct some new resolvent iterative algorithms for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is the unique solution of the problem of extended general nonlinear mixed variational inequalities. We study convergence analysis of the suggested iterative schemes under some suitable conditions. We also suggest and analyze a class of extended general resolvent dynamical systems associated with the extended general nonlinear mixed variational inequalities and show that the trajectory of the solution of the extended general resolvent dynamical system converges globally exponentially to the unique solution of the extended general nonlinear mixed variational inequalities. The results presented in this paper extend and improve some known results in the literature.     

Tunable zeroth-order resonator based on a ferrite metamaterial structure

This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.