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.     

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.     

Spin transfer torque in the semiconductor/ferromagnetic structure in the presence of Rashba effect

Spin transfer torque in magnetic structure occurs when the transverse component of the spin current that flows from the nonmagnetic medium to ferromagnetic medium is absorbed by the interface. In this paper, considering the Rashba effect on the semiconductor region, we discuss the spin transfer torque in semiconductor/ferromagnetic structure and obtain the components of spin-current density for two models:(i) single electron and(ii) the distribution of electrons. We show that no matter whether the difference in Fermi surface between semiconductor and Fermi spheres for the up and down spins in ferromagnetic increases, the transmission probability decreases. The obtained results for the values used in this article illustrate that Rashba effect increases the difference in Fermi sphere between semiconductor and Fermi sphere for the up and down spins in ferromagnetic. The results also show that the Rashba effect, brings an additional contribution to the components of spin transfer torque, which does not exist in the absence of the Rashba interaction. Moreover, the Rashba term has also different effects on the transverse components of the spin torque transfer.     

A Timoshenko beam reduced order model for shape tracking with a slender mechanism

We consider a flexible bio-inspired slender mechanism, modeled as a Timoshenko beam. It is coupled to the environment by a continuous distribution of compliant elements. We derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the Timoshenko beam. The coupling with the substrate allows us to formulate the problem in a control framework, and eventually to treat the system as a sensor to reconstruct the profile of the substrate through the deformation of the body. The coupling is modeled in the framework of two parameters elastic foundations. The convergence of the reduced order model with increasing number of basis functions is addressed in a suitable H¹ error norm. A closed loop force control is simulated for shape morphing when the system is coupled with a smooth substrate.     

Synthesis of Some Novel γ-Spirolactones

Summary. We report on the addition of dialkyl acetylenedicarboxylate to 1-alkylisatins or tryptanthrine in the presence of triphenylphosphine which leads to highly functionalised novel unsaturated -spirolactones.     

In Silico and Experimental Characterization of Chimeric Bacillus thermocatenulatus Lipase with the Complete Conserved Pentapeptide of Candida rugosa Lipase

Lipases are one of the highest value commercial enzymes as they have broad applications in detergent, food, pharmaceutical, and dairy industries. To provide chimeric Bacillus thermocatenulatus lipase (BTL2), the completely conserved pentapeptide (¹¹²Ala-His-Ser-Gln-Gly¹¹⁶) was replaced with similar sequences (²⁰⁷Gly-Glu-Ser-Ala-Gly²¹¹) of Candida rugosa lipase (CLR) at the nucleophilic elbow region. For this purpose, three mutations including A112G, H113E, and Q115A were inserted in the conserved pentapeptide sequence of btl2 gene. Based on the crystal structures of 2W22, the best structure of opened form of the chimeric lipases were garnered using the MODELLER v9.10 software. The native and chimeric lipases were docked to a set of ligands, and a trial version of Molegro Virtual Docker (MVD) software was used to obtain the energy values. Docking results confirmed chimeric lipase to be better than the native lipase. Following the in silico study, cloning experiments were conducted and expression of native and chimeric btl2 gene in Pichia pastoris was performed. The native and chimeric lipases were purified, and the effect of these mutations on characteristics of chimeric lipase studied and then compared with those of native lipase. Chimeric lipase exhibited 1.6-fold higher activity than the native lipase at 55 °C. The highest percentage of both lipases activity was observed at 60 °C and pH of 8.0. The ion Ca²⁺ slightly inhibited the activity of both lipases, whereas the organic solvent enhanced the lipase stability of chimeric lipase as compared with the native lipase. According to the results, the presence of two glycine residues at the conserved pentapeptide region of this chimeric lipase (¹¹² Gly-Glu-Ser-Ala-Gly ¹¹⁶) may increase the flexibility of the nucleophilic elbow region and affect the enzyme activity level.     

Structural, theoretical and multinuclear NMR study of mercury(II) complexes with a new ambidentate phosphorus ylide

The reaction of the new ambidentate ylide, Ph₃PCHCOCH₂COOC₂H₅ (EAPPY), with HgX₂ (X = Cl, Br and I) in equimolar ratios using methanol as the solvent leads to binuclear complexes of the type [EAPPY·HgX₂]₂ (X = Cl (1), Br (2) and I (3)). Single crystal X-ray analysis reveals the presence of a centrosymmetric dimeric structure containing the ylide and HgX₂ (X = Br or I)_. The IR and NMR data of the product [(EAPPY)·HgCl₂]₂ (1), formed by the reaction of mercury(II) chloride with the same ylide, are similar to those of 2 and 3. Analytical data indicate a 1:1 stoichiometry between the ylide and Hg(II) halide in each of the three products. Theoretical studies indicate that the nature of the R group in ylides of the type Ph₃PCHCOR has a weak effect on the Hg-C(ylide) bond length in binuclear Hg₂L₂I₄ complexes.     

Adsorption Studies of Radionuclides and Toxic Metal Ions on a Modified Mesoporous Lanthanum(III) Silicate

A new adsorbent, modified mesoporous lanthanum(III) silicate, has been prepared with various molar ratios of Si/La (10, 20, 40, 80) and cethyltrimethylammonium bromide (CTAB) as structure directing agent. XRD, nitrogen sorption, SEM, IR, thermogravimetry and sorption of radionuclides and toxic metal ions have been studied. The results show that adsorption amount of some element such as Pb(II) and Th(IV) has been increased significantly by incorporation of lanthanum ions in the framework of adsorbent. Separation of Co(II)‐Th(IV), Co(II)‐U(VI) and Mo(VI)‐U(VI) has been developed on columns of this adsorbent.