Generalized Bosbach states: part I

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics.     

Optical Fiber Excitation of Fano Resonances in a Silicon Microsphere

In this article, Fano lineshape whispering gallery modes were observed in the light scattering spectrum of a silicon microsphere in near-infrared telecommunication wavelengths. A simple model is presented to explain the transition from Lorentzian lineshape to the Fano lineshape resonances with the coupled-mode theory of multiple whispering gallery modes. Polar mode spacing of 0.23 nm is observed in the spectra, which correlates well with the calculated value. The quality factor of the Lorentzian and Fano resonances are on the order of 10⁵. By using an appropriate interface design for the microsphere coupling geometries, Fano lineshape optical resonances herald novel device applications for silicon volumetric lightwave circuits.     

On Dedekind Modules

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.     

Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings

Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, 2003) considered an iterative approach to finding a nearest common fixed point of infinitely many nonexpansive mappings in a Hilbert space. Very recently, Takahashi and Takahashi (J. Math. Anal. Appl. 331, 506–515, 2007) introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, motivated by these authors’ iterative schemes, we introduce a new iterative approach to finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space. The main result of this work is a strong convergence theorem which improves and extends results from the above mentioned papers.     

Chloro-Modified Magnetic Fe3O4@MCM-41 Core–Shell Nanoparticles for L-Asparaginase Immobilization with Improved Catalytic Activity,Reusability, and Storage Stability

This paper describes a new support that permits to efficient immobilization of L-asparaginase (L-ASNase). For this purpose, Fe₃O₄ magnetic nanoparticles were synthesized and coated by MCM-41. 3-chloropropyltrimethoxysilane (CPTMS) was used as a surface modifying agent for covalent immobilization of L-ASNase on the magnetic nanoparticles. The chemical structure; thermal, morphological, and magnetic properties; chemical composition; and zeta potential value of Fe₃O₄@MCM-41-Cl were characterized by Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), differential thermal analysis (DTA), differential scanning calorimetry (DSC), vibrating sample magnetometer (VSM), scanning electron microscope (SEM), energy dispersive X-ray (EDX), X-ray diffraction patterns (XRD), and zeta-potential measurement. The immobilization efficiency onto Fe₃O₄@MCM-41-Cl was detected as 63%. The reusability, storage, pH, and thermal stabilities of the immobilized L-ASNase were investigated and compared to that of soluble one. The immobilized enzyme maintained 42.2% of its original activity after 18 cycles of reuse. Furthermore, it was more stable towards pH and temperature compared with soluble enzyme. The Michaelis–Menten kinetic properties of immobilized L-ASNase showed a lower V_max and a similar K_m compared to soluble L-ASNase. Immobilized enzyme had around 47 and 32.5% residual activity upon storage a period of 28 days at 4 and 25 °C, respectively. In conclusion, the Fe₃O₄@MCM-41-Cl@L-ASNase core–shell nanoparticles could successfully be used in industrial and medical applications.

     

Comparing Singlet Oxygen Generation of Schiff Base Substituted Novel Silicon Phthalocyanines by Sonophotochemical and Photochemical Applications

Although the sonophotodynamic method has an effective therapeutic outcome for anticancer treatment compared with the photodynamic method, there are not enough related studies in the literature and this study aims to contribute to the development of sonophotodynamic studies. For this purpose, the Schiff base substituted silicon phthalocyanines were designed and synthesized as effective sensitizer candidates and the photophysicochemical and sonophotochemical features of the phthalocyanines were examined to increase singlet oxygen efficiency. The calculated Φ_Δ values indicate that the contribution of substituent groups improved the production of singlet oxygen compared with silicon (IV) phthalocyanine dichloride (SiPcCI₂) and also the sonophotochemical applications increased the singlet oxygen yields. The Φ_Δ values (Φ_Δ = 0.76 for axially bis-{4-[(E)-(pyridin-3-ylimino)methyl]phenol} substituted silicon (IV) phthalocyanine ( 2a ), 0.68 for axially bis-4-[(E)-{[(pyridin-3-yl)methyl]imino}methyl]phenol substituted silicon (IV) phthalocyanine ( 2b ) in photochemical study) reached to Φ_Δ = 0.98 for 2a , 0.94 for 2b in sonophotochemical study. This article will enrich the literature on increasing singlet oxygen yield.     

Swelling of <Emphasis Type="Italic">N</Emphasis>-vinylcaprolactam-dodecyl methacrylate gel in {heptane + toluene} mixtures

A copolymer gel has been synthesized from N-vinylcaprolactam and dodecyl methacrylate in ethanol using the free radical cross-linking polymerization method. Characterizations of the gel were performed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal gravimetric analysis (TGA) techniques. Swelling behavior of the gel was investigated in heptane, toluene, and their binary mixtures with different compositions. Swelling value in toluene is higher than that in heptane and swelling value increases with the increasing initial content of toluene in the binary mixture with heptane. The swelling values are correlated by the first- and second-order differential equations, and the best model correlating the experimental results is a second-order one. Diffusion coefficients have also been calculated for heptane and toluene at each concentration by power-law and first-order equations. While the diffusion mechanism of the gel in heptane is a Fickian one, the gel swelled in toluene exhibits a non-Fickian character. Diffusion mechanisms of the gels in binary mixtures are much more complicated. Because of the higher swelling degree in toluene compared to that in heptane, selectivity of the gel in different {heptane + toluene} mixtures with selectivity close to 1 has also been taken into consideration.     

Theoretical investigation of the Anti-Parkinson drug rasagiline and its salts: conformations and infrared spectra

The conformational analysis of rasagiline [N-propargyl-1(R)-aminoindan] was performed by the density functional theory (DFT) B3LYP method using the 6–31++G (d,p) basis set. A single point energy calculations based on the B3LYP optimized geometries were also performed at MP2/6-31++G (d, p) level. The vibrational frequencies of the most stable conformer of rasagiline was calculated at the B3LYP level and vibrational assignments were made for normal modes on the basis of scaled quantum mechanical force field (SQM) method. The influence of mesylate and ethanedisulfonate salts on the geometry of rasagiline free base and its normal modes are also discussed.      

Degenerate molecular shuttles with flexible and rigid spacers

The preparation and dynamic behavior of degenerate rotaxane molecular shuttles are described in which a benzylic amide macrocycle moves back and forth between two naphthalimide-glycine units along a diphenylethyne spacer or an aliphatic spacer consisting of a C(9), C(12), or C(26) alkyl chain. Subtle differences in the (1)H NMR spectra of the rotaxanes can be related to the presence of conformers in which the macrocycle interacts simultaneously with both glycines, especially in the case of the C(9) spacer. The kinetic data of the shuttling behavior in the C(26) rotaxane were obtained from dynamic NMR spectroscopy. The Eyring activation parameters were found to be ΔH(?) = 10 ± 1 kcal mol(-1), ΔS(?) = -6.5 ± 2.0 cal mol(-1) K(-1), ΔG(?)(298) = 11.9 ± 0.2 kcal mol(-1). For the systems with the shorter spacers, the shuttling rates were higher. Also in the diphenylethyne, rotaxane shuttling is rapid on the NMR time scale, indicating that the rigid unit does not impose a large barrier to the translocation of the macrocycle.