Summability on Mellin-type nonlinear integral operators

In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the summability methods defined by Bell. Considering the Haar measure with variation semi-norm in Tonelli's sense, we approach to the functions of bounded variation. Similar results are also obtained for uniformly continuous and bounded functions. Using suitable function classes we investigate the rate of convergence in the approximation. Finally, we give a non-trivial application verifying our approach.     

Biological distribution of iodo-allyl gabapentin and iodo-gabapentin

Gabapentin (GBP) is an anticonvulsant and is widely used in the treatment of epilepsy. In this study, GBP and an allyl derivative of GBP were radioiodinated with ¹³¹I using the iodogen method; then their radiopharmaceutical potential in rats and rabbits was investigated. The radiochemical purity of ¹³¹I-GBP and its derivatives was determined by RTLC. The labeling yield was 95±2%. Biological evaluation was performed in normal rats and rabbits. Labeled compounds were intravenously injected into two rabbits via the ear vein after anesthetizing. The dynamic and static scintigrams were obtained using a gamma camera at different time. Then the labeled compounds were administered intravenously into the rats. The distribution was studied by counting the radioactivity in the removed organs. The results of biodistribution in the rats showed the clearance of ¹³¹I-ALGBP was faster than ¹³¹I-GBP. On the other hand, the uptake of ¹³¹I-ALGBP in the brain was higher than ¹³¹I-GBP at 60 minutes.     

A summability process on Baskakov-type approximation

The summability process introduced by Bell (Proc Am Math Soc 38: 548–552, 1973) is a more general and also weaker method than ordinary convergence. Recent studies have demonstrated that using this convergence in classical approximation theory provides many advantages. In this paper, we study the summability process to approximate a function and its derivatives by means of a wider class of linear operators than a family of positive linear operators. Our results improve not only Baskakov’s idea in (Mat Zametki 13: 785–794, 1973) but also the Korovkin theory based on positive linear operators. In order to verify this we display a specific sequence of approximating operators by plotting their graphs.     

Investigation of interactions between some anionic dyes and cationic surfactants by conductometric method

The interactions of cationic surfactants with anionic dyes were studied by conductometric method. Benzyltrimethylammonium chloride (BTMACl), benzyltriethylammonium chloride (BTEACl) and benzyltributylammonium chloride (BTBACl) were used as cationic surfactants and indigo carmine (IC) and amaranth (Amr) were chosen as anionic dyes. The specific conductance of dye–surfactant mixtures was measured at 25, 35 and 45 °C. A decrease in measured specific conductance values of dye–surfactant mixture was caused by the formation of non-conducting or less-conducting dye–surfactant complex. The equilibrium constants, K₁, the standard free energy changes, ΔG₁°$\mathrm{\Delta }{G}_1°$, the standard enthalpy changes, ΔH₁°$\mathrm{\Delta }{H}_1°$ and the standard entropy changes, ΔS₁°$\mathrm{\Delta }{S}_1°$ for the first association step of dye–surfactant complex formation were calculated by a theoretical model. The results showed that the equilibrium constants and the negative standard free energy change values for all systems decreased as temperature increased. Also these values decreased for all systems studied with increasing alkyl chains of surfactants due to the steric effect. When the equilibrium constant values, K₁, for the first association step of IC–surfactant and Amr–surfactant systems with the same surfactant were compared, the values of K₁ for IC–surfactant system were higher than that of Amr–surfactant system.     

Statistical Approximation by Double Poisson–Cauchy Singular Integral Operators

In this paper we show that it is possible to approximate a continuous and 2π-periodic function on the disk centered at origin with radius π by means of double Poisson–Cauchy singular integral operators which do not need to be positive in general. Our results cover not only the classical approximation but also the statistical approximation process.     

Methyl 4‐O‐β‐D‐mannopyranosyl β‐D‐xylopyranoside

Methyl β‐D‐mannopyranosyl‐(1→4)‐β‐D‐xylopyranoside, C₁₂H₂₂O₁₀, (I), crystallizes as colorless needles from water, with two crystallographically independent molecules, (IA) and (IB), comprising the asymmetric unit. The internal glycosidic linkage conformation in molecule (IA) is characterized by a ϕ′ torsion angle (O5′_Man—C1′_Man—O1′_Man—C4_Xyl; Man is mannose and Xyl is xylose) of −88.38 (17)° and a ψ′ torsion angle (C1′_Man—O1′_Man—C4_Xyl—C5_Xyl) of −149.22 (15)°, whereas the corresponding torsion angles in molecule (IB) are −89.82 (17) and −159.98 (14)°, respectively. Ring atom numbering conforms to the convention in which C1 denotes the anomeric C atom, and C5 and C6 denote the hydroxymethyl (–CH₂OH) C atom in the β‐Xylp and β‐Manp residues, respectively. By comparison, the internal glycosidic linkage in the major disorder component of the structurally related disaccharide, methyl β‐D‐galactopyranosyl‐(1→4)‐β‐D‐xylopyranoside), (II) [Zhang, Oliver & Serriani (2012). Acta Cryst. C 68 , o7–o11], is characterized by ϕ′ = −85.7 (6)° and ψ′ = −141.6 (8)°. Inter‐residue hydrogen bonding is observed between atoms O3_Xyl and O5′_Man in both (IA) and (IB) [O3_Xyl...O5′_Man internuclear distances = 2.7268 (16) and 2.6920 (17) Å, respectively], analogous to the inter‐residue hydrogen bond detected between atoms O3_Xyl and O5′_Gal in (II). Exocyclic hydroxymethyl group conformation in the β‐Manp residue of (IA) is gauche–gauche, whereas that in the β‐Manp residue of (IB) is gauche–trans.     

Varying the Stiffness and Diffusivity of Rod-Shaped Microgels Independently through Their Molecular Building Blocks

Microgels are water-swollen, crosslinked polymers that are widely used as colloidal building blocks in scaffold materials for tissue engineering and regenerative medicine. Microgels can be controlled in their stiffness, degree of swelling, and mesh size depending on their polymer architecture, crosslink density, and fabrication method—all of which influence their function and interaction with the environment. Currently, there is a lack of understanding of how the polymer composition influences the internal structure of soft microgels and how this morphology affects specific biomedical applications. In this report, we systematically vary the architecture and molar mass of polyethylene glycol-acrylate (PEG-Ac) precursors, as well as their concentration and combination, to gain insight in the different parameters that affect the internal structure of rod-shaped microgels. We characterize the mechanical properties and diffusivity, as well as the conversion of acrylate groups during photopolymerization, in both bulk hydrogels and microgels produced from the PEG-Ac precursors. Furthermore, we investigate cell-microgel interaction, and we observe improved cell spreading on microgels with more accessible RGD peptide and with a stiffness in a range of 20 kPa to 50 kPa lead to better cell growth.     

The Urbach tails and optical absorption in layered semiconductor TlGaSe<Subscript>2</Subscript> and TlGaS<Subscript>2</Subscript> single crystals

TlGaSe₂ and TlGaS₂ single crystals were grown by the modified Bridgman-Stockbarger method. We report the result of an experimental study of the optical absorption of TlGaSe₂ and TlGaS₂ crystals. The absorption measurements were performed in steps of 10 K. The direct and indirect band gaps for TlGaSe₂ and TlGaS₂ samples were calculated as a function of temperature. The phonon energies in TlGaSe₂ and TlGaS₂ crystals were calculated as (39±4) and (9±4) meV at 240 K, respectively. At 10 K, direct and indirect band gaps were found as 2.294 and 2.148 eV for TlGaSe₂, 2.547 and 2.521 eV for TlGaS₂ crystals, respectively. The abrupt changes were observed in the direct and indirect band gaps in the some temperature ranges. These changes were interpreted as phase transformation temperatures. The steepness parameters and Urbach energy for TlGaSe₂ and TlGaS₂ samples increased with increasing sample temperature in the range (10–320) K.