Uniqueness of uniform norm and C*-norm in L p (G, ω)

Let G be a locally compact abelian group with a fixed Haar measure and ω be a weight on G. For 1 < p < ∞, we study uniqueness of uniform and C*-norm properties of the invariant weighted algebra L ^p (G, ω).     

A strict topology on Orlicz spaces

Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology (in the sense of Sentilles‐Taylor) on the Orlicz function space and investigate various properties of this locally convex topology. We also study the Orlicz space of a locally compact group G with a left Haar measure under the strict topology and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on under the topology and other natural ones.     

Compact right multipliers on a Banach algebra related to locally compact semigroups

For a locally compact semigroup \({\mathcal{S}}\), let \(L_{0}^{\infty}({\mathcal{S}},M_{a}({\mathcal{S}}))\) be the Banach space of all μ-measurable (\(\mu\in M_{a}({\mathcal{S}})\)) functions vanishing at infinity, where \(M_{a}({\mathcal{S}})\) denotes the algebra of all measures in the measure algebra \(M({\mathcal{S}})\) of \({\mathcal{S}}\) with continuous translations. Here, we study right compact multipliers on the Banach algebra \(L_{0}^{\infty}({\mathcal{S}},M_{a}({\mathcal{S}}))^{*}\) equipped with an Arens product.     

The Dual of Semigroup Algebras with Certain Locally Convex Topologies

In this paper, we deal with the dual of the semigroup algebras for an extensive class of locally compact semigroups S under certain locally convex topologies. We first introduce and study a locally convex topology on under which the Banach space can be identified with its strong dual. We then show that, except for the case where S is finite, there are infinitely many such locally convex topologies on . Finally, we characterize the spectrum of in terms of semicharacters on S.     

Certain strict topologies on the space of regular Borel measures on locally compact groups

Let G   denote a locally compact Hausdorff group and M(G)$M(G)$ be the space of all bounded complex-valued regular Borel measures on G  . In this paper, we define two strict topologies on M(G)$M(G)$ and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G)$M(G)$ and consider various continuity properties for the convolution product on M(G)$M(G)$ under these topologies.     

Porosity and products of Orlicz spaces

Let $(\Omega , \Sigma , \mu )$ be a measure space and let $\varphi _1, \ldots , \varphi _n$ and $\varphi $ be Young functions. In this paper, we, among other things, prove that the set $E=\{(f_1, \ldots ,f_n)\in M^{\varphi _1}\times \cdots \times M^{\varphi _n}:\, N_\varphi (f_1\cdots f_n)<\infty \}$ is a $\sigma $ - $c$ -lower porous set in $M^{\varphi _1}\times \cdots \times M^{\varphi _n}$ , under mild restrictions on the Young functions $\varphi _1, \ldots , \varphi _n$ and $\varphi $ . This generalizes a recent result due to G? a? b and Strobin (J Math Anal Appl 368:382–390, 2010) to more general setting of Orlicz spaces. As an application of our results, we recover a sufficient and necessary condition for Orlicz spaces to be closed under the pointwise multiplication due to Hudzik (Arch Math 44:535–538, 1985) and Arens et al. (J Math Anal Appl 177:386–411, 1993).     

Synthesis of star-shaped CuO nanoparticles supported on magnetic functionalized graphene: Catalytic and antibacterial activity

In this study, graphene oxide was modified during consecutive functionalization steps with 1,4-diphenylamine, cyanuric chloride, and ethylenediamine. Then, star-shaped CuO nanoparticles were synthesized on modified graphene oxide using the seed-mediated growth method in which nucleation, growth stages, and reduction of graphene oxide to graphene occurred simultaneously. After ensuring successful synthesis of CuO nanoparticles and to facilitate recycling, a magnetization process was utilized by adding iron oxide nanoparticles. This nanocomposite was characterized by transmission electron microscopy, X-ray powder diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy. The prepared heterogeneous catalyst was investigated for the reduction of organic dyes in the presence of NaBH₄ as a reducing reagent. The kinetic data obtained for the reduction of methyl orange (MO), methylene blue (MB), 4-nitrophenol (4-NP), and rhodamine 6G (Rh6G) were fitted to first-order rate equations, and the calculated rate constants for the reduction of MO, MB, 4-NP and Rh6G were as follows: −0.091, −0.071, −0.045, and 0.040, respectively. As star-shaped CuO nanoparticles showed a higher antibacterial effect compared to spherical-shaped CuO nanoparticles, the antibacterial activity of star-shaped CuO nanoparticles immobilized on magnetic functionalized graphene was evaluated against Gram-positive and Gram-negative bacteria through an agar well diffusion assay and demonstrated more antibacterial activity against gram-positive bacteria.     

The evolution of γ-Mg17Al12 intermetallic compound during accumulative back extrusion and subsequent ageing treatment

Accumulative back extrusion (ABE) processing, as a novel severe plastic deformation (SPD) method, has been recently justified to be capable of modifying the microstructural characteristics of alloys. In line to its ongoing researches, the present work has been planned to study the evolution of γ-Mg₁₇Al₁₂ intermetallic phase during ABE and subsequent ageing treatment in a high Al-bearing Mg–Al–Zn alloy. The behaviour of γ intermetallic has been systematically examined as following points of view: (i) strain–temperature-dependent morphology changes, (ii) strain-induced dissolution, and (iii) re-ageing behaviour as a function of time and temperature. Aiming to analyse the morphology of eutectic γ compound with respect to the strain and temperature, 2D projections of effective diameter, shape factor and globularity have been made in strain/temperature graphs. The processing conditions (strain and temperature) corresponding to the desired and undesired morphologies are introduced and microstructurally explained through underlying plasticity mechanisms, i.e., ‘necking-thinning-particle separation’ and ‘brittle fragmentation.’ The former mechanism is suggested to be in relation with partial strain-induced dissolution of eutectic γ phase, leading to generation of a supersaturated solid solution. This has resulted to the observation of ‘off-stoichiometry’ phenomena in Mg₁₇Al₁₂ phase and has been justified through dislocation-assisted deformation mechanism at elevated temperature. Surprisingly, a unique re-ageing behaviour has been found for the obtained solid solutions, where a modified kinetics and morphology of γ phase precipitation were characterized. The altered precipitation behaviour is attributed to the specific defect structure achieved by SPD acting as fast diffusion channel for Al solutes.     

Enhancement of Human γ-Interferon Production in Recombinant <Emphasis Type="Italic">E. coli</Emphasis> Using Batch Cultivation

Development of inexpensive and simple culture media and appropriate induction conditions are always favorable for industry. In this research, chemical composition and stoichiometric data for γ-interferon production and recombinant Escherichia coli growth were used in order to achieve a simple medium and favorable induction conditions. To achieve this goal, the effects of medium composition and induction conditions on the production of γ-interferon were investigated in batch culture of E. coli BL21 (DE3) [pET3a-ifnγ]. These conditions were considered as suitable conditions for the production of γ-interferon: 2.5× M9 medium, supplemented with a mixture of amino acids (milligram per liter), including glutamic acid 215, aspartic acid 250, lysine 160, and phenylalanine 90, and induction at late-log phase (OD₆₀₀ = 4.5). Under these conditions, dry cell weight of 6 ± 0.2 g/l and γ-interferon concentration of 2.15 ± 0.1 g/l were obtained. Later, without changing the concentration ratio of amino acids and glucose, the effect of increase in the primary glucose concentration on productivity of γ-interferon was investigated. It was found that 25 g/l glucose will result in maximum attainable biomass and recombinant human γ-interferon. At improved conditions, a dry cell weight of 14 ± 0.2 g/l, concentration and overall productivity of γ-interferon 4.2 ± 0.1 g/l and 420 ± 10 mg/l h, respectively, were obtained.     

Synthesis,Spectroscopy, X‐ray Crystallography,and DFT Computations of Nanosized Phosphazenes

Nanoparticles of nine phosphazenes with general formula 4‐CH₃C₆H₄S(O)₂N=PX₃ [X = Cl ( A ), NC₄H₈ ( 1 ), NC₆H₁₂ ( 2 ), NC₄H₈N–C(O)OC₂H₅ ( 3 ), NC₄H₈N–C(O)OC₆H₅ ( 4 ), NC₄H₈O ( 5 ), NHCH₂–C₄H₇O ( 6 ), N(CH₃)(C₆H₁₁) ( 7 ), NHCH₂–C₆H₅ ( 8 ), and 2‐NH‐NC₅H₄ ( 9 )] were synthesized using ultrasonic method and characterized by ¹H, ¹³C, ³¹P NMR, FT‐IR, fluorescence, as well as UV/Vis spectroscopy and additionally with XRD, FE‐SEM, N₂ sorption, and elemental analysis. The ³¹P NMR spectra of compounds 1 – 9 reveal the most up field shift δ(³¹P) for 9 at –11.45 ppm reflecting the most electron donation of 2‐aminopyridinyl rings through resonance to the phosphorus atom. The ¹H, ¹³C NMR spectra of 7 exhibit two sets of signals for the hydrogen and carbon atoms of its two isomers present in the solution state in 1:4 ratio. The FE‐SEM micrographs illustrate that the nanoparticles of compounds 1 – 9 have spherical morphology and a size of 27–42 nm. From the XRD patterns, the crystal sizes were estimated to about 24–86 nm. The highest bandgap was measured for 3 (3.81 eV) whereas the smallest was measured for 8 (3.50 eV). The structures of two polymorphs of compound 5 ( 5 , 5′ ) were determined by X‐ray crystallography at 120 K. Both of these polymorphs are triclinic with P1 space group but 5 has a doubled unit cell volume and two symmetrically independent molecules ( 5a and 5b ). In structures 5a and 5′ , the phosphorus and all endocyclic atoms of two morpholinyl rings display disorder, whereas the molecule 5b does not show disorder. The strong intermolecular O–H ··· O hydrogen bonds plus weak intermolecular C–H ··· O and C–H ··· N interactions create three‐dimensional polymers in the crystalline networks of 5 and 5′ . The DFT computations illustrate that molecule 5b is more stable than 5a by –1.1062 and –0.9779 kcal · mol^–1 at B3LYP and B3PW91 levels, respectively. The NBO calculations presented sp³d hybridization for phosphorus and sulfur atoms and sp², sp³ hybrids for the nitrogen and oxygen atoms.