Some approximation properties by a class of bivariate operators

Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.     

Centralisateur d'un élément dans un hypergroupe réversible

The purpose of this paper is to define the centralizer notion and to present some of its properties, in the context of reversible hypergroups.     

Comparison of BLADE and conventional T2-TSE sequences for the sagittal visualization of the cervical spinal cord in multiple sclerosis patients — A case report

The purpose of this study is to report the significant differences found in the identification of lesions in cervical spinal cord of two patients with multiple sclerosis when using the BLADE T2-TSE and BLADE T2-TIRM sequences as opposed to the conventional T2-TSE and T2-TIRM sequences for sagittal acquisition at 1.5 T. In both patients, one more lesion was identified with the BLADE sequences than with the conventional ones. Consequently, we suggest the use of BLADE T2-TSE and BLADE T2-TIRM sequences in place of conventional ones for sagittal examination of the cervical spinal cord of multiple sclerosis patients. The advantages of ΤΙRΜ to reveal the pathology of the cervical spinal cord and the advantage of BLADE sequences to improve image quality should be combined in a sequence that could be ideal for cervical spinal cord examinations.     

To be or to become: how dynamic geometry changes discourse

In this article, we investigate the impact of the introduction of a dynamic geometry environment on mathematical thinking by identifying changes in discourse engendered by its introduction in a high school geometry class. Our focus is on the teacher, and we find significant differences between static and dynamic geometry in terms of the ways in which the teacher talks about geometric objects, makes use of visual artifacts and models geometric reasoning. Even though these changes have major implications for the geometry being studied, they are made only very implicitly in the classroom.     

Preparation of siloxane‐based urethane dimethacrylates carrying carboxylic groups and the effect of silver nanoparticles on the properties of composite polymer films

This work reports on the synthesis of three acid oligosiloxane‐urethane dimethacrylates and their use to obtain hybrid nanocomposite films, in which the presynthesized silver nanoparticles (NPs) were incorporated before photopolymerization, or produced via in situ photoreduction of the silver nitrate (AgNO₃) precursor into the formulation, without any conventional reducing agent. All samples were characterized by ¹H NMR, FT‐infrared and UV spectroscopies, photodifferential scanning calorimetry (photo‐DSC), transmission electron microscopy (TEM), and energy‐dispersive X‐ray (EDX) analysis. Fourier transformed infrared spectroscopy and photo‐DSC results showed that dimethacrylates having hydrophilic segment of poly(ethylene oxide) type in structure are more reactive than the acid oligosiloxane dimethacrylate. When another urethane dimethacrylate is taken as a comonomer, the photopolymerization rate (0.112–0.132 s^?1) and the degree of conversion (82–93%) significantly increased. Experimental evidence of the existence of nanosilver into the polymer matrix generated upon UV irradiation has been supported by UV spectroscopy, EDX and TEM analysis, the last allowing a visualization of the formation of silver NPs with size between 2 and 15 nm. Mechanical parameters and wettability of the photocrosslinked films are also discussed in the prospect of further potential applications in the biomedical field. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Preparation of sol�Cgel hybrid materials from ��-methacryloxypropyltrimethoxysilane and tetramethyl orthosilicate: study of the hydrolysis and condensation reactions

Organic?Cinorganic hybrid materials suitable for the development of sol?Cgel coatings for metallic surfaces were prepared by hydrolysis and condensation of ??-methacryloxypropyltrimethoxysilane (MAPTMS) and tetramethyl orthosilicate (TMOS). The hydrolysis of MAPTMS/TMOS was carried out in an ethanol/water solution. The prehydrolysis stage of MAPTMS/TMOS system was monitored by Fourier transform infrared spectroscopy (FTIR) and liquid-state ²⁹Si and ¹³C nuclear magnetic resonance (²⁹Si and ¹³C NMR). FTIR analysis indicated that the hydrolysis of MAPTMS/TMOS was accomplished as far as the (SiOMe) band corresponding to unhydrolyzed silane disappeared. The concentration of the alkoxy groups and the extent of self-condensation of mono-, di-, and trisubstituted siloxanes (T species) in the sol were estimated by using liquid-state ²⁹Si NMR spectroscopy. The hydrolysis of the prepared sol was also evaluated by liquid-state ¹³C NMR spectroscopy. The results indicated that under the adopted synthesis strategy conditions, the hydrolysis process requires 4?h to be completed.     

Chemical profile and biological activities of Peltigera horizontalis (Hudson) Baumg. thallus and apothecia extracts

Abstract

The aim of this study was to determine, for the first time, the chemical composition of Peltigera horizontalis thallus and apothecia extracts (ether, ethyl acetate, dichloromethane and acetone) by HPLC-UV and GC-MS, and evaluate activity of genotoxic, anticholinesterase, antioxidant and antibacterial potential of acetone extracts. Major constituents of thallus extracts were gyrophoric acid, and methyl gyrophorate while dominant component of apothecia extracts was tenuiorin. The predominant volatile compounds in extracts were methyl orsellinate, dodecyl acrylate, orcinol and orcinol monomethyl ether. The thallus acetone extract at concentration of 2.0 µg mL^?1 gave the greatest decrease in the micronuclei frequency (22.4%) of all tested extracts. Apothecia extract showed stronger antioxidant activity as compared to thallus extract. Tested extracts at concentration of 10?mg mL^?1 exhibited inhibitory effect (16.5% for thallus and 12.8% for apothecia) on pooled human serum cholinesterase. P. horizontalis acetone extracts had no activity against the tested five bacteria strains.     

Effects of Sodium Butyrate on Cell Death Induced by Photodynamic Therapy in U373-MG and D54-MG Astrocytoma Cell Lines

The damage induced by end products of photodynamic therapy (PDT) in astrocytoma tumors leads to cytotoxicity and cell death. Chromatin modifiers such as sodium butyrate (NaB) induce several genes involved in apoptosis, among others. The PDT improvement was evaluated by the measurement of its effectiveness in the treatment of U373-MG and D54-MG astrocytoma cell lines exposed to NaB. Cells exposed to 80 μg mL⁻¹ of δ-aminolevulinic acid (ALA) as precursor of endogenous photosensitizer (PS), protoporphyrin IX (PpIX), induced 16.67% and 28.9% of mortality in U373-MG and D54-MG, respectively. The mortality increased to 70.62% and 96.7%, respectively, when U373-MG and D54-MG cells were exposed for 24 h to 8 m m NaB prior to ALA-induction. In this condition, re-expression of some genes related to apoptosis in U373-MG, and differentiation in D54-MG were induced. PpIX accumulation was higher than ALA-induction and the acetylation of histone H4 induced by NaB was verified by immunocytochemistry in both cells. It can be concluded that modified chromatin and genes induced by NaB increment the cellular death induced by PDT in astrocytoma cells using PpIX as endogenous PS.