Radical of filters in BL‐algebras

In this paper, the notion of the radical of a filter in BL‐algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV‐algebra if and only if D_s(A) ? F. After that we define the notion of semi maximal filter in BL‐algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL‐algebra. Moreover, we prove that A/F is a semi simple BL‐algebra if and only if F is a semi maximal filter of A. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Improved efficacy of bio‐mineralization of human mesenchymal stem cells on modified PLLA nanofibers coated with bioactive materials via enhanced expression of integrin α2β1

Current therapeutic interventions in bone defects are mainly focused on finding the best bioactive materials for inducing bone regeneration via activating the related intracellular signaling pathways. Integrins are trans‐membrane receptors that facilitate cell‐extracellular matrix (ECM) interactions and activate signal transduction. To develop a suitable platform for supporting human bone marrow mesenchymal stem cells (hBM‐MSCs) differentiation into bone tissue, electrospun poly L‐lactide (PLLA) nanofiber scaffolds were coated with nano‐hydroxyapatite (PLLA/nHa group), gelatin nanoparticles (PLLA/Gel group), and nHa/Gel nanoparticles (PLLA/nHa/Gel group) and their impacts on cell proliferation, expression of osteoblastic biomarkers, and bone differentiation were examined and compared. MTT data showed that proliferation of hBM‐MSCs on PLLA/nHa/Gel scaffolds was significantly higher than other groups (P < .05). Alkaline phosphatase activity was also more increased in hBM‐MSCs cultured under osteogenic media on PLLA/nHa/Gel scaffolds compared to others. Gene expression evaluation confirmed up‐regulation of integrin α2β1 as well as the osteogenic genes BGLAP, COL1A1, and RUNX2. Following use of integrin α2β1 blocker antibody, the protein level of integrin α2β1 in cells seeded on PLLA/nHa/Gel scaffolds was decreased compared to control, which confirmed that most of the integrin receptors were bound to gelatin molecules on scaffolds and could activate the integrin α2β1/ERK axis. Collectively, PLLA/nHa/Gel scaffold is a suitable platform for hBM‐MSCs adhesion, proliferation, and osteogenic differentiation in less time via activating integrin α2β1/ERK axis, and thus it might be applicable in bone tissue engineering.     

Highly efficient one-pot synthesis of dihydropyran heterocycle

Diammonium hydrogen phosphate and potassium carbonate-catalyzed one-pot synthesis of 1,4- phenylene-bis（2-amino-4H-pyran-3-carbonitrile and 2-amino-4-aryl-4H-pyran-3-carbonitrile deriva- tives has been achieved by a three-component cyclocondensation of aldehydes, malononitrile, and different nucleophiles in aqueous medium in high yields.     

Al(HSO4)3: an efficient and heterogeneous reusable catalyst for the synthesis of 1-amidoalkyl-2-naphthols under thermal solvent-free conditions

An efficient green protocol for the synthesis of 1-amidoalkyl-2-naphthols using a three-component, one-pot condensation reaction of 2-naphthol, aromatic aldehyde and amides in the presence of Al(HSO₄)₃ as heterogeneous catalyst under thermal solvent-free conditions has been described. The present procedure offers advantages such as shorter reaction times, simple work-up procedure, excellent yields, recovery and reusability of catalyst.     

Some results in BL ‐algebras

We define the set of double complemented elements in BL‐algebras and state and prove some theorems which determines properties of these sets. We introduce the notion of an almost top element and study the properties of these elements (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pt(II)-catalyzed synthesis of 1,2-dihydropyridines from aziridinyl propargylic esters

Pt(II)-catalyzed cycloisomerization of aziridinyl propargylic esters affords 1,2-dihydropyridines with regiodefined installation of substituents. A mild conversion of the 1,2-dihydropyridines to the corresponding substituted pyridines as well as chirality retention from the aziridinyl propargylic ester substrates have been demonstrated.     

A stochastic collocation method for the second order wave equation with a discontinuous random speed

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems.