Spectrum of a linear fourth‐order differential operator and its applications

In this paper, we apply the disconjugacy theory and Elias's spectrum theory to study the positivity and the spectrum structure of the linear operator coupled with the clamped beam boundary conditions (1.2). We also study the positivity and the spectrum structure of the more general operator coupled with (1.2). As the applications of our results on positivity and spectrum of fourth‐order linear differential operators, we show the existence of nodal solutions for the corresponding nonlinear problems via Rabinowitz's global bifurcation theorem.     

An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions

We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L²[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd.     

Extended Gini-Type Measures of Risk and Variability

ABSTRACT

The aim of this paper is to introduce a risk measure, Extended Gini Shortfall (EGS), that extends the Gini-type measures of risk and variability by taking risk aversion into consideration. Our risk measure is coherent and catches variability, an important concept for risk management. The analysis is made under the Choquet integral representations framework. We expose results for analytic computation under well-known distribution functions. Furthermore, we provide a practical application.     

On the class of positive almost weak Dunford–Pettis operators

We introduce and study the class of almost weak Dunford–Pettis operators and we derive the following interesting consequence: other characterizations of the weak Dunford–Pettis property. After that we characterize pairs of Banach lattices for which the adjoint of almost weak Dunford–Pettis operator is almost Dunford–Pettis. Finally, we establish a necessary and sufficient conditions on the pair of Banach lattices E and F which guarantees that if T : E → F is a positive almost weak Dunford–Pettis then T is almost Dunford–Pettis.     

Synthesis of modified peptidoglycan precursor analogues for the inhibition of glycosyltransferase

The peptidoglycan glycosyltransferases (GTs) are essential enzymes that catalyze the polymerization of glycan chains of the bacterial cell wall from lipid II and thus constitute a validated antibacterial target. Their enzymatic cavity is composed of a donor site for the growing glycan chain (where the inhibitor moenomycin binds) and an acceptor site for lipid II substrate. In order to find lead inhibitors able to fill this large active site, we have synthesized a series of substrate analogues of lipid I and lipid II with variations in the lipid, the pyrophosphate, and the peptide moieties and evaluated their biological effect on the GT activity of E. coli PBP1b and their antibacterial potential. We found several compounds able to inhibit the GT activity in vitro and cause growth defect in Bacillus subtilis . The more active was C16-phosphoglycerate-MurNAc-(L-Ala-D-Glu)-GlcNAc, which also showed antibacterial activity. These molecules are promising leads for the design of new antibacterial GT inhibitors.     

Integrated 3D-QSAR,molecular docking,and molecular dynamics simulation studies on 1,2,3-triazole based derivatives for designing new acetylcholinesterase inhibitors

Alzheimer’s disease (AD) is a multifactorial and polygenic disease. It is the most prevalent reason for dementia in the aging population. A dataset of twenty-six 1,2,3-triazole-based derivatives previously synthetized and evaluated for acetylcholinesterase inhibitory activity were subjected to the three-dimensional quantitative structure-activity relationship (3D-QSAR) study. Good predictability was achieved for comparative molecular field analysis (CoMFA) (Q² = 0.604, R² = 0.863, r_ext² = 0.701) and comparative molecular similarity indices analysis (CoMSIA) (Q² = 0.606, R² = 0.854, r_ext² = 0.647). The molecular features characteristics provided by the 3D-QSAR contour plots were quite useful for designing and improving the activity of acetylcholinesterase of this class. Based on these findings, a new series of 1,2,3-triazole based derivatives were designed, among which compound A1 with the highest predictive activity was subjected to detailed molecular docking and compared to the most active compound. The selected compounds were further subjected to 20 ns molecular dynamics (MD) simulations to study the comparative conformation dynamics of the protein after ligand binding, revealing promising results for the designed molecule. Therefore, this study could provide worthy guidance for further experimental analysis of highly effective acetylcholinesterase inhibitors.     

Nearby Lagrangians with vanishing Maslov class are homotopy equivalent

We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to the zero section in the Fukaya category with integral coefficients. We then study an extension of the Fukaya category in which Lagrangians equipped with local systems of arbitrary dimension are admitted as objects, and prove that this extension is generated, in the appropriate sense, by local systems over a cotangent fibre. Whenever the cotangent bundle is simply connected, this generation statement is used to prove that every closed exact Lagrangian of vanishing Maslov index is simply connected. Finally, we borrow ideas from coarse geometry to develop a Fukaya category associated to the universal cover, allowing us to prove the result in the general case.     

Translation surfaces in the 3-dimensional space satisfying Δ III r i = μ i r i

In this paper we study the translation surfaces in the 3-dimensional Euclidean and Lorentz-Minkowski space under the condition ${\Delta ^{III}r_{i} = \mu _{i}r_{i},\mu _{i} \in \mathbb{R}}$ , where Δ ^III denotes the Laplacian of the surface with respect to the third fundamental form III. We show that in both spaces a translation surface satisfying the preceding relation is a surface of Scherk.     

Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying Δr i ?=?λ i r i

In this paper we classify the factorable surfaces in the three-dimensional Euclidean space ${\mathbb{E}^{3}}$ and Lorentzian ${\mathbb{E}_{1}^{3}}$ under the condition ??r _i ?=??? _i r _i , where ${\lambda_{i}\in\mathbb{R}}$ and ?? denotes the Laplace operator and we obtain the complete classification for those ones.     

Porous Polysaccharide‐Based Scaffolds for Human Endothelial Progenitor Cells

Human ECFCs contribute to vascular repair. For this reason, they are considered as valuable cell therapy products in ischemic diseases. Porous scaffolds are prepared that are composed of natural polysaccharides, pullulan and dextran, by chemical crosslinking without use of organic solvents. These porous scaffolds, which have pores with an average size of 42 µm and a porosity of 21%, preserve the viability and the proliferation of cord‐blood ECFCs. After 7 d of culture in porous scaffolds, ECFCs express endothelial markers (CD31 and vWf) and maintain endothelial functions. The cultured cells can be easily retrieved by enzymatic degradation of the porous scaffolds. In vitro results suggest that the porous scaffold could allow cell delivery of ECFCs for treatment of vascular diseases.