On the minimaxness and coatomicness of local cohomology modules

Czechoslovak Mathematical Journal - Let R be a commutative Noetherian ring, I an ideal of R and M an R-module. We wish to investigate the relation between vanishing, finiteness, Artinianness,...     

Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential

This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type

$$\begin{aligned} \triangle ^2 u-\lambda M(\Vert \nabla u\Vert ^2)\triangle u-\frac{\mu }{\vert x\vert ^4}u=\frac{h(x)}{u^\gamma }+k(x)u^\alpha , \end{aligned}$$

under Navier boundary conditions, \(u=\triangle u=0\). Here \(\varOmega \subset {\mathbf {R}}^N\), \(N\ge 1\) is a bounded \(C^4\)-domain, \(0\in \varOmega \), h(x) and k(x) are positive continuous functions, \(\gamma \in (0,1)\), \(\alpha \in (0,1)\) and \(M:{\mathbf {R}}^+\rightarrow {\mathbf {R}}^+\) is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for \(\lambda > \frac{\mu }{\mu ^*m_0}\) and \(0<\mu <\mu ^*\). Here \(\mu ^*=\Big (\frac{N(N-4)}{4}\Big )^2\) is the best constant in the Hardy inequality. Besides, if \(\mu =0\), \(\lambda >0\) and h, k are Lipschitz functions, we show that this problem has a positive smooth solution. If \(h,k\in C^{2,\,\theta _0}(\overline{\varOmega })\) for some \(\theta _0\in (0,1)\), then this problem has a positive classical solution.

     

On stem covers and the universal central extensions of Lie crossed modules

In this article, we investigate stem covers and the universal central extensions of Lie crossed modules. In particular, a cover for the direct sum of two Lie crossed modules in term of given covers of them will be constructed. Using the results obtained, we give some properties of covers and the universal relative central extensions of pairs of Lie algebras.     

An electrospun degradable scaffold based on a novel hydrophilic polyester for tissue-engineering applications

Scaffolds based on a novel functionalized polyester, pHMGCL, are electrospun and characterized morphologically and physically. In vitro degradation studies of pHMGCL films show considerable mass loss and molecular weight reduction within 70 weeks. Scaffolds composed of fibers with uniform diameter (≈ 900 nm) and with melting temperatures higher than body temperature are prepared. As an indication for the feasibility of this material for regenerative medicine approaches, articular chondrocytes are seeded onto electrospun pHMGCL scaffolds. Chondrocytes attach to the fibers and re-differentiate as demonstrated by the production of GAG and collagen type II within four weeks of in vitro culture. Hydrophilic pHMGCL scaffolds may thus be useful for tissue engineering applications.     

Synthesis of 2,20'-arylmethylene bis (3-hydroxy-5,5-dimethyl-2-cyclohexene-1-one) in aqueous medium at room temperature

The reaction of dimedone with various aromatic aldehydes produces 2,2'-arylmethylene bis (3-hydroxy-5,5-dimethyl-2-cyclohexene-1-one) in excellent yields. The reactions occur in water as solvent at room temperature and avoiding the addition of any catalyst. The workup procedure is very simple and the products do not required further purification.     

A robust negative obstacle detection method using seed-growing and dynamic programming for visually-impaired/blind persons

Though a significant amount of work has been done on detecting obstacles, not much attention has been given to the detection of drop offs, e.g., sidewalk curbs, downward stairs, and other hazards. In this paper, we propose algorithms for detecting negative obstacles in an urban setting using stereo vision and two-stage dynamic programming (TSDP) technique. We are developing computer vision algorithms for sensing important terrain features as an aid to blind navigation, which interpret visual information obtained from images collected by cameras mounted on camera legs nearly as high as young person. This paper focuses specifically on a novel computer vision algorithm for detecting negative obstacles (i.e. anything below the level of the ground, such as holes and drop-offs), which are important and ubiquitous features on and near sidewalks and other walkways. The proposed algorithm is compared to other algorithms such as belief propagation and random growing correspondence seeds (GCS). According to the results, the proposed method achieves higher speed, more accurate disparity map and lower RMS errors. The speed of the proposed algorithm is about 28% higher than the random GCS algorithm. We demonstrate experimental results on typical sidewalk scenes to show the effectiveness of the proposed method.     

Electrochemical deposition of Ni on F-doped SnO<Subscript>2</Subscript> substrate and its post-annealing for use as current collector of dye-sensitized solar cell

Current collector is an important part of nanostructured dye-sensitized solar cells (DSSCs), which reduces ohmic loss. In the present work, Ni current collector was electrochemically deposited on fluorine-doped tin oxide (FTO) for use as current collector of DSSC. The adhesion of Ni to FTO was improved by post-annealing in ambient atmosphere. A new method was proposed to prevent Ni coating from oxidation during annealing. According to this method, a carbon over-layer was applied on Ni coating, which protected Ni from oxidation. Visual inspection and X-ray diffraction (XRD) results showed the effectiveness of this method in protection of Ni coating from oxidation. Furthermore, the effect of current collector on photovoltaic performance of DSSCs was investigated using current density-voltage curve measurement and electrochemical impedance spectroscopy methods. It was observed that post-annealing in ambient atmosphere, under protection of carbon over-layer, improves both the adhesion of Ni current collector to FTO and the photovoltaic performance of DSSC. However, Ni oxidation during post-annealing of Ni current collector, without carbon over-layer, significantly decreased the photovoltaic parameters of DSSC. The above observations were explained by considering the series resistance of DSSC.