On the no-slip boundary conditions for squeeze flow of viscous fluids

A typical class of boundary conditions for squeeze flow problems in lubrication approximation is the one in which the squeezing rate and the width between the squeezing plates are constant. This hypothesis is justified by claiming that the plates moves so slowly that they can be considered static. In this short note we prove that this assumption leads to a contradiction and hence cannot be used.     

A Sort of Gray-scale Morphological Dilations and Erosions

We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as the commuting property with translation and homothety, of these operators are discussed as well.     

Crystallization behavior and electroactive properties of PVDF,P(VDF-TrFE) and their blend films

PVDF, poly(vinylidene fluoride), as a semi-crystalline polymer, has interesting electroactive properties but usual melt and solution processing techniques result in its thermodynamically favored non-polar α-phase. By comparison, poly(vinylidene fluoride-trifluoroethylene) P(VDF-TrFE), PT for short, directly crystallizes in the polar β-phase under the same conditions as PVDF. In this study, blend thin films comprising PVDF and P(VDF-TrFE) were prepared by solvent casting method. The difference in the crystallization behavior is comprehensively investigated between the polymers: PVDF, P(VDF-TrFE), and the resulting blend films. It is found that replacement of the fluoride atom in TrFE monomer induces a strong steric hindrance that may alter the crystallization process to become more favorable for nucleation of the PVDF β-phase. To figure out the effect of TrFE content on the crystallization behavior and electroactive properties, films with different blend ratios of PVDF and P(VDF-TrFE) were prepared. We found that the PVDF films exhibit higher crystallization activation energy (ΔE) as PT content increases. The atomic force microscopy (AFM) in the piezoresponse force microscopy (PFM) mode illustrated that P5T5 films with equal contents of PVDF and P(VDF-TrFE) induced the highest d₃₃ values.     

A characterization of generalized derivations of JSL algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.     

An ensemble learning framework for potential miRNA-disease association prediction with positive-unlabeled data

To explore the pathogenic mechanisms of MicroRNA (miRNA) on diverse diseases, many researchers have concentrated on discovering the potential associations between miRNA and disease using machine learning methods. However, the prediction accuracy of supervised machine learning methods is limited by lacking of experimentally-validated uncorrelated miRNA-disease pairs. Without these negative samples, training a highly accurate model is much more difficult. Different from traditional miRNA-disease prediction models using randomly selected unknown samples as negative training samples, we propose an ensemble learning framework to solve this positive-unlabeled (PU) learning problem. The framework incorporates two steps, i.e., a novel semi-supervised Kmeans (SS-Kmeans) to extract reliable negative samples from unknown miRNA-disease pairs and subagging method to generate diverse training sample sets to make full use of those reliable negative samples for ensemble learning. Combined with effective random vector functional link (RVFL) network as prediction model, the proposed framework showed superior prediction accuracy comparing with other popular approaches. A case study on lung and gastric neoplasms further confirms the framework’s efficacy at identifying miRNA disease associations.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.