Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces

In this work, we consider two classes of non-self-mappings, which are called proximal weakly contractive and proximal nonexpansive mappings, and study the existence of solutions of a minimization problem. Existence results of best proximity points for these two classes of non-self-mappings in metric and Banach spaces are also obtained.     

Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Higher-Order Fourier Analysis Of {\mathbb{F}_{p}^n} And The Complexity Of Systems Of Linear Forms

In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets A of the group \mathbbF_pⁿ{\mathbb{F}_{p}^n} . It is possible to express these densities as certain analytic averages involving 1 _A , the indicator function of A. In the higher-order Fourier analytic approach, the function 1 _A is decomposed as a sum f ₁ + f ₂ where f ₁ is structured in the sense that it has a simple higher-order Fourier expansion, and f ₂ is pseudo-random in the sense that the k-th Gowers uniformity norm of f ₂, denoted by ||f₂||_U^k{\|{f_2}\|_{U^k}}, is small for a proper value of k.     

Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005     

Electron–electron interaction induced spin thermalization in quasi-low-dimensional spin valves

We study the spin thermalization, i.e., the inter-spin energy relaxation mediated by electron–electron scattering in small spin valves. When one or two of the dimensions of the spin valve spacer are smaller than the thermal coherence length, the direct spin energy exchange rate diverges and needs to be regularized by the sample dimensions. Here we consider two model systems: a long quasi-1D wire and a thin quasi-2D sheet.     

New class of hybrid BDF methods for the computation of numerical solutions of IVPs

A new class of hybrid BDF-like methods is presented for solving systems of ordinary differential equations (ODEs) by using the second derivative of the solution in the stage equation of class 2 + 1hybrid BDF-like methods to improve the order and stability regions of these methods. An off-step point, together with two step points, has been used in the first derivative of the solution, and the stability domains of the new methods have been obtained by showing that these methods are A-stable for order p, p =?3,4,5,6,7and A(α)-stable for order p, 8 ≤ p ≤?14. The numerical results are also given for four test problems by using variable and fixed step-size implementations.     

Experimental investigation and prediction of the thermal conductivity of water-based oxide nanofluids with low volume fractions

Journal of Thermal Analysis and Calorimetry - Although there are already many models for prediction of the thermal conductivity of nanoparticle suspension, most of them only consider the cases for...     

Poly(styrene-co-butyl acrylate)/mesoporous diatomaceous earth mineral nanocomposites by in situ AGET ATRP

Journal of Thermal Analysis and Calorimetry - Mesoporous diatomite platelets were used for in situ copolymerization of styrene and butyl acrylate by activators generated by electron transfer for...     

Fluorine-Boosted Kinetic and Selective Molecular Sieving of C6 Derivatives

Porous molecular sorbents have excellent selectivity towards hydrocarbon separation with energy saving techniques. However, to realize commercialization, molecular sieving processes should be faster and more efficient compared to extended frameworks. In this work, we show that utilizing fluorine to improve the hydrophobic profile of leaning pillararenes affords a substantial kinetic selective adsorption of benzene over cyclohexane (20 : 1 for benzene). The crystal structure shows a porous macrocycle that acts as a perfect match for benzene in both the intrinsic and extrinsic cavities with strong interactions in the solid state. The fluorinated leaning pillararene surpasses all reported organic molecular sieves and is comparable to the extended metal–organic frameworks that were previously employed for this separation such as UIO-66. Most importantly, this sieving system outperformed the well-known zeolitic imidazolate frameworks under low pressure, which opens the door to new generations of molecular sieves that can compete with extended frameworks for more sustainable hydrocarbon separation.