Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Detectability conditions for output-only subspace identification

ABSTRACT

The scope of output-only/blind identification is restricted to stochastic/statistical processes, but for the first time in this study, the detectability conditions for general output-only subspace identification are investigated. This aids the range of input sources to be extended in a much realistic manner, beyond the only stochastic inputs. For this purpose, the subspace framework is assigned to make a connection between the output signal contents and the LTI system order. A few substantial hypotheses and algebraic statements are propounded affirming the sufficiency of the genuine output sequences for the identification purpose. This can be perceived as the cornerstone of state-space model reconstruction. In order to consolidate the notions according to reality, several examples are studied and examined for different input classes with stochastic disturbance.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

Strong solutions to 3D compressible magnetohydrodynamic equations with Navier‐slip condition

We consider the short time strong solutions to the compressible magnetohydrodynamic equations with initial vacuum, in which the velocity field satisfies the Navier‐slip condition. The Navier‐slip condition differs in many aspects from no‐slip conditions, and it has attracted considerable attention in nanoscale and microscale flows research. Inspired by Kato and Lax's idea, we use the Lax–Milgram theorem and contraction mapping argument to prove local existence. Moreover, under the Navier‐slip condition, we establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of L^∞ norm of the deformation tensor D(u). Copyright © 2015 John Wiley & Sons, Ltd.     

Minimum-norm fixed point of nonexpansive mappings with applications

The purpose of this paper is to present two new iterative algorithms to find the minimum norm fixed point of nonexpansive nonself-mappings in the framework of Hilbert spaces. The results presented in this paper improve and extend the corresponding ones announced by Yao and Xu [Yao Y, Xu HK. Iterative methods for finding minimum norm fixed point of mappings with applications. Optimization. 2011;60:645–658] and many others. Some applications to convex minimization and split feast problems(SFP) are also included.     

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

Adaptive mesh refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR, better prediction can be obtained with much less labor work and cost compared to manually remeshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh, which is heavily used in the high‐Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high‐order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last, the mesh suitable for the solver is output. Generating refined elements in the parametric space with high‐order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, 3‐dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the 2‐dimensional airfoil and 3‐dimensional full aircraft, the current AMR method proves to be accurate, simple, and robust.     

Strong covalent bonding modulated graphene oxide/epoxy interfacial enhancement and advanced corrosion resistance

Abstract

Chemically functionalized graphene oxide [multi-amino functionalized graphene oxide (MAGO)] was achieved by building covalent bonds between graphene oxide (GO) and a small molecule containing benzene structure and multi-amino groups. Fourier transform infrared, X-ray diffraction, X-ray photo electron spectroscopy and TEM-EDX results certified that the molecule was successfully grafted onto GO nanosheets. Subsequently, functionalized GO was incorporated into waterborne epoxy (EP) coating through ball-milling method. This molecular design can significantly improve the dispersion of MAGO in EP matrix, as well as the compatibility and interaction between MAGO and EP. Compared with GO/EP, the water absorption of MAGO/EP decreased from 4.38 to 2.59%, the adhesion strength of MAGO/EP increased from 4.72 to 6.32?MPa after immersion of 40?days in 3.5% NaCl solution. Incorporation of 1?wt% of MAGO into EP matrix prominently improved the long-term corrosion resistance. The impedance modulus of GO/EP coating decreased by four orders after 40 days immersion, while that of MAGO/EP coating only decreased by one order. The impedance modulus was still 1.47?×?10⁸ Ω cm², and two-time constant wasn’t detected for MAGO/EP coating. This research developed a novel green anticorrosion coating with enhanced durability for metal protection.     

Self-assembly and aggregation of ATRP prepared amphiphilic BAB tri-block copolymers contained nonionic ethylene glycol and fluorescent 9,10-di(1-naphthalenyl)-2-vinyl-anthracene/1-vinyl-pyrene segments

Two novel amphiphilic BAB-type block copolymers, ADN-PEG3400-ADN and Py-PEG3400-Py containing deep blue and bluish-green fluorescent moieties were prepared using atom transfer radical polymerization (ATRP) (where, ADN = poly(9,10-di(1-naphthalenyl)-2-vinylanthracene), Py = poly(1-vinyl pyrene) and PEG3400 = poly(ethylene glycol) with M_n = 3400 g/mol). The GPC number averaged molecular weights (MW) of the block copolymers were M_n = 9600 and 13,800 g/mol, respectively, based on polystyrene MW standards. The PEG3400 segment has a melting temperature (T_m peak) at 64–65 °C, whereas the glass transition temperatures (T_g midpoint) of the ADN and Py segments were found to be 230 °C and 193 °C, respectively, and are similar to their respective homopolymers indicating complete microphase segregration. The photoluminescence (PL) emission of the copolymers ADN-PEG3400-ADN exhibited two maxima at 423.5 nm and 441.5 nm while Py-PEG3400-Py has a maximum at 488.5 nm. Both copolymers form individual spherical micelles with diameter from 30 to 90 nm for Py-PEG3400-Py and 40–160 nm for ADN-PEG3400-ADN. The micelles, however, transform into cross-linked pearl-necklace-like aggregates at polymer concentrations above 1000 ppm, which may be attributed to the physical cross-linking between adjacent spherical micelles caused by the PEG3400 segments.