τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES

The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.     

Comparison of Eu(NO<Subscript>3</Subscript>)<Subscript>3</Subscript> and Eu(acac)<Subscript>3</Subscript> precursors for doping luminescent silica nanoparticles

In this study, we report the comparison between Eu³⁺-doped silica nanoparticles synthesized by Stöber method using Eu(NO₃)₃ or Eu(acac)₃ as precursors. The impact of different europium species on the properties of the final silica nanospheres is investigated in details in terms of size, morphology, reachable doping amount, and luminescence efficiency. Moreover, the results obtained for different thermal treatments are presented and discussed. It is shown that the organic complex modify the silica growing process, leading to bigger and irregular nanoparticles (500–800 nm) with respect to the perfectly spherical ones (400 nm) obtained by the nitrate salt, but their luminescence intensity and lifetime is significantly higher when 800–900 °C annealing is performed.     

Overcoming acid–base copolymer neutralization using mesoporous carbon and its catalytic activity in the tandem deacetalization–Knoevenagel condensation reaction

Research on Chemical Intermediates - Acid–base copolymer materials are of considerable interest because of their fundamental implications for acid–base bifunctional catalysis...     

Enhancing optomechanical force sensing via precooling and quantum noise cancellation

We theoretically investigate optomechanical force sensing via precooling and quantum noise cancellation in two coupled cavity optomechanical systems.We show that force sensing based on the reduction of noise can be used to dramatically enhance the force sensing and that the precooling process can eifectively improve the quantum noise cancellation.Specifically,we examine the effect of optomechanical cooling and noise reduction on the spectral density of the noise of the force measurement;these processes can significantly enhance the performance of optomechanical force sensing,and setting up the system in the resolved sideband regime can lead to an optimization of the cooling processes in a hybrid system.Such a scheme serves as a promising platform for quantum back-action-evading measurements of the motion and a framework for an optomechanical force sensor.     

The Multi-point Optimization of Shock Control Bump with Constant-Lift Constraint Enhanced with Suction and Blowing for a Supercritical Airfoil

Both shock control bump (SCB) and suction and blowing are flow control methods used to control the shock wave/boundary layer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. A SCB uses a small local surface deformation to reduce the shock-wave strength, while suction decreases the boundary-layer thickness and blowing delays the flow separation. Here a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of SCB and suction and blowing. These flow control methods are used separately or together on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of all devices. It is shown that the simultaneous application of blowing and SCB (hybrid blowing/SCB) improves the average aerodynamic efficiency at off-design conditions by 18.2 % in comparison with the clean airfoil, while this increase is only 16.9 % for the hybrid suction/SCB. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.     

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

The multigrid method is one of the most efficient techniques for convergence acceleration of iterative methods. In this method, a grid coarsening algorithm is required. Here, an agglomeration scheme is introduced, which is applicable in both cell‐center and cell‐vertex 2 and 3D discretizations. A new implicit formulation is presented, which results in better computation efficiency, when added to the multigrid scheme. A few simple procedures are also proposed and applied to provide even higher convergence acceleration. The Euler equations are solved on an unstructured grid around standard transonic configurations to validate the algorithm and to assess its superiority to conventional explicit agglomeration schemes. The scheme is applied to 2 and 3D test cases using both cell‐center and cell‐vertex discretizations. Copyright © 2009 John Wiley & Sons, Ltd.     

Best approximation in vector spaces

In this paper, we obtain some results on best f-approximation in quotient spaces of vector spaces and determine under what conditions f-proximinality can be transmitted to and from quotient spaces. Also, in conclusion, we consider the relationship between f-approximation subsets and linear functionals on X.     

Bioresource Polymer Composite for Energy Generation and Storage: Developments and Trends

The ever-growing demand of human society for clean and reliable energy sources spurred a substantial academic interest in exploring the potential of biological resources for developing energy generation and storage systems. As a result, alternative energy sources are needed in populous developing countries to compensate for energy deficits in an environmentally sustainable manner. This review aims to evaluate and summarize the recent progress in bio-based polymer composites (PCs) for energy generation and storage. The articulated review provides an overview of energy storage systems, e. g., supercapacitors and batteries, and discusses the future possibilities of various solar cells (SCs), using both past research progress and possible future developments as a basis for discussion. These studies examine systematic and sequential advances in different generations of SCs. Developing novel PCs that are efficient, stable, and cost-effective is of utmost importance. In addition, the current state of high-performance equipment for each of the technologies is evaluated in detail. We also discuss the prospects, future trends, and opportunities regarding using bioresources for energy generation and storage, as well as the development of low-cost and efficient PCs for SCs.     

An investigation on the influence of the shape of the vortex generator on fluid flow and turbulent heat transfer of hybrid nanofluid in a channel

Journal of Thermal Analysis and Calorimetry - The purpose of this study is to numerically investigate flow field and turbulent heat transfer of hybrid nanofluid, water–DWCNT–TiO2 in a...