On Solvability of a Boundary Value Problem for Singular Integral Equations

This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05     

Partial hybrid finite elements for composite laminates

Three types of partial hybrid finite elements are presented in order to set up a global/local finite element model for analysis of composite laminates. In the global/local model, a composite laminate is divided into three different regions: global, local, and transition regions. These are modeled using three different elements. In the global region, a 4-node degenerated plate/shell element is used to model the overall response of the composite laminate. In the local region, a multilayer element is used to predict detailed stress distribution. In the transition region, a multilayer transition element is used to smoothly connect the two previous elements. The global/local finite element model satisfies the compatibility of displacement at the boundary between the global region and the local region. It also satisfies the continuity of transverse stresses at interlaminar surfaces and traction conditions on the top and bottom surfaces of composite laminates. The global/local finite element model has high accuracy and efficiency for stress analysis of composite laminates. A numerical example of analysis of a laminated strip with free edge is presented to illustrate the accuracy and efficiency of the model.     

Vibration frequency of a curved blade with weighted edge

The natural vibration frequencies and mode shapes of a curved cylindrical blade with a weighted edge are investigated. A finite element method is used, in which curved cylindrical shell finite elements are utilized to model the blade. The weighted edge is modelled as a beam with its stiffness and mass added into the stiffness and mass of the blade. Vibration frequencies and mode shapes for blades with different boundary conditions and with different radii of curvature are obtained. Finite element results are compared with experimental results.     

An extended transfer matrix-finite element method for free vibration of plates

A combination of extended transfer matrix and finite element methods is proposed for obtaining vibration frequencies of structures. This method yields the value of the frequency once a trial value is assumed. By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller computer can be used. Besides, no plotting of the values of the determinants corresponding to each assumed frequency is necessary. A worked example is given for the case of vibration of a cantilever plate. The results show fast convergence from the assumed value to the true natural frequency.     

A remark on ψ–Hilfer fractional differential equations with non-instantaneous impulses

We present a reasonable concept for solutions of non-instantaneous impulsive Cauchy problems with a ψ–Hilfer fractional derivative. Also, we provide a new sufficient condition for the existence, uniqueness, and stability of solutions for the given problem.     

To the theory of operator monotone and operator convex functions

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ⁺ into ℝ⁺ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra.     

Facile synthesis of SnO2–ZnO core–shell nanowires for enhanced ethanol-sensing performance

The design of core–shell heteronanostructures is powerful tool to control both the gas selectivity and the sensitivity due to their hybrid properties. In this work, the SnO₂–ZnO core–shell nanowires (NWs) were fabricated via two-step process comprising the thermal evaporation of the single crystalline SnO₂ NWs core and the spray-coating of the grainy polycrystalline ZnO shell for enhanced ethanol sensing performance. The as-obtained products were investigated by X-ray diffraction, scanning electron microscopy, and photoluminescence. The ethanol gas-sensing properties of pristine SnO₂ and ZnO–SnO₂ core–shell NW sensors were studied and compared. The gas response to 500 ppm ethanol of the core–shell NW sensor increased to 33.84, which was 12.5-fold higher than that of the pristine SnO₂ NW sensor. The selectivity of the core–shell NW sensor also improved. The response to 100 ppm ethanol was about 14.1, whereas the response to 100 ppm liquefied petroleum gas, NH₃, H₂, and CO was smaller, and ranged from 2.5 to 5.3. This indicates that the core–shell heterostructures have great potential for use as gas sensing materials.     

Bidirectional Wavelength Reconfigurable Module Based on Tunable Fiber Bragg Grating and Remote Pump Amplifier

Abstract

This article presents a novel bidirectional wavelength reconfigurable optical network utilizing a remotely pumped erbium-doped fiber amplifier and tunable fiber Bragg gratings. The system is experimentally demonstrated at a 10-Gb/s per channel over 20-km fiber span that verifies the metro-network range system performance. The achieved power penalty is less than 1 dB when compared to the back-to-back transmission link. An example of practical application where the proposed module is used as an add/drop multiplexer and a remote node in the bidirectional wavelength division multiplexing passive optical network system is described.