Convolution theorems associated with some integral operators and convolutions

In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.     

Exact tail asymptotics for fluid models driven by an M/M/c queue

Queueing Systems - In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is...     

App-based scaffolds for writing two-column proofs

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving and were capable of facilitating proof-writing skills in geometry.     

Interlaboratory Study of Digital Volume Correlation Error Due to X-Ray Computed Tomography Equipment and Scan Parameters: an Update from the DVC Challenge

Experimental Mechanics - The quality of Digital Volume Correlation (DVC) full-field displacement measurements depends directly on the characteristics of the X-ray Computed Tomography (XCT)...     

Morley’s trisector Theorem for isosceles tetrahedron

We extend Morley’s trisector theorem in the plane to an isosceles tetrahedron in three-dimensional space. We will show that the Morley tetrahedron of an isosceles tetrahedron is also isosceles tetrahedron. Furthermore, by the formula for distance in barycentric coordinate, we introduce and prove a general theorem on an isosceles tetrahedron.

     

Enhancement of free space optical link in heavy rain attenuation using multiple beam concept

Free space optics (FSO) has attracted a lot of attention for a variety of applications in telecommunications area, and it is dream of every researcher and telecommunication society to make it a real alternative solution for the last mile problem, to replace fiber optics. FSO is much preferred because of its low maintenance cost and deployment time. FSO with single-beam system is vulnerable to atmospheric attenuation, so to overcome this, a multiple-beam FSO transceiver system has become prominent and is usually used. In this paper, average rain attenuation is evaluated from the collected rain intensity data which are collected for a period of seven months, and implemented in the study concerning results relating link distance, and received optical power of using multiple-beam FSO system in tropical rainy weather. Comparison is made in terms of received optical power, geometrical losses, atmospheric losses, and bit error rate (BER) on using different number of optical beams, based on simulation at data rate of 1 Gb/s. From the results it is clear that the quality of received power is improved by using up to four beams, along with link distance up to 1141.2 m as compared to one-beam, two-beam, and three-beam, with link distances 833.3 m, 991.0 m, 1075.4 m, respectively.     

An improved least square channel estimation algorithm for coherent optical OFDM system

This paper presents an improved processing added to conventional least square (LS) channel estimation to modify its performance for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. By testing selected limitation factors of the existing algorithms, the influence of our improved algorithm to the performance of CO-OFDM system were studied and compared with other published algorithms. The simulation results of the study demonstrated that the proposed approaches achieved better channel estimation performance and are considered as a more appropriate alternative for CO-OFDM system with the tradeoff between complexity and performance.     

Surface-enhanced Raman scattering effect of gold nanoparticle arrays: The influence of annealing temperature,excitation power and array thickness

Gold nanoparticle arrays are fabricated for surface-enhanced Raman scattering (SERS) and the effect of the annealing temperature, the thickness of nanoparticle array and the exciting power on the SERS signals are investigated. The particle distribution and particle size are dense and uniform on the glass substrate when the 10 nm gold film was annealed at 250 °C and strong SERS signals for Rhodamine 6G were achieved via a 532 nm excitation with a 10 mW power. The SERS signal at 1650 cm⁻¹ is enhanced more than 10 times as compared to that of the gold film without annealing. The strong SERS behavior of gold nanoparticle arrays may broaden the SERS applications in biomedical and analytical chemistry.     

Photoluminescence and Raman spectroscopy studies of Eu3+-doped rutile TiO2 nanocrystals at high pressures

Nanocrystal samples (particle size about 90 nm) of Eu³⁺-doped rutile titanium dioxide (TiO₂) nanocrystals (rutile Eu³⁺/TiO₂ nanocrystals) were synthesized by the sol–gel method with hydrothermal treatment. The pressure effect on photoluminescence (PL) and Raman spectra of the rutile Eu³⁺/TiO₂ nanocrystals was investigated with a diamond anvil cell under hydrostatic pressure condition. Raman spectra of the samples at high pressures indicated that the critical pressure for the transition from the rutile phase to a new baddeleyite-type phase was between 10 and 14.2 GPa. The position of Raman bands shifted to high wavenumbers and the PL intensity of ⁵D ₀→⁷F ₂ transition of Eu³⁺ decreased down to zero with the increase of pressure before the phase transition occurred. After releasing the pressure, the rutile phase was not recovered and a α-PbO₂-type phase was observed at ambient pressure.     

Nanoscale gap filling for phase change material by pulsed deposition and inductively coupled plasma etching

The gap filling of phase change material has become a critical module in the fabrication process of phase change random access memory (PCRAM) as the device continues to scale down to 45 nm and below. However, conventional physical vapor deposition process cannot meet the nanoscale gap fill requirement anymore. In this study, we found that the pulsed deposition followed by inductively coupled plasma etching process showed distinctly better gap filling capability and scalability than single-step deposition process. The gap filling mechanism of the deposit–etch–deposit (DED) process was briefly discussed. The film redeposition during etching step was the key ingredient of gap filling improvement. We achieved void free gap filling of phase change material on the 30 nm via with aspect ratio of 1:1 by two-cycle DED process. The results provided a rather comprehensive insight into the mechanism of DED process and proposed a potential gap filling solution for 45 nm and below technology nodes for PCRAM.