New convolutions associated with the Mellin transform and their applications in integral equations

In this paper, we introduce two new convolutions associated with the Mellin transform which exhibit factorization properties upon the use of certain weight functions. This is applied to the solvability analysis of classes of integral equations. In particular, we present sufficient conditions for the solvability of an integral equation and a system of integral equations of convolution type.publishe

A profiling analysis of contributions of cigarette smoking, dietary calcium intakes, and physical activity to fragility fracture in the elderly

Fragility fracture and bone mineral density (BMD) are influenced by common and modifiable lifestyle factors. In this study, we sought to define the contribution of lifestyle factors to fracture risk by using a profiling approach. The study involved 1683 women and 1010 men (50+ years old, followed up for up to 20 years). The incidence of new fractures was ascertained by X-ray reports. A “lifestyle risk score” (LRS) was derived as the weighted sum of effects of dietary calcium intake, physical activity index, and cigarette smoking. Each individual had a unique LRS, with higher scores being associated with a healthier lifestyle. Baseline values of lifestyle factors were assessed. In either men or women, individuals with a fracture had a significantly lower age-adjusted LRS than those without a fracture. In men, each unit lower in LRS was associated with a 66% increase in the risk of total fracture (non-adjusted hazard ratio [HR] 1.66; 95% CI, 1.26 to 2.20) and still significant after adjusting for age, weight or BMD. However, in women, the association was uncertain (HR 1.30; 95% CI, 1.11 to 1.53). These data suggest that unhealthy lifestyle habits are associated with an increased risk of fracture in men, but not in women, and that the association is mediated by BMD

New convolutions for an oscillatory integral operator on the half-line

The main purpose of this work is to present three new convolutions for oscillatory integral operators defined on the positive half-line and in the framework of L1 Lebesgue spaces. Therefore, such new functions introduced by the new convolutions will have factorization properties when considering the oscillatory integral operators under consideration. Moreover, some fundamental and operational properties of the mentioned integral operator are also studied in the first part of the paper.publishe

The simulation of aerosol Lidar developed at the Institute of Geophysics

Lidar is an active remote-sensing system that uses laser radiation in the ultraviolet, visible and near-infrared wavelength domain. It allows the measurement of the physical properties of the atmosphere with spatial and temporal resolution. We have simulated the system and researched the initial design of the Lidar system to monitor the aerosol with the main parameters: high power Nd - YAG pulse laser emitted at the 532 nm wavelength. The system includes 28 cm diameter optical glass, photomultiplier tube (PMT) - H6780-03 photodetector, and optical components for convergence and filtering of reflected reflections. Initial measurements show that the Lidar system is highly sensitive, which determines important atmospheric properties such as the distribution and physical properties of the aerosol and height of ABL (atmospheric boundary layer)

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table