The Bivariate Transmuted Family of Distributions: Theory and Applications

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way to model models. The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed. The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon. Statistical properties of the new family of distributions are explored which include marginal and conditional distributions, conditional moments, product and ratio moments, bivariate reliability and bivariate hazard rate functions. The maximum likelihood estimation (MLE) for parameters of the family is also carried out. The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull (BTW) distribution. The new bivariate transmuted Weibull distribution is explored in detail. Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions, product, ratio and conditional momenst. The hazard rate function of the BTW distribution is obtained. Parameter estimation of the BTW distribution is also done. Finally, real data application of the BTW distribution is given. It is observed that the proposed BTW distribution is a suitable fit for the data used.     

Biomathematical study of time-dependent flow of a Carreau nanofluid through inclined catheterized arteries with overlapping stenosis

Journal of Central South University - This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon (angioplasty) with time-variant overlapping...     

Momentum in nonlinear optics

Abstract

Although it is well known that light carries momentum and exerts a pressure on objects, a conservation of momentum principle is apparently rarely used in optics. In nonlinear optics light waves interact and may exchange both energy and momentum. We demonstrate that a conservation of momentum principle holds in these cases and in fact its use is widespread but generally unrecognized in the standard mathematical methods. In both the cases of linear basis waves interacting nonlinearly, e.g. coupled-wave theory and frequency mixing, and fully nonlinear waves, we demonstrate that a governing Hamiltonian is related to momentum. Action principles are used to discuss the generality of these results.     

High-efficiency remediation of cadmium (Cd2+) from aqueous solution using poultry manure– and farmyard manure–derived biochars

Farmyard manure (FYM-BC) and poultry manure (PM-BC) derived biochars were applied as adsorbents to remove Cd²⁺ from water. Results indicated that PM-BC was a more efficient adsorbent than FYM-BC at all experimental conditions. Maximum Cd²⁺ adsorption was observed at pH 4, temperature 318 K and contact time 1 h, regardless of biochar type. The Langmuir model predicted maximum adsorption capacity of 90.09 mg g^?1 for PM-BC. The data fitting to pseudo-second-order model proposed chemisorption of Cd²⁺ onto biochars. Thermodynamics indicated that adsorption was spontaneous and endothermic. Post-adsorption analysis provided evidences of strong chemical interactions between biochars’ functional groups and Cd²⁺ ions.     

Theranostic Interpolation of Genomic Instability in Breast Cancer

Breast cancer is a diverse disease caused by mutations in multiple genes accompanying epigenetic aberrations of hazardous genes and protein pathways, which distress tumor-suppressor genes and the expression of oncogenes. Alteration in any of the several physiological mechanisms such as cell cycle checkpoints, DNA repair machinery, mitotic checkpoints, and telomere maintenance results in genomic instability. Theranostic has the potential to foretell and estimate therapy response, contributing a valuable opportunity to modify the ongoing treatments and has developed new treatment strategies in a personalized manner. “Omics” technologies play a key role while studying genomic instability in breast cancer, and broadly include various aspects of proteomics, genomics, metabolomics, and tumor grading. Certain computational techniques have been designed to facilitate the early diagnosis of cancer and predict disease-specific therapies, which can produce many effective results. Several diverse tools are used to investigate genomic instability and underlying mechanisms. The current review aimed to explore the genomic landscape, tumor heterogeneity, and possible mechanisms of genomic instability involved in initiating breast cancer. We also discuss the implications of computational biology regarding mutational and pathway analyses, identification of prognostic markers, and the development of strategies for precision medicine. We also review different technologies required for the investigation of genomic instability in breast cancer cells, including recent therapeutic and preventive advances in breast cancer.     

Structural Characterization of Oat Bran (1→3), (1→4)-β-D-Glucans by Lichenase Hydrolysis Through High-Performance Anion Exchange Chromatography with Pulsed Amperometric Detection

Cereal mixed linkages (1 → 3) (1 → 4)-β-D-glucan is a linear polysaccharide composed of glucose units. Oat β-glucan is a natural polymer. The main products of β-glucanase are oligosaccharides with DP3 and DP4, i.e., 3-Ob-cellobiosyl-D-glucose and 3-Ob-cellotriosyl-D-glucose, which represent over 90% of the molecule. Keeping in mind all the benefits of oat bran, the present study was planned to investigate the structural properties of oat bran, high-performance anion exchange chromatography with pulsed amperometric detection was used to examine these oligosaccharides. The structural analysis of oat bran of two oat varieties revealed that the ratio of soluble and insoluble triose to tetraose in β-glucan fraction was 1.44 and 1.78, respectively, for Avon variety; while the ratio of soluble and insoluble triose to tetraose in β-glucan fraction for Sargodha-81 was 1.49 and 1.77. The major units determined were cellotriose and cellotetraose. Other units cellopentaose and hexaoses were also existed but in minor fractions. Lichenase hydrolysis high-performance anion exchange chromatography with pulsed amperometric detection appeared to be the best choice for structural analysis of purified samples of mixed-linkage β-glucan.     

Exchange Bias, Memory and Freezing Effects in NiFe2O4 Nanoparticles

Single-phase NiFe₂O₄ nanoparticles embedded in SiO₂ matrix have been synthesized by sol-gel method. Average particle size lies in the range 8?C12 nm. Magnetic measurements are taken by SQUID-magnetometer with a maximum applied field of ??7 T and temperature down to 4.2 K. An exchange bias effect in nanoparticles is due to the existence of strong core-shell interactions and it vanishes as the particle size decreases (<4?nm). Spin disorder and frustration appear at the core-shell interface due to broken bonds on the surface. We have observed the exchange bias effect via hysteresis loop shift, when the sample is cooled in an applied field of 5?T. In both AC and DC fields, our system exhibit memory effects at the halted temperatures. Furthermore, a sharp increase of coercivity at low temperatures (<50 K) is observed, which is attributed to increased surface anisotropy at low temperatures. For saturation magnetization vs. temperature data, Bloch??s T ^3/2 law (M(T)=M(0)?(1?BT ^b )) is fitted well and yields: B=4??10^?05 K^?3/2 and b=1.53. All these measurements prove the presence of exchange bias (core-shell interactions), memory effects, validation of Bloch??s T ^3/2 law and freezing effects in nickel ferrite nanoparticles dispersed in SiO₂ matrix.     

Structural,viscoelastic, and vulcanization study of sponge ethylene–propylene–diene monomer composites with various carbon black loadings

In this article, we report the effect of various carbon nanoparticle concentrations on the structural, curing, tan δ, viscosity variation during vulcanization, thermal, and mechanical characteristics of ethylene–propylene–diene monomer polymer sponge composites. The purpose of this study was to develop high‐strength, foamy‐structure polymer composites with an optimum filler to matrix ratio for advanced engineering applications. We observed that the structural, vulcanization, viscoelastic, and mechanical properties of the fabricated composites were efficiently influenced with the progressive addition of carbon content in the rubber matrix. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39423.     

Exact Analysis of Non-Linear Fractionalized Jeffrey Fluid. A Novel Approach of Atangana-Baleanu Fractional Model

It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence of relative parameters on fluid flow and temperature distribution is shown graphically. As special cases, and for the sake of correctness, the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained. It is interesting to note that fractional parameter α provides more than one line as compared to the classical model. This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model. It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.