Sub-dimensional Mardia measures of multivariate skewness and kurtosis

The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets

Pterocarpus angolensis: Botanical, Chemical and Pharmacological Review of an Endangered Medicinal Plant of India

Herbal products for primary health care are gaining huge interests of the people and the various healthcare professionals. This is mainly because of the local availability and cost-effectiveness of plant remedies over expensive modern treatments. Pterocarpus angolensis, a deciduous plant belonging to the family of Fabaceae is mainly found in the tropical regions of Africa. This tree is rich in medicinal properties which are immensely used by the locals in Africa for the treatment of ringworm infections, ulcers, urinary schistosomiasis, skin injury, etc. The extracts of   P. angolensis are treasured in Africa for their effectiveness against many diseases like gonorrhea, mouth diseases, diarrhea, etc. It is reported to have inhibitory activity against various pathogens like Escherichia coli, Staphylococcus aureus, and Salmonella typhimurium because of the high concentration of bioactive compounds like flavonoids, tannins, and other phenolic compounds in the bark and leaves of the tree. Various research papers demonstrated the polar and nonpolar constituents of this plant showing antimicrobial, anti-plasmodial activities against Streptococcus agalactiae, Candida krusei, etc. In India, very few of these plants have been reported to be alive in the Darjeeling district, West Bengal. But, lack of proper documentation or research paper led to negligence related to the importance of this species and it has already been listed in the IUCN Red List of threatened species. The main objective of this review is to spread awareness about the conservation of the plant possessing such remarkable properties. Secondly, to provide an overview of the phytochemical screening of various important medicinal constituents that this plant possesses and this might lead to change in the field of modern medicine

Implications of solid phase interaction mechanisms on momentum, heat and solute transport in semi-solid materials processing

In this work, the problem of mathematical modeling of transport phenomena during semi-solid metal processing is investigated from a fundamental approach. The phenomenon of solid phase interaction is modeled by an evolution equation of an internal state variable. The formation of an interconnected network of agglomerated solid fragments at high values of solid fraction is also accounted for, leading to a more realistic prediction of momentum transport in comparison to other standard models reported in the literature. Numerical simulations are performed based on two separate momentum transport models. One of the models essentially neglects solid phase interaction mechanisms, whereas the other one incorporates the associated transport features, in order to capture the implications of solid phase agglomeration in a semi-solid slurry processing. A detailed analysis of the results reveals a profound impact of agglomeration and break-up on the transport phenomena, which need to be effectively captured

Numerical simulation of transport phenomena in electromagnetically stirred semi-solid materials processing

A continuum based integrated mathematical model is developed to analyse momentum, heat and solute transport during an electromagnetically stirred semi-solid materials processing operation. Separate conservation equations are solved to determine the solid phase velocity. Simultaneously, a solid fraction transport equation is solved to take into account the transport of fragmented dendrites and solidification of liquid phases present in the respective elemental volumes. Numerical simulations are performed to reveal the relative contributions of buoyancy and electromagnetic forces. The mathematical model is also tested by confronting present numerical results with reported experimental observations; an excellent agreement can be observed in this regard, thereby establishing the authenticity of the proposed formulation

Attempts to recognize the two different isomers of a photoswitchable dyad, 1-(4-bromo-phenyl)-3-(2-methoxy-naphthalen-1-yl)-propenone, by using TiO2 nanoparticles

Steady state, time-resolved spectroscopic measurements and theoretical computations on a photoswitchable organic dyad, 1-(4-bromo-phenyl)-3-(2-methoxy-naphthalen-1-yl)-propenone demonstrate the formations of the two different isomers in the excited singlet state though NMR study reveals the presence of only one isomer in the ground state. The present Letter describes how by combining with semiconductor TiO2 nanoparticles the presence of two different isomers of the photoswitchable dyad could be recognized in the form of various yields

Physics behind the Barrier to Internal Rotation of an Acetyl Chloride Molecule: A Combined Approach from Density Functional Theory, Car–Parrinello Molecular Dynamics, and Time-Resolved Wavelet Transform Theory

The physics behind the barriers to internal rotation of acetyl chloride (AC) molecule has been reported. The AC molecule closely resembles the molecular structure of acetaldehyde; the only subtle difference is the presence of a heavy chlorine atom in place of the hydrogen atom of the aldehyde group for the latter. This paper aims to study the effect of substitution of the heavy chlorine atom on the barrier energetics of the AC molecule. The reason behind the barrier for the AC molecule has been estimated for the first time from the unified approach using barrier energetics, natural bond orbital, nuclear virial, and relaxation analyses using density functional theory, Car–Parrinello molecular dynamics, and wavelet transform theory. Complete analyses reveal the concomitant relaxations of both the in-plane C_methyl–C₁ and C_methyl–H₄ bonds toward understanding the origin of the barrier due to internal rotation for the AC molecule. The large negative value of “<i>V</i>₆” further suggests that both the abovementioned degrees of freedom are coupled with the −CH₃ torsional vibration of the molecule. The coupling matrix (<i>H</i>₁₂) element has also been estimated. Time-resolved band stretching frequencies of C_methyl–C₁ and C₁–Cl₃ bonds of the AC molecule, as obtained from wavelet transformation analysis, primarily preclude the possibility of coupling between the C₁–Cl₃ bond and the torsional motion associated with the methyl group of the molecule