Volume 15 – Issue 4

In the present paper, we define adjoint of a Lorentzian matrix. We give a theorem to find the inverse of a matrix using adjoint of it. Also a shortcut to find the inverse of a 2×2 matrix is presented. Finally, we show that the inverse of a matrix can be found by changing the identity matrix with L-identity matrix in the augmented matrix and using GaussJordan elimination method. Furthermore, we introduce some new theorems related with adjoint and inverse of a matrix.

We construct a surface family possessing a natural lift of a given curve as a line of curvature. We obtain necessary and sufficient condition for the given curve such that its natural lift is a line of curvature on any member of the surface family. Finally, we present some illustrative examples

The main purpose of the article is to introduce an active teaching method, based on the nature of a familiar mathematical concept. Specifically, this paper presents the application of the visual image of convex function and concave function graphs concave function on demonstrating some inequality in the primary curriculum. Also, some results and comments concerning the proving method of such as inequalities are stated.

Assessment is one of the most powerful educational tools for promoting effective learning. But it must be used in the right way. We need to be on helping teachers use assessment as part of teaching and learning, in ways that will raise pupil’s achievement. This paper proposes some problems to assess student’s mathematical creative competency in grade 10 in Vietnam.

The present study was aimed to investigate phytochemical screening and to evaluate reducing power, cytotoxicity and antifungal activities of the petroleum ether and aqueous extracts of leaves and stems of Kalanchoe pinnata Linn (Crassulaceae). The qualitative phytochemical tests showed the presence of alkaloid, glycoside, gums, saponins, reducing sugar and tannins in the petroleum ether crude extract of Kalanchoe pinnata Linn while alkaloid, glycoside, steroid, saponins, tannins were present in the aqueous extract of Kalanchoe pinnata Linn. It was observed that both extracts of the studied plant possessed cytotoxic activity. In brine shrimp lethality bioassay, the LC50 (µg/ml) and LC90 (µg/ml) of the petroleum ether and aqueous extract of Kalanchoe pinnata Linn, were 25.12µg/ml& LC90: 177.83µg/ml respectively. The aqueous extract of the medicinal plant also showed lethality against the brine shrimp nauplii (LC50: 25.12µg/ml& LC90: 173.78µg/ml). Moreover, the extracts showed significant reducing power. It was also identified that the petroleum ether and aqueous extracts of Kalanchoe pinnata Linn showed antifungal activity. The obtained results provide a support for the use of this plant in traditional medicine. The plant studied can be a potential source of biologically active compounds as antifungal, anticancer agent and pesticide.

The superalloy BC1 (trademark of HAYNES International, Inc.) is an alloy used in the production processes of organic acids at high temperature, refining industry and a wide variety of chemical applications using hydrochloric and sulfuric acids.The HYBRIDBC1 is an alloy composed essentially of 62% of nickel, 22% of molybdenum and 15% of chromium. Its matrix is austenitic and its structure is face-centered cubic.The aim of this work is to study the influence of heat treatment on the structural and mechanical properties of the nickel based alloy. Indeed, four temperatures were chosen 700°C, 800°C, 900°C and 1000°C for a treatment time of 3 hours.The final hardness of the alloys treated at 700°C, 800°C, 900°C and 1000°C is equal respectively to 47.25 HRF, 47 HRF, 47 HRF and 47.5 HRF. The images obtained by optical microscopy after the iso-thermal treatments showed the presence of carbides at the joints and inside the grains in several morphologies, discontinuous transformations and eutectic precipitates. The X-ray diffraction spectra done during over aging consist of peaks of the austenite phase and precipitates.

The phenomenon of aging and overaging of PbCdBiMg alloys is characterized by continuous and discontinuous transformation, it is hardening and softening characterized by a precipitation of cadmium. In general, the magnesium addition increases the hardness and delays the kinetics of the hardening processing. Indeed, the study of the return to equilibrium of supersaturated hardened alloys PbCdBiMg was carried out by various experimental techniques: hardness, micro hardness, optical microscopy and X-ray diffraction. Two structural states were considered: raw casting alloys and rehomogenized alloys. The alloys concerned are: Pb2% Cd1% Bi and Pb 2% Cd3% Bi with various magnesium proportions: 0.12% Mg, 1% Mg, 2% Mg and 3% Mg. The experimental temperatures are 20 ° C and 80 ° C. Bismuth accelerates the curing reaction and magnesium slightly retards the transformation.