Volume 18 – Issue 3

In this research paper we introduce the numerical accuracy of solution one dimensional heat equation by different numerical scheme.The error analysis of different method also discussed. This study can be used to suggest the better accuracy for solving a partial differential equation. This comparative study provides better result for numerical solution of parabolic type equation.

In this paper, a new geometric method for ordering generalized trapezoidal fuzzy numbers with different left and right heights, based on the Gergonne point of a triangle is presented. The suggested method can order not only generalized trapezoidal fuzzy numbers but also crisp numbers and generalized triangular fuzzy numbers with the same centroid point. We also give an application of the proposed ordering method to the fuzzy matrix games, whose payoffs are represented by generalized trapezoidal fuzzy numbers with different left and right heights.

In this paper an efficient transformation, in combination with Exp-function method has been applied to construct generalized solitary and periodic wave solutions of the nonlinear Lax equation of fractional-order. First the nonlinear partial differential equation is converted into ordinary differential equation by a suitable transformation. Then desired solitary wave solutions has been obtained. Computational work and subsequent results reconfirm the efficiency of proposed algorithm. It is observed that suggested scheme is highly reliable and may be extended to other nonlinear differential equations of fractional order.

In this paper, we have expressed the transformation matrix between the Frenet frames of the spacelike curve with a spacelike binormal and its timelike involute curve as depend on lorentzian spacelike angle between the unit binormal vector and the Darboux vector of the spacelike evolute curve. Furthermore, some new characterizations with relation to the involute-evolute curve couple have been found.

In this work, by using Laplace integral representation of quadruple functionX^(4) _7 defined in [3], we introduced new generating functions involving some quadruple hypergeometric functions. Some particular cases and consequences of our main results are also considered

In this article two point fuzzy boundary value problems is defined under the approach generalized Hukuhara differentiability (gH-differentiability). The solution method of the fuzzy boundary value problem is examined with the aid of some initial value problems. This type of problem is associated with an operator in fuzzy Hilbert space. So, several theorems are given for the problem eigenvalues.

In this work, Lie symmetry analysis is applied on Lax’s fifth-order KdV and Hunter-Saxton equations. By using point symmetry, all of the geometric vector fields of these equations are presented. Then, on the basis of the optimal system, similarity reductions and exact solutions are obtained.

As a proper generalization of the modules with the properties (E) and (EE) that were introduced by Zöschinger in terms of supplements, we say that a module M has the property (WRE) (respectively,(WREE) if M has a weak Rad-supplement (respectively, ample weak Rad-supplements) in every extension. In this paper, we prove that if every submodule of a module M has the property (WRE) , then has the property (WREE) . We show that a ring R is semilocal if and only if every left R-module has the property(WRE) . Also we prove that over a commutative Von Neumann regular ring a module M has the property(WRE) if and only if M is injective.

Beta functions are used in many fields such as computational and applied mathematics, statistics, physics and chemistry. In this paper we generalized Beta function to negative integers. We present some new relationships for the negation of Beta function for negative integers. We also give an algorithm for the computation of Beta function in terms of negative numbers.

The objective of this paper is to set up some finite integral formulas involving the generalized Bessel first kind function negative order of m, modified Bessel function and spherical Bessel function. The result is given in terms of generalized Wright’s Hypergeometric functions pΨq. These results are procured with the help of finite integral due to Lavoie and Trottier. Some interesting particular cases in terms of corollary are established here.

We consider weighted graphs, such as graphs where the edge weights are positive definite matrices of the same order in this paper. The signless Laplacian eigenvalues of a graph are the eigenvalues of the signless Laplacian matrix of a graph G . Then, we have give some bound and found different upper bounds for the signless Laplacian radius of weighted graphs. We have obtained some results by characterizing these upper bounds.

In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial Q(j)= j^2-aj-bl on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we obtain a metallic Riemannian manifold with respect to the Riemannian metric.

In this study we define Gaussian balancing numbers and Gaussian Lucasbalancing numbers. Then we obtain Binet-like formulas, generating functions and some identities related with Gaussian balancing numbers and Gaussian Lucas-balancing numbers. Moreover, we give the new properties of Gaussian balancing numbers and Gaussian Lucasbalancing numbers in relation with balancing matrix formula.

In this study, a hybrid matrix-collocation method based on Dickson polynomials of the second kind along with Taylor polynomials is proposed to solve pantograph type functional differential equations with mixed delays under the initial conditions. The parameter-α in Dickson polynomials is interpreted for obtaining the optimum solutions. An error estimation related with the residual function and the mean-value theorem is implemented and also some illustrative examples are presented. It is observed that the proposed method is easy to be applied.

The awareness of the socio-environmental effects of forest exploitation is essential for better resource management and a sustainable management system for forestry. We started the present research with a theoretical documentation based on the knowledge of the legislation in the field and a descriptive analysis of the evolution of the forest fund of our country and the analyzed area. We strengthen the results of this research through the information obtained based on empirical research in the upper Aries river basin. For our statistical approach, we choose the questionnaire as a relevant research tool. The analysis was made using SPSS program, and statistical variables, including crosstable, the Spearman’s correlation coefficient and the χ2 (chi-square) test to test the relationship between two variables, both measured on a categorical scale. Through the qualitative analysis and interpretation of information obtained from the processing of questionnaires we indent to identify the main socio-environmental effects of forestry activity, the need to implement programs to exploit forest resources, the main factors that prevent exploitation of forest resources and also obtain relevant conclusions regarding measures needed to improve the area studied.

The beginning of the zero-grade experiment consists in the fact that some parents want to register their children early in school because they feel they are ready. Thus, according to the Education Law of 2010, was approved the passing of the preparatory class to the primary school and, implicitly, its transformation into the zero-grade. The implementation of the preparatory class aims to strengthen the knowledge already acquired by children, to socialize and to adapt to novelty. This paper aims to determine the degree of satisfaction of the parents and teachers involved in the proper development of the teaching activities specific to the preparatory class at the Ocnita Gymnasium School.

Gebel el-Silsila north of Aswan and is one of the most important archaeological sites in the world. It is considered the main quarry for sandstone in ancient Egypt. Also, it contains hundreds of graffiti, rock art, and rock-cut panels that suffer from several types of deterioration aspects due to the internal and the external deterioration factors dominating at the site. Different scientific methods such as: PM, SEM, XRD, EDX and FTIR have been used to study and determine the chemical and mineralogical components of those monuments and their deterioration aspects. The obtained results show that the chemical and mineralogical transformations were the main aspects in the deterioration and degradation of rock-cut panels

Viscosity study has been widely studied by scientist and engineers on various purposes. These include polymer science, heat transfer phenomena, petroleum reservoir development, coatings; scale modeling of magnetic intrusion, oil degradation, lubrication, etc. This article proposes four relationships of dynamic viscosity – temperature dependence for soybean oil. The purpose of this study was to find an exponential dependence between temperature and dynamic viscosity of soybean oil, using the equations. Equation constants η0, A1 and t1 were determined by fitting exponential. The correlation coefficients thus obtained varied between 0.7864 and 0.9999.

Marine algae are an important resource for the marine ecosystem to be used for public health. Studying marine habitats is necessary to ensure the safety of a good marine biomass. In this paper the classification of protected areas with the specification of the six protected areas from the Romanian Black Sea coast is presented, according to European norms with Decision 2009 / 92 / EC on marine habitats. For marine algae habitats the following results for physico-chemical parameters studied on samples, such as dry matter, conductivity, pH and salinity are presented. The variables of nutrients concentrations recorded for 2016 (concentrations for nitrites and nitrates, ammonium and phosphates) are investigated as well. Marine algae, used in this study, were Cystoseira barbata, Ceramium rubrum, Ulva lactuca, and Cladophora vagabunda all gathered from Black Sea. The station network has remained steady since 2009, with sampling from Vadu to Vama Veche from depths between 0-3 m during the summer season in 2016.

Micro analysis of pigments, plaster layers and binding media using SEMEDX, XRD and FTIR within Elshinawy palace proved that blue pigment is cobalt blue, green pigment is malachite yellow pigment is goethite, and binding medium is animal glue. These paintings were carried out on a ground layer of gypsum with animal glue as binding medium, in addition to a portion of calcite added deliberately to increase brightness of gypsum. The protein materials of animal glue gave in alkaline medium and in presence of copper a blue violet or purple color called Birut Molecules.

Even though the Internet is an enormous online library, discrimination between the accurate, scientific data and misleading information can be a serious issue even for a well- trained person. Unfortunately, a plethora of false information related to the chemical compounds with major impact on our lives is distributed on online environment. The main purpose of this paper is to review a few of the most encountered urban myths related to the “dangerous, carcinogenic, toxic” substances or, on the contrary, “panacea compounds”. Thus, the paper does analyze the popular (unconfirmed) facts and statements versus scientific evidence covering hot topics such as parabens, monosodium glutamate (MSG), Saccharin, amygdalin and Laetril, resveratrol, and rheosmin (raspberry ketone). Furthermore, the paper emphasizes the role of the high – school teachers in ensuring that students do access the most relevant and valid sources of information, while providing specific tools to discriminate between accurate, scientific data and false and dangerous statements with negative consequences from the educational perspective and beyond. Last but not least, the paper highlights the importance of using reliable sources of information from well-established institutions such as the EFSA (European Food Safety Authority, www.efsa.europa.eu), EMA (European Medicine Agency, http://www.ema.europa.eu), FDA (Food and Drug Administration, www.fda.gov), the EPA (Environmental Protection Agency, www.epa.gov), the IARC (International Agency for Research on Cancer, www.iarc.fr), the ANM (National Medicines Agency, http://www.anpm.ro), WHO (World Health Organization, www.who.int), EMA (European Medicine Agency), Mayo Clinic.

There are various techniques to determine the associated factors for oral cancer data. One of the most common techniques (in medical research) that always used is the prognostic model of the survival. Through the cox proportional hazards regression, we can investigate the association between the survival times of patients with the potential predictor variables. Current research nowadays is being focused on the most efficient model for the right decision making. To optimize the gained results, a combination method is being considered which consist of the fuzzy approach to the prognostic model of the survival. This promising technique had given a full attention because of its ability to give the best results. The model which gained from the proposed method is employed to estimate the potential factors that contribute to the oral cancer case. This provides useful information for the determination of potential factors that lead to oral cancer.

In this research work, the combined effects of thermal radiation and chemical reaction on an unsteady hydromagnetic mixed convective flow of incompressible and electrically conducting fluids past an infinite vertical porous plate has been made in presence of Soret and Dufour numbers. Energy equation takes into account of viscous dissipation, thermal radiation and Dufour effects. The governing differential equations are transformed into a set of non – linear coupled ordinary differential equations and solved using similarity analysis with finite difference numerical technique using appropriate boundary conditions for various physical parameters. Numerical solutions have been derived for the effects of different physical flow parameters on the velocity, temperature and concentration fields, skin – friction, rate of heat and mass transfer are discussed through graphs and results are physically interpreted.

High definition optical coherence tomography (HD-OCT) is a non-invasive imaging technique, with significant relevance in different area, mainly ophthalmology. In recent years OCT has become a promising tool also for the in vivo evaluation and diagnosis of different skin diseases, especially skin cancers. HD OCT can be used as a reliable diagnosis method that provides useful information on the architecture of cutaneous layers and sometimes on cellular morphology in the epidermis and other structures of the skin. Our work brings new information about the value of HD-OCT in describing in vivo pattern of basal cell carcinoma, one of the most frequent non-melanocytic skin cancers, compared with histopathology and dermoscopy.

This study shows the effects of heat treatment on the manganese steel which microstructure consists essentially of 18.447% of manganese, 0.745% of chromium, and 1.169% of carbon. The techniques used are: X-ray diffraction, optical microscope, scanning electron microscope.After heat treatment at 600 °C and 1050 °C for 30 minutes, metallurgical analysis will connect the microstructural changes occurring during the temperature maintenance to the mechanical behavior of the material. The characterization of the microstructures and the surface morphology of the alloy before and after the heat treatment determine that this treatment process favors the dispersion of carbides in the austenitic matrix and the appearance of precipitates which causes structural hardening.