Trisection of an arbitrary angle is considered an impossible event in mathematical history. In this paper, we are trying to establish a general procedure for trisecting an arbitrary angle using only an unmarked straightedge and a compass. The basic geometrical compass constructions described in our main results section will ensure the possibilities of known and unknown angles trisection indeed. Before reaching the main results or general trisecting procedure, we will try to prove that Angles of sixty, thirty, seventy-five, forty-five, and ninety degrees can be trisected successfully by following the way of Archimedes and other discrete endeavors. Although based on algebra, Pierre Laurent Wantzel declared the verdict, “Arbitrary angle trisection is impossible.” we experienced that our achieved procedure was possibly not arrested by this verdict. After applying our general process to trisect an arbitrary angle, we hope readers can trust algebra cannot affect the successful geometrical constructions of angle trisection.

For the past millennia, various methods had been developed to solve quadratic equations with one unknown. Among high school mathematics curriculum worldwide, quadratic equations teaching and learning intensively utilizes the completing squares method. The present study compared Loh’s method to completing squares to examine the difference in students performance in solving quadratic equations. A random sample of 21 students were put into control (n=11) and experimental groups (n=10). The experimental group solved two essay type questions using Loh’s method whiles the control group used completed squares. Students test scores were analysed non-parametrically by Mann-Whitney U test. The results revealed statistically significant difference in test scores between control group (median=2.00,n=11) and experimental group (median=5.00,n=10). The median for the experimental group was significantly higher than that of the control group. The study recommended that teachers, curriculum developers and policy makers should be highly interested in intuitive approaches, particularly Loh’s method, that discourage rote memorization.

This survey assessed the direct effects of teaching quality, teaching competence and mathematics connection on mathematics achievement motivation in Senior high School students in Ghana. A descriptive survey was used in the study, which included 329 senior high school students from Barekese Senior High School. Prior to the main model estimation, preliminary studies such as Confirmatory Factor Analysis, convergent validity, discriminant validity, and internal consistency (Cronbach’s Alpha) were computed. Amos (v.23) was used to do structural equation modeling (SEM) in order to assess the various assumptions. The results of path estimations revealed that mathematics connection positively and significantly influenced mathematics achievement motivation. However, teaching quality and teaching competence has no significant impact on mathematics achievement motivation.

Soft set theory, introduced by Molodtsov, is as an efficacious mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspect. Since its inception, different kinds of soft set operations are defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise gamma operation and we investigate its basic algebraic properties. Moreover by examing the distribution rules, it is aimed to contribute to the soft set literature by obtaining the relationships between this new soft set operation and other types of soft set operations such as extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations. This paper can be regarded as a theoritical study of soft set theory.

Field distribution in respect of LP11 mode in the dispersion controlled fibers in the appearance and in disappearance of Kerr category nonlinearity. The estimation involves totally the mathematical expression for the field of LP11 mode as prescribed in the Chebyshev method. Mathematical solution in connection with the relevant characteristics are described. The method of iterative repetition is applied for the required estimation at the state of said class of nonlinearity. The connected assessment using the prescribed mathematical exercise needs a little computations. But, the derived results exhibit extremely close proximity to the actual values obtained by a methodology namely finite element. As a result, our simple and precise formalism provides ample scope for analyzing various Kerr class nonlinear dual-mode optical fiber properties.

There are numerous methods for numerically solving a fifth-order ordinary differential equation. We show in this paper that the Bessel matrix polynomials method is a powerful tool for numerically solving this equation. Our method is tested on examples, and it is compared to other methods. It is demonstrated that the Bessel matrix polynomials method produces good results.

The single-index model is a portfolio optimization method that uses each asset’s beta’. In general, the beta is estimated using the return data by the least square method. However, the return data frequently contains several outliers, so the estimation resulting from the least square method is inaccurate. This study examines several beta estimators from robust regression methods, namely the least absolute value estimator, M-estimator, LMS-estimator, LTS-estimator, MM-estimator, and Tau estimator to estimate the beta of each asset and make an optimal portfolio based on this estimated value. We also evaluate the effect of robust beta estimators on the stability and performance of each portfolio. We present the Sharpe ratio and some turnover measures, namely the l-period portfolio turnover, maximum turnover, lower bound single-asset turnover, and lower bound multiple-asset turnover. Among various estimators used here, the Tau estimator is the best estimator to replace the OLS for estimating the beta.

This work proposes a new computational method, namely the He-Elzaki transform method (HETM) formulated by He’s variation iteration method and modified Laplace transform called Elzaki integral transform to solve nonlinear fractional Zakharov-Kuznetsov equations. The fractional derivatives are described by Caputo sense. The beauty of this technique is that one has no need to evaluate the Lagrange multiplier by integration or taking the convolution theorem. The suggested method is implemented on two examples and the results obtained are compared with those of the Variation iteration method (VIM), homotopy perturbation transform method (HPTM), and new iteration Sumudu transform method (NISTM), and optimum homotopy analysis method (OHAM). The innovative computational technique is an efficient high accurate method and facilitates solving fractional differential equations.

Electromagnetic Radiation comes out from different electrical, or electronics gadget used for Lab as well as household purposes. As many circuits of household, industrial, and communication systems operate at close proximity of each other and one such circuit can affect the performance of other nearby circuits adversely via inadvertent couplings of their signal through near and far region, propagating electromagnetic fields. Electromagnetic waves generated by different wireless systems like mobile systems, satellite systems, other microwave links, etc. facilitates our communications throughout the world. Thus the hazard of electromagnetic radiation causes interference among these instruments and at the same time affects the living cells which includes both plant and animal cells. Here our research is to study the electromagnetic radiation of all these instruments including mobile phones on the plant cells. For the purpose of this study, here Hibiscus Flower is taken, exposed to electromagnetic radiation for the different time interval with a constant power and at certain temperature. It is observed that the physical condition of the flower as well as dielectric constants is changed. Here, in this case the dielectric properties have been measured on a flower named Hibiscus (petals) using open ended coaxial probe technique at four different temperature levels i.e. at 0th hour, after 1hour, after 2hours and after 3 hours. There are the dielectrics properties for mentioned flowers have been measured and plotted graphically within frequency range of 0.02 GHz to 8.5 GHz at many sample points. Another important observation is that the condition of Hibiscus petals at different time interval after exposing electronic magnetic radiation from Horn Antenna. From this study we can get an idea that how electromagnetic radiation can be affected for plants.

Cloud computing is a platform for dynamically enhancing capabilities and increasing potentialities without requiring the addition of new hardware, employees, or software. Additionally, cloud computing began as a business notion and later became a successful IT innovation. Concerns have been expressed about the security of the cloud environment, though, considering that the cloud contains a lot of information about people and businesses. Although cloud computing has received a lot of attention, clients are still hesitant to move their businesses there. However, the only significant issue preventing greater adoption of cloud computing is a lack of protection. Additionally, the market is wary about cloud computing due to the intricacy with which it controls data protection and confidentiality. When used in a cloud context, the cloud model architecture jeopardises the security of current technology. Therefore, cloud service customers should be aware of the risks associated with uploading data into this novel environment. Therefore, several areas of cryptography that endanger cloud computing are examined in this work. This paper provides an overview of the specific security concerns that using cryptography in a cloud computing system raises.