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The Trisection of an Arbitrary Angle: A Classical Geometric Solution
Get PDFThis paper presents an elegant classical geometric solution to the ancient Greek's problem of angle trisection. Its primary objective is to provide a provable construction for resolving the trisection of an arbitrary angle, based on the restrictions governing the problem. The angle trisection problem is believed to be unsolvable for compass-straightedge construction. As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem. The goal of the presented solution is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greek's tools of geometry (a classical compass and straightedge) by changing the problem from the algebraic impossibility classification to a solvable plane geometrical problem. Fundamentally, this novel work is based on the fact that algebraic irrationality is not a geometrical impossibility. The exposed methods of proof have been reduced to the Euclidean postulates of classical geometry
Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces
Get PDFIn this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples
SOLUTIONS OF FRATIONAL EMDEN-FOWLER EQUATIONS BY HOMOTOPY ANALYSIS METHOD
Get PDFIn this paper, we have solved the singular initial value problems of fractional Emden-Fowler type equations by using the homotopy analysis method. The approximate analytical solution of this type equations are obtained
TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems
Get PDFTOPSIS (technique for order preference similarity to ideal solution) is considered one of the known classical multiple criteria decision making (MCDM) methods to solve bi-level non-linear fractional multi-objective decision making (BL-NFMODM) problems, and in which the objective function at each level is considered nonlinear and maximization type fractional functions. The proposed approach presents the basic terminology of TOPSIS approach and the construction of membership function for the upper level decision variable vectors, the membership functions of the distance functions from the positive ideal solution (PIS) and of the distance functions from the negative ideal solution (NIS). Thereafter a fuzzy goal programming model is adopted to obtain compromise optimal solution of BL-NFMODM problems. The proposed approach avoids the decision deadlock situations in decision making process and possibility of rejecting the solution again and again by lower level decision makers. The presented TOPSIS technique for BL-NFMODM problems is a new fuzzy extension form of TOPSIS approach suggested by Baky and Abo-Sinna (2013) (Applied Mathematical Modelling, 37, 1004-1015, 2013) which dealt with bi -level multi-objective decision making (BL-MODM) problems. Also, an algorithm is presented of the new fuzzy TOPSIS approach for solving BL-NFMODM problems. Finally, an illustrative numerical example is given to demonstrate the approach
Median Double Ranked Set Sampling Method
Get PDFIn environmental monitoring and assessment, the main focus is to achieve observational economy and to collect data with unbiased, efficient and cost-effective sampling methods. Ranked set sampling (RSS) is one traditional method that is mostly used for accomplishing observational economy. In this article, we suggested new sampling method called median double ranked set sampling (MDRSS). The newly suggested sampling method MDRSS is compare to the simple random sampling (SRS), RSS, double ranked set sampling (DRSS), median ranked set sampling (MRSS). When the underlying distributions are symmetric and asymmetric, it is shown that, the variance of the mean estimator under MDRSS is always less than the variance of the mean estimator based on SRS and the other methods
The Availability of Systems with Bathtub Hazard Rate Function
Get PDFIn our normal life we can see that the most realistic systems possess useful time governed by hazard rateof bathtub shaped. The hazard rate function, however, plays a vital role in the computation of theavailability function. The repair time, however, could be modeled as any statistical distribution. In thispaper I will investigate the nature of availability function and points of availability of systems with bathtubhazard function and exponential distribution repair time using Markovian method
Thermal Conductivity Modeling of Propylene Glycol - Based Nanofluid Using Artificial Neural Network
Get PDFThe article introduces artificial neural network model that simulates and predicts thermal conductivity and particle size of propylene glycol - based nanofluids containing Al2O3 and TiO2 nanoparticles in a temperature rang 20 - 80oc. The experimental data indicated that the nanofluids have excellent stability over the temperature scale of interest and thermal conductivity enhancement for both nanofluid samples. The neural network system was trained on the available experimental data. The system was designed to find the optimal network that has the best training performance. The nonlinear equations which represent the relation between the inputs and output were obtained. The results of neural network model and the theoretical models of the proposed system were performed and compared with the experimental results. The neural network system appears to yield the best fit consistent with experimental data. The results of the paper demonstrate the ability of neural network model as an excellent computational tool in nanofluid field
A A Novel Layered System to Prevent High-Energy, Ionizing Radioactive Photon Transmissions and Control Particle Behavior With The Utilization of Monte Carlo Transport Modeling Via SPENVIS-Based Modular Implementation
No full textToday, mass nuclear weapons and reactor plants are becoming more prominent. However, current methods of radiation shielding are not viable due to heavy cost and ineffective means of weakening photon momentum. Therefore, it becomes necessary to design structures resistant to the behavior of radiation from exposing to human life. Specifically, 280 computational experiments were conducted in a SPENVIS environment utilizing Multi-Layered Shielding Simulation (MULASSIS) and Geant4 Radiation Analysis for Space (GRAS) on multiple shielding models. These thirteen models tested against nuclear, artificially-generated incident particles under single and multi-ray analyses with four angular photon distributions in comparison to SHEILDOSE, a current standard for cosmic radiation shielding developed by the European Space Agency. These designs using stainless steel, lead, slightly-radioactive bismuth, and lithium-hydride prevented over 99% of particle detection compared to SHIELDOSE, which conversely increased the neutron-energy dose by over 700%, and insufficiently reduced high-energy gamma ray penetration. Per kilogram, my model is 144 times cheaper and only a small fraction of the thickness of either SHIELDOSE or metal foams. Thus, the potential of enhanced nuclear plants, further space exploration, and an overall safer approach to utilizing or preventing exposure to atomic particles such as with multi-disaster protection buildings can become more readily available, thus saving millions of lives that are in impending danger
The The Anisotropy of Electron Scattering in Uniaxially Deformed N-Si Single Crystals with Radiation Defects
No full textThe tensoresistance at the uniaxial pressure along the crystallographic direction [100] for n-Si single crystals, which were irradiated by the different doses of gamma quants was investigated. On the basis of the theory of anisotropic scattering and experimental data of the tensoresistance the dependences of the parameter of mobility anisotropy on the uniaxial pressure for the data of single crystals are obtained. It has been shown that for unirradiated n-Si single crystals, the parameter of mobility anisotropy does not depend on uniaxial pressure since the alloying impurities of phosphorus will be completely ionized at T=77 K. For the gamma - irradiated n-Si single crystals the parameter of mobility anisotropy will decrease with an increase in exposure dose by reducing the screening effect. In this case, it is necessary to take into account the mechanisms of electron scattering on the impurity ions, impurity complexes, which consist of several ions of the impurity and on the fluctuation potential, which leads to the appearance of gradients of resistivity. The changing of relative contribution of these the scattering mechanismsat at the uniaxial pressure determines the obtained dependences of the parameter of mobility anisotropy and the tensoelectric properties of gamma-irradiated n-Si single crystals
Influence of Alloying Additives on The Adhesive Properties of Steels: Atomic Level Simulation
Get PDFIn the present work we report atomistic molecular dynamics simulation results on adhesion force between self-mated iron/iron, iron/vanadium, iron-cementite and iron/titanium surfaces has been determined and we found that iron/cementite surface exhibits lower adhesive force than that of iron/iron surface. The results showed that adhesion, quantified by the work of adhesion, decreased as the vanadium content increased and highest reduction was obtained for 10 at.% vanadium and 7.5 at.% for titanium. Furthermore, the variation of adhesion force with temperature was studied in the temperature range between 300-700 K and we found that the adhesive force generally is lowered at higher temperature