Search results for: symmetric algebra

Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: Saida Dorbani, M'hammed Badaoui, Djilali Benouar

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This paper deals with the effect of the building design and epicentral distance on the storey lateral displacement, for several reinforced concrete buildings (6, 9 and 12 stories), with three floor plans: symmetric, mono symmetric, and unsymmetrical. These structures are subjected to seismic accelerations from the Boumerdes earthquake (Algeria, May 21st, Mw=6.5). The objective of this study is to highlight the impact of the fundamental period and epicentral distance on storey displacements for a given earthquake. The seismic lateral displacement is carried out in both longitudinal and transverse direction by the response spectrum method.

Keywords: natural period, epicenter distance, reinforced concrete buildings, storey displacement

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Authors: Gonzalo García-Reyes

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Conformastat spherically symmetric exact solutions of Einstein's field equations representing matter distributions made of fluid both perfect and anisotropic from given solutions of Poisson's equation of Newtonian gravity are investigated. The approach is used in the construction of new relativistic models of thick spherical shells and three-component models of galaxies (bulge, disk, and dark matter halo), writing, in this case, the metric in cylindrical coordinates. In addition, the circular motion of test particles (rotation curves) along geodesics on the equatorial plane of matter configurations and the stability of the orbits against radial perturbations are studied. The models constructed satisfy all the energy conditions.

Keywords: general relativity, exact solutions, spherical symmetry, galaxy, kinematics and dynamics, dark matter

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Authors: Kerem Ok, Cem Cevikbas, Vedat Coskun, Mohammed Alsadi, Busra Ozdenizci

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Un-keyed SIM cards do not contain the required security infrastructure to provide end-to-end encryption with Service Providers. Hence, new, emerging, or smart services those require end-to-end encryption between SIM card and a Service Provider is impossible. SIMSec key exchange protocol creates symmetric keys between SIM card and Service Provider. After a successful protocol execution, SIM card and Service Provider creates the symmetric keys and can perform end-to-end data encryption when required. In this paper, our aim is to analyze the SIMSec protocol’s security. According to the results, SIM card and Service Provider can generate keys securely using SIMSec protocol.

Keywords: End-to-end encryption, key exchange, SIM card, smart card

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Authors: Triloki Nath, R. K. Gupta, L. P. Singh

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The aim of this paper is to find the new exact solution of the blast wave problem in one-dimensional unsteady adiabatic flow for generalized geometry in a compressible, inviscid ideal gas with dust particles. The density of the undisturbed region is assumed to vary according to a power law of the distance from the point of explosion. The exact solution of the problem in form of a power in the distance and the time is obtained. Further, the behaviour of the total energy carried out by the blast wave for planar, cylindrically symmetric and spherically symmetric flow corresponding to different Mach number of the fluid flow in dusty gas is presented. It is observed that the presence of dust particles in the gas yields more complex expression as compared to the ordinary Gasdynamics.

Keywords: shock wave, blast wave, dusty gas, strong shock

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Kailash Ghimire, Manoj Thapa

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This study focuses on early identification of deficiencies in pre-required areas of students who are enrolled in College Algebra and Calculus I classes. The students were given pre-diagnostic tests on the first day of the class before they are provided with the syllabus. The tests consist of prerequisite, uniform and advanced content outlined by the University System of Georgia (USG). The results show that 48% of students in College Algebra are lacking prerequisite skills while 52% of Calculus I students are lacking prerequisite skills but, interestingly these students are prior exposed to uniform content and advanced content. The study is still in progress and this paper contains the outcome from Fall 2017 and Spring 2018. In this paper, early intervention used in these classes: two days vs three days meeting a week and students’ self-assessment using exam wrappers and their effectiveness on students’ learning will also be discussed. A result of this study shows that there is an improvement on Drop, Fail and Withdraw (DFW) rates by 7%-10% compared to those in previous semesters.

Keywords: student at risk, diagnostic tests, identification, intervention, normalization gain, validity of tests

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Moussa Hamdan, Abdulati Abdullah

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This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.

Keywords: surface plasmons, optical waveguides, semiconductor lasers, refractive index, slab dialectical

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Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

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Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: Hsueh-Cheng Yang

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The generation and design of compound involute spur gearings can be used in gear pump. A compound rack cutter with asymmetric involute teeth is presented for determining the mathematical model of compound gear pumps. This paper covers the following topics: (a) generation and geometry of compound rack cutter is presented and used to generate a compound gear and a compound pinion. (b) Based on the developed compound gears, stress analysis was performed for the symmetric gears and the asymmetric gears. Comparing the results of the stress analysis for the asymmetric involute teeth is superior to the symmetric involute teeth. A numerical example that illustrates the developed compound rack cutter is represented.

Keywords: compound, involute teeth, gear pump, rack cutter

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Authors: Wafa' Alsharafat, Suhila Farhan Abu-Owida

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Genetic algorithm (GA) is a powerful evolutionary searching technique that is used successfully to solve and optimize problems in different research areas. Genetic Algorithm (GA) considered as one of optimization methods used to solve Travel salesman Problem (TSP). The feasibility of GA in finding a TSP solution is dependent on GA operators; encoding method, population size, termination criteria, in general. In specific, crossover and its probability play a significant role in finding possible solutions for Symmetric TSP (STSP). In addition, the crossover should be determined and enhanced in term reaching optimal or at least near optimal. In this paper, we spot the light on using a modified crossover method called modified sequential constructive crossover and its impact on reaching optimal solution. To justify the relevance of a parameter value in solving the TSP, a set comparative analysis conducted on different crossover methods values.

Keywords: genetic algorithm, crossover, mutation, TSP

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Authors: Sai Charan Kamana, Harsha Vardhan Nakkina, B.R. Chandavarkar

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In a highly secure and robust key generation process, a key role is played by randomness and random numbers when current real-world cryptosystems are observed. Most of the present-day cryptographic protocols depend upon the Random Number Generators (RNG), Pseudo-Random Number Generator (PRNG). These protocols often use noisy channels such as Disk seek time, CPU temperature, Mouse pointer movement, Fan noise to obtain true random values. Despite being cost-effective, these noisy channels may need additional hardware devices to continuously communicate with them. On the other hand, Hash functions are Pseudo-Random (because of their requirements). So, they are a good replacement for these noisy channels and have low hardware requirements. This paper discusses, some of the key generation methodologies, and their drawbacks. This paper explains how hash functions can be used in key generation, how to combine Key Derivation Functions with hash functions.

Keywords: key derivation, hash based key derivation, password based key derivation, symmetric key derivation

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Authors: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Amir Alirezaei, Shahram Vahdani

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This study estimates the seismic demands of tall buildings with central symmetric setbacks by using nonlinear time history analysis. Three setback structures, all 60-story high with setback in three levels, are used for evaluation. The effects of irregularities occurred by setback, are evaluated by determination of global-drift, story-displacement and story drift. Story-displacement is modified by roof displacement and first story displacement and story drift is modified by global drift. All results are calculated at the center of mass and in x and y direction. Also the absolute values of these quantities are determined. The results show that increasing of vertical irregularities increases the global drift of the structure and enlarges the deformations in the height of the structure. It is also observed that the effects of geometry irregularity in the seismic deformations of setback structures are higher than those of mass irregularity.

Keywords: deformation demand, drift, setback, tall building

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Authors: Abdullah Al Mamun, Talal Alkharobi

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As data size is growing up, people are became more familiar to store big amount of secret information into cloud storage. Companies are always required to need transfer massive business files from one end to another. We are going to lose privacy if we transmit it as it is and continuing same scenario repeatedly without securing the communication mechanism means proper encryption. Although asymmetric key encryption solves the main problem of symmetric key encryption but it can only encrypt limited size of data which is inapplicable for large data encryption. In this paper we propose a probable approach of pretty good privacy for encrypt big data using both symmetric and asymmetric keys. Our goal is to achieve encrypt huge collection information and transmit it through a secure communication channel for committing the business and personal privacy. To justify our method an experimental dataset from three different platform is provided. We would like to show that our approach is working for massive size of various data efficiently and reliably.

Keywords: big data, cloud computing, cryptography, hadoop, public key

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Authors: Zia R. Tahir, P. Mandal

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This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0°/+45°/-45°/0°] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

Keywords: CFRP composite cylindrical shell, asymmetric meshing technique, primary buckling, secondary buckling, linear eigenvalue analysis, non-linear riks analysis

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Authors: B. Prashantha, S. Anish

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The aim of the present study is to computationally evaluate the hemodynamic factors which affect the formation of atherosclerosis and plaque rupture in the human artery. An increase of atherosclerosis disease in the artery causes geometry changes, which results in hemodynamic changes such as flow separation, reattachment, and adhesion of new cells (chemotactic) in the artery. Hence, geometry plays an important role in the determining the nature of hemodynamic patterns. Influence of stenosis in the non-bifurcating artery, under pulsatile flow condition, has been studied on an idealized geometry. Analysis of flow through symmetric and asymmetric stenosis in the artery revealed the significance of oscillating shear index (OSI), flow separation, low WSS zones and secondary flow patterns on plaque formation. The observed characteristic of flow in the post-stenotic region highlight the importance of plaque eccentricity on the formation of secondary stenosis on the arterial wall.

Keywords: atherosclerotic plaque, oscillatory shear index, stenosis nature, wall shear stress

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Authors: Muddser Ghaffar

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In material science, synthetic chiral polymers are becoming increasingly significant due to their distinct properties that distinguish them from other polymer materials. One special technique for producing well-defined chiral polymers is asymmetric kinetic resolution polymerization (AKRP), which adds stereo regularity to a polymer chain by the kinetic resolution of a race mate preferentially polymerizing one enantiomer. Apart from making it possible to characterize chiral polymers enantioselective, AKRP can synthesize chiral polymers with high stereo selectivity. This review includes the literature on the use of enzymes, chiral metal complexes, and organ catalysts as AKRP promoters. One enantiomer reacts more quickly than the other in this kind of polymerisation, quickly entering the expanding polymer chain, while the kinetically less reactive enantiomer stays unreactive and is readily separated using straightforward purification techniques. The degree of chiral induction and overall chirality of the chiral polymers that are generated may be assessed using the enantiomeric excess (ee) of the initial monomer, which is frequently determined by chiral HPLC analysis, throughout the polymerisation process.

Keywords: stereo regularity, polymers, dynamical, symmetric

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Authors: B. V. Bhaskara Rao, Rodrigo Espinoza

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The rapid development of renewable energy sources has drawn great attention to energy storage devices, especially supercapacitors, because of their high power density and rate performance. This work focus on Fe₃O₄ nanoparticles synthesized by reverse co-precipitation and MWCNTs functionalized by –COOH acid functionalization. The results show that Optimized 25wt% Fe₃O₄@FMWCNT show high specific capacitance 100 mF/cm² at one mA/cm² whereas 15wt% Fe₃O₄@FMWCNT showed high stability (80% retention capacity) over 5000 cycles. The electrolyte used in the coin cell is LiPF6 and the thickness of the electrode is 30 microns. The optimized Fe₃O₄@FMWCNT bucky papers coin cell electrochemical studies suggest that 25wt% Fe₃O₄@FMWCNT could be a good candidate for high-capacity supercapacitor devices. This could be further tested for flexible and planar supercapacitor device application with gel electrolytes.

Keywords: self-standing electrode, Fe₃O4@FMWCNT, supercapacitor, symmetric coin-cell

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Authors: Yaxiao Zhang, Yangzhou Chen

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This study investigate the formation problem for high-order continuous-time multi-robot with bounded symmetric time-varying delay protocol under switched directed communication topology. By using a linear transformation, the formation problem is transformed to stability analysis of a switched delay system. Under the assumption that each communication topology has a directed spanning tree, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) that the multi-robot system can achieve a desired formation by the trade-off among the pre-exist topologies with the help of the scheme of average dwell time. A numeral example is presented to illustrate the effectiveness of the obtained results.

Keywords: multi-robot systems, formation, switched directed topology, symmetric time-varying delay, average dwell time, linear matrix inequalities (lmis)

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: Soofia Malik

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The purpose of this study is to develop an instrument to measure undergraduate students’ attitudes toward mathematics (MAT) and to assess the data collected from the instrument for validity and reliability. The instrument is developed using five subscales: anxiety, enjoyment, self-confidence, value, and technology. The technology dimension is added as the fifth subscale of attitude toward mathematics because of the recent trend of incorporating online homework in mathematics courses as well as due to heavy reliance of higher education on using online learning management systems, such as Blackboard and Moodle. The sample consists of 163 (M = 82, F = 81) undergraduates enrolled in College Algebra course in the summer 2017 semester at a university in the USA. The data is analyzed to answer the research question: if and how do undergraduate students’ attitudes toward mathematics load using Principal Components Analysis (PCA)? As a result of PCA, three subscales emerged namely: anxiety/self-confidence scale, enjoyment, and value scale. After deleting the last five items or the last two subscales from the initial MAT scale, the Cronbach’s alpha was recalculated using the scores from 20 items and was found to be α = .95. It is important to note that the reliability of the initial MAT form was α = .93. This means that employing the final MAT survey form would yield consistent results in repeated uses. The final MAT form is, therefore, more reliable as compared to the initial MAT form.

Keywords: college algebra, Cronbach's alpha reliability coefficient, Principal Components Analysis, PCA, technology in mathematics

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Authors: Evariste Boj, Jan Schee

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We present the temperature anisotropy of the cosmic microwave background radiation due to the inhomogeneity region constructed on a 3-brane in the framework of a Randall-Sundrum one brane immersed into a 5D bulk $AdS_5$ spacetime. We employ the Brane-World Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model to describe the cosmic expansion on the brane. The inhomogeneity is modeled by the static, spherically symmetric spacetime that replaces the spherically symmetric part of a dust-filled universe and is connected to the FLRW spacetime through the junction conditions. As the vacuum region expands it induces an additional frequency shift to a CMBR photon passing through this inhomogeneity in comparison to the case of a photon propagating through a pure FLRW spacetime. This frequency shift is associated with the effective temperature change of the CMBR in the corresponding direction. We give an estimate of the CMBR effective temperature changes with the change of the value of the tidal charge parameter.

Keywords: CMBR, Randall-Sundrum model, Rees-Sciama effect, Braneworld

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Authors: Shehret Tilvaldyev, Jorge Flores-Garay, Alfredo Villanueva, Erwin Martinez, Lazaro Rico

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The efficiency of modern transportation is severely compromised by the prevalence of turbulent drag. The high level of turbulent skin-friction occurring, e.g., on the surface of an aircraft, automobiles or the carriage of a high-speed train, is responsible for excess fuel consumption and increased carbon emissions. The environmental, political, and economic pressure to improve fuel efficiency and reduce carbon emissions associated with transportation means that reducing turbulent skin-friction drag is a pressing engineering problem. The dynamic pressure of subsonic airflow around solid objects creates lift, but also induces drag force. This paper is presenting the results of laboratory experiments, investigating appearance and magnitude of dynamic pressure in micro scale of subsonic air flow around right cylinder and symmetrical airfoil.

Keywords: airflow, dynamic pressure, micro scale, symmetric object

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Authors: Nathi Ram, Saurabh K. Yadav

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In turbomachinery, the turbulent flow occurs due to the use of high velocity of low kinematic viscosity lubricants and used in many industrial applications. In the present work, the performance of symmetric slot-entry hybrid worn journal bearing under laminar and turbulent lubrication has been investigated. For turbulent lubrication, the Reynolds equation has been modified using Constantinescu turbulent model. This modified equation has been solved using the finite element method. The effect of turbulent lubrication on bearing’s performance has been presented for symmetric hybrid journal bearing. The slot-entry hybrid worn journal bearing under turbulent/laminar regimes have been investigated. It has been observed that the stiffness and damping coefficients are more for the bearing having slot width ratio (SWR) of 0.25 than the bearing with SWR of 0.5 and 0.75 under the turbulent regime. Further, it is also observed that for constant wear depth parameter, stability threshold speed gets increased for bearing operates at slot width ratio 0.25 under turbulent lubrication.

Keywords: hydrostatic bearings, journal bearings, restrictors, turbulent flow models, finite element technique

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Authors: Sabina Garayeva

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To determine the significant risk factors for intrauterine growth restriction (IUGR), we carried out a thorough study of the social status of the parents of children with IUGR. We observed 315 mothers who gave birth to children with (IUGR), of which 172 mothers with asymmetric type and 143 mothers with symmetric type of IUGR. Through a detailed survey was gathered detailed information about education of parents. The results show that the majority of mothers with IUGR had secondary education (44,8 ± 2,8%), and fathers - higher education (35,2 ± 2,7%). Whereas in the control group, the largest number of parents had higher education (mother 35,3 ± 4,4%, fathers 42,9 ± 4,5%). Number of mothers with secondary education with IUGR was significantly (p1 <0,01; χ2 = 22,67) differs from the number of mothers with physiological pregnancy with the same level of education. Meanwhile, in the group with a symmetrical embodiment of IUGR mothers with secondary formation of significantly greater 53,1 ± 4,2%, than the asymmetric embodiment IUGR 37,8 ± 3,7% (p2 <0,05; χ2 = 8 06). Among fathers with secondary education significant difference was noted in the symmetric version of IUGR 37,8 ± 4,1% more than in the control group (p1 <0,05), and among parents of children with asymmetric IUGR option prevailed fathers with higher education - 37 2 ± 3,7%. Thus, our results revealed a low educational level of the mother as a risk factor for IUGR, which further help to develop preventive and therapeutic measures to eliminate the severity of its consequences. As seen from the data presented, mothers of children with asymmetric IUGR had a school education and fathers - higher education, while in the symmetric type of both parents had secondary education. It is found that frequency of children, born with IUGR, of mothers - housewives and fathers, engage in physical labor, was high. Thus, the analysis conducted by the social status of the parents with IUGR revealed a low level of education and unemployed mothers as risk factors for this disease, which in the future will help to develop preventive and therapeutic measures to eliminate the severity of its.

Keywords: intrauterine growth restriction, education of mothers, education influence, IUGR

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