APAV - Academy of Sciences, Letters, Arts and Technology (E-Journals)
Not a member yet
757 research outputs found
Sort by
On some computational and applications of finite fields
Get PDFFinite field is a wide topic in mathematics. Consequently, none can talk about the whole contents of finite fields. That is why this research focuses on small content of finite fields such as polynomials computational, ring of integers modulo p where p is prime or a power of prime. Most of the times, books which talk about finite fields are rarely to be found, therefore one can know how arithmetic computational on small finite fields works and be able to extend to the higher order. This means how integer and polynomial arithmetic operations are done for Z p such as addition, subtraction, division and multiplication in Z p followed by reduction of p (modulo p). Since addition is the same as subtraction and division is treated as the inverse of the multiplication, thus in this paper, only addition and multiplication arithmetic operations are applied for the considered small finite fields (Z 2 − Z 17 ). With polynomials, one can learn from this paper how arithmetic computational through polynomials over finite fields are performed since these polynomials have coefficients drawn from finite fields. The paper includes also construction of polynomials over finite fields as an extension of finite fields with polynomials. This lead to arithmetic computational tables for the finite fields F q [x]/f(x), where f(x) is irreducible over F q . From the past decades, many researchers complained about the applications of some topics in pure mathematics and therefore the finite fields play more important role in coding theory, which involves error-coding detection and error-correction as well as cyclic codes. As a result, this research paper shows these applications among others
Determine the value d(M(G)) for non-abelian p-groups of order q = pnk of Nilpotency c
Get PDFIn this paper we prove that if n, k and t be positive integer numbers such that t < k < n and G is a non abelian p-group of order pnk with derived subgroup of order pkt and nilpotency class c, then the minimal number of generators of G is at most p1 2 ((nt+kt−2)(2c−1)(nt−kt−1)+n. In particular, |M(G)| _ p1 2 (n(k+1)−2)(n(k−1)−1)+n, and the equality holds in this last bound if and only if n = 1 and G = H ×Z, where H is extra special p-group of order p3n and exponent p, and Z is an elementary abelian p-group
Are low testosterone and sex differences in immune responses causing mass hysteria during the coronavirus pandemic?
Get PDFBy integrating the entire body of research in human sexual dynamics, immune responses, and sociocultural behavior, we can conclude that the mass hysteria our society is currently experiencing originates in our evolved psychological adaptations to pandemic conditions[i]. A lack of hormonal balance[ii], due to a collapse in testosterone levels, may cause a disproportionate immune response that leads to the destruction of our cherished sociopolitical institutions—the very institutions that are design to protect human liberty and prosperity. What is playing out at a societal level is similar to an excessive immune response that causes the body to attack itself: decreased testosterone causing the kind of auto-immune response that is more prevalent in females.[i] Barzilai, R. (2020). Low Solar Activity, Winter Flu Conditions, Pandemics and Sex Wars: A Holistic View of Human Evolution. Science & Philosophy, 8(1). Doi: 10.23756/sp.v8i1.514 [ii] Barzilai, R. (2019). Solar cycles, light, sex hormones and the life cycles of civilization: Toward integrated chronobiology. Science & Philosophy, 7(2). doi: 10.23756/sp.v7i2.48
Low Solar Activity, Winter Flu Conditions, Pandemics and Sex Wars: A Holistic View of Human Evolution
Get PDFThe current spread of coronavirus has caught our modern world by surprise, which leads to widespread panic, fear and confusion. However, if we view the unfolding of these events from a scientific historical perspective of past human evolution, we may discover the reoccurring patterns of the environmental conditions that give rise to such epidemics. Hence, we can figure out better methods to prepare and react to the infectious agents that spread diseases that have shaped the course of human history before. Here, I propose a holistic view of human evolution, with an interdisciplinary approach that studies how cyclic variation in solar UV energy affects the evolution of viruses and shapes the symbiotic dynamics of human life on earth
The history and the meaning of Einstein’s Principle of Equivalence
Get PDFWe review from a historical and a didactic point of view the Equivalence Principle, which was considered by Einstein as the corner stone of his new theory of Gravitation: the General Relativity. Before and after the enormous success of his theory, this principle was the subject of studies and discussions. Still today, after more than one century, the debate about its interpretation, application and generalization is very fertile. Einstein soon understood the revolutionary significance of his idea and defined it as “the happiest thought of my life”
Geometrical foundations of the sampling design with fixed sample size
Get PDFWe study the sampling design with fixed sample size from a geometric point of view. The first-order and second-order inclusion probabilities are chosen by the statistician. They are subjective probabilities. It is possible to study them inside of linear spaces provided with a quadratic and linear metric. We define particular random quantities whose logically possible values are all logically possible samples of a given size. In particular, we define random quantities which are complementary to the Horvitz-Thompson estimator. We identify a quadratic and linear metric with regard to two univariate random quantities representing deviations. We use the α-criterion of concordance introduced by Gini in order to identify it. We innovatively apply to probability this statistical criterion
New structure of norms on R^n and their relations with the curvature of the plane curves
Get PDFLet be fixed nonzero real-valued functions on , the real numbers. Let , where . We show that has properties similar to a norm on the normed linear space. Although is not a norm on in general, it induces a norm on . For the nonzero function , a curvature formula for the implicit curve at any regular point is given. A similar result is presented when is a nonzero function from to . In continued, we concentrate on . It is shown that the curvature of when is a positive multiple of . Particularly, we observe that is an elliptic integral of the second kind
CAS wavelet approximation of functions of Holder class and solutions of Fredholm integral equation
No full textIn this paper, cosine and sine wavelet is considered. Two new CAS wavelet estimators E(1) 2k;2M+1(f) and E(2) 2k;2M+1(f) for the approximation of a function f whose first derivative f' and second derivative f '' belong to Hölder's class Hα [0; 1) of order 0 <α≤1, have been obtained. These estimators are sharper and best in wavelet analysis.Using CAS wavelet a computational method has been developed to solve Fredholm integral equation of second kind. In this process, Fredholm integral equations are reduced into a system of linear equations. Approximation of function by CAS wavelet method is applied in obtaining the solution of Fredholm integral equation of second kind. CAS wavelet coefficient matrices are prepared using the properties of CAS wavelets.Two examples are illustrated to show the validity and efficiency of the technique discussed in this paper
Modelling the shape of sunspot cycle using a modified Maxwell-Boltzmann probability distribution function
Get PDFAbstractThe 11 year sunspot number cycle has been a fascinating phenomenon for many scientists in the last three centuries. Various mathematical functions have been used for modelling the 11 year sunspot number cycles. In this paper, we present a new model, which is derived from the well known Maxwell-Boltzmann probability distribution function. A modification has been carried out by introducing a new parameter, called area parameter to model sunspot number cycle using Maxwell-Boltzmann probability distribution function. This parameter removes the normality condition possessed by probability density function, and fits an arbitrary sunspot cycle of any magnitude. The new model has been fitted in the actual monthly averaged sunspot cycles and it is found that, the Hathaway-Wilson-Reichmann measure, goodness of fit is high. The estimated parameters of the sunspot number cycles 1 to 24 has been presented in this paper. A Monte Carlo based simple random search is used for nonlinear parameter estimation. Prediction has been carried out for the next sunspot number cycles 25 through a model by averaging of recent cycle’s model parameters. This prediction can be used for simulating a more realistic sunspot cycle profile. Through extensive Monte Carlo simulations, large number of sunspot cycle profile could be generated and these can be used in the orbital dynamics studies
Mathematics and the Liberal Arts
Get PDFThe Liberal Arts deal with the human being as a whole and hence with what lies at the essence of being human. As a result, the Liberal Arts have a far greater capacity to do good than other fields of study, fortheir foundation in philosophy enables them to bring students into contact with the ultimate questions which they are free to accept (or reject). Even if these questions have little or no ‘market value’, itshould be obvious that the way they are taught and learned is going to have a powerful impact upon the future of the students and society. It is suggested here that mathematics has an integral role in the study of the liberal arts in a first degree at a university where the ‘meal ticket’ is subsequently studied in the graduate or professional school