Mathematics

The problem of scheduling a timetable is a complex job that is considered as an NP-hard problem, i.e., not verifiable in polynomial time. This is a typical scheduling problem that appears to be a strenuous job in every academic institute. The Genetic Algorithm, being an adaptive algorithm, can improve its efficiency as it progresses. A timetable should satisfy a particular number of constraints that are specific to the organization that it has been subjected to. Here, the university that is associated with our college, Kerala Technological University (KTU), has just been established and it is essential to have a timetable scheduler of its own to ease the burden of colleges to specify its norms and amount of subjects it deals with every year.

Tracing the origins of the Mayan Calendar, I discovered that European medieval paintings, Greek vessels, rock art and texts such as the Bible and the Torah, contain mathematical codes hidden in designs and stories. The astronomical mathematical mechanisms that allow us to decipher, the hidden at plain sight messages, are the Mayan and the Aztec calendar.Recognizing that all ancestral religions shared the same knowledge, deprives us of arguments to discuss, and invites us to dialogue.The oldest astronomical map in the world, suggests that America was inhabited earlier than we imagined, by an advanced culture.The oldest rock art in the world suggests that the Neanderthals also used this calendar, and that the intellectual challenge that gave us humanity, was our astonishment at the movement of the stars.

First paragraph: Students of cognitive evolution and of twentieth century thought are fortunate in the simultaneous appearance of these two biographies. No doubt the simultaneity is mostly coincidence. The physicist Richard Feynman is most widely known, alas, for two autobiographical collections of anecdotes which reveal him to be a waggish and riggish anti-establishment sort; he is most deeply known for his contributions to quantum electrodynamics. John von Neumann was a thoroughly establishment sort - soldiers guarded his hospital room as he lay dying of brain cancer just in case he let out defense secrets in his sleep - and is most widely know as the name which appears in phrases like “computers using the von Neumann architecture.” The two men crossed paths in Los Alamos, where they worked on the atomic bomb.  That crossing is a reasonable place to begin our review.

Publication Date: June 22 , 2020                            Number of Pages: 24
The subject matter of this paper , is a number theory problem that was
featured in the 2015-16 Mathematical Olympiad of Croatia.
This problem is published as Problem 112 in the collection of problems
under the title , "Number theory problems in Mathematical
  Competitions , 2015-2016" , by author Amir  Hossein  Parvardi.
  We state Problem 112 below as PROBLEM 1.
                                            PROBLEM 1( Problem 112)
                    Croatia Final  Round National Competition  2015 - 2016
        Determine all pairs (m , n) of positive integers for which there
                exist integers a , b , and c that  satisfy
                a + b + c = 0    and      a^2 + b^2 + c^2 = (2^m)(3^n) .
    The Solution/Answer to this problem is stated on page 6 of
                this paper; it is the direct consequence of Results 4 and 5.
    Results 4 and 5 are stated on pages 4 and 5; we prove them in
  Sections 4 and 5 respectively; pages 11-13 and 14-24.
            According to the Solution/Answer stated on page 6; the positive
            integer pairs (m , n) for which the conditions are satisfied , are
                          precisely those in which m is odd.
        Specifically , consider the 3-variable , 2-equation symmetric system
                              x+y+z=0  and  x^2 + y^2 + z^2 =(2^m)(3^n) ,
                                    where m and n  are positive integers. Then:
        1) If m is even , the above system has no integer solution.
        2) If m is odd and n even;  m=2u + 1 and n = 2t; where u is a
            non-negative integer and t is a positive integer; then the above
                          system has exactly six integer solutions:
                  Let  A= (2^u)(3^t). Then the six integer solutions. are:
                (x , y , z) = (A , - A , 0) , (-A , A , 0) , (A , 0 , -A) , (-A , 0 , A) ,
                                    (0 , A , -A) , and (0 , -A , A) .
        3) If n and m are both odd ;  m = 2t + 1  and  n = 2q + 1; where
                        t and q are non-negative integers; then the above system
                      has exactly six integer solutions:
                    Let  B = (2^t)(3^q)  and C =[2^(t+1)](3^q)= 2B .
              The six integer solutions are:
        (x , y , z) = (B , B , - C) , (-B , -B , C) , (B , -C , B) , (-B , C , -B ) ,
                              (- C , B , B ) , and (C , -B , - B ) .

Applied Mathematics and Sciences: An International Journal (MathSJ ) aims to publish original research papers and survey articles on all areas of pure mathematics, theoretical applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.

The fixation probability of a mutation in a population network is a widely-studied phenomenon in evolutionary dynamics. This mutation model following a Moran process finds a compelling application in modeling information propagation through human networks. Here we present a stochastic model for a two-state human population in which each of N individual nodes subscribes to one of two contrasting messages, or pieces of information. We use a mutation model to describe the spread of one of the two messages labeled the mutant, regulated by stochastic parameters such as talkativity and belief probability for an arbitrary fitness r of the mutant message. The fixation of mutant information is analyzed for an unstructured well-mixed population and simulated on a Barabási-Albert graph to mirror a human social network of N = 100 individuals. Chiefly, we introduce the possibility of a single node speaking to multiple information recipients or listeners, each independent of one another, per a binomial distribution. We find that while in mixed populations, the fixation probability of the mutant message is strongly correlated with the talkativity (sample correlation ρ = 0.96) and belief probability (ρ = −0.74) of the initial mutant, these correlations with respect to talkativity (ρ = 0.61) and belief probability (ρ = −0.49) are weaker on BA graph simulations. This indicates the likely effect of added stochastic noise associated with the inherent construction of graphs and human networks.

It is proved that the dichotomy of good and evil is ostensible, that the “universe of information” cannot be divided into two disjoint sets, so that in one there is no “evil” and in the other there is no “good”. Quotes I write because good-evil can be replaced by any opposites such as: truth-lie, big-small, empty-full, and so on. Also, the proof of Gödel's incompleteness theorem is given, or the non-existence of the set of all sets (Russell's paradox) and the like (concerning the universe of information).

Movimientos trapezoidales no lineales en el campo de las ciencias cuánticas Estoy realizando algunas investigaciones científicas sobre la posible existencia de movimientos trapezoidales no lineales en el campo de las ciencias cuánticas. Al contrario de los movimientos uniformes, sería un movimiento con características irregulares. Sería posible observar movimientos cuánticos repentinos o inesperados en los laboratorios cuánticos en el futuro próximo. En la física clásica podemos observar movimientos repentinos o inesperados en el cuerpo humano, lo que altera el manejo de las cargas, de manera verificable. Por lo tanto, considero que el ser humano puede estudiar los movimientos trapezoidales no rectilíneos cuánticos para poder manejar estos movimientos cuánticos en un tiempo tal vez no muy lejano. Aunque pueda parecer ilógico (o paralógico), los movimientos repentinos y la brusquedad añadidos al factor Inesperado existen en nuestro propio 3D en relación cuántica con 4D, sin descartar ninguna otra dimensión. Creo que esta premisa se atribuye al movimiento espacial de los ovnis, erróneamente, ya que el ser humano tiene la capacidad de estudiar, investigar y aplicar el conocimiento que proporcionará esta premisa cuántica. A diferencia de muchos de mis colegas, mi posición será llegar a nuevos conocimientos en Ciencia, Ingeniería y Técnicas Cuánticas basadas en el conocimiento de la Ciencia y las Técnicas Clásicas (tradicionales). Una gran cantidad de fenómenos no visibles que ocurren en nuestro 3D, como el mal funcionamiento repentino que altera o descompone, por ejemplo, el funcionamiento de los circuitos electrónicos de los paneles eléctricos se debe a la irrupción de las cargas electromagnéticas cuánticas y los operadores cuánticos que aún se desconocen.. Todavía hay muchas brechas y brechas, tal vez debido a la ausencia de conexión o vínculo entre el mundo clásico y

Busto Zapico, M. (2020). Standardisation and units of measurement used in pottery production: the case of the post-medieval botijuela or Spanish olive jar made in Seville. Post-medieval Archaeology, 54(1), 42-59. doi:https://doi.org/10.1080/00794236.2020.1750145

The aim of this paper is to determine the degree of standardization of pottery production and the units of measure that regulated their production. The group chosen to test this methodology is known as the Spanish olive jar. It is a series of productions manufactured in the south of the Iberian Peninsula throughout the Early Modern Period. The methodology begins with the morphometric characterisation of each vessel around a series of quantitative variables. Then, the Test for Normality is performed, and the Product-Moment Correlation Coefficient is calculated. Subsequently, a Cluster Analysis identifies different groups of Spanish olive jars. The Principal Component Analysis provides additional information that allows for a deeper understanding of the groups obtained. As a final step, calculating the Coefficient of Variation allows us to know the degree of standardization of each variable. Finally, once all these data are known, the possible units of measure that governed the production system of the Spanish olive jar can be recognized.

[El objetivo de este trabajo es determinar el grado de estandarización de una producción cerámica y las unidades de medida que regulan su producción. El grupo elegido para probar esta metodología se conoce como Spanish olive jar o botijuela, fabricada en el sur de la Península Ibérica a lo largo del período moderno temprano. La metodología hace una caracterización morfométrica de cada vasija usando varias variables cuantitativas. Después se realiza la ‘prueba de normalidad’, y se calcula el coeficiente de ‘correlación producto momento’; a éste sigue un análisis de grupos de las diversas botijuelas. El análisis de componentes principales identifica además diversos grupos de botijuelas, mientras el análisis de componentes principales ayuda a entender mejor dichos grupos. También se calcula el coeficiente de variación para identificar el grado de estandarización de cada variable. Finalmente, con todos estos datos se pueden identificar las posibles unidades de medida que regían el sistema de producción de estas botijuelas.]

The hyperbolic and circular trigonometric functions exhibit periodicity under repeated differentiation. The hyperbolic sine and cosine functions, whilst distinct from their first derivatives, are each equal to their own second derivative. Similarly, the circular sine and cosine functions are each equal to their own fourth derivative. Very little appears in the literature about functions of a real variable that are equal to their own third derivative. The purpose of this note is to define three such functions and to investigate their properties.

During the spring semester, Choi and classmates junior Natalie Medina and postbaccalaureate student Lily Tanara enrolled in prerequisite coursework for CSUF’s credential program that prepares students for middle school or high school teaching careers. The five-course sequence covers topics in education such as equity and multicultural education, adolescent development, and disciplinary literacy, a course taught by Alison Dover, associate professor of secondary education.

Cancer has become a leading cause of death worldwide. To deal with medical images to discover tumors and their types, Authors need a distinct experience in understanding medical images. Authors need machine learning techniques to reach great accuracy and speed to analyse these images to avoid a lack of experience or errors. In this paper, Authors will study a (SVM) of machine learning techniques used to classify brain images. SVM will be used in this paper to analyse brain images and discover Benign Tumor and Malignant tumor by using Matlab software. The results of the experiments conducted showed the accuracy of the system provided for the classification of tumor types (Benign, Malignant) found in medical brain images. Authors will adhere in this research that the images to be classified are limited by the presence of only two types of tumors. In the future, some pre-processing procedures will be added to the brain's medical images prior to the classification process.

Publication Date: June 17 , 2020                          Number of Pages : 21
In this paper , we study and solve two problems by this author.
The first problem , PROBLEM 1 , is a Diophantine system of two
equations and four variables. The second problem , PROBLEM 2 , deals
with a Diophantine equation with two variables.
                                      PROBLEM 1
    Determine the set of all positive integer pairs (x , y) such that the sum
  of their reciprocals is the reciprocal of an integer; and their product xy
is a perfect square. Equivalently , determine the set of all positive
integer solutions of the 2-equation , 4-variable system ,
                                          1/x + 1/y = 1/z ; and ,
                                                xy = w^2 .
  Result 5 is stated on page 6 of this paper; we prove it in Section 3 ,
  pages  12 and 13. According to Result 5 , the set of all positive integer
                    solutions of the above system can be described in terms
                          of three integer parameters k , m , and t as follows :
    x = t(k^2)[(k^2) + (m^2)} , y=t(m^2)[(k^2) + (m^2)] ,
    z=t(k^2)(m^2)  ,  w= tkm[(k^2) + (m^2)] ;  where t can be any positive
integer; and k and m can be any relatively prime positive integers. 
                                                    PROBLEM 2
      Let p be prime number greater than 5; equivalently , p>(or=) 7.
                      Determine the set of all positive integer solutions of the
                              2-variable equation,
                                                  2/x + 3/y = 5/p .
          Result 6 is stated on pages 7 and 8 of this paper. We prove  it  in
                            Section 4 , pages 14-21.
          According to Result 6 , the above equation has exactly two
                        positive integer solutions. Specifically:
        1) If the prime p is of the form , p=5a + 1; a a positive integer; the two solutions are:    (x , y)= (2a+1, (5a+1)(2a+1)) , ((5a+1)(3a+1) , 3a+1).
      2) If p=5b+2 ; b a positive integer ; then the two solutions are:
      (x , y)= (2b+1 , 3(5b+2)(2b+1)) , (2(b+1) , (5b+2)(b+1)) .
  3) If p=5c+2 ; c a positive integer ; then the two solutions are:
      (x , y)=(2(5c+3)(3c+2) , 3c+2) . ((5c+3)(c+1) , 3(c+1)) .
    4) If p=5d+1 ; d a positive integer; the two solutions are:
      (x , y)= (2(d+1) , 3(5d+4)(d+1)) ,  (2(5d+4)(d+1) , 3(d+1)) .