Mathematics

Tesis doctoral sobre el mal en Platón. ¿Qué es el mal para Platón? ¿Cuántos tipos de mal existen? ¿Cómo podemos remediar los males que acontecen? ¿Será posible evitarlos? Platón sugiere que mediante la música, la matemática y la gimnasia podemos encontrar el camino hacia el bien.

Eigendistributions of a co∼event, and the new Bayesian theorem in the theory of experience and chance.
Example. An experientially random experiment is conducted in which a group of M = 4 experienced experts (observers) ranks a random collection of N = 5 trees (observations) into two ranks: «to be cut» (×) and «not to be cut».

Publication Date: October 25 , 2019                            Number of  Pages: 16
In this work , we study  and solve a  Diophantine  problem which is part
of the Problem Collection entitled , 
"1220  Number Theory Problems (The J 29 Project)" ,  by  authors
      Amir  Hossein  Parvardi  and  Ben (bluecarneal).
  The said problem is Problem 122 in the above described collection.
                  We state the problem below as PROBLEM 1:
                                          PROBLEM 1(Problem 122)
                          Find all the integer solutions  of  the  equation
                                            (x - y)^3 =  x^2 +  y^2.
      Observe that the above equation is  anti-symmetric:
      If (a , b) is a solution , then  (- b , - a)  is also a solution .
                  There are  five results in this paper Results 1, 2 , 3 , 4 , and 5.
                  All five results are stated on  pages 2-5  of this paper.
                  We present proofs of Results 1 -4 ; in  Sections 2-5.
      Result 5  is the immediate consequence of Results 1 through 5.
                Result 5  provides a comprehensive answer to PROBLEM 1.
                                      Let us state Result 5:
          Let S  be the set  all  integer solutions of the  2-variable equation ,
                                          (x - y)^3  =  x^2 + y^2 .
              Then S  is the union of three sets F , P , and N;
                                          S = FUPUN , where:
    1) F = { (0 , 0) , (1 , 0) , ( - 1 , 0 ) .
    2) P is the set of all ordered pairs of the form ,
            (x , y) = ( (t+1)[2(t^2)+2t +1] , t[2(t^2) + 2t + 1] ) ;  where t can be
                        any positive integer: t = 1 , 2 , 3 , ......
      3) N is the set of all ordered pairs of the form ,
            (x , y) = ( (-1)(t+1)[2(t^2)+2t +1] , (-1)t[2(t^2) + 2t + 1] ) ; where
                            t can be any positive integer.

Tesis doctoral, defendida en junio de 2019 en la Universidad de Buenos Aires, en la que se analiza el problema de la existencia de los objetos matemáticos. Se estudian las posturas actuales y se propone una solución propia basada en el convencionalismo.

Individuation and Meta-systems in relation to the Foundational Mathematical Categories

-- Abstract:  On Transduction and Ontogenesis of Simondon and General Economies of Bataille in relation to Fundamental Ontology and in light of the structure of the Emergent Event as seen in the Foundational Mathematical Categories.

-- Key Words: Emergent Event, Foundational Mathematical Categories, Emergent Meta-system, Orthogonal Centering Dialectic, Hegel, Sartre, Badiou, Derrida, Deleuze, Philosophy of Science, Kantian Meta-episteme

Publication Date: October 23 , 2019                      Number of Pages: 21
In this paper , we study and solve two problems. Each of the two problems
involves a one-variable trigonometric equation. The first problem , stated
below as PROBLEM 1 , was featured in the AMERICAN INVITATIONAL
MATHEMATICS EXAMINATION (AIME) of 1996; and it is published in the
September 1996 issue of the journal CRUX  MATHEMATICORUM;
Issue No 5 , Volume 22 , page 200. The second problem , PROBLEM 2 ,
is created by this author. Let us state the two problems.
PLEASE NOTE: all angles in this paper and in this abstract are measured
                                        in  DEGREES.
                                              PROBLEM 1
                        14th ANNUAL AMERICAN  INVITATIONAL
                                        MATHEMATICS EXAMINATION (AIME) 
                                              Thursday , March 28 , 1996
            Problem#10: Find the smallest positive integer solution to
                                  tan(19x) =cos(96) + sin(96)]/[cos(96) - sin(96)] .
                                                PROBLEM 2
                            Let k be a positive integer. Determine all the integer
                                  solutions of the one-variable equation ,
          tan(19x) = [cos(90+9k) + sin(90+9k)]/[cos(90+9k )- sin(90+9k)] .
          PLEASE NOTE: For the remainder of this abstract , we will refer
                          to the equation of PROBLEM 1 as Equation (1) ; and to
                                the equation of PROBLEM 2  as Equation (2).
            There are seven results in this paper; Results 1-7.
                      Result 2 plays a key role in the solutions of both problems.
                          Let us state the second result:
                                                                Result 2
                                  Let  c be the degree measure of an angle; with
                            c not of the form  180d + 135 (degrees) ; where d is
                                          an integer. Then , and only then ,
                  [cos(90+c) +  sin(90+c]/[cos(90+c) - sin(90+c) = tan(135 + c).
      We prove Result 2 in Section 2 , pages 9-10.
  Using Results 2 and 3 ; in Section 4 , page 15, we prove Result 4 ;
                        Which provides the answer to PROBLEM 1:
                                                        Result 4
                          All the integer solutions to Equation (1) are given
                                    by  x = 3(60t - 7) = 180 t - 21; where t can be any
                                                integer.
                                Therefore , the smallest positive integer solution
                                          of Equation (1) is obtained for t=1:
                                                        x=159  is the minimum positive
                                  integer solution of  Equation (1).
                  On page 8 , we show that the right hand-side of Equation (2)
                            is defined as a real number if , and only if , the positive
                                    integer k is non-congruent to 15 modulo 20.
                            Under this assumption on k , Result 6 gives all the
                                        integer solutions of Equation (2); and
                                                Result 7 provides the least or smallest
                                        positive integer solution to Equation (2).

SPUI25 are hosting an event on October 31st in Amsterdam at 20.00 with Prof. Stefaan Missinne,  Fellow of the Royal Geographical Society, da Vinci expert, and author of The Da Vinci Globe. Published recently by Cambridge Scholars, the book brings the reader along a fabulous journey of scholars, maps, and riddles, to present painstaking evidence that one of the world’s earliest known globes – found after a chance discovery at a London map fair in 2012 – was in fact crafted by Leonardo da Vinci.


https://www.spui25.nl/gedeelde-content/evenementen/evenementen/2019/10/de-wereldbol-van-leonardo-da-vinci.html

https://cambridgescholarsblog.wordpress.com/2019/10/08/event-in-amsterdam-the-da-vinci-globe/

In this multidisciplinary investigation we show how an evidence-based perspective of quantification-in terms of algorithmic verifiability and algorithmic computability-admits evidence-based definitions of well-definedness and effective com-putability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA-over the structure N of the natural numbers-that are complementary, not contradictory. The first yields the weak, standard, interpretation I_P A(N, SV) of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under I_P A(N, SV). The second yields a strong, finitary, interpretation I_P A(N, SC) of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under I_P A(N, SC). We situate our investigation within a broad analysis of quantification visávisá vis: • Hilbert's ε-calculus • Gödel's ω-consistency • The Law of the Excluded Middle • Hilbert's ω-Rule • An Algorithmic ω-Rule • Gentzen's Rule of Infinite Induction • Rosser's Rule C • Markov's Principle • The Church-Turing Thesis • Aristotle's particularisation (defined as the postulation that from the provability of a formula [(∀x)F (x)] in a formal theory L, we may conclude the existence of some unspecified object a, in the domain of any well-defined interpretation I of L, for which the interpretation F * (a) of [F (a)] is true) • Wittgenstein's perspective of constructive mathematics • An evidence-based perspective of quantification. By showing how these are formally interrelated , we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's ε-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines.

Whether and in what way enumeration processes differ for small and large sets of objects is still a matter of debate. In order to shed light on this issue, EEG data were obtained from 60 normally developing elementary school children. Adopting a standard non-symbolic numerical comparison paradigm allowed us to manipulate numerical distance between stimulus arrays for different quantity ranges, i.e. the subitizing, counting and estimation ranges. In line with the existing literature, the amplitudes of parietal positive going ERP components showed systematic effects of numerical distance, which did not depend on set size. In contrast to the similarities in surface distribution of electrophysiological activity across all number ranges, applying source localization we found distance related current density effects in inferior parietal processing systems to be similar for all numerical ranges, there was, however, considerable variation in the involvement of medial parietal and lateral occipital regions. The precuneus, which is known to be involved in visual imagery, showed distance effects exclusively for numerical comparisons on large set sizes. In contrast, the processing of small quantities and stimulus arrays arranged into canonical patterns relied on lateral occipital areas that are linked to higher-level shape recognition. These findings suggest, on the one hand, that for explicit numerical decisions an involvement of domain-specific resources does not depend on quantity features of the visual input. On the other hand, it seems that the recruitment of mediating perceptual systems differs between the apprehension of small quantities and the enumeration of large sets of objects.

THE MILITARY TECHNICAL COURIER / VOJNOTEHNIČKI GLASNIK (ISSN 0042-8469, e-ISSN 2217-4753, UDC 623+355/359, DOI: 10.5937/VojnotehnickiGlasnik; https://doi.org/10.5937/VojnotehnickiGlasnik) is a multidisciplinary scientific journal of the Ministry of Defence of the Republic of Serbia. It publishes scientific and professional papers as well as technical data on modern weapon systems and military technologies.
The journal covers inter-service technical support to the Army on the principle of logistic system support; fundamental, applied and development research; production and use of weapons and military equipment as well as other theoretical and practical achievements leading to professional development of all members of Serbian, regional and international academic communities, members of the Ministry of Defence and the Army of Serbia in particular.

Modular hip implants allows for the adjustment of leg length, offset, and the ability to remove the head for acetabular exposure during primary and revision surgery. The design of the Morse taper facilitates the intimate contact of the conical trunnion of the femoral stem (male component), with the conical bore of the femoral head (female component). Orthopaedic trunnion tapers are not standardized and vary in length, taper angle, and base dimension. Variations in the design and surface characteristics of the trunnion, will directly reflect on the interface at the taper junction and can influence the likelihood of subsequent wear, corrosion and longevity of the implant. The effect of surface topography of trunnions on commercially available hip stems has not yet been considered as a possible contributing factor in the corrosion observed at taper junctions. In this study we analyzed the surface topography and surface roughness of randomly selected commercially available femoral hip stem trunnions to obtain a greater insight into their surface characteristics.

Origami is the art of paper folding originated from Japan. It is, based on previous research has many benefits, especially in the learning of mathematics in the classroom. Therefore, there is a need to study about the possibility of application of origami in the process of learning mathematics in Indonesia. This study aimed to find out and analyze the possibility of application of origami in the Indonesian education system, especially in the subjects of mathematics at junior high school. This research is the first (first year) research within two phases (2 years) of research. The research method was done by a means of surveying technique, by spreading the questionnaire to the junior high school mathematics teachers via Google Spreadsheet, the analysis of BSE mathematics junior high school books, and discussion with some mathematics teachers. The result of this research shows that there is a huge chance for origami to be applied in mathematics learning process in junior high school level in Indonesia because based on the result of the questionnaire, 87.5% of respondents stated that they have never used origami as learning media. In addition, from the results of the analysis of 6 mathematics BSE books of junior high school level in Indonesia, it was found that origami or paper folding art is only applied to one activity and become an example of the origami-based problem. It is concluded that the development of secondary-school mathematics learning model by using origami has a huge opportunity to be implemented.