Mathematics

This short article gives an introduction to binary linear block codes for error detection and error correction.  Various codes are discussed and compared, including repetition codes, Hamming codes, and Reed-Muller codes.

A version of this article was published by the Radio Society of Great Britain in their members' magazine/journal, 'RadCom'.

Les impressions et les interprétations d'artefacts archéologiques dépendent en grande partie de l'expérience personnelle. Elles ne font appel à aucune autorité dogmatique, car elles adhèrent étroitement à la vérité recherchée par les scientifiques qui veulent expliquer les paléo environnements en fonction de l’expérience des données recueillies. Dans le cas présent, l'analyse des données et les conclusions ont permis de confectionner ce que l'on pourrait, par exemple, appeler le discours des os d'Ishango. L'objectif de ce travail est d'améliorer la compréhension du petit os d'Ishango en confrontant le déchiffrement de ses caractéristiques et une feuille de ponctuation d'un thème géomantique. La méthode géomantique qui consiste à faire une série de petites lignes verticales a alors été appliquée à la lecture et à l'analyse du symbolisme du petit os d’Ishango. La lecture visuelle de la morphologie structurale du petit os d'Ishango a été réalisée en utilisant le corpus ésotérique des connaissances de la religion universelle transmises dans le secret initiatique depuis la nuit des temps. Les analogies confirment un lien fort entre les connaissances occultes, la géomancie et les mathématiques dans la conception des os d'Ishango qui a eu lieu aux confins des Grands lacs africains il y a au moins 25 ka.

It has never been accomplished to describe our behavior mathematically. Due to the fact that human behavior is highly erratic even the understanding of its causes are still sketchy. Assuming that we are all equal in our regulation of thought and behavior there are simply too many differences and partially inconsistencies, the attempts stopped in its onset. For having defined the five major groups of mankind, the sociopath, the artist, the median, the, and the psychopath［1］each group is related to each other but his decision making is hardwired differently and thou probably more easy to grasp than sticking to the consistency of all appearance for the regulation of behavior is quite similar in the five groups but different in its limits. Using the more formalistic tools of mathematics, this can open the review of the equations in verifying or falsifying the predictions on future behavior in an individual, at least after defining the group affiliation. Therefore a self-test has been established［2］to predetermine the group. In a hybrid-species ［3］, the eight main neuro-receptors in each group to have two optional origins. Measuring each by its own dominating patterns not only the amalgamation in each group can be defined but also the native patterns of the non-hybrid ancestry ［4］. Not only the variance of possible combination can distribute to the limits of brain-equations but also the time-axis of our memory, being rather different, illuminating the highly different decision making among offspring of hunters and farmers. A phenomenon probably explaining the variance in processing memory by peripheral distributed groups of ADHD and autism for ADHD memorizes in combining data with importance and such is been given an emotional response to the recall, while autism is mainly been given the exact time reference stored in a continuous frame of time-preference. The latter therefore have problems to distinguish between important and not important and the former lacks a passing timeframe, mirroring the primary form of acquiring resource, farming or hunting. With the boundaries set the graphs of the equation on resource-projection looks highly different by only changing its limits. Having not only focussed on the designation of human groups but also in behavioral shifts over time (from social to non-social) and the exact denomination of similar behavior, some rather simple equation could be defined to predict and consequently proof the predicate. Not only the proper use of words is necessary but also awareness that non-social individuals will often not answer truthfully. A topic that also can be mathematically predicted. The outcome will revolutionize our perception of mankind and ourselves, dawning more than one academic discipline, probably enabling us to go virtual and back again.

On considère ici le sujet de l'imagination et de ses relations avec des théories particulières (qui ont été utilisées dans une grande variété de domaines) en donnant l'exemple d'Alan Turing, qui a envisagé un modèle de la morphogenèse pour expliquer le développement des êtres vivants et un moyen pour visualiser ce mécanisme à l'aide d'un ordinateur et d'une feuille quadrillée.
De cette façon, il a pu reconstruire plusieurs des stades du développement d'un système stochastique qui est capable de décrire un grand nombre de processus naturels et qui a été appliqué récemment aussi à la forme des villes et à la création d'objets qui font partie du design morphogénétique. Dans tous ces cas, on peut retrouver la même logique d’émergence d’une forme à partir d’une matière qui n’est pas inerte comme dans le modèle hylémorphique aristotélicien, un mécanisme qui nous permet d’analyser les analogies qui sont à la base de nos catégories eidétiques.

The old practices of interpretation have been exhausted, and the humanities and social sciences are facing a crisis. Is there a way out of the labyrinth of reading? In this book, Professor Neuman presents a challenging approach to interpreting texts and reading literature through the spectacles of conceptual mathematics. This approach strives to avoid the simplicity of a quantitative approach to the analysis of literature as well as both the relativistic and the ideological dangers facing a qualitative reading of a text. The approach is introduced in a rigorous and accessible manner and woven with insights gained from various fields. Taking us on a challenging journey from Ovid's Metamorphoses to Nick Cave's The Death of Bunny Munro, the book shows how we may gain a deeper understanding of literature and the aesthetic experience of reading.


"Conceptual Mathematics and Literature employs an interdisciplinary mathematical approach that is a uniquely insightful interpretive analysis of literary works. It offers novel ways of comprehending previously unnoticed underlying patterns of meaning. Numerous figures illustrate and reinforce the author's brilliant and illuminating mode of critical inquiry."-Frank Nuessel, Professor of Modern Languages and Linguistics, University Scholar at the University of Louisville

Nowadays, people are connected to the cloud, i.e., back end servers to implement various tasks such as storage of important data, running applications of higher compatibility and so on. While performing such tasks, a number of hosts within the system may encounter various faults resulting in their downfall. Once a system failure occurs, it has an effect on the execution of the tasks performed by the failed components such as hosts or virtual machines. Subsequently, establishing a requirement for a cloud climate that helps in running various hosts or virtual machines effectively in a cloud computing framework independent of the fault or failure happening inside the parts of the framework.

In this modern era, mostly all wireless software applications are hacked and injected because of several harmful activities. Henceforth, different frameworks were developed to measure the security level in software systems. Especially, the penetration testing (PT) model is mostly worn by all applications to make the attack vulnerability assessment. To secure the system, initially the behaviour of attacks should be analysed and that is trained in specific agent or software module. Based on the trained activities the specific verification system can predict the present malicious activities. Furthermore, the verification agent or system should be automated to find the harmful activities in any time. Also, the PT is utilized in both hardware and software gadgets, it is processed based on the support of software functions. In other case, the Machine Learning (ML) and Reinforcement Learning (RL) model is functioned to process the attack behaviour in software systems. Moreover, in this review the usage of PT is elaborated in dissimilar ways for different applications. Subsequently, the performance of PT framework is differed based on its each software or applications.

Discussion is about the relative energy and time in the context of probability and information. The first, which increases with vitality, the information of a given particle and decreases with probability, and the second (time), which disappears with increasing probability.

The aim of this study was to investigate the association between school connectedness and performance in standardized test scores and whether this association was moderated by ethnic private regard. The study combines self-report data with school district reported data on standardized test scores in reading and math and free and reduced lunch status. Participants included 436 Mexican-origin youth attending a middle school in a southwestern U.S. state. Participants were on average 12.34 years of age (SD = .95) and 51.8% female and 48.2% male. After controlling for age, gender, free and reduced lunch status, and generational status, school connectedness and ethnic private regard were both positive predictors of standardized test scores in reading and math. Results also revealed a significant interaction between school connectedness and ethnic private regard in predicting standardized test scores in reading, such that participants who were low on ethnic private regard and low on school...

Publication Date: December1 , 2020                        Number of Pages: 22
The subject matter of this paper is the equation  y^3 + p^3 = x^2 ,  where
  x and y  are positive integer variables ; and p is an odd prime .
  There are seven results in this paper , Results 1-7.
    Let us start with Result 7 , which is described in the title of this paper:
                                                          Result 7
                        Let  p be a prime congruent to 5 or 7 modulo12.
              Consider  the  2-variable equation    y^3 + p^3 = x^2 ,  with
                                    x and y being positive integer variables and under
                                    the condition that y is not divisible by p.
                                Then , the  above equation has no solution.
            Result 7 is stated in the introduction of this paper , on page 5.
                We prove Result 7 in Section 5 , pages 13-22.
                  In the proof of Result 7 , we use Results 2-6; see a brief
                          description below for Results 2-6.
                          In Section 2 , pages 6-8 ; we briefly describe the concepts
                                of a quadratic residue; and a quadratic non-residue
                                      modulo an odd prime number p .
          On page 8 , we State Result 1 which the Quadratic Reciprocity Law
                            in the case of two odd primes p and q.
            Using Result1 , in Section 3 , on page 9 , we prove Result 2:
                            If p is a prime number congruent  to 5 or 7 mod12 ;
                        Then  the number 3 is a quadratic non-residue of p.
          The third result , Result 3 , is stated on page 2 , and proved in
                        Section 4 , pages 10-12. Here is Result3:
                        Let a and b be relatively prime positive integers.
                          And let  d= g.c.d(a+b , a^2 - ab + b^2)  . Then:
                        (i) If a+b is not divisible by 3 ;  d=1.
                        (ii) If a+b is divisible by 3 ,  d=3 ; and in fact , a^2 -ab + b^2
                                  is exactly divisible by 3.
            Now , let us say a few words about Results 4 , 5 , 6. They are all
                        well known and stated in the introduction without proof.
            1) Result 4 : It states that if an integer n is not divisible by an odd
                          prime p ; then n has a multiplicative inverse modulo p.
            2) Result5: If the product of two relatively prime positive integers
                      is a perfect square; then each of the two integers must be
                                  a perfect square.
            3) Result 6: A quadratic trinomial with integer coefficients has
                                      a rational root , and therefore two rational roots;
                    If and only if , its discriminant is a perfect square.

There are now well-established examples of carriers and pores which facilitate the transfer of ions across thin lipid membranes. In the absence of such agents, lipid bilayer membranes are extremely impermeable to the common inorganic ions. Thus, the conductance of a pure lecithin + decane or glyceryl mono-oleate + decane membrane in M/10 NaCl is less than10−9Ω −1 cm−2. However, on the addition of small lipid-soluble molecules such as valinomycin, or surface-active polypeptides such as gramicidin A, the conductance may become so high (> 10−1 ω−l cm−2) that the resistance of the membrane merges into that of the aqueous phase. This review is concerned with the extent to which we now understand how these added substances transfer ions across lipid membranes. Attention has been concentrated on the simpler systems, i.e. the lipid-soluble ions, the 1–1 carriets, a simple pore and, with some loss of simplicity, a substance which prodeces interacting pores. Only molecules of known primary structure are discussed.