Scientific and Practical Approaches to Improving Noise Muffler Designs of Piston Internal Combustion Engines Based on Theory of Numbers

A methodological method based on the use of the theory of preferred numbers has been proposed in order to improve the most important parameters of the working bodies of noise mufflers. As a result of many years of scientific research, the authors have established a previously unknown theoretical relationship between the main series of preferred numbers, golden ratio and Fibonacci series numbers. A new direction in the development of number theory has been considered in the paper, its classification has been compiled, including the geometric theory of numbers, preferred numbers, containing a new basic series of preferred numbers using the Fibonacci sequence. New formulas have been obtained to determine the denominators of geometric progressions for the series of preferred numbers and the area of a circle. Determining the area of a circle using the new formula allows to get more accurate values. A new formula for determining the circumference of a circle has also been derived. The designs of perforated partitions have been developed, in which the laws of the new basic series of preferred numbers are used. Determining the area of a circle using the new formula allows you to get more accurate values. A new formula for determining the circumference of a circle is also obtained. The designs of perforated partitions have been developed, in which the regularities of the new basic series of preferred numbers have been used. A calculated substantiation of the main geometric and structural dimensions of noise mufflers is given using a mathematical model of a perforated golden partition and new basic series of preferred numbers, which allow to obtain a noise muffler design that has the lowest possible aerodynamic resistance with the maximum possible reduction in the noise level of exhaust gases from internal combustion engines. An innovative model of a noise muffler for reciprocating internal combustion engines with improved hydraulic and acoustic characteristics based on the theory of numbers is proposed in the paper. The theory of preferred numbers applies to any technical device.

Srinivas Ramanujan: An Indigenous Mathematician

The paper undertaken for the deliberation of International stature on December 22, 2020 rivets attention on the topic of THE CONTRIBUTION OF RAMANUJAN in the arena of MATHEMATICS. He is remembered for India’s greatest mathematical genii. He made significant contribution to the analytical theory of numbers elliptical functions, continued fractions and infinite series. Ramanujan left a slew of unpublished note books enfolding theorems that future generation of mathematical world have been exploring continuously. He is an icon of a self-studied, self learnt, self-taught mathematical genius who is a living legend and ennobling soul for the posterity. He is known as child prodigy. Owing to his ingenuous acumen and surprising accomplishments in the field of Mathematics, Indian govt. decided to celebrate his birthday 22nd December as National Mathematics Day.

ON THE METHODOLOGY APPLICATION OF MODERN COMPUTING TECHNOLOGIES IN STUDYING THE THEORY OF NUMBERS

Обсуждаются проблемы, связанные с компьютерным поиском псевдопростых чисел. Предлагаются новые машинные способы быстрого поиска псевдопростых чисел Кармайкла-Черника с использованием пакета символьных математических вычислений Maple. The problems associated with the computer search for pseudo-simple numbers are discussed. New machine methods are proposed to quickly find Carmichael-Chernick numbers using the Maple symbolic mathematical computation package.

Analisis Penguasaan Objek Matematika dalam Penerapan Lesson Study (Kajian Pada 3 Mahasiswa PIPM Angkatan X Semester Ganjil T.A 2017/2018 di Prodi S2 Pendidikan Matematika FKIP Universitas Bengkulu)

Penelitian ini bertujuan untuk mengidentifikasi penguasaan objek langsung dan tidak langsung dalam 2 mata pelajaran matematika kepada 3 siswa yang mengikuti Praktek Inovasi Pembelajaran Matematika (PIPM) Angkatan X Semester Ganjil TA TA 2017/2018 Prodi S2 Pendidikan Matematika Universitas FKIP Universitas Muhammadiyah Malang Bengkulu, dan faktor-faktor yang mempengaruhinya. Sampel penelitian ini adalah 3 siswa yang mengikuti Praktek Inovasi Pembelajaran Matematika (PIPM) bersama Pamong Drs.M.Fachruddin.S, MPd. Hasil penelitian menunjukkan bahwa objek langsung pada 2 mata pelajaran matematika (Teori Bilangan dan Capita Selekta Matematika tingkat Pendidikan Dasar) yang terdiri dari penguasaan konsep, operasi, dan prinsip matematika dikategorikan sangat baik. Demikian pula penguasaan objek tidak langsung dalam dua mata pelajaran matematika (Teori Bilangan dan Kapita Selekta Matematika tingkat Pendidikan Dasar) yang meliputi kemampuan pemecahan masalah dan kemampuan penalaran ke dalam kategori tinggi. Ada tiga faktor yang menyebabkan penguasaan objek matematika, yaitu (1) kualifikasi dan kompetensi guru, (2) kualitas pembelajaran / perkuliahan, dan (3) budaya belajar siswa. This study aims to identify the direct and indirect object mastery in 2 mathematics courses in the application of lesson study on 3 students who follow the Practice of Mathematics Learning Innovation (PIPM) Force X Odd Semester FY 2017/2018 Prodi S2 Mathematics Education FKIP University of Bengkulu, and the factors that influence it. The sample of this research is 3 students who follow the Practice of Innovation of Mathematics Learning (PIPM) with Pamong Drs.M.Fachruddin.S, MPd. The result of the research shows that the direct object in 2 mathematics subjects (Theory of Numbers and Capita Selekta Matematika level of Basic Education) consisting of mastery of concept, operation, and mathematics principle is categorized very good. Similarly, the mastery of indirect objects in two mathematics courses (Theory of Numbers and Kapita Selekta Matematika level of Basic Education) which includes problem-solving ability and reasoning ability into high category. There are three factors causing the mastery of mathematical objects, namely (1) qualification and competence of teachers, (2) the quality of learning / lectures and (3) student learning culture.

The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡

In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics.

Joseph Melia’s nominalism and the indexing theory of numbers

According to the Quine-Putnam indispensability argument, we are committed to all the entities that are indispensable to our best scientific theory. John Melia argues contra Quine-Putnam by claiming that even though such entities as numbers are indispensable to our best science, there is reason to deny their existence. In order to defend Melia?s theory from criticism put forth by Mark Colyvan, who demands that Melia provide a nominalistically acceptable paraphrase of our best scientific theory, supporters of this view have argued for the stronger claim that numbers are not indispensable. They all claim that numbers have an indexing role in the scientific explanation. In this article, I will consider some of the arguments for the indexing theory and point out its inadequacies.

Generating relations and multivariable Aleph-function

Srivastava and Panda have studied the simple and multiple generating relations concerning the multivariable H-function. The aim of this paper is to derive the various classes of simple and multiple generating relations involving the multivariable Aleph-function. The generating function is used in the theory of numbers, in physics and other fields of mathematics. We see the particular cases concerning the multivariable I-function, the Aleph-function of two variables and the I-function of two variables.