Numerical Solution with Non-Polynomial Cubic Spline Technique of Order Four Homogeneous Parabolic Partial Differential Equations

An innovative technique of NPCS are being used in engineering, computer sciences and natural sciences field to solve PDEs and ODEs Problems. There are many problems not having exact solution or not much stable and convergent exact solution, to solve such problem one apply different approximation, iterative and many other methods. The developed technique is one of them and implemented on some homogeneous parabolic PDEs of different dimensions and getting results will compare with exact solution and one other existing method, by tabular and graphically as well. Graphs and Mathematical result are found by using MATHEMATICA. Copyright(c) The Authors

Easing COVID-19 lockdown measures while protecting the older restricts the deaths to the level of the full lockdown

Guided by a rigorous mathematical result, we have earlier introduced a numerical algorithm, which using as input the cumulative number of deaths caused by COVID-19, can estimate the effect of easing of the lockdown conditions. Applying this algorithm to data from Greece, we extend it to the case of two subpopulations, namely, those consisting of individuals below and above 40 years of age. After supplementing the Greek data for deaths with the data for the number of individuals reported to be infected by SARS-CoV-2, we estimated the effect on deaths and infections in the case that the easing of the lockdown measures is different for these two subpopulations. We found that if the lockdown measures are partially eased only for the young subpopulation, then the effect on deaths and infections is small. However, if the easing is substantial for the older population, this effect may be catastrophic.

‘PARALLEL PROPORTIONS’ IN J. S. BACH'S MUSIC

ABSTRACTRecent studies propose that J. S. Bach established ‘parallel proportions’ in his music – ratios of the lengths of movements or of pieces in a collection intended to reflect the perfection of divine creation. Before we assign meaning to the number of bars in a work, we need to understand the mathematical and musical basis of the claim.First we need to decide what a ‘bar’ is and what constitutes a ‘movement’. We have explicit evidence from Bach on these points for Bach's 1733 Dresden Missa, and his own tallies do not agree with those in the theory. There are many ways to count, and the numbers of movements or bars are analytical results dependent on choices by the analyst, not objective data.Next, chance turns out to play an enormous role in ‘parallel proportions’. Under certain constraints almost any set of random numbers that adds up to an even total can be partitioned to show a proportion, with likelihoods better than ninety-five per cent in sets that resemble the Missa. These relationships are properties of numbers, not musical works. We thus need to ask whether any apparent proportion is the result of Bach's design or is simply a statistically inevitable result, and the answer is clearly the latter. For pieces or sets with fewer movements the odds are less overwhelming, but the subjective nature of counting and the possibility of silently choosing from among many possibilities make even these results questionable.Theories about the number of bars in Bach's music and possible meanings are interpretative, not factual, and thus resistant to absolute disproof. But a mathematical result of the kind claimed for ‘parallel proportions’ is essentially assured even for random sets of numbers, and that makes it all but impossible to label such relationships as intentional and meaningful.

Defects in the 3-dimensional toric code model form a braided fusion 2-category

It was well known that there are e-particles and m-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ2 topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.

A Study on Misconception of Using Brackets in Arithmetic Expression

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and algebra. If the bracket is not used properly, the value of the mathematical result is completely changed. The concept of this bracket is inserted into the students while learning school-based mathematics. So at the beginning of the bracket learning process, school-based textbooks, curriculum, and teachers are of great importance. The methodology of the proposed study is based on the document-based analysis. This study employed including studying international and national journals, library consultation, expert opinion, online journals, periodical, newspapers, and documents. Finally, the researcher suggested the importance, precaution, and effectiveness of using brackets in arithmetic.

Penerapan Pembelajaran Think Talk Write Untuk Meningkatkan Hasil Belajar Matematika

This study aims to improve the learning process and the student’s mathematical result by applying Think-Talk-Write strategy in cooperative learning. The research subject were 34 students of class VIII1 SMPN 12 Pekanbaru. This study was conducted in the odd semester of the academic year 2019/2020. This research is Classromm Action Research with two cycles and each of cycle has four stages: planning, implementation, observation, and reflection. Data in this research are teacher and student activity sheets and student’s mathematical result data. The research instuments consists of learning device (Syllabus, Lesson Plans, and Student Activity Sheets) and instruments for data collecting (teacher and students observation sheet and mathematics learning outcome test). The data analysis technique used is descriptive narrative analysis which is done by describing the data collected on the observation sheet. Based on analysis of teacher and student activity sheets was obtained that implementation of learning process on cycle II better than cycle I. The results of this research showed an increasing the number of students who reach the Minimum Completeness Criteria from the base score to cycle I and cycle II. The number of students who reached Minimum Competeness Criteria on the base score was 8 person, in cycle I was 17 person and in cycle II was 27 person. Results of this research indicates that the implementation of Think-Talk-Write strategy in cooperative learning to improve the learning process and improve the student’s mathematics result at class VIII1 SMPN 12 Pekanbaru.

Why Aggregate Using Weighted Averages?

This chapter defends the claim that we should aggregate an individual’s different utility functions at different times by taking a weighted average of them. It introduces the Principle of Minimal Mutilation, which says that an aggregate of a collection of attitudes should lie as close as possible to the attitudes it aggregates. By giving a mathematically precise account of the distance between different utility functions, the chapter appeals to a mathematical result to show that only weighted averages do this. It then defends the practice of taking weighted averages in the case of credences against objections due to Elkin & Wheeler (2016) ‘Resolving Peer Disagreements Through Imprecise Probabilities’, Noûs, May, among others.

Modified signomial geometric programming (MSGP) and its applications

A "signomial" is a mathematical function, contains one or more independent variables. Richard J. Duffin and Elmor L. Peterson introduced the term "signomial". Signomial geometric programming (SGP) optimization technique often provides a much better mathematical result of real-world nonlinear optimization problems. In this research paper, we have proposed unconstrained and constrained signomial geometric programming (SGP) problem with positive or negative integral degree of difficulty. Here a modified form of signomial geometric programming (MSGP) has been developed and some theorems have been derived. Finally, these are illustrated by proper examples and applications.

On Insolvability of the 4-th Hilbert Problem for Hyperbolic Geometries

The article proves the insolvability of the 4-th Hilbert Problem for hyperbolic geometries. It has been hypothesized that this fundamental mathematical result (the insolvability of the 4-th Hilbert Problem) holds for other types of non-Euclidean geometry (geometry of Riemann (elliptic geometry), non-Archimedean geometry, and Minkowski geometry). The ancient Golden Section, described in Euclid’s Elements (Proposition II.11) and the following from it Mathematics of Harmony, as a new direction in geometry, are the main mathematical apparatus for this fundamental result. By the way, this solution is reminiscent of the insolvability of the 10-th Hilbert Problem for Diophantine equations in integers. This outstanding mathematical result was obtained by the talented Russian mathematician Yuri Matiyasevich in 1970, by using Fibonacci numbers, introduced in 1202 by the famous Italian mathematician Leonardo from Pisa (by the nickname Fibonacci), and the new theorems in Fibonacci numbers theory, proved by the outstanding Russian mathematician Nikolay Vorobyev and described by him in the third edition of his book “Fibonacci numbers”.

Alarming Dangerous Situation by Air Pollution-I

Day by day increasing air pollution is creating serious problem in our life. This pollution affects all living things. There are so many reasons for air pollution. Since air pollution is one kind among various types of pollution but it affects directly to all human kinds. The air pollution produced by automobiles makes tremendous harmful effects on the health of peoples and environment. In this paper the mathematical result for amount of production of CO2 by burning of petrol from 2-Wheelers is elaborated.