scholarly journals The Maximal Prime Gaps Supremum and the Firoozbakht's Hypothesis No 30

2020 ◽  
Author(s):  
Jan Feliksiak
Keyword(s):  
Upper Bound ◽  
Prime Numbers ◽  
Heuristic Argument ◽  
Mathematical Problems ◽  
The Subject ◽  
Prime Gaps ◽  
Theoretical Results

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

STUDI DESKRIPTIF MINAT CALON GURU SEKOLAH DASAR TERHADAP PENGGUNAAN ALAT PERAGA MATEMATIKA SETELAH PERKULIAHAN MEDIA DAN MODEL PEMBELAJARAN MATEMATIKA SD

2015 ◽  
Vol 8 (1) ◽  
pp. 19
Author(s):  
Isna Rafianti ◽  
Etika Khaerunnisa
Keyword(s):  
Elementary Teachers ◽  
Elementary Mathematics ◽  
Mathematics Learning ◽  
Learning Model ◽  
Prospective Elementary Teachers ◽  
Descriptive Research ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
The Subject ◽  
Object Of Study

This research is motivated by the lack of interest of teachers in the use of props in the process of learning mathematics in elementary school. In accordance with the demands of the curriculum in 2013 and supported by the developed learning theory, learning mathematics is abstract object of study, students need an intermediary that props math-ematics, so that students can more easily understand the concepts that will be pre-sented, and in the end it can deliver students to solve mathematical problems, not only that proposed by the teacher but also the problems in life. The purpose of this study was to determine the interest of prospective elementary teachers on the use of props mathematics after getting lectures media and elementary mathematics learning model. By knowing the interest of prospective elementary teachers will be developed further realization of the state of the subject being studied. The method used is descriptive research, then the instruments used were questionnaires and interviews. The results of this study stated that the interest of prospective elementary teachers on the use of props after attending lectures media and elementary mathematics learning model is high over-all with a percentage of 76.70%.Keywords : Interest, Props Mathematics

PENGARUH METODE EKSPOSITORI TERHADAP PEMAHAMAN KONSEP MATEMATIKA MAHASISWA PGSD

2018 ◽  
Author(s):  
Daswarman Daswarman
Keyword(s):  
Research Design ◽  
Experimental Research ◽  
Mathematical Abilities ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
The Subject

The aim of learning mathematics in universities is to improve students' mathematical abilities. One of the important mathematical abilities of students is understanding the concept. With an understanding of the concept, students will easily solve mathematical problems. This research is an experimental research design with One Group Pretest-Posttest Design. In the design of this study, researchers used one class as the subject of research. Before being given treatment, the pretest is first performed, then given treatment within a certain period, then given a posttest. The results showed that there was an increase in students' understanding of the concept after being given the application of the expository method.

scholarly journals PROFIL PENALARAN ANALOGI SISWA DALAM PEMECAHAN MASALAH MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

MATHEdunesa ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 35-39
Author(s):  
Tri Wilfi Iqlima ◽  
Susanah Susanah
Keyword(s):  
Descriptive Study ◽  
Qualitative Approach ◽  
Mathematical Ability ◽  
Target Problem ◽  
Mathematical Abilities ◽  
School Year ◽  
Mapping Process ◽  
Mathematical Problems ◽  
The Subject ◽  
The Difference

Analogy reasoning is the process of thinking logically and analytically in drawing conclusions based on the similarities between the two things being compared. The purpose of this study is to describe the analogy reasoning of students in solving mathematical problems in terms of high, medium, and low mathematical abilities. This research is a descriptive study with a qualitative approach. Data collection was carried out in class IX-H of SMP Negeri 5 Surabaya in the 2019/2020 school year by 33 students and each subject was selected for each category of mathematical ability. The results of the analysis of Problem Solving Tests and interviews show that students with high, medium, and low mathematical abilities mention information that is known and what is asked for logical reasons on the source and target problem, and explain the relations between the information. This indicates that each subject has an encoding process. Each subject also mentions and explains the concepts used to solve source problems, which means each subject has an inferring process. The difference is, subjects with high mathematical ability mention the same concepts between the source problem and the target problem and explain the concepts used to solve the target problem, then students can complete the target problem. This means that the subject is doing two other processes, namely mapping and applying. Subjects with medium mathematical abilities are mentioning the same concept between the source problem and the target problem but cannot explain the concept used in the target problem. However, the subject only did one of the two indicators in the mapping process, so the analogy reasoning process carried out by the subject was encoding and inferring. While students with low mathematical abilities are stopped in the encoding and inferring processes. Keywords: Analogy Reasoning, Mathematical Abilitiy

THE ALLOCATION OF CUSTOMERS IN A DISCRETE-TIME MULTI-SERVER QUEUEING SYSTEM

2010 ◽  
Vol 27 (06) ◽  
pp. 649-667 ◽  
Author(s):  
WEI SUN ◽  
NAISHUO TIAN ◽  
SHIYONG LI
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Allocation Problem ◽  
Optimal Outcome ◽  
The Subject ◽  
Multi Server ◽  
Theoretical Results

This paper, analyzes the allocation problem of customers in a discrete-time multi-server queueing system and considers two criteria for routing customers' selections: equilibrium and social optimization. As far as we know, there is no literature concerning the discrete-time multi-server models on the subject of equilibrium behaviors of customers and servers. Comparing the results of customers' distribution at the servers under the two criteria, we show that the servers used in equilibrium are no more than those used in the socially optimal outcome, that is, the individual's decision deviates from the socially preferred one. Furthermore, we also clearly show the mutative trend of several important performance measures for various values of arrival rate numerically to verify the theoretical results.

On the Iwasawa λ-invariant of the cyclotomic ℤ2-extension of ℚ(pq) and the 2-part of the class number of ℚ(pq,2 + 2)

2020 ◽  
pp. 1-28
Author(s):  
Naoki Kumakawa
Keyword(s):  
Upper Bound ◽  
Class Number ◽  
Number Fields ◽  
Prime Numbers

In this paper, we study the Iwasawa [Formula: see text]-invariant of the cyclotomic [Formula: see text]-extension of [Formula: see text], where [Formula: see text] are distinct odd prime numbers satisfying certain arithmetic conditions. Moreover, we obtain an upper bound of the [Formula: see text]-part of the class number of certain quartic number fields by calculating the Sinnott index explicitly.

scholarly journals The Study of the Theoretical Size and Node Probability of the Loop Cutset in Bayesian Networks

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1079 ◽  
Author(s):  
Jie Wei ◽  
Yufeng Nie ◽  
Wenxian Xie
Keyword(s):  
Probability Theory ◽  
Graph Theory ◽  
Bayesian Inference ◽  
Bayesian Networks ◽  
Numerical Simulations ◽  
Complete Graph ◽  
Upper Bound ◽  
Numerical Algorithms ◽  
Theoretical Research ◽  
Theoretical Results

Pearl’s conditioning method is one of the basic algorithms of Bayesian inference, and the loop cutset is crucial for the implementation of conditioning. There are many numerical algorithms for solving the loop cutset, but theoretical research on the characteristics of the loop cutset is lacking. In this paper, theoretical insights into the size and node probability of the loop cutset are obtained based on graph theory and probability theory. It is proven that when the loop cutset in a p-complete graph has a size of p − 2 , the upper bound of the size can be determined by the number of nodes. Furthermore, the probability that a node belongs to the loop cutset is proven to be positively correlated with its degree. Numerical simulations show that the application of the theoretical results can facilitate the prediction and verification of the loop cutset problem. This work is helpful in evaluating the performance of Bayesian networks.

Thermodynamics of Non-Dilute Polymer Solutions

1967 ◽  
Vol 40 (1) ◽  
pp. 1-35 ◽  
Author(s):  
D. Patterson
Keyword(s):  
Polymer Solution ◽  
Polymer Solutions ◽  
Solution Thermodynamics ◽  
General Interest ◽  
Chain Molecules ◽  
Dilute Polymer Solutions ◽  
Mathematical Problems ◽  
The Subject ◽  
Further Development ◽  
Θ Point

Abstract An excellent new text, “Macromolecules in Solution,” by A. Morawetz emphasizes advances in polymer solution thermodynamics since publication of standard texts such as those of Tompa and Flory. Detailed development of the subject from 1950 may be followed in articles on polymers in Annual Reviews of Physical Chemistry, and particularly in the articles appearing every three years specially devoted to solution properties: Flory and Krigbaum (1951), Wall and Hiller (1954), Hermans (1957), Casassa (1960) and Hughes and von Frankenberg (1963). The articles on solutions of non-electrolytes are, of course, always of general interest and often deal directly with polymer solutions or mixtures of chain molecules. Because of this very satisfactory situation, the author has decided that the best thing is to review in more detail the single topic which is most interesting to him. This is the thermodynamics of non-dilute solutions where it is usually supposed that the quasi-lattice theories of the 40's are quite adequate at concentrations greater than about 10 per cent. For fifteen years or so, interest has centered on very dilute polymer solutions and the dimensions of isolated polymer molecules, particularly at temperatures near the θ point. Increasingly difficult mathematical problems have followed the McMillan-Mayer comparison of solutions and imperfect gases first applied to polymer solutions by Zimm and Stockmayer. Polymer solution thermodynamics seems to have moved far beyond the intuitive questions of Meyer as to why a polymer solution differs from an ideal solution or from a mixture of a monomeric solute and solvent. However, certain results, apparently not very widely known, make one feel that such qualitative questions are not out of date and that the thermodynamics of concentrated polymer solutions may be open to much further development.

scholarly journals Contact lines over random topographical substrates. Part 1. Statics

2011 ◽  
Vol 672 ◽  
pp. 358-383 ◽  
Author(s):  
NIKOS SAVVA ◽  
GRIGORIOS A. PAVLIOTIS ◽  
SERAFIM KALLIADASIS
Keyword(s):  
Numerical Experiments ◽  
Random Variable ◽  
Contact Angles ◽  
Contact Lines ◽  
Substrate Roughness ◽  
Random Functions ◽  
Flat Substrate ◽  
The Subject ◽  
Influence Of Substrate ◽  
Theoretical Results

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

scholarly journals NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS

2014 ◽  
Vol 33 (2) ◽  
pp. 83 ◽  
Author(s):  
Federico Camerlenghi ◽  
Vincenzo Capasso ◽  
Elena Villa
Keyword(s):  
Numerical Experiments ◽  
Random Sets ◽  
Density Estimator ◽  
Absolutely Continuous ◽  
Minkowski Content ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Spatially Inhomogeneous ◽  
The Subject ◽  
Theoretical Results

Many real phenomena may be modelled as random closed sets in ℝd, of different Hausdorff dimensions. The problem of the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous, random sets with Hausdorff dimension n < d, has been the subject of extended mathematical analysis by the authors. In particular, two different kinds of estimators have been recently proposed, the first one is based on the notion of Minkowski content, the second one is a kernel-type estimator generalizing the well-known kernel density estimator for random variables. The specific aim of the present paper is to validate the theoretical results on statistical properties of those estimators by numerical experiments. We provide a set of simulations which illustrates their valuable properties via typical examples of lower dimensional random sets.

scholarly journals An S-type upper bound for the largest singular value of nonnegative rectangular tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 925-933 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Upper Bound ◽  
Singular Value ◽  
Numerical Examples ◽  
Rectangular Tensors ◽  
Theoretical Results

AbstractAn S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.

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