Collatz Iterative Trajectories of All Odd Numbers Attain Bounded Values

The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slope being less than 1. An odd number N that satisfies the condition of a slope less than 1 after nth Collatz iterations is defined as an n-step odd number. Through statistical analysis, it is found that after nth Collatz iterations, the iterative value of any n-step odd number N that is greater than 1 is less than N, which proves that the slope less than 1 is a sufficient and necessary condition for Collatz iteration convergence.

STATISTICAL AND COMPOSITE ANALYSIS OF RELATIONSHIP BETWEEN THE NUMBER OF CONVECTIVE CORES AND THE CHARACTERISTICS OF TBB WITHIN THE TROPICAL CYCLONE CIRCULATION AND ITS INTENSITY

Based on the data(including radius of maximum winds) from the JTWC(Joint Typhoon Warning Center),the tropical cyclones(TCs) radii of the outermost closed isobar, TCs best tracks from Shanghai Typhoon Institute and the Black Body Temperature(TBB) of the Japanese geostationary meteorological satellite M1 TR IR1, and combining13 tropical cyclones which landed in China again after visiting the island of Taiwan during the period from 2001 to2010, we analyzed the relationship between the number of convective cores within TC circulation and the intensity of TC with the method of convective-stratiform technique(CST) and statistical and composite analysis. The results are shown as follows:(1) The number of convective cores in the entire TC circulation is well corresponding with the outer spiral rainbands and the density of convective cores in the inner core area increases(decreases) generally with increasing(decreasing) TC intensity. At the same time, the number of convective cores within the outer spiral rainbands is more than that within the inner core and does not change much with the TC intensity. However, the density of convective cores within the outer spiral rainbands is lower than that within the inner core.(2) The relationship described above is sensitive to landing location to some extent but not sensitive to the structure of TC.(3) The average value of TBB in the inner core area increases(decreases) generally with increasing(decreasing) of TC intensity, which is also sensitive to landing situation to some extent. At the same time, the average value of TBB within the outer spiral rainbands is close to that within the entire TC circulation, and both of them are more than that within the inner core. However, they do not reflect TC intensity change significantly.(4) The results of statistical composite based on convective cores and TBB are complementary with each other, so a combination of both can reflect the relationship between TC rainbands and TC intensity much better.

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation （DNS） of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed. The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers （Pτ = 0.71, 1.5, and 3.0） and a shear Reynolds number （Reτ = 180）. Some typical thermal statistics, including normalized mean temperature and their fluctuations, turbulent heat fluxes, Nusselt number and so on, are analyzed. The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number. Two reasons can explain this. First, the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases, and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field. Second, the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number, and the thermal feedback of the particles to turbulence becomes weak.

Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables

We study a new family of random variables that each arise as the distribution of the maximum or minimum of a random number N of i.i.d. random variables X1, X2,…, XN, each distributed as a variable X with support on [0, 1]. The general scheme is first outlined, and several special cases are studied in detail. Wherever appropriate, we find estimates of the parameter θ in the one-parameter family in question.

A CLASS OF RANDOM NUMBER GENERATORS BASED ON WEYL SEQUENCE

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.

A Binomial Model Approach: Comparing the R0 Values of SARS-CoV-2 rRT-PCR Data from Laboratories across Northern Cyprus

Northern Cyprus has implemented relatively strict measures in the battle against the outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The measures were introduced at the beginning of the COVID-19pandemic, in order to prevent the spread of the disease. One of these measures was the use of two separate realtime reverse transcription polymerase chain reaction (rRT-PCR) tests for SARS-CoV-2 referred to as the doublescreening procedure, which was adopted following the re-opening of the sea, air and land borders for passengersafter the first lockdown. The rRT-PCR double screening procedure involved reporting a negative rRT-PCR testwhich was carried in 72 to 120 h before departure whilst presenting no known symptoms of the COVID-19and performing a second rRT-PCR test at the point of arrival. This study compares the results of SARS-CoV-2rRT-PCR tests performed on incoming flight passengers from the 1st July to 9th of September 2020 to NorthernCyprus. The rRT-PCR test results collected by the Near East University (NEU) DESAM COVID-19 laboratory werecompared with the rRT-PCR test results collected by the Ministry of Health and/or private COVID-19 laboratoriesin Northern Cyprus. This comparative study was conducted using binomial distribution. In addition, by applyingthe Susceptible-Exposed-Infected-Removed (SEIR) model to Northern Cyprus, overall basic reproduction number(R0) value of the COVID-19 was analysed for the same time period to act as a threshold for this comparison.In both the statistical and SEIR mathematical model, R0 was calculated. It was assumed that, the more similarthe R0 results of NEU DESAM COVID-19 laboratory and other laboratories were with the overall R0 value ofNorthern Cyprus, the more reliable the results would be. We calculated that the median R0 values of the NEUDESAM COVID-19 laboratory and other laboratories performing the SARS-CoV-2 rRT-PCR on air passengersduring the studied period to be 0.96 and 1.29, respectively, compared to Northern Cyprus median R0 value whichwas 0.99. The rRT-PCR screening results from the NEU DESAM COVID-19 laboratory were closely aligned withthe screening results of Northern Cyprus whereas the screening results reported by other laboratories were not in afit with the regional pattern. This study also aimed to point out the importance of the rRT-PCR screening procedure since asymptomatic positive SARS-CoV-2 cases entery to Northern Cyprus was inhibited and this prevented thespread of the disease within the population.

Clarifications for the Published Article: “A Solution to the Famous Twin’s Problem” in the APM of SCIRP at 24 September of 2019

This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.

Ideal Statistically Pre-Cauchy Triple Sequences of Fuzzy Number and Orlicz Functions

In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that x = {xijk} is ideal statistically pre-Cauchy if and only if D (xijk, xpqr) ≥ ε, i ≤ m, j ≤ n, t ≤ k}| ≥ δ} ∈I. At the same time, we have proved x = {xijk} is ideal statistically convergent to x0 if and only if . Also, some properties of these new sequence spaces are investigated.

STATISTICS OF CHINA'S TEXTILE JOURNALS

This paper deals with the number of China’s textile journals,and the distribution of journalsincluding the content,region and publishing organization.Based on investigation,the number ofjournals now probably exceeds 300,their contents cover all the textile fields,and the publishing or-ganizations with various form are all over the country.

A Theoretical Foundation for the Widely Linear Processing of Quaternion-Valued Data

In this paper, we will give a theoretical foundation for a quaternion-valued widely linear estimation framework. The estimation error obtained with the quaternion-valued widely linear estimation method is proved to be smaller than that obtained using the usual quaternion-valued linear estimation method.

Mathematical Model of the Spread of the Coronavirus Disease 2019 (COVID-19) in Burkina Faso

In this paper, we develop a mathematical model of the COVID-19 pandemic in Burkina Faso. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also the cumulative number of reported cases. We use public policies in model in order to reduce the contact rate, this allows to show how the reduction of the daily report of infectious cases goes, so we would like to draw the attention of decision makers for a rapid treatment of reported cases.

Weighted (<i>λ</i>, <i>μ</i>)-Ideal Statistical Convergence and Strongly Weighted (<i>λ</i>, <i>μ</i>)-Ideal Convergence of Double Sequences of Fuzzy Numbers

The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ, μ)-ideal statistical convergence and strongly weighted (λ, μ)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.

Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

FORMULATION OF STATISTICAL EVOLUTION OF MICROCRACKS IN SOLIDS

The paper presents a principal formulation of statistical evolution of microcracks, occurring in solids, subjected to external loading. In particular, the concept of ideal microcracks is elaborated, in order to describe the fundamental features of damage resulting from nucleation and extension of microcracks. Relevant average damage functions are also discussed.

Testing of Elliptical Symmetry

In this paper, some test statistics of skewness and kurtosis based on Projection Pursuit technique are proposed for the testing problem of elliptical symmetry of a high-dimensional distribution, the limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternatives. The asymptotic properties of Bootstrap approximation are investigated. Furthermore, for computational reasons, the Number theoretic method is used in approximation for the statistics. Several simulation experiments are performed.

STATISTICAL MECHANICS MODEL OF LIQUID BINARY ALLOY AND ITS PARAMETERS

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Minimum Quadratic Distance Methods Using Grouped Data for Parametric Families of Copulas

Minimum quadratic distance (MQD) methods are used to construct chi-square test statistics for simple and composite hypothesis for parametric families of copulas. The methods aim at grouped data which form a contingency table but by defining a rule to group the data using Quasi-Monte Carlo numbers and two marginal empirical quantiles, the methods can be extended to handle complete data. The rule implicitly defines points on the nonnegative quadrant to form quadratic distances and the similarities of the rule with the use of random cells for classical minimum chi-square methods are indicated. The methods are relatively simple to implement and might be useful for applied works in various fields such as actuarial science.

Automatic estimation and removal of noise on digital image

An spatially adaptive noise detection and removal algorithm is proposed.Under the assumption that an observed image and its additive noise have Gaussian distribution,the noise parameters are estimated with local statistics from an observed degraded image,and the parameters are used to define the constraints on the noise detection process.In addition,an adaptive low-pass filter having a variable filter window defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image.Experimental results demonstrate the capability of the proposed algorithm.

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

数智驱动的零售电商平台供应链发展研究

选取国内零售电商企业为研究对象,基于供应链视角,采用熵值法及描述性统计方法对当前数智驱动背景下零售电商平台供应链发展新格局对经济市场的辐射作用,以及国内零售电商上市公司供应链发展情况进行研究.研究结果发现,数智驱动下的零售电商企业供应链整体发展稳中求进,也证明了数智化对供应链发展具有重要的推动作用,数智驱动下的供应链仍然有发展进步空间与实际研究价值,提出电商平台供应链发展建议,对于零售电商企业具有实际参考价值.