Origin of Sexy Prime Numbers, Origin of Cousin Prime Numbers, Equations from Supposedly Prime Numbers, Origin of the Mersenne Number, Origin of the Fermat Number

We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.

The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures

This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.

Establishment of Real-Time Quantitative PCR Method for the Determination of Transposon Copy Number in Cronobacter sakazakii

[Objective] This study aimed to establish a Real-Time quantitative PCR method for the determination of transposon copy number in C. sakazakii. [ Method ] With single-copy housekeeping gene atpD as the reference gene, recombinant plasmid containing both single-copy housekeeping gene atpD and EZ-TN5 transposon was constructed; based on the established standard curves for real-time quantitative detection of atpD gene and EZ-TN5 transposon, copy number of atpD gene and EZ-TN5 transpason in three C. sakazakii mutants was detected and the ratio was calculated. [ Result] Correlation coefficients of the standard curves for real-time quantitative detection of atpD gene and EZ-TN5 transposon were 0. 999 and 0.998, respectively ; the ratios of copy number of atpD gene and EZ-TN5 transposon in three C. sakazakii mutants were 0.98, 1.17 and 0.91, respectively, which indicates that EZ-TN5 transpeson in C. sakakii mutants is a single-copy. [ Conclusion] Real-time quantitative PCR method established in this study had high availability and could replace the Southern blot method to detect the copy num- ber of EZ-TN5 transposon in different bacteria.

Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN

In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.

Prediction of Kappa Number in Eucalyptus Kraft Pulp Continuous Digester Using the Box &Jenkins Methodology

The quality of the resulting pulping continuous digesters is monitored by measuring the Kappa number, which is a reference of residual lignin. The control of the kappa number is carried out mainly in the top of the digester, therefore it is important to get some indication of this analysis beforehand. In this context, the aim of this work was to obtain a prediction model of the kappa number in advance to the laboratory results. This paper proposes a new approach using the Box & Jenkins methodology to develop a dynamic model for predicting the kappa number from a Kamyr continuous digester from an eucalyptus Kraft pulp mill in Brazil. With a database of 1500 observations over a period of 30 days of operation, some ARMA models were studied, leading to the choice of ARMA (1, 2) as the best forecasting model. After fitting the model, we performed validation with a new set of data from 30 days of operation, achieving a model of 2.7% mean absolute percent error.

Probabilistic Modelling of COVID-19 Dynamic in the Context of Madagascar

We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 (COVID-19) in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolating all suspected cases and hospitalized confirmed case, we get an epidemic model with seven compartments: susceptible (S), Exposed (E), Infected (I), Asymptomatic (A), Hospitalized (H), Cured (C) and Death (D). In addition to the classical deterministic models used in epidemiology, the stochastic model offers a natural representation of the evolution of the COVID-19 epidemic. We inferred the models with the official data provided by the COVID-19 Command Center (CCO) of Madagascar, between March and August 2020. The basic reproduction number R0 and the other parameters were estimated with a Bayesian approach. We developed an algorithm that allows having a temporal estimate of this number with confidence intervals. The estimated values are slightly lower than the international references. Generally, we were able to obtain a simple but effective model to describe the spread of the disease.

IMAGING ANALYSIS OF FREQUENCY MODULATION CONTINUOUS WAVE SYNTHETIC APERTURE RADAR IN NEAR RANGE MODE

Frequency-Modulation Continuous-Wave Synthetic Aperture Radar(FMCW SAR)has shown great potential in the applications of civil and military fields because of its easy deployment and low cost.However,most of these work and analysis are concentrated on airborne FMCW SAR,where the characteristics of the imaging geometry and signal are much similar to that of traditional pulsed-SAR.As a result,a series of test campaigns of automobile-based FMCW SAR were sponsored by Institute of Electronics,Chinese Academy of Sciences(IECAS)in the autumn of 2012.In this paper,we analyze the imaging issues of FMCW SAR in automobile mode(named as near range mode),where a vehicle is used as moving platform and a large looking angle is configured.The imaging geometry and signal properties are analyzed in detail.We emphasize the difference of the near range mode from the traditional airborne SAR mode.Based on the analysis,a focusing approach is proposed in the paper to handle the data focusing in the case.Simulation experiment and real data of automobile FMCW SAR are used to validate the analysis.

基于Theil不等系数的C-IGOWLA算子的区间组合预测模型

传统的组合预测方法通常是针对非区间数据在最优准则下来建立最优预测模型的,但实际,中在不确定环境下样本数据和预测值序列均以区间数形式给出,因此有必要研究区间组合预测模型。文章引进连续区间诱导广义有序加权对数平均算子(C-IGOWLA)的概念,以Theil不等系数作为最优准则,提出了一种新的基于Theil不等系数的C-IGOWLA算子的区间组合预测模型,并结合实例验证了模型的有效性。

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

SOME PROBLEMS IN THE Z-C-X SPACE

The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.

Strong Law of Large Numbers under an Upper Probability

Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.

An NC Algorithm for Sorting Real Numbers in <em>O</em>(nlogn/√<span style="font-size: 14px;font-weight: bold;margin-left:-2px;margin-right:2px;border-top:2px solid black;">loglogn</span>) Operations

We apply the recent important result of serial sorting of n real numbers in time to the design of a parallel algorithm for sorting real numbers in time and operations. This is the first NC algorithm known to take operations for sorting real numbers.

Identification of chloroquine resistance Pfcrt-K76T and determination of Pfmdr1-N86Y copy number by SYBR Green I qPCR

Objective:To identify prevalence of chloroquine resistance point mutation at(Pfcrt,K76T)and(Pfindr1.N86Y) copy number variation.Methods:SYBR Green I based real time PCR was used.One hundred and thirty-three samples were analyzed for(Pfcrt,K76T) and(Pfmdr1.N86Y) copy number from dried blood spot.Parasite DNA was extracted using high pure DNA preparation kit.The amplification of DNA was done by using AccuPower 2* GreenStar '' qPCR Master mix.For quantification purpose a new primer pair was designed for 178 base pair template from complete genome sequence of Plasmodium falciparum strain 3D7 at NCBI.Absolute quantification method was used to determine the Pfmdr1-N86 Y copy number variations.Standard curve was built from strain3D7 gDNA since it has single copy of Pfindr1 per haploid genome.The known positive controls with single and multi-copy number of Pfindr1 gene were included in each experiment.The copy number ratio of the samples to the standard calibrator was made to obtain the fold difference among the samples with respect to copy number variation.Results:Out of 133 samples 73(54.89%) were confirmed as mutant(Pfcrt,76T) and the remaining 60(45.11%) were genotyped as wild type(Pfcrt,K76).The(Pfindr1.N86Y) copy number variation was determined for 133 clinical samples.Out of these samples 61(45.86%)had single copy and the remaining 72(54.14%) had multi-copy numbers higher than 1.5 copies per genome.Thirty-four(25.56%) multi-copies were between 1.5 and 2.5 copies per genome while 38(28.57%) were more than 2.5 copies per genome.The minimum and maximum copies per genome were 0.474 and 4.741.respectively.Conclusions:The study showed high prevalence level and fixation of Pfcrt.76 T mutation after chloroquine withdrawal.The prevalence of Pfindr1 copy number variant suggested that the presence of modulating factor for emergence of Plasmodium falciparum strains with higher copy numbers.However,the prevalence level was not statistically significant.

A New Algorithmic Approach for Detection and Identification of Vehicle Plate Numbers

This work proposes a method for the detection and identification of parked vehicles stationed. This technique composed many algorithms for the detection, localization, segmentation, extraction and recognition of number plates in images. It is acts of a technology of image processing used to identify the vehicles by their number plates. Knowing that we work on images whose level of gray is sampled with (120×180), resulting from a base of abundant data by PSA. We present two algorithms allowing the detection of the horizontal position of the vehicle: the classical method “horizontal gradients” and our approach “symmetrical method”. In fact, a car seen from the front presents a symmetry plan and by detecting its axis, that one finds its position in the image. A phase of localization is treated using the parameter MGD (Maximum Gradient Difference) which allows locating all the segments of text per horizontal scan. A specific technique of filtering, combining the method of symmetry and the localization by the MGD allows eliminating the blocks which don’t pass by the axis of symmetry and thus find the good block containing the number plate. Once we locate the plate, we use four algorithms that must be realized in order to allow our system to identify a license plate. The first algorithm is adjusting the intensity and the contrast of the image. The second algorithm is segmenting the characters on the plate using profile method. Then extracting and resizing the characters and finally recognizing them by means of optical character recogni-tion OCR. The efficiency of these algorithms is shown using a database of 350 images for the tests. We find a rate of lo-calization of 99.6% on a basis of 350 images with a rate of false alarms (wrong block text) of 0.88% by image.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Congruences for the class numbers of real cyclic sextic number fields

LetK 6 be a real cyclic sextic number field, andK 2,K 3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh - =h (K 6)/(h(K 2)h(K 3)) are obtained. In particular, when the conductorf 6 ofK 6 is a primep, $Ch^ - \equiv B\tfrac{{p - 1}}{6}B\tfrac{{5(p - 1)}}{6}(\bmod p)$ , whereC is an explicitly given constant, andB n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.

Bounds of the Ideal Class Numbers of Real Quadratic Function Fields

The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.

The Betti Numbers of Real Toric Varieties Associated to Weyl Chambers of Type B

The authors compute the(rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes p.

转基因草莓植株cNHX1基因表达水平和拷贝数的Real Time PCR分析

分析了转cNHX1基因的草莓不同植株的外源基因表达水平和cNHX1基因的拷贝数。结果表明:不同转基因株系cNHX1基因表达水平存在差异,而且这种差异随盐胁迫时间的延长而更明显。在6个株系中,T6株系有最高和最稳定的cNHX1基因表达水平,而T2株系的表达水平最低。对转基因植株基因组cNHX1基因拷贝数的分析表明,T3、T6、T8和T14的含量相似,而与T2株系相差289%～310%,推测T3、T6、T8和T14株系为单拷贝植株,而T2株系为3拷贝株系。

Web 2.0-Comet-Continuations模式在局部放电实时监测中的应用

针对传统Web模式的实时系统具有的用户体验不理想、数据延迟高和响应速度慢等缺点,通过对Ajax技术和Web工作模式深入分析研究,采用Web 2.0、Comet、Continuations相结合的方式,结合电缆终端局部放电实时监测系统例证,将三维谱图网格化并结合div技术模拟桌面应用程序局部刷新。该模式下系统具有无闪烁、实时性高的特点,并且即使在连接大量客户端时,服务器也只需消耗较少的CPU和内存资源。