The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it ...The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.展开更多
Increasing effective panicle number per plant(EPN)is one approach to increase yield potential in rice.However,molecular mechanisms underlying EPN remain unclear.In this study,we integrated mapbased cloning and genome-...Increasing effective panicle number per plant(EPN)is one approach to increase yield potential in rice.However,molecular mechanisms underlying EPN remain unclear.In this study,we integrated mapbased cloning and genome-wide association analysis to identify the EPN4 gene,which is allelic to NARROW LEAF1(NAL1).Overexpression lines containing the Teqing allele(TQ)of EPN4 had significantly increased EPN.NIL-EPN4^(TQ) in japonica(geng)cultivar Lemont(LT)exhibited significantly improved EPN but decreased grain number and flag leaf size relative to LT.Haplotype analysis indicated that accessions with EPN4-1 had medium EPN,medium grain number,and medium grain weight,but had the highest grain yield among seven haplotypes,indicating that EPN4-1 is an elite haplotype of EPN4 for positive coordination of the three components of grain yield.Furthermore,accessions carrying the combination of EPN4-1 and haplotype GNP1-6 of GNP1 for grain number per panicle showed higher grain yield than those with other allele combinations.Therefore,pyramiding of EPN4-1 and GNP1-6 could be a preferred approach to obtain high yield potential in breeding.展开更多
An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite nu...An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.展开更多
Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , ...Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.展开更多
Some haplotypes of the sucrose synthase gene TaSus1 are associated with thousand-grain weight(TGW)in wheat(Triticum aestivum L.).However,no mutations have been identified within the gene to test this association.The e...Some haplotypes of the sucrose synthase gene TaSus1 are associated with thousand-grain weight(TGW)in wheat(Triticum aestivum L.).However,no mutations have been identified within the gene to test this association.The effects of TaSus1 on grain number per spike(GNS)also are largely unknown.Our previous genome-wide association study identified TaSus-A1 as a candidate gene controlling fertile spikelet number per spike(FSN).In the present study,we generated two independent mutants for the three TaSus1 homoeologs by CRISPR/Cas9-mediated genome editing.The triple mutants displayed lower FSN,GNS,grain number per spikelet(GNST),and TGW than wild-type plants.In 306 hexaploid wheat accessions,two single-nucleotide polymorphisms in TaSus-A1 contributed differently to GNS.Introgression of the two alleles into a wheat genetic background confirmed their effects.The alleles differed in geographical distribution among the accessions.展开更多
Background Copy number variants(CNV)hold significant functional and evolutionary importance.Numerous ongoing CNV studies aim to elucidate the etiology of human diseases and gain insights into the population structure ...Background Copy number variants(CNV)hold significant functional and evolutionary importance.Numerous ongoing CNV studies aim to elucidate the etiology of human diseases and gain insights into the population structure of livestock.High-density chips have enabled the detection of CNV with increased resolution,leading to the identification of even small CNV.This study aimed to identify CNV in local Italian chicken breeds and investigate their distribution across the genome.Results Copy number variants were mainly distributed across the first six chromosomes and primarily associated with loss type CNV.The majority of CNV in the investigated breeds were of types 0 and 1,and the minimum length of CNV was significantly larger than that reported in previous studies.Interestingly,a high proportion of the length of chromosome 16 was covered by copy number variation regions(CNVR),with the major histocompatibility complex being the likely cause.Among the genes identified within CNVR,only those present in at least five animals across breeds(n=95)were discussed to reduce the focus on redundant CNV.Some of these genes have been associated to functional traits in chickens.Notably,several CNVR on different chromosomes harbor genes related to muscle development,tissue-specific biological processes,heat stress resistance,and immune response.Quantitative trait loci(QTL)were also analyzed to investigate potential overlapping with the identified CNVR:54 out of the 95 gene-containing regions overlapped with 428 QTL associated to body weight and size,carcass characteristics,egg production,egg components,fat deposition,and feed intake.Conclusions The genomic phenomena reported in this study that can cause changes in the distribution of CNV within the genome over time and the comparison of these differences in CNVR of the local chicken breeds could help in preserving these genetic resources.展开更多
Water is the key factor limiting dryland wheat grain yield.Mulching affects crop yield and yield components by affecting soil moisture.Further research is needed to determine the relationships between yield components...Water is the key factor limiting dryland wheat grain yield.Mulching affects crop yield and yield components by affecting soil moisture.Further research is needed to determine the relationships between yield components and soil moisture with yield,and to identify the most important factor affecting grain yield under various mulching measures.A long-term 9-yearifeld experiment in the Loess Plateau of Northwest China was carried out with three treatments:no mulch (CK),plastic mulch (M_(P)) and straw mulch (M_(S)).Yield factors and soil moisture were measured,and the relationships between them were explored by correlation analysis,structural equation modeling and significance analysis.The results showed that compared with CK,the average grain yields of M_(P) and M_(S) increased by 13.0and 10.6%,respectively.The average annual grain yield of the M_(P) treatment was 134 kg ha^(–1) higher than the M_(S) treatment.There were no significant differences in yield components among the three treatments (P<0.05).Soil water storage of the M_(S) treatment was greater than the M_(P) treatment,although the differences were not statistically signifiant.Soil water storage during the summer fallow period (SWSSF) and soil water storage before sowing (SWSS) of M_(S) were significantly higher than in CK,which increased by 38.5 and 13.6%,respectively.The relationship between M_(P) and CK was not statistically significant for SWSSF,but the SWSS in M_(P) was significantly higher than in CK.In terms of soil water storage after harvest (SWSH) and water consumption in the growth period(ET),there were no signi?cant differences among the three treatments.Based on the three analysis methods,we found that spike number and ET were positively correlated with grain yield.However,the relative importance of spike number to yield was the greatest in the M_(P )and M_(S) treatments,while that of ET was the greatest in CK.Suifcient SWSSF could indirectly increase spike number and ET in the three treatments.Based on these results,mulch can improve yield and soil water storage.The most important factor affecting the grain yield of dryland wheat was spike number under mulching,and ET with CK.These findings may help us to understand the main factors influencing dryland wheat grain yield under mulching conditions compared to CK.展开更多
Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also th...Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also the accuracy of models’outputs.Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web.In this study,three aggregation methods,including taxonomic aggregation(TA),structural equivalence aggregation(SEA),and self-organizing maps(SOM),were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo(LIM-MCMC)model.Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological net-work indices.Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices.The effects of aggregation methods were driven by the differences in species aggregation principles,which will alter food web structure and function through the redistribution of energy flow.According to the results of mean absolute percentage error(MAPE)which can be applied to evaluate the accuracy of the model,we found that MAPE in food web indices will increase with the reducing trophospecies number,and MAPE in food web function indices were smaller and more stable than those in food web structure indices.Therefore,trade-off between simplifying food webs and reflecting the status of ecosystem should be con-sidered in food web studies.These findings highlight the importance of aggregation methods and trophospecies number in the analy-sis of food web simplification.This study provided a framework to explore the extent to which food web models are affected by dif-ferent species aggregation,and will provide scientific basis for the construction of food webs.展开更多
Deep neural networks perform well in image recognition,object recognition,pattern analysis,and speech recog-nition.In military applications,deep neural networks can detect equipment and recognize objects.In military e...Deep neural networks perform well in image recognition,object recognition,pattern analysis,and speech recog-nition.In military applications,deep neural networks can detect equipment and recognize objects.In military equipment,it is necessary to detect and recognize rifle management,which is an important piece of equipment,using deep neural networks.There have been no previous studies on the detection of real rifle numbers using real rifle image datasets.In this study,we propose a method for detecting and recognizing rifle numbers when rifle image data are insufficient.The proposed method was designed to improve the recognition rate of a specific dataset using data fusion and transfer learningmethods.In the proposed method,real rifle images and existing digit images are fusedas trainingdata,andthe final layer is transferredto theYolov5 algorithmmodel.The detectionand recognition performance of rifle numbers was improved and analyzed using rifle image and numerical datasets.We used actual rifle image data(K-2 rifle)and numeric image datasets,as an experimental environment.TensorFlow was used as the machine learning library.Experimental results show that the proposed method maintains 84.42% accuracy,73.54% precision,81.81% recall,and 77.46% F1-score in detecting and recognizing rifle numbers.The proposed method is effective in detecting rifle numbers.展开更多
The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper inves...The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.展开更多
In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the br...In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.展开更多
The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean ...The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>=d<sup>2</sup> with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d<sup>2</sup> is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>+d<sup>2</sup>=e<sup>2</sup> and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d<sup>2</sup>, respectively, e<sup>2</sup>.展开更多
Buildings with large open spaces in which chemicals are handled are often exposed to the risk of explosions.Computational fluid dynamics is a useful and convenient way to investigate contaminant dispersion in such lar...Buildings with large open spaces in which chemicals are handled are often exposed to the risk of explosions.Computational fluid dynamics is a useful and convenient way to investigate contaminant dispersion in such large spaces.The turbulent Schmidt number(Sct)concept has typically been used in this regard,and most studies have adopted a default value.We studied the concentration distribution for sulfur hexafluoride(SF6)assuming different emission rates and considering the effect of Sct.Then we examined the same problem for a light gas by assuming hydrogen gas(H2)as the contaminant.When SF6 was considered as the contaminant gas,a variation in the emission rate completely changed the concentration distribution.When the emission rate was low,the gravitational effect did not take place.For both low and high emission rates,an increase in Sct accelerated the transport rate of SF6.In contrast,for H2 as the contaminant gas,a larger Sct could induce a decrease in the H2 transport rate.展开更多
Biological specimens are fundamental for taxonomy and flora/fauna research.More importantly,they also play crucial roles in recording environmental impacts on morphology and behavior,which is vital for biodiversity re...Biological specimens are fundamental for taxonomy and flora/fauna research.More importantly,they also play crucial roles in recording environmental impacts on morphology and behavior,which is vital for biodiversity research and conservation.However,there are few systematic studies on the patterns and drivers of bird specimen number at regional scales.This study is the first attempt to examine the relationships between bird specimen number and species traits as well as climate niche breadth in China,aiming to answer two questions:1)how do species’temperature niche breadth and precipitation niche breadth influence specimen number?2)which trait is most associated with bird specimen number?The associations between bird specimen number and explanatory variables were examined using ordinary least squares,generalized linear models,phylogenetic generalized linear mixed models,and multiple comparisons.The results showed that Muscicapidae was the family with the highest specimen number,and Passeriformes was the order with the highest specimen number.Bird specimen number significantly increased with larger temperature niche breadth and precipitation niche breadth.Specimen number was also positively associated with geographic range size,habitat specificity,hunting vulnerability and clutch size,but negatively associated with body size.These findings suggest that future bird specimen collection should pay more attention to birds with limited ecological niches,large body sizes,and small clutch sizes.This research enhances the use of bird specimen data to study and preserve biodiversity.展开更多
This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Co...This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.展开更多
We demonstrate the photon-number resolution(PNR)capability of a 1.25 GHz gated InGaAs single-photon avalanche photodiode(APD)that is equipped with a simple,low-distortion ultra-narrowband interference circuit for the ...We demonstrate the photon-number resolution(PNR)capability of a 1.25 GHz gated InGaAs single-photon avalanche photodiode(APD)that is equipped with a simple,low-distortion ultra-narrowband interference circuit for the rejection of its background capacitive response.Through discriminating the avalanche current amplitude,we are able to resolve up to four detected photons in a single detection gate with a detection efficiency as high as 45%.The PNR capability is limited by the avalanche current saturation,and can be increased to five photons at a lower detection efficiency of 34%.The PNR capability,combined with high efficiency and low noise,will find applications in quantum information processing technique based on photonic qubits.展开更多
Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ...Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .展开更多
In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Th...In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.展开更多
Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of...Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of chromosomal copy number variations.Methods:3551 naturally conceived singleton pregnant women who underwent NIPT were included in this study.The NIPT revealed abnormalities other than sex chromosome abnormalities and trisomy 13,18,and 21.Pregnant women with chromosome copy number variations underwent genetic counseling and prenatal ultrasound examination.Interventional prenatal diagnosis and chromosome microarray analysis(CMA)were performed.The clinical phenotypes and pregnancy outcomes of different prenatal diagnoses were analyzed.Additionally,a follow-up was conducted by telephone to track fetal development after birth,at six months,and one year post-birth.Results:A total of 53 cases among 3551 cases showed chromosomal copy number variation.Interventional prenatal diagnosis was performed in 36 cases:27 cases were negative and 8 were consistent with the NIPT test results.This indicates that NIPT’s positive predictive value(PPV)in CNVs is 22.22%.Conclusion:NIPT has certain clinical significance in screening chromosome copy number variations and is expected to become a routine screening for chromosomal microdeletions and microduplications.However,further interventional prenatal diagnosis is still needed to identify fetal CNVs.展开更多
针对任务风险难度量、评估信息不确定性强等问题,提出一种Z-number和改进DS证据理论的风险评估方法。利用Z-number方法描述评估指标,得到各风险等级的初始基本概率分配(basic probability assignment,BPA);基于信度熵和皮尔逊相关系数改...针对任务风险难度量、评估信息不确定性强等问题,提出一种Z-number和改进DS证据理论的风险评估方法。利用Z-number方法描述评估指标,得到各风险等级的初始基本概率分配(basic probability assignment,BPA);基于信度熵和皮尔逊相关系数改进DS证据理论克服悖论问题进行信息融合,确定风险的最终等级;接着,基于信息融合结果引入Joussleme距离求解专家可信度。最后,以重装空投任务为例,验证本文所提风险评估方法的合理性,并对比分析不同改进DS证据理论方法得到的结果,验证所提方法的有效性和准确性。展开更多
文摘The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.
基金This work was funded by the National Key Research and Development Program of China(2023YFF1000404)the Shenzhen Basic Research and Development Key Program of China(JCYJ20200109150713553)Hainan Key Research and Development in Modern Agriculture of China(ZDYF2021Y128).
文摘Increasing effective panicle number per plant(EPN)is one approach to increase yield potential in rice.However,molecular mechanisms underlying EPN remain unclear.In this study,we integrated mapbased cloning and genome-wide association analysis to identify the EPN4 gene,which is allelic to NARROW LEAF1(NAL1).Overexpression lines containing the Teqing allele(TQ)of EPN4 had significantly increased EPN.NIL-EPN4^(TQ) in japonica(geng)cultivar Lemont(LT)exhibited significantly improved EPN but decreased grain number and flag leaf size relative to LT.Haplotype analysis indicated that accessions with EPN4-1 had medium EPN,medium grain number,and medium grain weight,but had the highest grain yield among seven haplotypes,indicating that EPN4-1 is an elite haplotype of EPN4 for positive coordination of the three components of grain yield.Furthermore,accessions carrying the combination of EPN4-1 and haplotype GNP1-6 of GNP1 for grain number per panicle showed higher grain yield than those with other allele combinations.Therefore,pyramiding of EPN4-1 and GNP1-6 could be a preferred approach to obtain high yield potential in breeding.
文摘An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.
文摘Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.
基金This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences(XDA24010104-2).
文摘Some haplotypes of the sucrose synthase gene TaSus1 are associated with thousand-grain weight(TGW)in wheat(Triticum aestivum L.).However,no mutations have been identified within the gene to test this association.The effects of TaSus1 on grain number per spike(GNS)also are largely unknown.Our previous genome-wide association study identified TaSus-A1 as a candidate gene controlling fertile spikelet number per spike(FSN).In the present study,we generated two independent mutants for the three TaSus1 homoeologs by CRISPR/Cas9-mediated genome editing.The triple mutants displayed lower FSN,GNS,grain number per spikelet(GNST),and TGW than wild-type plants.In 306 hexaploid wheat accessions,two single-nucleotide polymorphisms in TaSus-A1 contributed differently to GNS.Introgression of the two alleles into a wheat genetic background confirmed their effects.The alleles differed in geographical distribution among the accessions.
基金supported by the project“Protection of biodiversity of Italian poultry breeds—TuBAvI”,funded in the framework of the PSRN 2014–2020,submeasure 10.2“Support for sustainable conservation,use and development of genetic resources in agriculture”.
文摘Background Copy number variants(CNV)hold significant functional and evolutionary importance.Numerous ongoing CNV studies aim to elucidate the etiology of human diseases and gain insights into the population structure of livestock.High-density chips have enabled the detection of CNV with increased resolution,leading to the identification of even small CNV.This study aimed to identify CNV in local Italian chicken breeds and investigate their distribution across the genome.Results Copy number variants were mainly distributed across the first six chromosomes and primarily associated with loss type CNV.The majority of CNV in the investigated breeds were of types 0 and 1,and the minimum length of CNV was significantly larger than that reported in previous studies.Interestingly,a high proportion of the length of chromosome 16 was covered by copy number variation regions(CNVR),with the major histocompatibility complex being the likely cause.Among the genes identified within CNVR,only those present in at least five animals across breeds(n=95)were discussed to reduce the focus on redundant CNV.Some of these genes have been associated to functional traits in chickens.Notably,several CNVR on different chromosomes harbor genes related to muscle development,tissue-specific biological processes,heat stress resistance,and immune response.Quantitative trait loci(QTL)were also analyzed to investigate potential overlapping with the identified CNVR:54 out of the 95 gene-containing regions overlapped with 428 QTL associated to body weight and size,carcass characteristics,egg production,egg components,fat deposition,and feed intake.Conclusions The genomic phenomena reported in this study that can cause changes in the distribution of CNV within the genome over time and the comparison of these differences in CNVR of the local chicken breeds could help in preserving these genetic resources.
基金supported financially by the National Key Research and Development Program of China(2021YFD1900703)the National Natural Science Foundation of China(31272250)。
文摘Water is the key factor limiting dryland wheat grain yield.Mulching affects crop yield and yield components by affecting soil moisture.Further research is needed to determine the relationships between yield components and soil moisture with yield,and to identify the most important factor affecting grain yield under various mulching measures.A long-term 9-yearifeld experiment in the Loess Plateau of Northwest China was carried out with three treatments:no mulch (CK),plastic mulch (M_(P)) and straw mulch (M_(S)).Yield factors and soil moisture were measured,and the relationships between them were explored by correlation analysis,structural equation modeling and significance analysis.The results showed that compared with CK,the average grain yields of M_(P) and M_(S) increased by 13.0and 10.6%,respectively.The average annual grain yield of the M_(P) treatment was 134 kg ha^(–1) higher than the M_(S) treatment.There were no significant differences in yield components among the three treatments (P<0.05).Soil water storage of the M_(S) treatment was greater than the M_(P) treatment,although the differences were not statistically signifiant.Soil water storage during the summer fallow period (SWSSF) and soil water storage before sowing (SWSS) of M_(S) were significantly higher than in CK,which increased by 38.5 and 13.6%,respectively.The relationship between M_(P) and CK was not statistically significant for SWSSF,but the SWSS in M_(P) was significantly higher than in CK.In terms of soil water storage after harvest (SWSH) and water consumption in the growth period(ET),there were no signi?cant differences among the three treatments.Based on the three analysis methods,we found that spike number and ET were positively correlated with grain yield.However,the relative importance of spike number to yield was the greatest in the M_(P )and M_(S) treatments,while that of ET was the greatest in CK.Suifcient SWSSF could indirectly increase spike number and ET in the three treatments.Based on these results,mulch can improve yield and soil water storage.The most important factor affecting the grain yield of dryland wheat was spike number under mulching,and ET with CK.These findings may help us to understand the main factors influencing dryland wheat grain yield under mulching conditions compared to CK.
基金supported by the National Key R&D Program of China(Nos.2019YFD0901204,2019YFD 0901205).
文摘Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also the accuracy of models’outputs.Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web.In this study,three aggregation methods,including taxonomic aggregation(TA),structural equivalence aggregation(SEA),and self-organizing maps(SOM),were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo(LIM-MCMC)model.Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological net-work indices.Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices.The effects of aggregation methods were driven by the differences in species aggregation principles,which will alter food web structure and function through the redistribution of energy flow.According to the results of mean absolute percentage error(MAPE)which can be applied to evaluate the accuracy of the model,we found that MAPE in food web indices will increase with the reducing trophospecies number,and MAPE in food web function indices were smaller and more stable than those in food web structure indices.Therefore,trade-off between simplifying food webs and reflecting the status of ecosystem should be con-sidered in food web studies.These findings highlight the importance of aggregation methods and trophospecies number in the analy-sis of food web simplification.This study provided a framework to explore the extent to which food web models are affected by dif-ferent species aggregation,and will provide scientific basis for the construction of food webs.
基金supported by the Future Strategy and Technology Research Institute(RN:23-AI-04)of Korea Military Academythe Hwarang-Dae Research Institute(RN:2023B1015)of Korea Military Academy,and Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2021R1I1A1A01040308).
文摘Deep neural networks perform well in image recognition,object recognition,pattern analysis,and speech recog-nition.In military applications,deep neural networks can detect equipment and recognize objects.In military equipment,it is necessary to detect and recognize rifle management,which is an important piece of equipment,using deep neural networks.There have been no previous studies on the detection of real rifle numbers using real rifle image datasets.In this study,we propose a method for detecting and recognizing rifle numbers when rifle image data are insufficient.The proposed method was designed to improve the recognition rate of a specific dataset using data fusion and transfer learningmethods.In the proposed method,real rifle images and existing digit images are fusedas trainingdata,andthe final layer is transferredto theYolov5 algorithmmodel.The detectionand recognition performance of rifle numbers was improved and analyzed using rifle image and numerical datasets.We used actual rifle image data(K-2 rifle)and numeric image datasets,as an experimental environment.TensorFlow was used as the machine learning library.Experimental results show that the proposed method maintains 84.42% accuracy,73.54% precision,81.81% recall,and 77.46% F1-score in detecting and recognizing rifle numbers.The proposed method is effective in detecting rifle numbers.
基金funded by King Khalid University through a large group research project under Grant Number R.G.P.2/449/44.
文摘The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274046,11874094,and 12147102)Chongqing Natural Science Foundation(Grant No.CSTB2022NSCQ-JQX0018)Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003).
文摘In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.
文摘The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>=d<sup>2</sup> with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d<sup>2</sup> is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>+d<sup>2</sup>=e<sup>2</sup> and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d<sup>2</sup>, respectively, e<sup>2</sup>.
基金funded by the National Natural Science Foundation of China and the Machinery Industry Innovation Platform Construction Project of China Machinery Industry Federation,Grant Numbers 52378103 and 2019SA-10-07.
文摘Buildings with large open spaces in which chemicals are handled are often exposed to the risk of explosions.Computational fluid dynamics is a useful and convenient way to investigate contaminant dispersion in such large spaces.The turbulent Schmidt number(Sct)concept has typically been used in this regard,and most studies have adopted a default value.We studied the concentration distribution for sulfur hexafluoride(SF6)assuming different emission rates and considering the effect of Sct.Then we examined the same problem for a light gas by assuming hydrogen gas(H2)as the contaminant.When SF6 was considered as the contaminant gas,a variation in the emission rate completely changed the concentration distribution.When the emission rate was low,the gravitational effect did not take place.For both low and high emission rates,an increase in Sct accelerated the transport rate of SF6.In contrast,for H2 as the contaminant gas,a larger Sct could induce a decrease in the H2 transport rate.
基金supported by the Natural Science Foundation of Inner Mongolia,China(2023JQ01)the National Key R&D Program of China(2019YFA0607103)+2 种基金the Central Government Guides Local Science and Technology Development Fund Projects(2022ZY0224)the Open Project Program of’Ministry of Education Key Laboratory of Ecology and Resources Use of the Mongolian Plateau(KF2023003)’the Major Science and Technology Project of Inner Mongolia Autonomous Region:Monitoring,Assessment and Early Warning Technology Research of Biodiversity in Inner Mongolia(2021ZD0011)。
文摘Biological specimens are fundamental for taxonomy and flora/fauna research.More importantly,they also play crucial roles in recording environmental impacts on morphology and behavior,which is vital for biodiversity research and conservation.However,there are few systematic studies on the patterns and drivers of bird specimen number at regional scales.This study is the first attempt to examine the relationships between bird specimen number and species traits as well as climate niche breadth in China,aiming to answer two questions:1)how do species’temperature niche breadth and precipitation niche breadth influence specimen number?2)which trait is most associated with bird specimen number?The associations between bird specimen number and explanatory variables were examined using ordinary least squares,generalized linear models,phylogenetic generalized linear mixed models,and multiple comparisons.The results showed that Muscicapidae was the family with the highest specimen number,and Passeriformes was the order with the highest specimen number.Bird specimen number significantly increased with larger temperature niche breadth and precipitation niche breadth.Specimen number was also positively associated with geographic range size,habitat specificity,hunting vulnerability and clutch size,but negatively associated with body size.These findings suggest that future bird specimen collection should pay more attention to birds with limited ecological niches,large body sizes,and small clutch sizes.This research enhances the use of bird specimen data to study and preserve biodiversity.
文摘This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.
基金supported by the National Natural Science Foundation of China(62250710162 and 12274406)the National Key Research and Development Program of China(2022YFA1405100).
文摘We demonstrate the photon-number resolution(PNR)capability of a 1.25 GHz gated InGaAs single-photon avalanche photodiode(APD)that is equipped with a simple,low-distortion ultra-narrowband interference circuit for the rejection of its background capacitive response.Through discriminating the avalanche current amplitude,we are able to resolve up to four detected photons in a single detection gate with a detection efficiency as high as 45%.The PNR capability is limited by the avalanche current saturation,and can be increased to five photons at a lower detection efficiency of 34%.The PNR capability,combined with high efficiency and low noise,will find applications in quantum information processing technique based on photonic qubits.
文摘Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .
文摘In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.
基金Dongguan City Social Development Project(Project number:20161081101023)。
文摘Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of chromosomal copy number variations.Methods:3551 naturally conceived singleton pregnant women who underwent NIPT were included in this study.The NIPT revealed abnormalities other than sex chromosome abnormalities and trisomy 13,18,and 21.Pregnant women with chromosome copy number variations underwent genetic counseling and prenatal ultrasound examination.Interventional prenatal diagnosis and chromosome microarray analysis(CMA)were performed.The clinical phenotypes and pregnancy outcomes of different prenatal diagnoses were analyzed.Additionally,a follow-up was conducted by telephone to track fetal development after birth,at six months,and one year post-birth.Results:A total of 53 cases among 3551 cases showed chromosomal copy number variation.Interventional prenatal diagnosis was performed in 36 cases:27 cases were negative and 8 were consistent with the NIPT test results.This indicates that NIPT’s positive predictive value(PPV)in CNVs is 22.22%.Conclusion:NIPT has certain clinical significance in screening chromosome copy number variations and is expected to become a routine screening for chromosomal microdeletions and microduplications.However,further interventional prenatal diagnosis is still needed to identify fetal CNVs.
文摘针对任务风险难度量、评估信息不确定性强等问题,提出一种Z-number和改进DS证据理论的风险评估方法。利用Z-number方法描述评估指标,得到各风险等级的初始基本概率分配(basic probability assignment,BPA);基于信度熵和皮尔逊相关系数改进DS证据理论克服悖论问题进行信息融合,确定风险的最终等级;接着,基于信息融合结果引入Joussleme距离求解专家可信度。最后,以重装空投任务为例,验证本文所提风险评估方法的合理性,并对比分析不同改进DS证据理论方法得到的结果,验证所提方法的有效性和准确性。
