Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

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.

Preliminary Identification of a Prime Number Other Than 2 and 3, the Origin of Twin Prime Numbers, the Structure of the Chain of Prime Numbers and the Set of Prime Numbers Less Than a Given Integer

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 Esp. 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 Enp. 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 Ep. 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.

A novel Effective Panicle Number per Plant 4 haplotype enhances grain yield by coordinating panicle number and grain number in rice

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.

How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)

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.

Binding Number and Fractional k-Factors of Graphs

In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.

The first factor affecting dryland winter wheat grain yield under various mulching measures: Spike number

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.

On Perron’s Formula and the Prime Numbers

The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.

Impacts of Aggregation Methods and Trophospecies Number on the Structure and Function of Marine Food Webs

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.

Analysis of pseudo-random number generators in QMC-SSE method

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.

Three- and Four-Dimensional Generalized Pythagorean Numbers

The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a2+b2=c2 with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a2+b2+c2=d2 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 d2 is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a2+b2+c2+d2=e2 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 d2, respectively, e2.

The Quantum Microverse: A Prime Number Framework for Understanding the Universe

This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.

High donor-number and low content electrolyte additive for stabilizing zinc metal anode

The aqueous zinc ion batteries(AZIBs)are thought as promising competitors for electrochemical energy storage,though their wide application is curbed by the uncontrollable dendrite growth and gas evolution side reactions.Herein,to stabilize both zinc anodes and water molecules,we developed a modified electrolyte by adding a trace amount of N,N-diethylformanmide(DEF)into the ZnSO_(4)electrolyte for the first time in zinc ion batteries.The effectiveness of DEF is predicted by the comparison of donor number and its preferential adsorption behavior on the zinc anode is further demonstrated by several spectroscopy characterizations,electrochemical methods,and molecular dynamics simulation.The modified electrolyte with 5%v.t.DEF content can ensure a stable cycling life longer than 3400 h of Zn‖Zn symmetric cells and an ultra-reversible Zn stripping/plating process with a high coulombic efficiency of 99.7%.The Zn‖VO_(2)full cell maintains a capacity retention of 83.5%and a 104 mA h g^(-1)mass capacity after 1000cycles.This work provides insights into the role of interfacial adsorption behavior and the donor number of additive molecules in designing low-content and effective aqueous electrolytes.

Distribution and Relation of Primes with Tesla Numbers 3, 6, and 9

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.

Bird specimen number linked with species trait and climate niche breadth

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.

GHz photon-number resolving detection with high detection efficiency and low noise by ultra-narrowband interference circuits

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.

A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

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.

OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

Computation of Stiffness and Damping Derivatives of an Ogive in a Limiting Case of Mach Number and Specific Heat Ratio

This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.

Relationship Between Gene-Phenotype and Clinical Manifestations of Chromosomal Copy Number Variations Indicated by Non-Invasive Prenatal Testing

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.

Defogging computational ghost imaging via eliminating photon number fluctuation and a cycle generative adversarial network

Imaging through fluctuating scattering media such as fog is of challenge since it seriously degrades the image quality.We investigate how the image quality of computational ghost imaging is reduced by fluctuating fog and how to obtain a high-quality defogging ghost image. We show theoretically and experimentally that the photon number fluctuations introduced by fluctuating fog is the reason for ghost image degradation. An algorithm is proposed to process the signals collected by the computational ghost imaging device to eliminate photon number fluctuations of different measurement events. Thus, a high-quality defogging ghost image is reconstructed even though fog is evenly distributed on the optical path. A nearly 100% defogging ghost image is obtained by further using a cycle generative adversarial network to process the reconstructed defogging image.