The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for ...The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.展开更多
Background The importance of sheep breeding in the Mediterranean part of the eastern Adriatic has a long tradition since its arrival during the Neolithic migrations.Sheep production system is extensive and generally c...Background The importance of sheep breeding in the Mediterranean part of the eastern Adriatic has a long tradition since its arrival during the Neolithic migrations.Sheep production system is extensive and generally carried out in traditional systems without intensive systematic breeding programmes for high uniform trait production(carcass,wool and milk yield).Therefore,eight indigenous Croatian sheep breeds from eastern Adriatic treated here as metapopulation(EAS),are generally considered as multipurpose breeds(milk,meat and wool),not specialised for a particular type of production,but known for their robustness and resistance to certain environmental conditions.Our objective was to identify genomic regions and genes that exhibit patterns of positive selection signatures,decipher their biological and productive functionality,and provide a"genomic"characterization of EAS adaptation and determine its production type.Results We identified positive selection signatures in EAS using several methods based on reduced local variation,linkage disequilibrium and site frequency spectrum(eROHi,iHS,nSL and CLR).Our analyses identified numerous genomic regions and genes(e.g.,desmosomal cadherin and desmoglein gene families)associated with environmental adaptation and economically important traits.Most candidate genes were related to meat/production and health/immune response traits,while some of the candidate genes discovered were important for domestication and evolutionary processes(e.g.,HOXa gene family and FSIP2).These results were also confirmed by GO and QTL enrichment analysis.Conclusions Our results contribute to a better understanding of the unique adaptive genetic architecture of EAS and define its productive type,ultimately providing a new opportunity for future breeding programmes.At the same time,the numerous genes identified will improve our understanding of ruminant(sheep)robustness and resistance in the harsh and specific Mediterranean environment.展开更多
Solid polymer electrolytes(SPEs)hold great application potential for solid-state lithium metal battery because of the excellent interfacial contact and processibility,but being hampered by the poor room-temperature co...Solid polymer electrolytes(SPEs)hold great application potential for solid-state lithium metal battery because of the excellent interfacial contact and processibility,but being hampered by the poor room-temperature conductivity(~10^(−7)S·cm^(−1))and low lithium-ion transference number(tLi+).Here,a lamellar composite solid electrolyte(Vr-NH_(2)@polyvinylidene fluoride(PVDF)LCSE)withβ-conformation PVDF is fabricated by confining PVDF in the interlayer channel of-NH_(2)modified vermiculite lamellar framework.We demonstrate that the conformation of PVDF can be manipulated by the nanoconfinement effect and the interaction from channel wall.The presence of-NH_(2)groups could induce the formation ofβ-conformation PVDF through electrostatic interaction,which serves as continuous and rapid lithium-ion transfer pathway.As a result,a high room-temperature ionic conductivity of 1.77×10^(−4)S·cm^(−1)is achieved,1-2 orders of magnitude higher than most SPEs.Furthermore,Vr-NH_(2)@PVDF LCSE shows a high tLi+of 0.68 because of the high dielectric constant,~3 times of that of PVDF SPE,and surpassing most of reported SPEs.The LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)||Li cell assembled by Vr-NH_(2)@PVDF LCSE obtains a discharge specific capacity of 137.1 mAh·g^(−1)after 150 cycles with a capacity retention rate of 93%at 1 C and 25℃.This study may pave a new avenue for high-performance SPEs.展开更多
This paper presents a further study of the Manning and Darcy-Weisbach resistance coefficients, as they play a significant role in assessing the cross-sectional mean velocity, conveyance capacity and determining the la...This paper presents a further study of the Manning and Darcy-Weisbach resistance coefficients, as they play a significant role in assessing the cross-sectional mean velocity, conveyance capacity and determining the lateral distribution of depth mean velocity and local boundary shear stress in compound channels. The relationships between the local, zonal and overall resistance coefficients, and a wide range of geometries and different roughness between the main channel and the flood plain are established by analyzing a vast amount of experimental data from a British Science and Engineering Research Council Flood Channel Facility （SERC-FCF）. And the experimental results also show that the overall Darcy-Weisbach resistance coefficient for a compound channel is the function of Reynolds number, but the function relationship is different from that for a single channel. By comparing and analyzing the conventional methods with the experimental data to predict composite roughness in compound channels, it is found that these methods are not suitable for compound channels. Moreover, the reason why the conventional methods cannot assess correctly the conveyance capacity of compound channels is also analyzed in this paper.展开更多
文摘The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.
基金supported by Croatian Science Foundation project IP-2018–01-8708-Application of NGS methods in the assessment of genomic variability in ruminants–“ANAGRAMS”the EU Operational Program Competitiveness and Cohesion 2014–2020 project KK.01.1.1.04.0058—Potential of microencapsulation in cheese productionthe project No.QK1919156 of the Ministry of Agriculture,Czech Republic.
文摘Background The importance of sheep breeding in the Mediterranean part of the eastern Adriatic has a long tradition since its arrival during the Neolithic migrations.Sheep production system is extensive and generally carried out in traditional systems without intensive systematic breeding programmes for high uniform trait production(carcass,wool and milk yield).Therefore,eight indigenous Croatian sheep breeds from eastern Adriatic treated here as metapopulation(EAS),are generally considered as multipurpose breeds(milk,meat and wool),not specialised for a particular type of production,but known for their robustness and resistance to certain environmental conditions.Our objective was to identify genomic regions and genes that exhibit patterns of positive selection signatures,decipher their biological and productive functionality,and provide a"genomic"characterization of EAS adaptation and determine its production type.Results We identified positive selection signatures in EAS using several methods based on reduced local variation,linkage disequilibrium and site frequency spectrum(eROHi,iHS,nSL and CLR).Our analyses identified numerous genomic regions and genes(e.g.,desmosomal cadherin and desmoglein gene families)associated with environmental adaptation and economically important traits.Most candidate genes were related to meat/production and health/immune response traits,while some of the candidate genes discovered were important for domestication and evolutionary processes(e.g.,HOXa gene family and FSIP2).These results were also confirmed by GO and QTL enrichment analysis.Conclusions Our results contribute to a better understanding of the unique adaptive genetic architecture of EAS and define its productive type,ultimately providing a new opportunity for future breeding programmes.At the same time,the numerous genes identified will improve our understanding of ruminant(sheep)robustness and resistance in the harsh and specific Mediterranean environment.
基金National Natural Science Foundation of China(No.U2004199)Joint Foundation for Science and Technology Research&Development Plan of Henan Province(Nos.222301420003 and 232301420038)+1 种基金China Postdoctoral Science Foundation(No.2022TQ0293)Key Science and Technology Project of Henan Province(No.221100240200-06).
文摘Solid polymer electrolytes(SPEs)hold great application potential for solid-state lithium metal battery because of the excellent interfacial contact and processibility,but being hampered by the poor room-temperature conductivity(~10^(−7)S·cm^(−1))and low lithium-ion transference number(tLi+).Here,a lamellar composite solid electrolyte(Vr-NH_(2)@polyvinylidene fluoride(PVDF)LCSE)withβ-conformation PVDF is fabricated by confining PVDF in the interlayer channel of-NH_(2)modified vermiculite lamellar framework.We demonstrate that the conformation of PVDF can be manipulated by the nanoconfinement effect and the interaction from channel wall.The presence of-NH_(2)groups could induce the formation ofβ-conformation PVDF through electrostatic interaction,which serves as continuous and rapid lithium-ion transfer pathway.As a result,a high room-temperature ionic conductivity of 1.77×10^(−4)S·cm^(−1)is achieved,1-2 orders of magnitude higher than most SPEs.Furthermore,Vr-NH_(2)@PVDF LCSE shows a high tLi+of 0.68 because of the high dielectric constant,~3 times of that of PVDF SPE,and surpassing most of reported SPEs.The LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)||Li cell assembled by Vr-NH_(2)@PVDF LCSE obtains a discharge specific capacity of 137.1 mAh·g^(−1)after 150 cycles with a capacity retention rate of 93%at 1 C and 25℃.This study may pave a new avenue for high-performance SPEs.
基金The project supported by the National Natural Science Foundation of China(50279024)the National Key Basic Research and Development Program of China(973 Program)(2003CB415202)the Specialized Research Fund for the Doctoral Program of Higher Education(2
文摘This paper presents a further study of the Manning and Darcy-Weisbach resistance coefficients, as they play a significant role in assessing the cross-sectional mean velocity, conveyance capacity and determining the lateral distribution of depth mean velocity and local boundary shear stress in compound channels. The relationships between the local, zonal and overall resistance coefficients, and a wide range of geometries and different roughness between the main channel and the flood plain are established by analyzing a vast amount of experimental data from a British Science and Engineering Research Council Flood Channel Facility （SERC-FCF）. And the experimental results also show that the overall Darcy-Weisbach resistance coefficient for a compound channel is the function of Reynolds number, but the function relationship is different from that for a single channel. By comparing and analyzing the conventional methods with the experimental data to predict composite roughness in compound channels, it is found that these methods are not suitable for compound channels. Moreover, the reason why the conventional methods cannot assess correctly the conveyance capacity of compound channels is also analyzed in this paper.
