Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers...Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.展开更多
A high-entropy alloy–ceramic gradient composite of TiC–TiB_2/75vol% Al_(0.3) CoCrFe Ni was successfully prepared by combustion synthesis under an ultra-high gravity field, which is a low-cost method with high effici...A high-entropy alloy–ceramic gradient composite of TiC–TiB_2/75vol% Al_(0.3) CoCrFe Ni was successfully prepared by combustion synthesis under an ultra-high gravity field, which is a low-cost method with high efficiency. The ceramic particles were gradient distributed in the Al_(0.3) CoCrFe Ni matrix, and the hardness of the composite material gradually decreased along the thickness direction. The anti-penetration performance of the gradient composites was simulated using the ANSYS/LS-DYNA explicit simulation program. The results demonstrate that the distribution of the ceramic particles strongly affected the mechanical properties and the anti-penetration performance of the composites. With the same total ceramic volume fraction, the gradient composites exhibit better anti-penetration performance than the corresponding ceramic–metal interlayer composites. The more uneven the ceramic distribution, the greater the elastic modulus and yield stress of the surface layer and, thus, the better the anti-penetration performance.展开更多
Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems us...Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.展开更多
RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different co...RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different colors.The problem is that these two systems are hard to use for manipulating any operations involving combinations of colors,and they lack the capacity for inter-changeability or unification.Based on prime number theory and Goldbach's conjecture,this study presents a universal color system(C235)using a number-based structure to encode,compute and unify all colors on a color wheel.The proposed C235 system offers a unified representation for the efficient encoding and effective manipulation of color.It can be applied to designing a high-rate LCD system and colorizing objects with multiple attributes and DNA codons,opening the door to manipulating colors and lights for even broader applications.展开更多
文摘Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.
基金financially supported by the Fundamental Research Funds for the Central Universities of China (FRF-GF-17-B21)
文摘A high-entropy alloy–ceramic gradient composite of TiC–TiB_2/75vol% Al_(0.3) CoCrFe Ni was successfully prepared by combustion synthesis under an ultra-high gravity field, which is a low-cost method with high efficiency. The ceramic particles were gradient distributed in the Al_(0.3) CoCrFe Ni matrix, and the hardness of the composite material gradually decreased along the thickness direction. The anti-penetration performance of the gradient composites was simulated using the ANSYS/LS-DYNA explicit simulation program. The results demonstrate that the distribution of the ceramic particles strongly affected the mechanical properties and the anti-penetration performance of the composites. With the same total ceramic volume fraction, the gradient composites exhibit better anti-penetration performance than the corresponding ceramic–metal interlayer composites. The more uneven the ceramic distribution, the greater the elastic modulus and yield stress of the surface layer and, thus, the better the anti-penetration performance.
基金Supported by the National Natural Science Foundation of China(12035006,12075098)the Natural Science Foundation of Hubei Province(2019CFB563)+1 种基金the Hubei Province Department of Education(D20201108)Hubei Province Department of Science and Technology(2021BLB171)。
文摘Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.
文摘RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different colors.The problem is that these two systems are hard to use for manipulating any operations involving combinations of colors,and they lack the capacity for inter-changeability or unification.Based on prime number theory and Goldbach's conjecture,this study presents a universal color system(C235)using a number-based structure to encode,compute and unify all colors on a color wheel.The proposed C235 system offers a unified representation for the efficient encoding and effective manipulation of color.It can be applied to designing a high-rate LCD system and colorizing objects with multiple attributes and DNA codons,opening the door to manipulating colors and lights for even broader applications.
