In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
Under quasispin scheme, a complete group theoretical classification of fermion states with symplectlc symmetry is proposed. Furthermore, the first and second order irreducible tensor operators are investigated in deta...Under quasispin scheme, a complete group theoretical classification of fermion states with symplectlc symmetry is proposed. Furthermore, the first and second order irreducible tensor operators are investigated in detail to approach the fermion states with explicit forms.展开更多
In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background...In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.展开更多
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
We present NeuralMag,a flexible and high-performance open-source Python library for micromagnetic simulations.NeuralMag leverages modern machine learning frameworks,such as PyTorch and JAX,to perform efficient tensor ...We present NeuralMag,a flexible and high-performance open-source Python library for micromagnetic simulations.NeuralMag leverages modern machine learning frameworks,such as PyTorch and JAX,to perform efficient tensor operations on various parallel hardware,including CPUs,GPUs,and TPUs.The library implements a novel nodal finite-difference discretization scheme that provides improved accuracy over traditional finite-difference methods without increasing computational complexity.NeuralMag is particularly well-suited for solving inverse problems,especially those with time-dependent objectives,thanks to its automatic differentiation capabilities.Performance benchmarks show that NeuralMag is competitive with state-of-the-art simulation codes while offering enhanced flexibility through its Python interface and integration with high-level computational backends.展开更多
In artificial neural networks,data structures usually exist in the form of vectors,matrices,or higher-dimensional tensors.However,traditional electronic computing architectures are limited by the bottleneck of separat...In artificial neural networks,data structures usually exist in the form of vectors,matrices,or higher-dimensional tensors.However,traditional electronic computing architectures are limited by the bottleneck of separation of storage and computing,making it difficult to efficiently handle large-scale tensor operations.The research team has developed a photonic tensor processing unit based on a single microring resonator,which performs tensor convolution operations in multiple dimensions of time,wavelength,and microwave frequency by precisely adjusting the operating state of multi-wavelength lasers.This innovative design increases the photonic computing density to 34.04 TOPS/mm²,significantly surpassing the performance level of existing photonic computing chips.展开更多
文摘In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
基金Supported by the National Natural Science Foundation of China
文摘Under quasispin scheme, a complete group theoretical classification of fermion states with symplectlc symmetry is proposed. Furthermore, the first and second order irreducible tensor operators are investigated in detail to approach the fermion states with explicit forms.
基金Supported in part by the National Science Foundation of China(NSFC)under Grant Nos.11690022 and 11475237Strategic Priority Research Program of the Chinese Academy of Sciences(CAS), under Grant No.XDB23030100+1 种基金Key Research Program QYZDYSSWSYS007the CAS Center for Excellence in Particle Physics(CCEPP)
文摘In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
基金the Austrian Science Fund (FWF) 10.55776/P34671, 10.55776/I6068, 10.55776/PAT3864023, and 10.55776/PIN1434524. For open access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submissionThis work has been supported by the Horizon Europe research and innovation program through MaMMoS grant agreement No 101135546 and Marie Skłodowska Curie grant agreement No 101152613. We gratefully acknowledge the wedding of the Koraltans for fruitful discussions and a great time, which led to this publication.
文摘We present NeuralMag,a flexible and high-performance open-source Python library for micromagnetic simulations.NeuralMag leverages modern machine learning frameworks,such as PyTorch and JAX,to perform efficient tensor operations on various parallel hardware,including CPUs,GPUs,and TPUs.The library implements a novel nodal finite-difference discretization scheme that provides improved accuracy over traditional finite-difference methods without increasing computational complexity.NeuralMag is particularly well-suited for solving inverse problems,especially those with time-dependent objectives,thanks to its automatic differentiation capabilities.Performance benchmarks show that NeuralMag is competitive with state-of-the-art simulation codes while offering enhanced flexibility through its Python interface and integration with high-level computational backends.
文摘In artificial neural networks,data structures usually exist in the form of vectors,matrices,or higher-dimensional tensors.However,traditional electronic computing architectures are limited by the bottleneck of separation of storage and computing,making it difficult to efficiently handle large-scale tensor operations.The research team has developed a photonic tensor processing unit based on a single microring resonator,which performs tensor convolution operations in multiple dimensions of time,wavelength,and microwave frequency by precisely adjusting the operating state of multi-wavelength lasers.This innovative design increases the photonic computing density to 34.04 TOPS/mm²,significantly surpassing the performance level of existing photonic computing chips.
