In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece...In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.展开更多
In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The bo...In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).展开更多
A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gat...A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.展开更多
This paper presents a short exploration of the phenomena of mass and heat increase, shedding light on the remarkable notion of an expanding universe. Aimed at physicists and mathematicians, this investigation draws on...This paper presents a short exploration of the phenomena of mass and heat increase, shedding light on the remarkable notion of an expanding universe. Aimed at physicists and mathematicians, this investigation draws on an innovative collaboration with ChatGPT, an AI language model trained using scientific knowledge, to enrich our understanding of these fundamental concepts. By delving into the Gravitational Constant, we unveil compelling evidence for an increase in mass and heat for all celestial objects within an isotropic and homogenous universe as a result of the Lorentz Transformation of mass energy (LTME). Traditionally, LTME has been considered relevant primarily for subatomic particles at high velocities. However, this study posits that LTME is equally applicable to celestial bodies, even at relatively low velocities. The journey commences with an examination of the Gamma Factor in the LTME, illuminating its significance in comprehending the expansion of the cosmos. Ultimately, this paper offers a comprehensive validation of “Expanding Matter” with responses from ChatGPT, illuminating the ever-growing nature of our universe. As physicists, embarking on this journey will lead to new perspectives on the profound mysteries that shape cosmic reality. This pursuit contemplates the possibility of an infinitely energetic universe, where energy metamorphoses into mass through M = E/c<sup>2</sup>. This interpretation proposes the existence of a Process of Continuously Created Matter, manifesting as an ongoing accretion, augmentation, and expansion, harmonizing with the universe’s ever-expansive nature. The study further incorporates state-of-the-art observational technologies to substantiate its claims, thereby opening new avenues for future research in both theoretical physics and cosmology.展开更多
Lorentz Invariance is a foundational principle in modern physics, but some recent quantum gravity theories have hinted that it may be violated at extremely high energies. Gamma-ray bursts (GRBs) provide a promising to...Lorentz Invariance is a foundational principle in modern physics, but some recent quantum gravity theories have hinted that it may be violated at extremely high energies. Gamma-ray bursts (GRBs) provide a promising tool for checking and constraining any deviations from Lorentz Invariance due to their huge energies and cosmological distances. Gamma-ray bursts, which are the most intense and powerful explosions in the universe, are traditionally divided into long bursts whose observed duration exceeds 2 s, and short bursts whose observed duration is less than 2 s. In this study, we employ a recent sample of 46 short GRBs to check for any deviation from Lorentz Invariance. We analyze the spectral lag of the bursts in our data sample and check for any redshift dependence in the GRB rest frame, which would indicate a violation of Lorentz Invariance. Our results are consistent, to within 1σ, with no deviation from Lorentz Invariance.展开更多
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.
基金supported by the NNSF of China(12271483,11961056)the NSF of Jiangxi Province(20192BAB201004)+1 种基金supported by the“Xin-Miao”Program of Zhejiang Province(2021R415027)the Innovation Fund of ZUST(2020yjskc06).
文摘In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).
基金supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)。
文摘A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.
文摘This paper presents a short exploration of the phenomena of mass and heat increase, shedding light on the remarkable notion of an expanding universe. Aimed at physicists and mathematicians, this investigation draws on an innovative collaboration with ChatGPT, an AI language model trained using scientific knowledge, to enrich our understanding of these fundamental concepts. By delving into the Gravitational Constant, we unveil compelling evidence for an increase in mass and heat for all celestial objects within an isotropic and homogenous universe as a result of the Lorentz Transformation of mass energy (LTME). Traditionally, LTME has been considered relevant primarily for subatomic particles at high velocities. However, this study posits that LTME is equally applicable to celestial bodies, even at relatively low velocities. The journey commences with an examination of the Gamma Factor in the LTME, illuminating its significance in comprehending the expansion of the cosmos. Ultimately, this paper offers a comprehensive validation of “Expanding Matter” with responses from ChatGPT, illuminating the ever-growing nature of our universe. As physicists, embarking on this journey will lead to new perspectives on the profound mysteries that shape cosmic reality. This pursuit contemplates the possibility of an infinitely energetic universe, where energy metamorphoses into mass through M = E/c<sup>2</sup>. This interpretation proposes the existence of a Process of Continuously Created Matter, manifesting as an ongoing accretion, augmentation, and expansion, harmonizing with the universe’s ever-expansive nature. The study further incorporates state-of-the-art observational technologies to substantiate its claims, thereby opening new avenues for future research in both theoretical physics and cosmology.
文摘Lorentz Invariance is a foundational principle in modern physics, but some recent quantum gravity theories have hinted that it may be violated at extremely high energies. Gamma-ray bursts (GRBs) provide a promising tool for checking and constraining any deviations from Lorentz Invariance due to their huge energies and cosmological distances. Gamma-ray bursts, which are the most intense and powerful explosions in the universe, are traditionally divided into long bursts whose observed duration exceeds 2 s, and short bursts whose observed duration is less than 2 s. In this study, we employ a recent sample of 46 short GRBs to check for any deviation from Lorentz Invariance. We analyze the spectral lag of the bursts in our data sample and check for any redshift dependence in the GRB rest frame, which would indicate a violation of Lorentz Invariance. Our results are consistent, to within 1σ, with no deviation from Lorentz Invariance.
