Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructio...Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.展开更多
We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce "fractal calculus" (or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce "fractal calculus" (or, p-type calculus, or, Gibbs-Butzer calculus). Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D(C Kp) and locally compact group Kp^+-(= Kp), so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ(Kp), σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr(Kp), σ≥0, 1≤r 〈∞, is shown.展开更多
Dear Editor,This letter introduces a value decomposition method based on a quadratic function for multi-agent reinforcement learning,aiming to derive cooperative policies among agents modeled by artificial neural netw...Dear Editor,This letter introduces a value decomposition method based on a quadratic function for multi-agent reinforcement learning,aiming to derive cooperative policies among agents modeled by artificial neural networks.By constructing a quadratic function with specific parameter constraints,it ensures that the function achieves a global maximum when the local optimal actions are used as inputs.Based on this structured quadratic function,a novel value decomposition algorithm is proposed to facilitate optimal cooperative policy training within the centralized training with decentralized execution(CTDE)framework.展开更多
摘要Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
摘要We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce "fractal calculus" (or, p-type calculus, or, Gibbs-Butzer calculus). Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D(C Kp) and locally compact group Kp^+-(= Kp), so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ(Kp), σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr(Kp), σ≥0, 1≤r 〈∞, is shown.
基金supported in part by the National Natural Science Foundation of China(62273077)the Natural Science Foundation of Sichuan Province(2024NSFJQ0013)the Sichuan Science and Technology Program(2025ZDZX0006)。
摘要Dear Editor,This letter introduces a value decomposition method based on a quadratic function for multi-agent reinforcement learning,aiming to derive cooperative policies among agents modeled by artificial neural networks.By constructing a quadratic function with specific parameter constraints,it ensures that the function achieves a global maximum when the local optimal actions are used as inputs.Based on this structured quadratic function,a novel value decomposition algorithm is proposed to facilitate optimal cooperative policy training within the centralized training with decentralized execution(CTDE)framework.