Suppose that Ip^α is the p-adic Riesz potential. In this paper, we established the boundedness of Ip^α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic R...Suppose that Ip^α is the p-adic Riesz potential. In this paper, we established the boundedness of Ip^α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential Ip^α and p-adic generalized Campanato functions. Keywords展开更多
Let K be a cyclic quartic number field, and k its quadratic subfield. Let h(L) denote theideal class number of field L. Ten congruenees for h^- = h(K)/h(k) are obtained. In par-ticular, if K = Q((p+s(p^(1/2))))^(1/2) ...Let K be a cyclic quartic number field, and k its quadratic subfield. Let h(L) denote theideal class number of field L. Ten congruenees for h^- = h(K)/h(k) are obtained. In par-ticular, if K = Q((p+s(p^(1/2))))^(1/2) with the prime number p = r^2+s^2 and s is even, then C_1h^-≡B_((p-1)/_4)B_(3(p-1)/4) (mod p) for p≡1 (mod 8); and C_2h^-≡E_((p-5)/8)E_((3p-7)/8)(mod p) for p≡5 (mod 8)where B_n and E_n are the Bernoulli and the Euler numbers. If the real K = Q((v(5+2(5^(1/2))))^(1/2),then C_3h^-≡h(Q((-v)^(1/2))) h (Q((-5v)^(1/2))) (mod 5). If 3 ramifies in K = Q(θ^(1/2)), then C_4h(K)≡h(K~*) (mod 3) with K~* = Q((-3θ^(1/2))). All the above C_i are explicitly given constants.Some relations between the factors of class numbers h^- are also obtained. These results forcyclic quartic fields are an extension of the results for quadratic fields obtained by Ankeny-Artin-Chowla, Kiselev, Carlitz and Lu Hong-wen from 1948 to 1983.展开更多
The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
Any bounded tile of the field Qp of p-adic numbers is a compact open set up to a set of zero Haar measure.In this note,we present two simple and direct proofs of this fact.
The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark...The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark energy via a golden mean scaling-super quantization of the electromagnetic field.展开更多
基金Acknowledgements The authors would like to express their gratitude to the referees for their very valuable comments. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11601035, 11471050）.
文摘Suppose that Ip^α is the p-adic Riesz potential. In this paper, we established the boundedness of Ip^α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential Ip^α and p-adic generalized Campanato functions. Keywords
基金Project supported by the National Natural Science Foundation of China.
文摘Let K be a cyclic quartic number field, and k its quadratic subfield. Let h(L) denote theideal class number of field L. Ten congruenees for h^- = h(K)/h(k) are obtained. In par-ticular, if K = Q((p+s(p^(1/2))))^(1/2) with the prime number p = r^2+s^2 and s is even, then C_1h^-≡B_((p-1)/_4)B_(3(p-1)/4) (mod p) for p≡1 (mod 8); and C_2h^-≡E_((p-5)/8)E_((3p-7)/8)(mod p) for p≡5 (mod 8)where B_n and E_n are the Bernoulli and the Euler numbers. If the real K = Q((v(5+2(5^(1/2))))^(1/2),then C_3h^-≡h(Q((-v)^(1/2))) h (Q((-5v)^(1/2))) (mod 5). If 3 ramifies in K = Q(θ^(1/2)), then C_4h(K)≡h(K~*) (mod 3) with K~* = Q((-3θ^(1/2))). All the above C_i are explicitly given constants.Some relations between the factors of class numbers h^- are also obtained. These results forcyclic quartic fields are an extension of the results for quadratic fields obtained by Ankeny-Artin-Chowla, Kiselev, Carlitz and Lu Hong-wen from 1948 to 1983.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
基金Supported by NSF of China(Grant Nos.11971190 and 11971192)the Fundamental Research Funds for the Central Universities(Grant No.CCNU19QN076)
文摘Any bounded tile of the field Qp of p-adic numbers is a compact open set up to a set of zero Haar measure.In this note,we present two simple and direct proofs of this fact.
文摘The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark energy via a golden mean scaling-super quantization of the electromagnetic field.
