In this paper, we define multiple Dedekind sums by products of Bernoulli functions. From the Fourie expansions of Bernoulli functions, we express the Dedekind sums as series representatios. Then by a combinatorial-geo...In this paper, we define multiple Dedekind sums by products of Bernoulli functions. From the Fourie expansions of Bernoulli functions, we express the Dedekind sums as series representatios. Then by a combinatorial-geometric method, we give a new proof of a Knopp-type identity for the Dedekind sums.展开更多
The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Re...The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.展开更多
In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the a...In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.展开更多
Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper...Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.展开更多
∑-protocol has been proved to be a very powerful cryptographic tool and widely used in nnmerous important cryptographic applications. In this paper, the authors make use of ∑-protocol as a main tool to resolve the f...∑-protocol has been proved to be a very powerful cryptographic tool and widely used in nnmerous important cryptographic applications. In this paper, the authors make use of ∑-protocol as a main tool to resolve the following difficult problems 1-3 and to construct three ettlcient cryptographic protocols 4 6：1） How to construct a protocol for proving a secret integer to be a Blum integer with form PQ, where P, Q are two different primes and both -- 3（mod 4）;2） How to construct a protocol for proving a secret polynomial with exact degree t - 1 iil a （t, n）- threshold secret sharing scheme：3） How to construct witness indistinguishable and witness hiding protocol not from zero-knowledge proof;4） A publicly verifiable secret sharing scheme with information-theoretic security;5） A delegateable signature scheme under the existence of one-way permutations;6） Non-interactive universal designated verifier signature schemes.展开更多
文摘In this paper, we define multiple Dedekind sums by products of Bernoulli functions. From the Fourie expansions of Bernoulli functions, we express the Dedekind sums as series representatios. Then by a combinatorial-geometric method, we give a new proof of a Knopp-type identity for the Dedekind sums.
文摘The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.
文摘In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.
基金sponsored by the National Natural Science Foundation of China (50608066)the National Science and Technology Pillar Program of China(2006BAC13B02)
文摘Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.
基金supported by the Foundation of tihe National Natural Science of China under Grant Nos 90604034 (Key Project), 10726012, 10871222, 10531040,and 10471156
文摘∑-protocol has been proved to be a very powerful cryptographic tool and widely used in nnmerous important cryptographic applications. In this paper, the authors make use of ∑-protocol as a main tool to resolve the following difficult problems 1-3 and to construct three ettlcient cryptographic protocols 4 6：1） How to construct a protocol for proving a secret integer to be a Blum integer with form PQ, where P, Q are two different primes and both -- 3（mod 4）;2） How to construct a protocol for proving a secret polynomial with exact degree t - 1 iil a （t, n）- threshold secret sharing scheme：3） How to construct witness indistinguishable and witness hiding protocol not from zero-knowledge proof;4） A publicly verifiable secret sharing scheme with information-theoretic security;5） A delegateable signature scheme under the existence of one-way permutations;6） Non-interactive universal designated verifier signature schemes.
