A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy...A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.展开更多
For a deeper understanding of the shear resistance performance of the steel-concrete-steel composite shear wall, the main influence factors such as the thicknesses of the steel plates and the concrete, the strength gr...For a deeper understanding of the shear resistance performance of the steel-concrete-steel composite shear wall, the main influence factors such as the thicknesses of the steel plates and the concrete, the strength grades of the concrete and the span-depth ratios of the composite wall, which have impacts on the shear resistance performance of the composite shear wail, are analyzed by the numerical simulation method. Meanwhile, the simplified calculation formulae of the initial elastic lateral-resisting stiffness and the shear bearing capacity of the composite shear wall are also proposed. The research shows that with the increase in the thicknesses of the steel plates and the concrete and the increase in the strength grades of the concrete, the shear performance of the shear wall improves obviously; the span-depth ratios of the composite wall have a significant effect on the initial elastic lateral- resisting stiffness, but a small effect on the shear bearing capacity. Comparing the results of the simplified calculation formulae with those of the nonlinear finite element method, it is obvious that the presented formulae are reasonable and meet the real force state of the structure. These conclusions can serve as a preliminary design reference for the steel-concrete- steel composite shear wall.展开更多
Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
This paper introduces a method of sieve which can be to calculate the number of residues of the integers 1,2,...,2a sifted by n paiwise coprime numbers.
Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. ...Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.展开更多
To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensive...To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensively studied in theory by virtue of related theories of hydromechanics and aerosol.According to actual measurements of flow coefficients and atomization angles of X-type swirl nozzle,computational formula was derived for atomized particle sizes of such a nozzle in conjunction with relevant empirical equation. Moreover, a mathematical model for applying high pressure atomization to dust removal in underground coal mine was also established to deduce theoretical computation formula of fractional efficiency. Then, Matlab was adopted to portray the relation curve between fractional efficiency and influence factors. In addition, a theoretical formula was also set up for removal efficiency of respirable dust and total coal dust based on dust size and frequency distribution equations. In the end,impacts of dust characteristic parameters on various dust removal efficiencies were analyzed.展开更多
As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonh...As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.展开更多
Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorpt ion equations was carried out to calculate their thermodynamic equilibrium constants. The calculation formulae ofthree thermo...Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorpt ion equations was carried out to calculate their thermodynamic equilibrium constants. The calculation formulae ofthree thermodynamic parameters, the standard molar Gibbs free energy change, the standard molar enthalpy change and the standard molar entropy change, of isothermal adsorption processes for Freundlich andTemkin isotherm models were deduced according to the relationship between the thermodynamic equilibriumconstats and the temperature.展开更多
In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theore...In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theoretical formula for the plastic zone of rocks surrounding a roadway. We also analyzed the distribution characteristics of the plastic zone under different levels of tectonic stress, vertical pressure, cohesion and friction angle of the surrounding rock. Secondly, we used numerical simulation to analyze the range and shape features of the plastic zone of rocks surrounding the roadway, given different tectonic stress levels. Finally we used a rock drilling detector to carry out field measurements on the broken state of rock surrounding the roadway at the –700 substation and channels in the Xinzhuang mine of the Shenhuo mining area. Given the measured ground stress, we analyzed the relationship between tectonic stress and the distribution of this plastic zone. Our results show that the range of the plastic zone at the top and bottom of the roadway increases with an increase in tectonic stress and this increase is especially obvious at the roadway corner.展开更多
Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel(CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the ...Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel(CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the underlying untreated stratum. Due to the changing permeability property of CFG piles, the whole consolidation process of the composite ground with CFG piles was divided into two stages, i.e., the early stage(permeable CFG pile bodies) and the later stage(impermeable pile bodies). Then, the consolidation equation of the composite foundation with CFG piles was established by using the Terzaghi one-dimensional consolidation theory. Consequently, the unified formula to calculate the excess pore water pressure was derived with the specific solutions for the consolidation degree of composite ground, reinforced area and underlying stratum under instant load obtained respectively. Finally, combined with a numerical example, influencing rules by main factors(including the replacement rate m, the treatment depth h1, the permeability coefficient Ks1, Kv2 and compression modulus Es1, Es2 of reinforced area and underlying stratum) on the consolidation property of composite ground with CFG piles were discussed in detail. The result shows that the consolidation velocity of underlying stratum is slower than that of the reinforced area. However, the consolidation velocity of underlying stratum is slow at first then fast as a result of the transferring of effective stress to the underlying stratum during the dissipating process of excess pore water pressure.展开更多
文摘A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.
基金The Basic Scientific Research Funds of Hohai University (No. B1020133)
文摘For a deeper understanding of the shear resistance performance of the steel-concrete-steel composite shear wall, the main influence factors such as the thicknesses of the steel plates and the concrete, the strength grades of the concrete and the span-depth ratios of the composite wall, which have impacts on the shear resistance performance of the composite shear wail, are analyzed by the numerical simulation method. Meanwhile, the simplified calculation formulae of the initial elastic lateral-resisting stiffness and the shear bearing capacity of the composite shear wall are also proposed. The research shows that with the increase in the thicknesses of the steel plates and the concrete and the increase in the strength grades of the concrete, the shear performance of the shear wall improves obviously; the span-depth ratios of the composite wall have a significant effect on the initial elastic lateral- resisting stiffness, but a small effect on the shear bearing capacity. Comparing the results of the simplified calculation formulae with those of the nonlinear finite element method, it is obvious that the presented formulae are reasonable and meet the real force state of the structure. These conclusions can serve as a preliminary design reference for the steel-concrete- steel composite shear wall.
文摘Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
文摘This paper introduces a method of sieve which can be to calculate the number of residues of the integers 1,2,...,2a sifted by n paiwise coprime numbers.
基金Project(14JJ4003) supported by the Natural Science Foundation of Hunan Province,ChinaProject(2013M531812) supported by China Postdoctoral Science Foundation+1 种基金Project supported by the Postdoctoral Foundation of Central South UniversityProject(14JJ4003) Project(2013SCEEKL001) supported by Foundation of Tianjin Key Laboratory of Soft Soil Characteristics and Engineering Environment,China
文摘Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.
基金Financial provided by the National Natural Science Foundation of China (Nos. 51574123 and U1361118)the China Postdoctoral Science Foundation (No. 2015M 582118)
文摘To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensively studied in theory by virtue of related theories of hydromechanics and aerosol.According to actual measurements of flow coefficients and atomization angles of X-type swirl nozzle,computational formula was derived for atomized particle sizes of such a nozzle in conjunction with relevant empirical equation. Moreover, a mathematical model for applying high pressure atomization to dust removal in underground coal mine was also established to deduce theoretical computation formula of fractional efficiency. Then, Matlab was adopted to portray the relation curve between fractional efficiency and influence factors. In addition, a theoretical formula was also set up for removal efficiency of respirable dust and total coal dust based on dust size and frequency distribution equations. In the end,impacts of dust characteristic parameters on various dust removal efficiencies were analyzed.
文摘As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.
文摘Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorpt ion equations was carried out to calculate their thermodynamic equilibrium constants. The calculation formulae ofthree thermodynamic parameters, the standard molar Gibbs free energy change, the standard molar enthalpy change and the standard molar entropy change, of isothermal adsorption processes for Freundlich andTemkin isotherm models were deduced according to the relationship between the thermodynamic equilibriumconstats and the temperature.
基金Financial support for this work, provided by the research fund of the State Key Laboratory of Coal Resources and Mine Safety of the China University of Mining & Technology (No.08kf11) is gratefully ac-knowledged
文摘In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theoretical formula for the plastic zone of rocks surrounding a roadway. We also analyzed the distribution characteristics of the plastic zone under different levels of tectonic stress, vertical pressure, cohesion and friction angle of the surrounding rock. Secondly, we used numerical simulation to analyze the range and shape features of the plastic zone of rocks surrounding the roadway, given different tectonic stress levels. Finally we used a rock drilling detector to carry out field measurements on the broken state of rock surrounding the roadway at the –700 substation and channels in the Xinzhuang mine of the Shenhuo mining area. Given the measured ground stress, we analyzed the relationship between tectonic stress and the distribution of this plastic zone. Our results show that the range of the plastic zone at the top and bottom of the roadway increases with an increase in tectonic stress and this increase is especially obvious at the roadway corner.
基金Project(51378197)supported by the National Natural Science Foundation of China
文摘Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel(CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the underlying untreated stratum. Due to the changing permeability property of CFG piles, the whole consolidation process of the composite ground with CFG piles was divided into two stages, i.e., the early stage(permeable CFG pile bodies) and the later stage(impermeable pile bodies). Then, the consolidation equation of the composite foundation with CFG piles was established by using the Terzaghi one-dimensional consolidation theory. Consequently, the unified formula to calculate the excess pore water pressure was derived with the specific solutions for the consolidation degree of composite ground, reinforced area and underlying stratum under instant load obtained respectively. Finally, combined with a numerical example, influencing rules by main factors(including the replacement rate m, the treatment depth h1, the permeability coefficient Ks1, Kv2 and compression modulus Es1, Es2 of reinforced area and underlying stratum) on the consolidation property of composite ground with CFG piles were discussed in detail. The result shows that the consolidation velocity of underlying stratum is slower than that of the reinforced area. However, the consolidation velocity of underlying stratum is slow at first then fast as a result of the transferring of effective stress to the underlying stratum during the dissipating process of excess pore water pressure.
