An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theore...An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theorem in combinatorics and some conclusions known to us in thecoloring of the distance graph, the chromatic number _X(G) is determined in this paper that is ofthe distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 andcontaining {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodiccolorings.展开更多
The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root ...We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.展开更多
Under certain condition, the inequality |λ_1p_1~2+λ_2p_2~2+λ_3p_3~2+λ_4p_4~2+μ_12^(x1)+…+μ_s2^(xs)+γ|＜ηhas infinitely many solutions in primes p_1,p_2,p_3,p_4 and positive integers x_1,…,x_s.
Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like disper...Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.展开更多
Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an...Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.展开更多
In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.
Deep hydrodesulfurization （HDS） is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/...Deep hydrodesulfurization （HDS） is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/or new types of reactors. In this work, the kinetics of dibenzothiophene （DBT） hydrodesulfurization over Ni-P/SBA-15/ cordierite catalyst was investigated at 340-380 ℃ and 3.0-5.0 MPa. The first-order reaction model with respect to both DBT and H2 was used to fit the kinetics data in a batch recycle operation system. It is found that both the activation energy and rate constant over the Ni-P monolithic catalyst under our operating conditions are close to those over conventionally used HDS catalysts. Comparative performance studies of two types of reactors, i.e., trickle bed reactor and monolithic reactor, were performed based on reactor modeling and simulation. The results indicate that the productivity of the monolithic reactor is 3 times higher than that of the trickle bed reactor on a catalyst weight basis since effective utilization of the catalyst is higher in the monolithic reactor, but the volumetric productivity of the monolithic reactor is lower for HDS of DBT. Based on simulation results, a two- reactor-in-series configuration for hydrodesulfurization is proposed, in which a monolithic reactor is followed by a tickled bed reactor so as to attain intensified performance of the system converting fuel oil of different sulfur-containing compounds. It is illustrated that the two reactor scheme outperforms the trickle bed reactor both on reactor volume and catalyst mass bases while the content of sulfur is reduced from 200 μg·g-1 to about 10 μ·g-1.展开更多
When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensio...When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.展开更多
文摘An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theorem in combinatorics and some conclusions known to us in thecoloring of the distance graph, the chromatic number _X(G) is determined in this paper that is ofthe distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 andcontaining {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodiccolorings.
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
基金Supported by the Foundation for University Key Teacher by the Ministry of Education(2000-2003)Supported by the National Natural Science Foundation of China(10061003)
文摘We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.
基金Supported by the National Natural Science Foundation of China(10171076)Supported by the Scientific and Technical Committee Foundation of Shanghai(03JC14027)
文摘Under certain condition, the inequality |λ_1p_1~2+λ_2p_2~2+λ_3p_3~2+λ_4p_4~2+μ_12^(x1)+…+μ_s2^(xs)+γ|＜ηhas infinitely many solutions in primes p_1,p_2,p_3,p_4 and positive integers x_1,…,x_s.
文摘Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.
基金Supported by the National Natural Science Foundations of China(19971096)
文摘In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.
基金Supported by the State Key Development Program for Basic Research of China(2006CB202503)
文摘Deep hydrodesulfurization （HDS） is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/or new types of reactors. In this work, the kinetics of dibenzothiophene （DBT） hydrodesulfurization over Ni-P/SBA-15/ cordierite catalyst was investigated at 340-380 ℃ and 3.0-5.0 MPa. The first-order reaction model with respect to both DBT and H2 was used to fit the kinetics data in a batch recycle operation system. It is found that both the activation energy and rate constant over the Ni-P monolithic catalyst under our operating conditions are close to those over conventionally used HDS catalysts. Comparative performance studies of two types of reactors, i.e., trickle bed reactor and monolithic reactor, were performed based on reactor modeling and simulation. The results indicate that the productivity of the monolithic reactor is 3 times higher than that of the trickle bed reactor on a catalyst weight basis since effective utilization of the catalyst is higher in the monolithic reactor, but the volumetric productivity of the monolithic reactor is lower for HDS of DBT. Based on simulation results, a two- reactor-in-series configuration for hydrodesulfurization is proposed, in which a monolithic reactor is followed by a tickled bed reactor so as to attain intensified performance of the system converting fuel oil of different sulfur-containing compounds. It is illustrated that the two reactor scheme outperforms the trickle bed reactor both on reactor volume and catalyst mass bases while the content of sulfur is reduced from 200 μg·g-1 to about 10 μ·g-1.
基金Projects(51878190,51779031,51678170)supported by the National Natural Science Foundation of China。
文摘When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.
