An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolu...An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.展开更多
Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n +t cop-ies of n” of Agarwal and Andrews (J. Combin. Theory Ser.A, 45(1987), No.1, 40-49). In this paper we use l...Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n +t cop-ies of n” of Agarwal and Andrews (J. Combin. Theory Ser.A, 45(1987), No.1, 40-49). In this paper we use lattice paths of Agarwal and Bressoud (Pacific J. Math. 136(2) (1989), 209-228) to provide new combinatorial interpretations of the same identities. This results in five new 3-way combinatorial identities.展开更多
The difference of energy and electronic structure of V, Nb, and Ta in different crystalline structures were investigated by different methods in density functional theory （DFT）. Lattice constants, total energies, an...The difference of energy and electronic structure of V, Nb, and Ta in different crystalline structures were investigated by different methods in density functional theory （DFT）. Lattice constants, total energies, and densities of states of these metals were calculated using the plane-wave pseudopotential method in DFT. Results were compared with those of projector augmented wave method, CALPHAD method, and experiments. Total energy and electronic structure analyses showed that valence electrons mostly transferred from s to p or d state, changing obviously with both the crystal structure and the elemental period number from V to Ta and leading to stronger cohesion, higher cohesive energy and more stable lattice of heavier metals.展开更多
In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a co...In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.展开更多
Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangul...Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangular,hexagonal,and kagome lattices.Here,we propose a strategy to engineer semiregular tessellation patterns in untwisted bilayer graphene by applying anisotropic epitaxial tensile strain(AETS)along crystallographic directions.Through force-field and firstprinciples calculations,we demonstrate that AETS can induce a rich variety of semiregular tessellation geometries,including truncated hextille,prismatic pentagon,and brick-phase arrangements.Characteristic electronic Dirac and flat bands of the lattice models associated with these semiregular tessellations are observed near the Fermi level,arising from interlayer interactions generated by the spatial rearrangement of AB,BA,and SP domains.Furthermore,the real-space observations of electronic kagome,distorted Lieb,brick-like,and one-dimensional stripe lattices demonstrate that AETS enables tunable semiregular tessellation lattices.Our study identifies AETS as a promising new degree of freedom in moiréengineering,offering a reproducible and scalable platform for exploring exotic electronic lattices in moirésystems.展开更多
In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as t...In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.展开更多
Blind signature allows a user to get a signature of a signer on an arbitrary message,and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message.Th...Blind signature allows a user to get a signature of a signer on an arbitrary message,and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message.This property is necessary when the user’s privacy needs protection,such as a bank bill,a trade secret,etc.As an alternative of public key infrastructure,the identity-based system can simplify the key management procedures in certificate-based public key systems.Inspired by the requirement of identity-based blind signature in the post quantum world,we research on identity-based blind signature based on hard lattice problems under the random Oracle model.We propose a construction built upon the blind signature by Rückert,and it is proved to be one-more unforgeable against selective identity and chosen message attacks（s ID-CMA）and unconditionally blind.The proposed scheme has 2 moves,and its security can be reduced to the small integer solution（SIS）problem.展开更多
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio...For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.展开更多
We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and ...We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.展开更多
In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is al...In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.展开更多
The electronic structures of three types of lattice defects in pyrites （i.e., As-substituted, Co-substituted, and intercrystalline Au py-rites） were calculated using the density functional theory （DFT）. In additio...The electronic structures of three types of lattice defects in pyrites （i.e., As-substituted, Co-substituted, and intercrystalline Au py-rites） were calculated using the density functional theory （DFT）. In addition, their band structures, density of states, and difference charge density were studied. The effect of the three types of lattice defects on the pyrite floatability was explored. The calculated results showed that the band-gaps of pyrites with Co-substitution and intercrystalline Au decreased significantly, which favors the oxidation of xanthate to dix-anthogen and the adsorption of dixanthogen during pyrite flotation. The stability of the pyrites increased in the following order： As-substituted 〈 perfect 〈 Co-substituted 〈 intercrystalline Au. Therefore, As-substituted pyrite is easier to be depressed by intensive oxidi-zation compared to perfect pyrite in a strongly alkaline medium. However, Co-substituted and intercrystalline Au pyrites are more difficult to be depressed compared to perfect pyrite. The analysis of the Mulliken bond population and the electron density difference indicates that the covalence characteristic of the S Fe bond is larger compared to the S S bond in perfect pyrite. In addition, the presence of the three types of lattice defects in the pyrite bulk results in an increase in the covalence level of the S Fe bond and a decrease in the covalence level of the S S bond, which affect the natural floatability of the pyrites.展开更多
This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary ...This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary condition and the relaxation time are tailored to the situation. The dynamic compaction process is vividly presented and the shock wave can be easily found in the simulation. The density is analyzed in order to explore the mechanism of the high velocity compaction.展开更多
文摘An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.
文摘Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n +t cop-ies of n” of Agarwal and Andrews (J. Combin. Theory Ser.A, 45(1987), No.1, 40-49). In this paper we use lattice paths of Agarwal and Bressoud (Pacific J. Math. 136(2) (1989), 209-228) to provide new combinatorial interpretations of the same identities. This results in five new 3-way combinatorial identities.
基金ACKNOWLEDGMENTS This work was supported by the Doctoral Discipline Foundation of the Ministry of Education of China （No.20070533118） and the National Natural Science Foundation of China （No.50871124）. The authors acknowledge Dr. Y. Z. Nie for his useful discussion in calculations.
文摘The difference of energy and electronic structure of V, Nb, and Ta in different crystalline structures were investigated by different methods in density functional theory （DFT）. Lattice constants, total energies, and densities of states of these metals were calculated using the plane-wave pseudopotential method in DFT. Results were compared with those of projector augmented wave method, CALPHAD method, and experiments. Total energy and electronic structure analyses showed that valence electrons mostly transferred from s to p or d state, changing obviously with both the crystal structure and the elemental period number from V to Ta and leading to stronger cohesion, higher cohesive energy and more stable lattice of heavier metals.
文摘In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.52461160327,92477205,12474173,and 12104313)the National Key R&D Program of China(Grant No.2023YFA1406500)+3 种基金the Department of Science and Technology of Guangdong Province(Grant No.2021QN02L820)Shenzhen Science and Technology Program(Grant No.RCYX20231211090126026,the Stable Support Plan Program 20220810161616001)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.22XNKJ30)。
文摘Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangular,hexagonal,and kagome lattices.Here,we propose a strategy to engineer semiregular tessellation patterns in untwisted bilayer graphene by applying anisotropic epitaxial tensile strain(AETS)along crystallographic directions.Through force-field and firstprinciples calculations,we demonstrate that AETS can induce a rich variety of semiregular tessellation geometries,including truncated hextille,prismatic pentagon,and brick-phase arrangements.Characteristic electronic Dirac and flat bands of the lattice models associated with these semiregular tessellations are observed near the Fermi level,arising from interlayer interactions generated by the spatial rearrangement of AB,BA,and SP domains.Furthermore,the real-space observations of electronic kagome,distorted Lieb,brick-like,and one-dimensional stripe lattices demonstrate that AETS enables tunable semiregular tessellation lattices.Our study identifies AETS as a promising new degree of freedom in moiréengineering,offering a reproducible and scalable platform for exploring exotic electronic lattices in moirésystems.
基金supported by the Department of Mathematics,Faculty of Science,Mahidol University,Thailand
文摘In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.
基金Supported by the National Natural Science Foundation of China(61472309,61572390,61672412,61402353)
文摘Blind signature allows a user to get a signature of a signer on an arbitrary message,and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message.This property is necessary when the user’s privacy needs protection,such as a bank bill,a trade secret,etc.As an alternative of public key infrastructure,the identity-based system can simplify the key management procedures in certificate-based public key systems.Inspired by the requirement of identity-based blind signature in the post quantum world,we research on identity-based blind signature based on hard lattice problems under the random Oracle model.We propose a construction built upon the blind signature by Rückert,and it is proved to be one-more unforgeable against selective identity and chosen message attacks（s ID-CMA）and unconditionally blind.The proposed scheme has 2 moves,and its security can be reduced to the small integer solution（SIS）problem.
基金supported by the National Key R and D Program of China(2020YFA0713100).
文摘For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50971101 and 51074127)the Research Fund of the State Key Laboratory of Solidification Processing(NPU)of China(Grant No.SKLSP201010)
文摘We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.
基金Project supported by the Natural Science Foundation of China(10461006)the Natural Science Foundation of Inner Mongolia(2004080201103)the High Education Science Research Programof Inner Mongolia(NJ02035)
文摘In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.
基金supported by the National Natural Science Foundation of China (No.u0837602)
文摘The electronic structures of three types of lattice defects in pyrites （i.e., As-substituted, Co-substituted, and intercrystalline Au py-rites） were calculated using the density functional theory （DFT）. In addition, their band structures, density of states, and difference charge density were studied. The effect of the three types of lattice defects on the pyrite floatability was explored. The calculated results showed that the band-gaps of pyrites with Co-substitution and intercrystalline Au decreased significantly, which favors the oxidation of xanthate to dix-anthogen and the adsorption of dixanthogen during pyrite flotation. The stability of the pyrites increased in the following order： As-substituted 〈 perfect 〈 Co-substituted 〈 intercrystalline Au. Therefore, As-substituted pyrite is easier to be depressed by intensive oxidi-zation compared to perfect pyrite in a strongly alkaline medium. However, Co-substituted and intercrystalline Au pyrites are more difficult to be depressed compared to perfect pyrite. The analysis of the Mulliken bond population and the electron density difference indicates that the covalence characteristic of the S Fe bond is larger compared to the S S bond in perfect pyrite. In addition, the presence of the three types of lattice defects in the pyrite bulk results in an increase in the covalence level of the S Fe bond and a decrease in the covalence level of the S S bond, which affect the natural floatability of the pyrites.
基金supported by the National Natural Science Foundation of China(Nos. 50874123 and 51174236)National Basic Research Program of China(No. 2011CB606306)
文摘This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary condition and the relaxation time are tailored to the situation. The dynamic compaction process is vividly presented and the shock wave can be easily found in the simulation. The density is analyzed in order to explore the mechanism of the high velocity compaction.
