In this paper,the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem.The tuning of the width and position of the bandgap is achieve...In this paper,the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem.The tuning of the width and position of the bandgap is achieved by changing the local structural parameters,i.e.,the rotation angle,the short beam length,and the beam thickness.In order to expand the regulation of the bandgap,the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed.The results show that the mass density and stiffness of the structure have significant effects on the bandgap,while Poisson’s ratio has no effect on the bandgap.By analyzing the first ten bands of the reference unit cell,it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction,and these bandgap widths are wider.The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure,and this dipole resonance originates from the coupling of the bending deformation of the beam elements.In the band structure,the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance,which is different from that with the conventional negative slope formed by the coupling of two resonance modes.This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials,as well as for the regulation of bandgaps and the suppression of elastic waves.展开更多
In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated ...In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.展开更多
This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have b...This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure. The transmission matrix for the N identical cascaded cells has been successfully used to obtain an efficient and easy-to-use formula giving the necessary number of cells such that they can be considered infinite. As an illustrative example, the formula is applied and verified to finite size TL periodically loaded with obstacles. Scattering parameters and the input impedance of the structure are expressed and plotted.展开更多
The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure....The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.展开更多
Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0...Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.展开更多
Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, ...Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, assuming the random variables to be discrete.展开更多
Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GET...Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.展开更多
As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid wi...As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH展开更多
基金supported by the National Natural Science Foundation of China(Nos.11872233,11472163,and 12102245)。
文摘In this paper,the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem.The tuning of the width and position of the bandgap is achieved by changing the local structural parameters,i.e.,the rotation angle,the short beam length,and the beam thickness.In order to expand the regulation of the bandgap,the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed.The results show that the mass density and stiffness of the structure have significant effects on the bandgap,while Poisson’s ratio has no effect on the bandgap.By analyzing the first ten bands of the reference unit cell,it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction,and these bandgap widths are wider.The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure,and this dipole resonance originates from the coupling of the bending deformation of the beam elements.In the band structure,the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance,which is different from that with the conventional negative slope formed by the coupling of two resonance modes.This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials,as well as for the regulation of bandgaps and the suppression of elastic waves.
文摘In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.
文摘This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure. The transmission matrix for the N identical cascaded cells has been successfully used to obtain an efficient and easy-to-use formula giving the necessary number of cells such that they can be considered infinite. As an illustrative example, the formula is applied and verified to finite size TL periodically loaded with obstacles. Scattering parameters and the input impedance of the structure are expressed and plotted.
文摘The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.
基金This work was supported by National Natural Science Foundation of China(11571369)。
文摘Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.
文摘Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, assuming the random variables to be discrete.
文摘Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.
基金the National Natural Science Foundation of China and the Military Science Foundation in Ministry of Electronic Industry of China.
文摘As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH
