Mathematics
1
2021, 51(6): 447-452.
DOI: 10.52396/JUST-2021-0076
Abstract：
A parabolic equation of fourth order on surfaces with conical singularities is considered. By the analysis of energy and approximations, the existence and uniqueness of the solution of this equation in a special space that has some approximation property are proved. Finally, it's proved that the property is equivalent to the finiteness of energy for some functions when β∈(-1,0).
A parabolic equation of fourth order on surfaces with conical singularities is considered. By the analysis of energy and approximations, the existence and uniqueness of the solution of this equation in a special space that has some approximation property are proved. Finally, it's proved that the property is equivalent to the finiteness of energy for some functions when β∈(-1,0).
2
2021, 51(5): 369-373.
DOI: 10.52396/JUST-2021-0040
Abstract：
Considering the action of the symmetric group Sn on M0,n, all the possible stable subgroups were obtained.
Considering the action of the symmetric group Sn on M0,n, all the possible stable subgroups were obtained.
3
2021, 51(5): 374-381.
DOI: 10.52396/JUST-2021-0119
Abstract：
A problem was proposed by Moore and West to determine whether every (k+1)-critical non-complete graph has a cycle of length 2 modulo k. We prove a stronger result that for k=4, 5, every (k+1)-critical non-complete graph contains cycles of all lengths modulo k.
A problem was proposed by Moore and West to determine whether every (k+1)-critical non-complete graph has a cycle of length 2 modulo k. We prove a stronger result that for k=4, 5, every (k+1)-critical non-complete graph contains cycles of all lengths modulo k.
4
2021, 51(5): 382-389.
DOI: 10.52396/JUST-2021-0026
Abstract：
A manifold extended t-process regression (meTPR) model is developed to fit functional data with a complicated input space. A manifold method is used to transform covariate data from input space into a feature space, and then an extended t-process regression is used to map feature from feature space into observation space. An estimation procedure is constructed to estimate parameters in the model. Numerical studies are investigated with both synthetic data and real data, and results show that the proposed meTPR model performs well.
A manifold extended t-process regression (meTPR) model is developed to fit functional data with a complicated input space. A manifold method is used to transform covariate data from input space into a feature space, and then an extended t-process regression is used to map feature from feature space into observation space. An estimation procedure is constructed to estimate parameters in the model. Numerical studies are investigated with both synthetic data and real data, and results show that the proposed meTPR model performs well.
5
Abstract：
The online updating method (ONLINE) is an efficient analysis approach applied to big data. We prove the asymptotic properties and conduct statistical inference of the ONLINE models in kernel density and kernel regression. Several algorithms are proposed to solve the problems of the bandwidth selection in kernel density and regression respectively. We verify the asymptotic normality of the ONLINE density model in simulation and apply the ONLINE linear kernel regression to the Volatility Index (VIX) prediction. The empirical results show that the ONLINE linear kernel regression model achieves a comparable performance in continuously arriving option data streams prediction with significantly lower complexity than the classical local linear regression model.
The online updating method (ONLINE) is an efficient analysis approach applied to big data. We prove the asymptotic properties and conduct statistical inference of the ONLINE models in kernel density and kernel regression. Several algorithms are proposed to solve the problems of the bandwidth selection in kernel density and regression respectively. We verify the asymptotic normality of the ONLINE density model in simulation and apply the ONLINE linear kernel regression to the Volatility Index (VIX) prediction. The empirical results show that the ONLINE linear kernel regression model achieves a comparable performance in continuously arriving option data streams prediction with significantly lower complexity than the classical local linear regression model.
6
Abstract：
The deletion-restriction method was used to classify hyperplane arrangements with the top degree Betti number of its complements being small.
The deletion-restriction method was used to classify hyperplane arrangements with the top degree Betti number of its complements being small.
7
Abstract：
The integrable mixed coupled nonlinear Schrödinger (MCNLS) equations is studied, which describes the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert (RH) approach, the N-soliton solutions of the MCNLS equations can be expressed explicitly when the jump matrix of a constructed RH problem is a 3×3 unit matrix. As a special example, the expression of one soliton and two solitons are displayed explicitly. More generally, as a promotion, an integrable generalized multi-component NLS system with its linear spectral problem is discussed.
The integrable mixed coupled nonlinear Schrödinger (MCNLS) equations is studied, which describes the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert (RH) approach, the N-soliton solutions of the MCNLS equations can be expressed explicitly when the jump matrix of a constructed RH problem is a 3×3 unit matrix. As a special example, the expression of one soliton and two solitons are displayed explicitly. More generally, as a promotion, an integrable generalized multi-component NLS system with its linear spectral problem is discussed.
8
Abstract：
A new type hybrid Hermite weighted essentially non-oscillatory (HWENO) schemes in the implicit method of lines transpose (MOLT) framework is designed for solving one-dimensional linear transport equations and further applied to the Vlasov-Poisson (VP) simulations via dimensional splitting. Compared with the WENO-based MOLT method given in J. Comput. Phys. [2016, 327: 337-367], the new proposed hybrid HWENO-based MOLT scheme has two advantages. The first is the HWENO schemes using the stencils narrower than those of the WENO schemes with the same order of accuracy. The second is that the schemes can adapt between the linear scheme and the HWENO scheme automatically. In summary, the hybrid HWENO scheme keeps the simplicity and robustness of the simple WENO scheme, while it has higher efficiency with less numerical errors in smooth regions and less computational costs as well. Benchmark examples are given to demonstrate the robustness and good performance of the proposed scheme.
A new type hybrid Hermite weighted essentially non-oscillatory (HWENO) schemes in the implicit method of lines transpose (MOLT) framework is designed for solving one-dimensional linear transport equations and further applied to the Vlasov-Poisson (VP) simulations via dimensional splitting. Compared with the WENO-based MOLT method given in J. Comput. Phys. [2016, 327: 337-367], the new proposed hybrid HWENO-based MOLT scheme has two advantages. The first is the HWENO schemes using the stencils narrower than those of the WENO schemes with the same order of accuracy. The second is that the schemes can adapt between the linear scheme and the HWENO scheme automatically. In summary, the hybrid HWENO scheme keeps the simplicity and robustness of the simple WENO scheme, while it has higher efficiency with less numerical errors in smooth regions and less computational costs as well. Benchmark examples are given to demonstrate the robustness and good performance of the proposed scheme.
9
2021, 51(3): 216-227.
DOI: 10.52396/JUST-2021-0053
Abstract：
Correctly identifying the subgroups in a heterogeneous population has gained increasing popularity in modern big data applications since studying the heterogeneous effect can eliminate the impact of individual differences and make the estimation results more accurate. Despite the fast growing literature, most existing methods mainly focus on the heterogeneous univariate regression and how to precisely identify subgroups in face of multiple responses remains unclear. Here, we develop a new methodology for heterogeneous multi-response regression via a concave pairwise fusion approach, which estimates the coefficient matrix and identifies the subgroup structure jointly. Besides, we provide theoretical guarantees for the proposed methodology by establishing the estimation consistency. Our numerical studies demonstrate the effectiveness of the proposed method.
Correctly identifying the subgroups in a heterogeneous population has gained increasing popularity in modern big data applications since studying the heterogeneous effect can eliminate the impact of individual differences and make the estimation results more accurate. Despite the fast growing literature, most existing methods mainly focus on the heterogeneous univariate regression and how to precisely identify subgroups in face of multiple responses remains unclear. Here, we develop a new methodology for heterogeneous multi-response regression via a concave pairwise fusion approach, which estimates the coefficient matrix and identifies the subgroup structure jointly. Besides, we provide theoretical guarantees for the proposed methodology by establishing the estimation consistency. Our numerical studies demonstrate the effectiveness of the proposed method.
10
Abstract：
An SEIQR epidemic model with the saturation incidence rate and hybrid strategies was proposed, and the stability of the model was analyzed theoretically and numerically. Firstly, the basic reproduction number R0 was derived, which determines whether the disease was extinct or not. Secondly, through LaSalle's invariance principle, it was proved that the disease-free equilibrium is globally asymptotically stable and the disease generally dies out when R0<1. By Routh-Hurwitz criterion theory, it was proved that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R0>1. Thirdly, according to the periodic orbit stability theory and the second additive compound matrix, it was proved that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R0>1. Finally, some numerical simulations were carried out to illustrate the results.
An SEIQR epidemic model with the saturation incidence rate and hybrid strategies was proposed, and the stability of the model was analyzed theoretically and numerically. Firstly, the basic reproduction number R0 was derived, which determines whether the disease was extinct or not. Secondly, through LaSalle's invariance principle, it was proved that the disease-free equilibrium is globally asymptotically stable and the disease generally dies out when R0<1. By Routh-Hurwitz criterion theory, it was proved that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R0>1. Thirdly, according to the periodic orbit stability theory and the second additive compound matrix, it was proved that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R0>1. Finally, some numerical simulations were carried out to illustrate the results.
11
Abstract：
The simple linear errors-in-variables (EV) model with φ-mixing random errors was mainly studied. By using the central limit theorem and the Marcinkiewicz-type strong law of large numbers for the φ-mixing sequence, the asymptotic normality of the least square (LS) estimators for the unknown parameters were established under some mild conditions. In addition, based on the strong convergence for weighted sums of φ-mixing random variables, the strong consistency of the LS estimators were obtained. Finally, the simulation study was provided to verify the validity of the theoretical results.
The simple linear errors-in-variables (EV) model with φ-mixing random errors was mainly studied. By using the central limit theorem and the Marcinkiewicz-type strong law of large numbers for the φ-mixing sequence, the asymptotic normality of the least square (LS) estimators for the unknown parameters were established under some mild conditions. In addition, based on the strong convergence for weighted sums of φ-mixing random variables, the strong consistency of the LS estimators were obtained. Finally, the simulation study was provided to verify the validity of the theoretical results.
12
Abstract：
The recursive equation Tn=Xn+Tn-1Yn was considered, in which Xn and Yn are two independent random variables, and Tn-1 on the right-hand side is independent of (Xn,Yn). Under the assumption that Xn follows a subexponential distribution with a nonzero lower Karamata index, and that (Xn,Yn) fulfills a certain dependence structure, some asymptotic formulas were obtained for the tail probabilities of Tn in this equation.
The recursive equation Tn=Xn+Tn-1Yn was considered, in which Xn and Yn are two independent random variables, and Tn-1 on the right-hand side is independent of (Xn,Yn). Under the assumption that Xn follows a subexponential distribution with a nonzero lower Karamata index, and that (Xn,Yn) fulfills a certain dependence structure, some asymptotic formulas were obtained for the tail probabilities of Tn in this equation.
13
2017, 47(11): 894-898.
DOI: 10.3969/j.issn.0253-2778.2017.11.002
Abstract：
An n-color 1-2-3 composition of positive integers is defined as an n-color composition with only parts of size 1, 2 or 3. An n-color 1-2-3 palindromic composition is an n-color 1-2-3 composition that reads the same forward as backward. Here the generating function, explicit formulas and recurrence relations for the number of n-color 1-2-3 compositions and the n-color 1-2-3 palindromic compositions of positive integers were obtained. In addition, a relation between the number of 1-2-3 compositions of a positive integer and the number of compositions of a positive integer with parts omitting all multiples of size 3 was given. Furthermore, the generalized relation was obtained.
An n-color 1-2-3 composition of positive integers is defined as an n-color composition with only parts of size 1, 2 or 3. An n-color 1-2-3 palindromic composition is an n-color 1-2-3 composition that reads the same forward as backward. Here the generating function, explicit formulas and recurrence relations for the number of n-color 1-2-3 compositions and the n-color 1-2-3 palindromic compositions of positive integers were obtained. In addition, a relation between the number of 1-2-3 compositions of a positive integer and the number of compositions of a positive integer with parts omitting all multiples of size 3 was given. Furthermore, the generalized relation was obtained.
14
Abstract：
The linear codes over the ring Fp+uFp+vFp+uvFp were studied, where p is a prime and u2=u, v2=v, uv=vu. A kind of Gray map and some weight enumerators and their relationships of linear codes over R were discussed. Moreover, an example was given to show the validity of the above weight enumerators formulas.
The linear codes over the ring Fp+uFp+vFp+uvFp were studied, where p is a prime and u2=u, v2=v, uv=vu. A kind of Gray map and some weight enumerators and their relationships of linear codes over R were discussed. Moreover, an example was given to show the validity of the above weight enumerators formulas.
15
2017, 47(11): 906-911.
DOI: 10.3969/j.issn.0253-2778.2017.11.004
Abstract：
Let α≥2 be an integer, p1 and p2 be odd prime numbers with p12. By using elementary methods and techniques, it was proved that there are no near-perfect numbers of the form 2α-1p12p22 with the redundant divisor d∈{1,p12,p22,p1p2,p1p22,p12p2}, and then an equivalent condition for near-perfect numbers of the form 2α-1p12p22 with the redundant divisor d∈{p1,p2} was obtained. Furthermore, for a fixed positive integer k≥ 2, by generalizing the definition of nearperfect numbers to be k-weakly-near-perfect numbers, it was proved that there are no k-weakly-near-perfect numbers of the form n=2α-1p12p22 when k≥ 3.
Let α≥2 be an integer, p1 and p2 be odd prime numbers with p1
16
2017, 47(11): 912-918.
DOI: 10.3969/j.issn.0253-2778.2017.11.005
Abstract：
A class of interpolation and approximation blending binary 6-point subdivision scheme was presented. The smoothness of the scheme was analyzed by the Laurent polynomial method. The limit curve can reach C4 continuous. The Holder exponent of the limit curves was also calculated. Compared with the existing binary 6-point subdivision schemes, the proposed scheme achieves higher continuity and better approximating results. Furthermore, the uniform subdivision scheme is extended to the non-uniform subdivision scheme. Experimental results illustrate the effectiveness of the subdivision scheme and the role of the shape parameters.
A class of interpolation and approximation blending binary 6-point subdivision scheme was presented. The smoothness of the scheme was analyzed by the Laurent polynomial method. The limit curve can reach C4 continuous. The Holder exponent of the limit curves was also calculated. Compared with the existing binary 6-point subdivision schemes, the proposed scheme achieves higher continuity and better approximating results. Furthermore, the uniform subdivision scheme is extended to the non-uniform subdivision scheme. Experimental results illustrate the effectiveness of the subdivision scheme and the role of the shape parameters.
17
Abstract：
Zero-difference balanced(ZDB) functions were introduced by Ding in connection with construction of optimal constant composition codes and optimal and perfect difference systems of sets. Based on such functions, people have been constructed optimal constant weight codes and optimal frequency hopping sequences. Here the zero-difference balanced function was generalized to the generalized zero-difference balanced (G-ZDB) function, and based on properties of p-cyclotomic cosets, several new classes of generalized zero-difference balanced functions were constructed.
Zero-difference balanced(ZDB) functions were introduced by Ding in connection with construction of optimal constant composition codes and optimal and perfect difference systems of sets. Based on such functions, people have been constructed optimal constant weight codes and optimal frequency hopping sequences. Here the zero-difference balanced function was generalized to the generalized zero-difference balanced (G-ZDB) function, and based on properties of p-cyclotomic cosets, several new classes of generalized zero-difference balanced functions were constructed.
18
Abstract：
A class of projectively flat Finsler metrics with three parameters was constructed, which generalizes a result obtained by Mo and Yang.
A class of projectively flat Finsler metrics with three parameters was constructed, which generalizes a result obtained by Mo and Yang.
19
Abstract：
The classifications of all the solutions to the linearized Yamabe equations and fractional Yamabe type equations are crucial to the proof of the compactness of the scalar curvature problems and the fractional scalar curvature problems respectively. These classifications, though having been proved in an analytical way before, have been proved by adopting some new geometric approaches from the perspective of conformal geometry.
The classifications of all the solutions to the linearized Yamabe equations and fractional Yamabe type equations are crucial to the proof of the compactness of the scalar curvature problems and the fractional scalar curvature problems respectively. These classifications, though having been proved in an analytical way before, have been proved by adopting some new geometric approaches from the perspective of conformal geometry.
20
Abstract：
Let D be the degree diagonal matrix of G, A be the adjacency matrix of G, Q=D+A be the signless Laplacian matrix of G. Let ξ(G) be the signless Laplacian spectral radius of G. Here the degree of graph was extended to k-degree, and average degree to k-average degree of a graph. A new upper and a new lower bound for the signless spectral radius of a graph G was obtained. Comparisons were made of the result with several classical results on the ξ(G).
Let D be the degree diagonal matrix of G, A be the adjacency matrix of G, Q=D+A be the signless Laplacian matrix of G. Let ξ(G) be the signless Laplacian spectral radius of G. Here the degree of graph was extended to k-degree, and average degree to k-average degree of a graph. A new upper and a new lower bound for the signless spectral radius of a graph G was obtained. Comparisons were made of the result with several classical results on the ξ(G).
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