ISSN 1673-3452
ISSN 1673-3576(Online)
CN 11-5739/O1
Postal Subscription Code 80-964
2018 Impact Factor: 0.565
Life activities are extremely complex phenomena in nature. From molecular signaling regulation to multi-cellular tissue formation and so on, the biological system consists of multiple temporal, spatial and functional scales. Multiscale mathematical models have extensive applications in life science research due to their capacity of appropriately simulating the complex multiscale biological systems. Many mathematical methods, including deterministic methods, stochastic methods as well as discrete or rule-based methods, have been widely used for modeling biological systems. However, the models at single scale are not sufficient to simulate complex biological systems. Therefore, in this paper we give a survey of two multiscale modeling approaches for biological systems. One approach is continuous stochastic method that couples ordinary differential equations and stochastic differential equations; Another approach is hybrid continuous-discrete method that couples agent-based model with partial differential equations. We then introduce the applications of these multiscale modeling approaches in systems biology and look ahead to the future research.
Given a connected graph G, the revised edge-revised Szeged index is defined as Sze∗(G)=∑e=uv∈EG(mu(e)+m0(e)2)(mv(e)+m0(e)2), where mu(e), mv(e) and m0(e) are the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u and the number of edges of G at the same distance to u and v, respectively. In this paper, by transformation and calculation, the lower bound of revised edge-Szeged index of unicyclic graphs with given diameter is obtained, and the extremal graph is depicted.
A combinatorial batch code has strong practical motivation in the distributed storage and retrieval of data in a database. In this survey, we give a brief introduction to the combinatorial batch codes and some progress.
Let k⩾1 be an integer. Assume that RH holds. In this paper we prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p23+p33+p43+p53, where p1,p2,p3,p4,p5 are prime numbers. This expands the previous results.
We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper. The construction techniques of iterative methods are induced by using linear approximation, integral interpolation, Adomian series decomposition, Taylor expansion, multi-step iteration, etc. The convergent conditions and proof methods, including majorizing sequences and recurrence relations, in semilocal convergence of iterative methods for nonlinear equations are discussed in the theoretical analysis. The majorizing functions, which are used in majorizing sequences, are also discussed in this paper.
Generalized exponential distribution is a class of important distribution in lifedata analysis, especially in some skewed lifedata. The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered. The maximum likelihood estimators are obtained using the EM algorithm. Some simulations are carried out to illustrate that the proposed algorithm is effective for the model. Finally, a set of medicine data is analyzed by generalized exponential distribution.
Determining the search direction and the search step are the two main steps of the nonlinear optimization algorithm, in which the derivatives of the objective and constraint functions are used to determine the search direction, the one-dimensional search and the trust domain methods are used to determine the step length along the search direction. One dimensional line search has been widely discussed in various textbooks and references. However, there is a less-known technique—arc-search method, which is relatively new and may generate more efficient algorithms in some cases. In this paper, we will survey this technique, discuss its applications in different optimization problems, and explain its potential improvements over traditional line search method.
In this paper, path-connectivity of the set of some special wavelets in L2(R), which is the topological geometric property of wavelets, is introduced. In particular, the main progress of wavelet connectivity in the past twenty years is reviewed and some unsolved problems are listed. The corresponding results of high dimension case and other cases are also briefly explained.
In this paper,we give all primitive solutions of a parameterized family of quartic Thue equations:
x4−4cx3y+(6c+2)x2y2+4cxy3+y4=96c+169,c>0.
The iterated spherical average Δ(A1)N is an important operator in harmonic analysis, and has very important applications in approximation theory and probability theory, where Δ is the Laplacian, A1 is the unit spherical average and (A1)N is its iteration. In this paper, we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space, and prove the boundedness of the operator in Triebel-Lizorkin space. Moreover, we use above conclusions to improve the existing results of the boundedness of this operator in Lp space.
It is not completely clear which elements constitute the frame sets of the B-splines currently, but some considerable results have been obtained. In this paper, firstly, the background of frame set is introduced. Secondly, the main progress of the frame sets of the B-splines in the past more than twenty years are reviewed, and particularly the progress for the frame set of the 2 order B-spline and the frame set of the 3 order B-spline are explained, respectively.
In this note, we consider a class of Fourier integral operators with rough amplitudes and rough phases. When the index of symbols in some range, we prove that they are bounded on L1 and construct an example to show that this result is sharp in some cases. This result is a generalization of the corresponding theorems of Kenig-Staubach and Dos Santos Ferreira-Staubach.
By utilizing the improvement function, we change the nonsmooth convex constrained optimization into an unconstrained optimization, and construct an infeasible quasi-Newton bundle method with proximal form. It should be noted that the objective function being minimized in unconstrained optimization subproblem may vary along the iterations (it does not change if the null step is made, otherwise it is updated to a new function). It is necessary to make some adjustment in order to obtain the convergence result. We employ the main idea of infeasible bundle method of Sagastizàbal and Solodov, and under the circumstances that each iteration point may be infeasible for primal problem, we prove that each cluster point of the sequence generated by the proposed algorithm is the optimal solution to the original problem. Furthermore, for BFGS quasi-Newton algorithm with strong convex objective function, we obtain the condition which guarantees the boundedness of quasi-Newton matrices and the R-linear convergence of the iteration points.
We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective, and also the properties for cluster-tilting objects in d-cluster categories. We get the following results: (1) When d>1, any almost complete cluster-tilting object in d-cluster category has only one complement. (2) Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras. We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category. (3) A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n−1(n>2). (4) The (2m+1)-cluster category of type D2n−1 admits a cluster-tilting object such that its endomorphism algebra is self-injective, and its stable category is equivalent to the (4m+2)-cluster category of type A4mn−4m+2n−1.
This paper gives the truncated version of the generalized minimum backward error algorithm (GMBACK)—the incomplete generalized minimum backward perturbation algorithm (IGMBACK) for large nonsymmetric linear systems. It is based on an incomplete orthogonalization of the Krylov vectors in question, and gives an approximate or quasi-minimum backward perturbation solution over the Krylov subspace. Theoretical properties of IGMBACK including finite termination, existence and uniqueness are discussed in details, and practical implementation issues associated with the IGMBACK algorithm are considered. Numerical experiments show that, the IGMBACK method is usually more efficient than GMBACK and GMRES, and IMBACK, GMBACK often have better convergence performance than GMRES. Specially, for sensitive matrices and right-hand sides being parallel to the left singular vectors corresponding to the smallest singular values of the coefficient matrices, GMRES does not necessarily converge, and IGMBACK, GMBACK usually converge and outperform GMRES.
In this paper, a three-term derivative-free projection method is proposed for solving nonlinear monotone equations. Under some appropriate conditions, the global convergence and R-linear convergence rate of the proposed method are analyzed and proved. With no need of any derivative information, the proposed method is able to solve large-scale nonlinear monotone equations. Numerical comparisons show that the proposed method is effective.
In this work, we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:
{TΔt−1ν(tΔν−1νx(t))=f(x(t+ν−1)),t∈[0,T]N0,x(ν−2)=[tΔν−1νx(t)]t=T=0.
The existence of nontrivial solutions is obtained in the case of super quadratic growth of the nonlinear term f by change of fountain theorem.
In many fields, we need to deal with hierarchically structured data. For this kind of data, hierarchical mixed effects model can show the correlation of variables in the same level by establishing a model for regression coefficients. Due to the complexity of the random part in this model, seeking an effective method to estimate the covariance matrix is an appealing issue. Iterative generalized least squares estimation method was proposed by Goldstein in 1986 and was applied in special case of hierarchical model. In this paper, we extend the method to the general hierarchical mixed effects model, derive its expressions in detail and apply it to economic examples.
As the extension of classical Hardy operator and Cesàro operator, Hausdorff operator plays an important role in the harmonic analysis, so it is significant to discuss the boundedness of this kind of operator on various function spaces. The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces. In addition, the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.
In this paper, a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined. Using the left and right index arrays, we divide the necklace words into 5 classes. We discuss finite-dimensional Lie subalgebras of necklace Lie algebras intensively and prove that some subalgebras are isomorphism to simple Lie algebra sl(n).
Let p and q be two distinct odd primes and let d=(p−1,q−1). In this paper, we construct d-ary generalized two-prime Sidelnikov sequences and study the autocorrelation values and linear complexity.