An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes

In the present study,we extend the order-preserving(OP)criterion proposed in our latest studies to the WENO-Z-type schemes.Firstly,we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Ztype weights in a uniform formula from the perspective of the mapping relation.Then,we naturally introduce the OP criterion to improve the WENO-Z-type schemes,and the resultant schemes are denoted as MOP-GMWENO-X,where the notation“X”is used to identify the version of the existing WENO-Z-type scheme in this paper.Finally,extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes.We draw the conclusion that,the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes.The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations.The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

On the Semigroups of Order-preserving and A-Decreasing Finite Transformations

For n E N, let On be the semigroup of all singular order-preserving mappings on [n] = （1, 2,..., n}. For each nonempty subset A of [n], let On （A） = （a ∈ On： （A k ∈ A） ka ≤ k} be the semigroup of all order-preserving and A-decreasing mappings on [n]. In this paper it is shown that On（A）is an abundant semigroup with n - 1 ＊-classes. Moreover, On（A） is idempotent-generated and its idempotent rank is 2n - 2 - IA／（n}l. Further, it is shown that the rank of On（A） is equal to n - 1 if 1 ∈ A, and it is equal to n otherwise.

On order-preserving and order-reversing mappings defined on cones of convex functions

In this paper,we first show that for a Banach space X,there is a fully order-reversing mapping T from conv(X)(the cone of all the extended real-valued lower semicontinuous proper convex functions defined on X)onto itself if and only if X is reflexive and linearly isomorphic to its dual X^(*).Then we further prove the following generalized Artstein-Avidan-Milman representation theorem:For every fully order-reversing mapping T:conv(X)→conv(X),there exist a linear isomorphism U:X→X^(*),x_(0)^(*),φ_(0)∈X^(*),α>0 and r_0∈R so that(Tf)(x)=α(Ff)(Ux+x_(0)^(*))+<φ_(0),x>+r_(0),■x∈X where T:conv(X)→conv(X^(*))is the Fenchel transform.Hence,these resolve two open questions.We also show several representation theorems of fully order-preserving mappings defined on certain cones of convex functions.For example,for every fully order-preserving mapping S:semn(X)→semn(X),there is a linear isomorphism U:X→X so that(Sf)(x)=f(Ux),■f∈semn(X),x∈X where semn(X)is the cone of all the lower semicontinuous seminorms on X.

基于数字签名与Trie的保序子矩阵约束查询

目前,基因芯片技术飞速发展,促使生物学家积累了大量的不同实验条件下的基因表达数据.事实证明,基因芯片数据分析在理解基因功能、基因调控和分子生命过程中发挥着重要作用.保序子矩阵(order-preserving submatrix,简称OPSM)是基因芯片数据分析技术中的一种有效模型,其可以发现在部分基因和不同实验条件下具有相同表达趋势的聚类.在分析基因表达机理的过程中,OPSM的检索无疑节省了生物学家的时间与精力.目前,OPSM的查询主要是基于关键词的检索方法,但是分析者对结果具有微弱的控制力.通常,分析者所能决定的临时的参数设置往往偏离其领域知识,致使检索结果与真实想要的结果相去甚远.为了解决上述问题,提出两类基于数字签名与Trie的OPSM索引与约束查询方法.在真实数据上进行了大量的实验,实验结果表明,所提出的方法具有良好的有效性与可扩展性.

Coupling for Markovian switching jump-diffusions

This work is concerned with coupling for a class of Markovian switching jump-diffusion processes.The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switching device.For this class of processes,we construct a successful coupling and an order-preserving coupling.

Order-Revealing Encryption:File-Injection Attack and Forward Security

Order-preserving encryption(OPE)and order-revealing encryption(ORE)are among the core ingredients for encrypted databases(EDBs).In this work,we study the leakage of OPE and ORE and their forward security.We propose generic yet powerful file-inject ion attacks(FI As)on OPE/ORE,aimed at the situations of possessing order by and range queries.Our FI As only exploit the ideal leakage of OPE/ORE(in particular,no need of data denseness or frequency).We also improve their efficiency with the frequency statistics using a hierarchical idea such that the high-frequency values will be recovered more quickly.We conduct some experiments on real datasets to test the performance,and the results show that our FI As can cause an extreme hazard on most of the existing OPEs and OREs with high efficiency and 100%recovery rate.We then formulate forward security of ORE,and propose a practical compilation framework for achieving forward secure ORE to resist the perniciousness of FIA.The compilation framework can transform most of the existing OPEs/OREs into forward secure OREs,with the goal of minimizing the extra burden incurred on computation and storage.We also present its security proof,and execute some experiments to analyze its performance.The proposed compilation is highly efficient and forward secure.

A General Improvement in the WENO-Z-Type Schemes

A new type offinite volume WENO schemes for hyperbolic problems was devised in[33]by introducing the order-preserving(OP)criterion.In this continuing work,we extend the OP criterion to the WENO-Z-type schemes.Wefirstly rewrite the formulas of the Z-type weights in a uniform form from a mapping perspective inspired by extensive numerical observations.Accordingly,we build the concept of the locally order-preserving(LOP)mapping which is an extension of the order-preserving(OP)mapping and the resultant improved WENO-Z-type schemes are denoted as LOP-GMWENO-X.There are four major advantages of the LOP-GMWENO-X schemes superior to the existing WENO-Z-type schemes.Firstly,the new schemes can amend the serious drawback of the existing WENO-Z-type schemes that most of them suffer from either producing severe spurious oscillations or failing to obtain high resolutions in long calculations of hyperbolic problems with discontinuities.Secondly,they can maintain considerably high resolutions on solving problems with high-order critical points at long output times.Thirdly,they can obtain evidently higher resolution in the region with high-frequency but smooth waves.Finally,they can significantly decrease the post-shock oscillations for simulations of some 2D problems with strong shock waves.Extensive benchmark examples are conducted to illustrate these advantages.