1-Norm/2-Norm约束及小波多尺度2D体波走时成像

在对浅地表复杂地下介质层析成像时,由于观测系统局限性及方法本身对特定岩石地球物理属性的不敏感性等因素,造成地球物理反演存在多解性。在地震走时成像中,地震射线数量在低速区域分布较少形成阴影区,造成其对低速区域成像分辨率较低。同时因为观测数据包含干扰信息以及不同反演方法的局限性等因素造成反演结果包含次生假异常。这里主要研究了空间域的L1-norm、L2-norm约束反演及小波域小波系数稀疏约束反演,对比不同反演方式及约束条件对地质模型的分辨能力。通过测试孤立异常模型、层状地层模型、倾斜地层模型,得出三种不同反演方式分别具有对不同特定模型的分辨特性。在实际资料成像中,可以通过使用多种反演方式,对比反演结果合理性以期达到更准确的地质构造解释。

1-TYPE LIPSCHITZ SELECTIONS IN GENERALIZED 2-NORMED SPACES

We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.

Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

The Aleksandrov Problem in Non-Archimedean 2-Fuzzy 2-Normed Spaces

We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.

Design of Polynomial Fuzzy Neural Network Classifiers Based on Density Fuzzy C-Means and L2-Norm Regularization

In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2,β)-BANACH SPACES

In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.

A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

On Felbin-type Fuzzy 2-normed Spacesand Its Fuzzy I-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.

THE L^2-NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2ND ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGULARITY

Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.

CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM

The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.

H^2-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach

The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H2- exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C norm are derived.

Angel estimation via frequency diversity of the SIAR radar based on Bayesian theory

The orthogonal signals of multi-carrier-frequency emission and multiple antennas receipt module are used in SIAR radar.The corresponding received echo is equivalent to non-uniform spatial sampling after the frequency diversity process.As using the traditional Fourier transform will result in the target spectral with large sidelobe,the method presented in this paper firstly makes the preordering treatment for the position of the received antenna.Then,the Bayesian maximum posteriori estimation with l2-norm weighted constraint is utilized to achieve the equivalent uniform array echo.The simulations present the spectrum estimation in angle precision estimation of multiple targets under different SNRs,different virtual antenna numbers and different elevations.The estimation results confirm the advantage of SIAR radar both in array expansion and angle estimation.

Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces

Abstract This paper studies the problem of minimizing a homogeneous polynomial （form） f（x） over the unit sphere Sn-1 = {x ∈ R^n： ｜｜X｜｜2 = 1}. The problem is NP-hard when f（x） has degree 3 or higher. Denote by fmin （resp. fmax） the minimum （resp. maximum） value of f（x） on S^n-1. First, when f（x） is an even form of degree 2d, we study the standard sum of squares （SOS） relaxation for finding a lower bound of the minimum .fmin ：max γ s.t.f（x）-γ.｜｜x｜｜2^2d is SOS.Let fos be be the above optimal value. Then we show that for all n ≥ 2d,Here, the constant C（d） is independent of n. Second, when f（x） is a multi-form and ^-1 becomes a muilti-unit sphere, we generalize the above SOS relaxation and prove a similar bound. Third, when f（x） is sparse, we prove an improved bound depending on its sparsity pattern; when f（x） is odd, we formulate the problem equivalently as minimizing a certain even form, and prove a similar bound. Last, for minimizing f（x） over a hypersurface H（g） = {x E lRn： g（x） = 1} defined by a positive definite form g（x）, we generalize the above SOS relaxation and prove a similar bound.

On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s T 2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however, the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the classical Hotelling’s T 2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L 2-norm based test. The asymptotic powers of the proposed L 2-norm based test and Hotelling’s T 2 test are derived and theoretically compared. Methods for implementing the L 2-norm based test are described. Simulation studies are conducted to compare the L 2-norm based test and Hotelling’s T 2 test when the latter can be well defined, and to compare the proposed implementation methods for the L 2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.

RUELLE'S INEQUALITY FOR THE ENTROPY OF RANDOM DIFFEOMORPHISMS

In this paper, we prove Ruelle’s inequality for the entropy and Lyapunov exponents of random diffeomorphisms. Y. Kefer has studied this problem in ergodic case, but his theorem and proof seem to be incorrect. A new discussion is given in this paper with some new ideas and methods to be introduced, especially for f∈Diff^2(M), we introduce a new definition of C^2-norm |f|c^2 and the concept of relation number r(f) which play an important role both in this paper and in general studies.