Bounds on Projections onto Bivariate Polynomial Spline Spaces with Stable Local Bases

L _& ∞ bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases are established. The general results are then applied to obtain error bounds for best L ₂ - and l ₂ -approximation by splines on quasi-uniform triangulations. March 8, 2000. Date revised: November 20, 2000. Date accepted: July 9, 2001.     

Continuity envelopes and sharp embeddings in spaces of generalized smoothness

We study continuity envelopes in spaces of generalized smoothness and . The results are applied in proving sharp embedding assertions in some limiting situations.     

Weighted BMO and Carleson measures on spaces of homogeneous type

In this paper we characterize the weighted BMO(ω)(X), with X a space of homogeneous type, through an adequate weighted Carleson measure. As a byproduct we can define the weighted Triebel-Lizorkin space and obtain the identification with the above space.     

Quintic spline technique for time fractional fourth‐order partial differential equation

Higher order non‐Fickian diffusion theories involve fourth‐order linear partial differential equations and their solutions. A quintic polynomial spline technique is used for the numerical solutions of fourth‐order partial differential equations with Caputo time fractional derivative on a finite domain. These equations occur in many applications in real life problems such as modeling of plates and thin beams, strain gradient elasticity, and phase separation in binary mixtures, which are basic elements in engineering structures and are of great practical significance to civil, mechanical, and aerospace engineering. The quintic polynomial spline technique is used for space discretization and the time‐stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence analysis are also discussed. The numerical results are given, which demonstrate the effectiveness and accuracy of the numerical method. The numerical results obtained in this article are also compared favorably well with the results of (S. S. Siddiqi and S. Arshed, Int. J. Comput. Math. 92 (2015), 1496–1518). © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 445–466, 2017     

New spline basis functions for sampling approximations

We describe a method of constructing a new kind of splines with compact support on . These basis functions consisting of a linear combination of the cardinal B-splines of mixed orders enable us to achieve simultaneously a good sampling approximation and an interpolation of any smooth function.     

The Sharkovski? Theorem for spaces of measurable functions

We formulate a generalization of the so-called Random Sharkovski? Theorem from paper by Jan Andres, which is the randomized version of the classical Sharkovski? Theorem. We use the method of transformation to deterministic case involving the Kuratowski-Ryll-Nardzewski selection theorem, which allows us to omit the assumption of completeness of the incorporated measurable space. Moreover, we formulate an analogue of the Sharkovski? Theorem for spaces of measurable functions and for Lp-spaces.     

模糊向量空间的商空间

在史和黄重新定义的模糊向量空间的模糊基和模糊维数的基础上,讨论模糊向量空间的模糊线性映射及其性质,定义模糊向量空间(V,μ)的商空间(V/K,μK)并研究了它的性质,证明公式dim(μK)+dim (k(e)ff)=dim(μ)成立,其中k(e)ff是模糊向量空间(V,μ)关于模糊线性映射f的模糊核空间.     

Metrizability of Spaces of ℝ-places of Function Fields of Transcendence Degree 1 Over Real Closed Fields

In this article we discuss the following question “When do different orderings of the rational function field R(X) (where R is a real closed field) induce the same ?-place?” We use this to show that if R contains a dense real closed subfield R′, then the spaces of ?-places of R(X) and R′(X) are homeomorphic. For the function field K = R(X), we prove that its space M(K) of ?-places is metrizible if and only if R contains a countable dense subfield. Moreover, we show that this condition is neccessary for the metrizability of M(F) for any function field F of transcendence degree 1 over R.     

Accelerated Failure Time Model for Arbitrarily Censored Data With Smoothed Error Distribution

This article develops a semiparametric procedure to estimate parameters of an accelerated failure time model. To express the density of the error distribution, we use the P-spline (B-splines with penalties) smoothing technique. To accommodate error densities with infinite support (and for other reasons) we replace the B-splines with their limits as the degree of the B-spline goes to infinity; namely, with normal densities. The spline coefficients as well as any number of regression parameters are quickly and accurately estimated via penalized maximum likelihood. The method directly provides predictive survival distributions for fixed values of covariates while allowing for left-, right-, and interval-censored data. The approach has been implemented as an R package and is applied here to the problem of predicting AIDS-free survival in the presence of interval censoring.     

修正样条小波最小二乘法用于分辨高噪声重叠峰

采用连续样条小波变换确定重叠信号的组分峰的数目和峰位置,将样条小波最小二乘法加以改进,使其成为既能滤出噪声又能分峰的新方法.对信噪比为1的重叠峰进行处理,得到满意结果.该方法只需对信号进行一次处理,处理速度快,且数据点无须为2n(n∈Z).应用于毛细管电泳电导信号的处理,得到满意结果.