Abstract
The concept of strong differential subordination was introduces in 1, 2 by Antonio and Romaguera and developed in 4. The object of the present paper is to investigate some inclusion ...relations and other interesting properties for p-valent functions defined in the open unit disk of the complex plane involving linear operator by using the principle of strong differential subordination
In this paper, we introduce a new analogue of Bernstein operators and we call it as (p, q)-Bernstein operators which is a generalization of q-Bernstein operators. We also study approximation ...properties based on Korovkin’s type approximation theorem of (p, q)-Bernstein operators and establish some direct theorems. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.
•A nonlinear sparse mode decomposition (NSMD) is proposed.•The proposed NSMD method can avoid modal aliasing and improve the orthogonality of decomposition.•NSMD method has good robustness and ...adaptability.
Traditional time-frequency analysis methods, including empirical mode decomposition (EMD), local characteristic-scale decomposition (LCD) and variable mode decomposition (VMD), have some limitations in nonlinear signal analysis. When the signal has strong noise, traditional time-frequency analysis methods will force the signal to be decomposed into several inaccurate components, and the achieved components usually suffer from the end effect problem. Considering the above pressing challenge, a new signal decomposition algorithm, nonlinear sparse mode decomposition (NSMD), is proposed in this protocol. The core of NSMD is that the local narrowband signal disappears under the action of the singular local linear operator, so the singular local linear operator can be applied to extract the local narrowband component of the detected signal. Meanwhile, the obtained local narrowband signal can be superposed as the basic signal to close to the original signal, realizing the adaptive decomposition of the signal with good robustness and adaptability. The analysis results of simulation signals and planetary gearbox fault signals indicate that the proposed NSMD method is effective for raw vibration signals.
We study the Steklov eigenvalue problem for the ∞-orthotropic Laplace operator defined on convex sets of RN, with N≥2, considering the limit for p→+∞ of the Steklov problem for the p-orthotropic ...Laplacian. We find a limit problem that is satisfied in the viscosity sense and a geometric characterization of the first non trivial eigenvalue. Moreover, we prove Brock-Weinstock and Weinstock type inequalities among convex sets, stating that the ball in a suitable norm maximizes the first non trivial eigenvalue for the Steklov ∞-orthotropic Laplacian, once we fix the volume or the anisotropic perimeter.
By Heyde's theorem, the class of Gaussian distributions on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given ...another. We prove an analogue of this theorem for two independent random vectors taking values in the space Rn. The obtained class of distributions consists of convolutions of Gaussian distributions and a distribution supported in a subspace, which is determined by coefficients of the linear forms.
For two Banach spaces X and Y, we denote by K(X,Y) (resp. B(X,Y)) the space of all compact (resp. bounded) linear operators from X to Y. In this paper, we show that for 1\leq p,q<\infty, K(\ell ..._{p},\ell _{q}) is an 8-Lipschitz retract of B(\ell _{p},\ell _{q}).
There are two notions of approximate Birkhoff–James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff–James orthogonality in the space of bounded linear ...operators defined on a normed space. A complete characterization of approximate Birkhoff–James orthogonality in the space of bounded linear operators defined on Hilbert space of any dimension is obtained which improves on the recent result by Chmieliński et al. (2017) 4, in which they characterized approximate Birkhoff–James orthogonality of linear operators on finite dimensional Hilbert space and also of compact operators on any Hilbert space.
The object of this paper is to introduce the concepts of weighted λ-statistical convergence and statistical summability (N¯λ,p). We also establish some inclusion relations and some related results ...for these new summability methods. Further, we determine a Korovkin type approximation theorem through statistical summability (N¯λ,p) and we show that our approximation theorem is stronger than classical Korovkin theorem by using classical Bernstein polynomials.
In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin ...norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain various bounds for the Berezin radius of bounded linear operators, which improve on the earlier bounds. Further, we obtain a Berezin radius inequality for the sum of the product of operators, from which we derive new Berezin radius bounds.
Celotno besedilo
Dostopno za:
BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
10.
Conditional Functional Graphical Models Lee, Kuang-Yao; Ji, Dingjue; Li, Lexin ...
Journal of the American Statistical Association,
2023, Letnik:
118, Številka:
541
Journal Article
Recenzirano
Odprti dostop
Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. The changes of graph structure can often be attributed to external variables, ...such as the diagnosis status or time, the latter of which gives rise to the problem of dynamic graphical modeling. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity due to the external variables. In this article, we introduce a conditional graphical model for multivariate random functions, where we treat the external variables as conditioning set, and allow the graph structure to vary with the external variables. Our method is built on two new linear operators, the conditional precision operator and the conditional partial correlation operator, which extend the precision matrix and the partial correlation matrix to both the conditional and functional settings. We show that their nonzero elements can be used to characterize the conditional graphs, and develop the corresponding estimators. We establish the uniform convergence of the proposed estimators and the consistency of the estimated graph, while allowing the graph size to grow with the sample size, and accommodating both completely and partially observed data. We demonstrate the efficacy of the method through both simulations and a study of brain functional connectivity network.
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