Results 81 to 90 of about 434,525 (329)

Norms of elementary operators [PDF]

Proceedings of the American Mathematical Society, 2007
Let A i and B i , 1 ≤ i < n, be bounded linear operators acting on a separable Hilbert space H. In this note, we prove that sup{∥Σ n i=1 A i XB i ∥ X ∈ B(H),∥X∥ < 1} = sup{∥Σ n i=1 AiUB i ∥:UU* = U*U = IU ∈ B(H)}. Moreover, we prove that there exists an operator X o with ∥ X 0 ∥ = 1 such that ∥ Σ n i=1 A i X 0 B i ∥= sup{∥ Σ n i=1 AiXBi:X ∈
Gui-Bao Gao, Hong-Ke Du, Yue-Qing Wang
openaire   +2 more sources

Machine learning for identifying liver and pancreas cancers through comprehensive serum glycopeptide spectra analysis: a case‐control study

Molecular Oncology, EarlyView.
This study presents a novel AI‐based diagnostic approach—comprehensive serum glycopeptide spectra analysis (CSGSA)—that integrates tumor markers and enriched glycopeptides from serum. Using a neural network model, this method accurately distinguishes liver and pancreatic cancers from healthy individuals.
Motoyuki Kohjima, Yuko Takami, Ken Kawabe, Kazuhiro Tanabe, Chihiro Hayashi, Mikio Mikami, Tetsuya Kusumoto   +6 more
wiley   +1 more source

Linear extension operators for Sobolev spaces on radially symmetric binary trees

Advanced Nonlinear Studies, 2023
Let ...
Fefferman Charles, Klartag Bo’az
doaj   +1 more source

On operator norms for hyperbolic groups [PDF]

Journal of Topology and Analysis, 2017
We estimate the operator norm of radial non-negative functions on hyperbolic groups. As a consequence, we show that several forms of Haagerup’s inequality are optimal.
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Comprehensive profiling of lncRNAs and mRNAs enriched in small extracellular vesicles for early noninvasive detection of colorectal cancer: diagnostic panel assembly and extensive validation

Molecular Oncology, EarlyView.
Small extracellular vesicles are a promising source of diagnostic molecules. We conducted a comprehensive study, including transcriptome profiling and RT‐qPCR validation on large cohorts of samples. Diagnostic panels enabling sensitive detection of colorectal cancer and precancerous lesions were established. Some molecules were differentially expressed
Petra Vychytilova‐Faltejskova, Marketa Pavlikova, Lucie Pifkova, Robin Jugas, Tana Machackova, Lenka Radova, Milana Sachlova, Renata Bartosova, Tetiana Samoilenko, Zuzana Feckova, Jana Orlickova, Erika Slamova, Elleni Ponechal Michu, Dagmar Al Tukmachi, Michaela Ruckova, Martina Vodinska, Jan Kotoucek, Tina Catela Ivkovic, Marie Boudna, Lucia Bohovicova, Teodor Stanek, Jana Halamkova, Martin Svoboda, Vladimir Prochazka, Tomas Grolich, Zdenek Kala, Ondrej Slaby   +26 more
wiley   +1 more source

Learning neural operators on Riemannian manifolds

National Science Open
Learning mappings between functions (operators) defined on complex computational domains is a common theoretical challenge in machine learning. Existing operator learning methods mainly focus on regular computational domains, and have many components ...
Chen Gengxiang, Liu Xu, Meng Qinglu, Chen Lu, Liu Changqing, Li Yingguang   +5 more
doaj   +1 more source

On the Norm of Certain Weighted Composition Operators on the Hardy Space

Abstract and Applied Analysis, 2009
We obtain a representation for the norm of certain compact weighted composition operator 𝐶𝜓,𝜑 on the Hardy space 𝐻2, whenever 𝜑(𝑧)=𝑎𝑧+𝑏 and 𝜓(𝑧)=𝑎𝑧−𝑏. We also estimate the norm and essential norm of a class of noncompact weighted composition operators ...
M. Haji Shaabani, B. Khani Robati
doaj   +1 more source

Multi‐omic profiling of squamous cell lung cancer identifies metabolites and related genes associated with squamous cell carcinoma

Molecular Oncology, EarlyView.
Using multi‐omic characterization, we aimed to identify key regulators specific to squamous cell lung carcinoma (SqCC). SqCC‐specific differentially expressed genes were integrated with metabolics data. High expression of the creatine transporter SLC6A8, along with elevated creatine levels, appeared to be a distinct metabolic feature of SqCC.
Johan Staaf, Daniel Ehinger, Hans Brunnström, Mats Jönsson, Frida Rosengren, Marija Kotevska, Anna Karlsson, Mattias Aine, Christian Frezza, Maria Planck, Elsa Arbajian   +10 more
wiley   +1 more source

A General Norm on Extension of a Hilbert’s Type Linear Operator

Journal of Mathematical Extension, 2010
The main purpose of this paper is to study a general norm on extension of a Hilbert’s type linear operator in the continuous and discrete form. In addition to expressing the norm of a Hilbert’s type linear operator T : L 2 (0,∞) → L 2 (0,∞), a ...
Z. Jokar, J. Behboodian
doaj  

Maximal norm Hankel operators

Journal of Mathematical Analysis and Applications
A Hankel operator $\mathbf{H}_φ$ on the Hardy space $H^2$ of the unit circle with analytic symbol $φ$ has minimal norm if $\|\mathbf{H}_φ\|=\|φ\|_2$ and maximal norm if $\|\mathbf{H}_φ\| = \|φ\|_\infty$. The Hankel operator $\mathbf{H}_φ$ has both minimal and maximal norm if and only if $|φ|$ is constant almost everywhere on the unit circle or ...
Brevig, Ole Fredrik, Seip, Kristian
openaire   +4 more sources