Results 71 to 80 of about 7,157,448 (338)

On A Matrix Hypergeometric Differential Equation

مجلة العلوم البحتة والتطبيقية, 2021
In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation.
Salah Hamd, Faisal Saleh Abdalla, Ahmed Shletiet   +2 more
doaj   +1 more source

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

, 2013
The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution.
Krishnamurthy, Subramanian, Pati, G. S., Shahriar, M. S., Tseng, S., Tu, Y., Wang, Ye   +5 more
core   +1 more source

Detecting homologous recombination deficiency for breast cancer through integrative analysis of genomic data

Molecular Oncology, EarlyView.
This study develops a semi‐supervised classifier integrating multi‐genomic data (1404 training/5893 validation samples) to improve homologous recombination deficiency (HRD) detection in breast cancer. Our method demonstrates prognostic value and predicts chemotherapy/PARP inhibitor sensitivity in HRD+ tumours.
Rong Zhu, Katherine Eason, Suet‐Feung Chin, Paul A. W. Edwards, Raquel Manzano Garcia, Richard Moulange, Jia Wern Pan, Soo Hwang Teo, Sach Mukherjee, Maurizio Callari, Carlos Caldas, Stephen‐John Sammut, Oscar M. Rueda   +12 more
wiley   +1 more source

Matrix equation representation of the convolution equation and its unique solvability

Special Matrices
We consider the convolution equation F*X=BF* X=B, where F∈R3×3F\in {{\mathbb{R}}}^{3\times 3} and B∈Rm×nB\in {{\mathbb{R}}}^{m\times n} are given and X∈Rm×nX\in {{\mathbb{R}}}^{m\times n} is to be determined. The convolution equation can be regarded as a
Satake Yuki, Sogabe Tomohiro, Kemmochi Tomoya, Zhang Shao-Liang   +3 more
doaj   +1 more source

Solution to Several Split Quaternion Matrix Equations

Mathematics
Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties.
Xin Liu, Tong Shi, Yang Zhang
doaj   +1 more source

Space--time fluctuations and the spreading of wavepackets

, 2009
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric.
Abel Camacho, Alfredo Macias, Birell N D, Bonifacio Paolo M, Breuer H-P, Claus Lämmerzahl, Ertan Göklü, Göklü E, Hogan C J, Lämmerzahl C Rademaker P, Novikov E A, Novikov E A, Sonego S, Wang C H-T   +13 more
core   +1 more source

Tumor clusters with divergent inflammation and human retroelement expression determine the clinical outcome of patients with serous ovarian cancer

Molecular Oncology, EarlyView.
Analysis of treatment‐naïve high‐grade serous ovarian carcinoma (HGSOC) and control tissues for ERVs, LINE‐1 (L1), inflammation, and immune checkpoints identified five clusters with diverse patient recurrence‐free survivals. An inflammation score was calculated and correlated with retroelement expression, where one novel cluster (Triple‐I) with high ...
Laura Glossner, Markus Eckstein, Christoph Mark, Matthias W. Beckmann, Arndt Hartmann, Pamela L. Strissel, Reiner Strick   +6 more
wiley   +1 more source

Matrix iteration algorithms for solving the generalized Lyapunov matrix equation

Advances in Difference Equations, 2021
In this paper, we first recall some well-known results on the solvability of the generalized Lyapunov equation and rewrite this equation into the generalized Stein equation by using Cayley transformation.
Juan Zhang, Huihui Kang, Shifeng Li
doaj   +1 more source

Structural Analysis by Modified Signature Matrix for Integro-differential-algebraic Equations [PDF]

, 2023
Wenqiang Yang, Wenyuan Wu, Greg Reid
openalex   +1 more source

Stability of the matrix Dyson equation and random matrices with correlations [PDF]

, 2016
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum.
Oskari Ajanki, L. Erdős, Torben Krüger
semanticscholar   +1 more source