Results 81 to 90 of about 756,333 (330)

A method for constructing a complete bifurcation picture of a boundary value problem for nonlinear partial differential equations: application of the Kolmogorov-Arnold theorem [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика
The purpose of this study is to develop a numerical method for bifurcation analysis of nonlinear partial differential equations, based on the reduction of partial differential equations to ordinary ones, using the Kolmogorov-Arnold theorem.
Gromov, Vasily Alexandrovich, Tomashchuk, Korney Kirillovich, Beschastnov, Yury Nikolaevich, Sidorenko, Artem Aleksandrovich, Kakurin, Vasily Vladimirovich   +4 more
doaj   +1 more source

A large‐scale retrospective study in metastatic breast cancer patients using circulating tumour DNA and machine learning to predict treatment outcome and progression‐free survival

Molecular Oncology, EarlyView.
There is an unmet need in metastatic breast cancer patients to monitor therapy response in real time. In this study, we show how a noninvasive and affordable strategy based on sequencing of plasma samples with longitudinal tracking of tumour fraction paired with a statistical model provides valuable information on treatment response in advance of the ...
Emma J. Beddowes, Mario Ortega Duran, Solon Karapanagiotis, Alistair Martin, Meiling Gao, Riccardo Masina, Ramona Woitek, James Tanner, Fleur Tippin, Justine Kane, Jonathan Lay, Anja Brouwer, Stephen‐John Sammut, Suet‐Feung Chin, Davina Gale, Dana W. Y. Tsui, Sarah‐Jane Dawson, Nitzan Rosenfeld, Maurizio Callari, Oscar M. Rueda, Carlos Caldas   +20 more
wiley   +1 more source

Inhomogeneous Schrödinger system with inverse square potential in three space dimensions

Journal of Inequalities and Applications
This work studies the inhomogeneous Schrödinger coupled system with inverse square potential i ∂ t u j + Δ u j − λ | x | 2 u j = ± | x | − τ ( ∑ k = 1 m a j k | u k | p ) | u j | p − 2 u j . $$ i\partial _{t} u_{j} +\Delta u_{j}-\frac{\lambda}{|x|^{2}}u_{
Salah Boulaaras, Radhia Ghanmi, Tarek Saanouni   +2 more
doaj   +1 more source

On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup

AIMS Mathematics
This study explored the time asymptotic behavior of the Schrödinger equation with an inhomogeneous energy-critical nonlinearity. The approach follows the concentration-compactness method due to Kenig and Merle.
Saleh Almuthaybiri, Radhia Ghanmi , Tarek Saanouni   +2 more
doaj   +1 more source

On a linear system of differential equations

Вестник КазНУ. Серия математика, механика, информатика, 2019
The linear systems of partial differential equations of the first order with the identical main parts is considered. Аpplying the well-known relation between a normal system of ordinary differential equations and a linear system of partial differential
T. М. Aldibekov, M. M. Aldazharova
doaj   +1 more source

Multidimensional OMICs reveal ARID1A orchestrated control of DNA damage, splicing, and cell cycle in normal‐like and malignant urothelial cells

Molecular Oncology, EarlyView.
Loss of the frequently mutated chromatin remodeler ARID1A, a subunit of the SWI/SNF cBAF complex, results in less open chromatin, alternative splicing, and the failure to stop cells from progressing through the cell cycle after DNA damage in bladder (cancer) cells. Created in BioRender. Epigenetic regulators, such as the SWI/SNF complex, with important
Rebecca M. Schlösser, Florian Krumbach, Eyleen Corrales, Geoffroy Andrieux, Christian Preisinger, Franziska Liss, Alexandra Golzmann, Melanie Boerries, Kerstin Becker, Ruth Knüchel, Stefan Garczyk, Bernhard Lüscher   +11 more
wiley   +1 more source

Chemoresistome mapping in individual breast cancer patients unravels diversity in dynamic transcriptional adaptation

Molecular Oncology, EarlyView.
This study used longitudinal transcriptomics and gene‐pattern classification to uncover patient‐specific mechanisms of chemotherapy resistance in breast cancer. Findings reveal preexisting drug‐tolerant states in primary tumors and diverse gene rewiring patterns across patients, converging on a few dysregulated functional modules. Despite receiving the
Maya Dadiani, Gilgi Friedlander, Gili Perry, Nora Balint‐Lahat, Shlomit Gilad, Dana Morzaev‐Sulzbach, Anjana Shenoy, Noa Bossel Ben‐Moshe, Anya Pavlovsky, Rinat Bernstein‐Molho, Eytan Domany, Iris Barshack, Tamar Geiger, Bella Kaufman, Einav Nili Gal‐Yam   +14 more
wiley   +1 more source

Global solutions for bi-harmonic inhomogeneous non-linear Schrödinger equations in Lebesgue spaces

Journal of Inequalities and Applications
This paper studies the inhomogeneous bi-harmonic nonlinear Schrödinger equation i u ˙ + Δ 2 u ± | x | − τ | u | p − 1 u = 0 , $$ \mbox{i}\dot{u} +\Delta ^{2} u\pm |x|^{-\tau}|u|^{p-1}u=0, $$ where u : = u ( t , x ) : R × R N → C $u:=u(t,x):\mathbb{R ...
Radhia Ghanmi, Salah Boulaaras, Tarek Saanouni   +2 more
doaj   +1 more source

Superprocesses and Partial Differential Equations

The Annals of Probability, 1993
This is a survey of recent developments on measure-valued Markov processes including a number of the author's important contributions. This subject has its origins in the paper of \textit{S. Watanabe} [J. Math. Kyoto Univ. 8, 141-167 (1968; Zbl 0159.462)] in which a class of measure-valued branching processes was constructed based on a family of ...
openaire   +2 more sources

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