Results 111 to 120 of about 13,830,771 (328)

Stability and asymptotic properties of a linear fractional difference equation

, 2012
This paper discusses qualitative properties of the two-term linear fractional difference equation ∇α0y(n)=λy(n), where α,λ∈R ...
J. Cermák, Tomáš Kisela, Luděk Nechvátal   +2 more
semanticscholar   +1 more source

KRAS and GNAS mutations in cell‐free DNA and in circulating epithelial cells in patients with intraductal papillary mucinous neoplasms—an observational pilot study

Molecular Oncology, Volume 19, Issue 7, Page 2144-2153, July 2025.
This study demonstrates that KRAS and GNAS mutations are more prevalent in patients with resected intraductal papillary mucinous neoplasms (IPMN) compared to those under clinical surveillance. GNAS mutations significantly differ between the two patient cohorts, indicating that their absence may serve as a potential biomarker to support conservative ...
Christine Nitschke, Marie Tölle, Philipp Walter, Kira Meißner, Mara Goetz, Jolanthe Kropidlowski, Andreas W. Berger, Jakob R. Izbicki, Felix Nickel, Thilo Hackert, Klaus Pantel, Harriet Wikman, Faik G. Uzunoglu   +12 more
wiley   +1 more source

From differential to difference equations for first order ODEs [PDF]

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation.
Freed, Alan D., Walker, Kevin P.
core   +1 more source

Qualitative approximation of solutions to difference equations of various types

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper we study the asymptotic behavior of solutions to difference equations of various types. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, and establish some results concerning ...
Janusz Migda
doaj   +1 more source

Cellular liquid biopsy provides unique chances for disease monitoring, preclinical model generation and therapy adjustment in rare salivary gland cancer patients

Molecular Oncology, Volume 19, Issue 7, Page 2056-2073, July 2025.
We quantified and cultured circulating tumor cells (CTCs) of 62 patients with various cancer types and generated CTC‐derived tumoroid models from two salivary gland cancer patients. Cellular liquid biopsy‐derived information enabled molecular genetic assessment of systemic disease heterogeneity and functional testing for therapy selection in both ...
Nataša Stojanović Gužvić, Florian Lüke, Steffi Treitschke, Andrea Coluccio, Martin Hoffmann, Giancarlo Feliciello, Adithi Ravikumar Varadarajan, Xin Lu, Kathrin Weidele, Catherine Botteron, Silvia Materna–Reichelt, Felix Keil, Katja Evert, Florian Weber, Thomas Schamberger, Michael Althammer, Jirka Grosse, Dirk Hellwig, Christian Schulz, Stephan Seitz, Peter Ugocsai, Anke Schlenska‐Lange, Roman Mayr, Ulrich Kaiser, Wolfgang Dietmaier, Bernhard Polzer, Jens Warfsmann, Kamran Honarnejad, Tobias Pukrop, Daniel Heudobler, Christoph A. Klein, Christian Werno   +31 more
wiley   +1 more source

On the local dynamics of polynomial difference equations with fading stochastic perturbations [PDF]

, 2010
We examine the stability-instability behaviour of a polynomial difference equa- tion with state-independent, asymptotically fading stochastic perturbations. We find that the set of initial values can be partitioned into a stability region, an instability
Appleby, John A.D., Kelly, C., Mao, Xuerong, Rodkina, A.   +3 more
core  

Circulating tumor DNA (ctDNA) trajectories predict survival in trifluridine/tipiracil‐treated metastatic colorectal cancer patients

Molecular Oncology, Volume 19, Issue 7, Page 2120-2132, July 2025.
The authors applied joint/mixed models that predict mortality of trifluridine/tipiracil‐treated metastatic colorectal cancer patients based on circulating tumor DNA (ctDNA) trajectories. Patients at high risk of death could be spared aggressive therapy with the prospect of a higher quality of life in their remaining lifetime, whereas patients with a ...
Matthias Unseld, Stefan Kühberger, Ricarda Graf, Christine Beichler, Markus Braun, Nadia Dandachi, Ellen Heitzer, Gerald W. Prager   +7 more
wiley   +1 more source

An Ap\'ery-like difference equation for Catalan's constant

, 2002
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational coefficients, we obtain a second-order difference equation for these forms ...
Zudilin, Wadim
core   +5 more sources

Integrative analysis of circulating tumor cells (CTCs) and exosomes from small‐cell lung cancer (SCLC) patients: a comprehensive approach

Molecular Oncology, Volume 19, Issue 7, Page 2038-2055, July 2025.
This study simultaneously investigated circulating tumor cells (CTCs) and exosomes from small‐cell lung cancer (SCLC) patients. The elevated expression of JUNB and CXCR4 in CTCs was a poor prognostic factor for SCLC patients, whereas exosomal overexpression of these biomarkers revealed a high discrimination ability of patients from healthy individuals,
Dimitrios Papakonstantinou, Argyro Roumeliotou, Evangelia Pantazaka, Athanasios‐Nasir Shaukat, Athina Christopoulou, Angelos Koutras, Foteinos‐Ioannis Dimitrakopoulos, Vassilis Georgoulias, Anastasia Xagara, Evangelia Chantzara, Fillipos Koinis, Athanasios Kotsakis, Constantinos Stathopoulos, Galatea Kallergi   +13 more
wiley   +1 more source

On Invariants for Difference Equations and Systems of Difference Equations of Rational Form

Journal of Mathematical Analysis and Applications, 1999
AbstractC. J. Schinas (J. Math. Anal. Appl.,216(1997), 164–179) has presented some invariants for difference equations and systems of difference equations of rational form with constant and periodic coefficients (of certain period). We report that the presented invariants as well as their difference equations can be generalized.
openaire   +2 more sources