Results 41 to 50 of about 4,643,635 (279)
Molecular Oncology, EarlyView.Matched spatial transcriptomics and single‐nuclei RNA‐seq were generated for anaplastic and BRAFV600E papillary thyroid cancers revealing generic and tumor‐specific states occurring in cancer cells and in the tumor microenvironment. In this context, cancer dedifferentiation mirrored organoid maturation through ordered thyroid marker gain/loss ...
Adrien Tourneur +11 more
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Characteristics of Conservation Laws for Difference Equations [PDF]
, 2013 Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the ...
Hydon, PE +3 more
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Invariants for Difference Equations and Systems of Difference Equations of Rational Form
Journal of Mathematical Analysis and Applications, 1997 The author consideres the system of difference equations \[ x_{n+1} = \frac{a_n y_n + A}{x_{n-1}}, \qquad y_{n+1} = \frac{b_n x_n + A}{y_{n-1}}, n = 0, 1,\dots\tag{1} \] where the coefficients \(\{a_n\}\) and \(\{b_n\}\) are periodic sequences of positive numbers of period 2 and \(A\) is a positive constant. Some invariants for system (1) are presented.
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Molecular Oncology, EarlyView.Detecting circulating tumor cells (CTCs) in blood before surgery may help predict outcomes in patients with head and neck squamous cell carcinoma (HNSCC). Here, we show when combined with tumor size and lymph node involvement from routine imaging, CTC status identifies high‐risk patients with poorer survival—offering a simple, minimally invasive tool ...
Susanne Flach +9 more
wiley +1 more source
Global Behavior of a Rational Difference Equation
四川大学学报. 自然科学版, 2018 In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of a rational difference equation x_(n+1)=(x_n x_(n-k))/(αx_n+βx_(n-(k+1)) ), where inter k∈N, inter n∈N∪{0},α,β are real ...
CHEN Wei-Wei
doaj
Analysis of the Convergence and Periodicity of a Rational Difference Equation
Journal of Mathematical Sciences and Modelling, 2019 The exact solutions of most difference equations cannot be obtained sometimes. This can be attributed to the fact that there is no a specific approach from which one can find the exact solution.
Mohammed Almatrafi, Marwa Alzubaidi
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Molecular Oncology, EarlyView.This study identifies somatostatin receptor 4 (Sstr4) as a critical tumor suppressor against skin and head/neck cancers (HNSCC, cSCC, and BCC). The loss of Sstr4 removes a check on cell growth, causing hyperactivation of the MAPK‐ERK signaling pathway (↑).
Ali Taqvi +6 more
wiley +1 more source
Rate of convergence of solutions of rational difference equation of second order
Advances in Difference Equations, 2004 We investigate the rate of convergence of solutions of some special cases of the equation , with positive parameters and nonnegative initial conditions.
Kalabušić S +1 more
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Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation
Complexity, 2019 Let k be a nonnegative integer and c a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c), n≥0, with positive initial ...
Wen-Xiu Ma
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The Form of the Solutions of System of Rational Difference Equation
Journal of Mathematical Sciences and Modelling, 2018 In this article, we study the form of the solutions of the system of difference equations $x_{n+1}=((y_{n-8})/(1+y_{n-2}x_{n-5}y_{n-8}))$, $y_{n+1}=((x_{n-8})/(\pm1\pm x_{n-2}y_{n-5}x_{n-8}))$, with the initial conditions are real numbers.
E. M. Elsayed, Marwa M. Alzubaidi
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