Results 31 to 40 of about 3,220 (237)

Linear forms in logarithms and exponential Diophantine equations [PDF]

Hardy-Ramanujan Journal, 2020
This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations. Secondly how this theory is the culmination of a series of greater and smaller discoveries.
openaire   +3 more sources

Repdigits as Euler functions of Lucas numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.
Bravo Jhon J., Faye Bernadette, Luca Florian, Tall Amadou   +3 more
doaj   +1 more source

On the Diophantine Equation $\left(9d^2 + 1\right)^x + \left(16d^2 - 1\right)^y = (5d)^z$ Regarding Terai's Conjecture

Journal of New Theory
This study proves that the Diophantine equation $\left(9d^2+1\right)^x+\left(16d^2-1\right)^y=(5d)^z$ has a unique positive integer solution $(x,y,z)=(1,1,2)$, for all $d>1$.
Murat Alan, Tuba Çokoksen
doaj   +1 more source

The Efficacy and Safety of Bevacizumab/Irinotecan/Temozolomide (BIT) for Relapsed/Refractory Neuroblastoma: The UK Children's Cancer and Leukaemia Group Experience

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Patients with high‐risk neuroblastoma who either are refractory to induction chemotherapy or relapse following multi‐modal treatment have a dismal prognosis. Based on data from the BEACON trial, since 2021 the UK national guidelines recommend bevacizumab, irinotecan, and temozolomide (BIT) for patients with relapsed/refractory ...
Thomas J. Jackson, Menna Shamma, Upeka Senanayake, Shaimaa Sahmoud, Kathleen Duffin, Victoria Howard, David King, Ayesha Fathani, Blanche Lumb, Andrei Pobischan, Irum Latif Memon, Monzir Ahmed, Rhian Thomas, Gerard Millen, Yasmeen Alomari, Sucheta Vaidya, Lynley V. Marshall, Sally L. George, Ramya Ramanujachar, Juliet Gray, Paola Angelini   +20 more
wiley   +1 more source

Hypergeometric transformations of linear forms in one logarithm

Functiones et Approximatio Commentarii Mathematici, 2008
We discuss hypergeometric constructions of rational approximations to values of the logarithm function.
Viola, Carlo, Zudilin, Wadim
openaire   +4 more sources

Inhibiting stearoyl‐CoA desaturase suppresses bone metastatic prostate cancer by modulating cellular stress, mTOR signaling, and DNA damage response

FEBS Letters, EarlyView.
Bone metastasis in prostate cancer (PCa) patients is a clinical hurdle due to the poor understanding of the supportive bone microenvironment. Here, we identify stearoyl‐CoA desaturase (SCD) as a tumor‐promoting enzyme and potential therapeutic target in bone metastatic PCa.
Alexis Wilson, Mackenzie K Herroon, Shane Mecca, Laimar C Garmo, Jacob Lindquist, Shrila Rajendran, Steve M. Patrick, Izabela Podgorski   +7 more
wiley   +1 more source

On a few Diophantine equations, in particular, Fermat's last theorem

International Journal of Mathematics and Mathematical Sciences, 2003
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
doaj   +1 more source

Linear forms in elliptic logarithms

Journal of Number Theory, 1985
The author studies lower bounds for linear forms in elliptic integrals in the case of complex multiplications, and related estimates for dependence relations of such numbers. His results considerably improves on the previous works of D. Masser and M. Anderson on these topics, the main feature being a sharp dependence on the heights of the corresponding
openaire   +2 more sources

Calpain small subunit homodimerization is robust and calcium‐independent

FEBS Letters, EarlyView.
Calpains dimerize via penta‐EF‐hand (PEF) domains. Using single‐molecule force spectroscopy, we measured the strength and kinetics of PEF–PEF homodimer binding. The interaction is robust, shows a transient conformational step before dissociation, and remains largely insensitive to Ca2+.
Nesha May O. Andoy, Trina Dykstra‐MacPherson, Mathias A. Bell, Peter L. Davies, Ruby May A. Sullan   +4 more
wiley   +1 more source

Aggressive prostate cancer is associated with pericyte dysfunction

Molecular Oncology, EarlyView.
Tumor‐produced TGF‐β drives pericyte dysfunction in prostate cancer. This dysfunction is characterized by downregulation of some canonical pericyte markers (i.e., DES, CSPG4, and ACTA2) while maintaining the expression of others (i.e., PDGFRB, NOTCH3, and RGS5).
Anabel Martinez‐Romero, Ane Martinez‐Larrinaga, Joaquim Grego‐Bessa, Saioa Garcia‐Longarte, Hielke van Splunder, Ianire Astobiza, Amaia Ercilla, Laura Bozal‐Basterra, Isabel Mendizabal, Pilar Villacampa, Arkaitz Carracedo, Mariona Graupera   +11 more
wiley   +1 more source