Results 41 to 50 of about 542,394 (229)

Smooth solutions to the abc equation: the xyz Conjecture [PDF]

, 2011
This paper studies integer solutions to the ABC equation A+B+C=0 in which none of A, B, C has a large prime factor. Set H(A,B, C)= max(|A|,|B|,|C|) and set the smoothness S(A, B, C) to be the largest prime factor of ABC.
Lagarias, Jeffrey C., Soundararajan, K.
core   +2 more sources

Expression of the pro-angiogenic factors vascular endothelial growth factor and interleukin-8/CXCL8 by human breast carcinomas is responsive to nutrient deprivation and endoplasmic reticulum stress

Molecular Cancer, 2004
Background The expression of pro-angiogenic cytokines, such as vascular endothelial growth factor (VEGF) and interleukin-8/CXCL8 (IL-8), plays an important role in tumor growth and metastasis.
Abcouwer Steve F, Bobrovnikova-Marjon Ekaterina V, Marjon Philip L   +2 more
doaj   +1 more source

On the largest prime factor of $n^2+1$

Journal of the European Mathematical Society, 2022
We show that the largest prime factor of n^2+1 is infinitely often greater than n^{1.279} .
openaire   +3 more sources

On SA, CA, and GA numbers [PDF]

, 2012
Gronwall's function $G$ is defined for $n>1$ by $G(n)=\frac{\sigma(n)}{n \log\log n}$ where $\sigma(n)$ is the sum of the divisors of $n$. We call an integer $N>1$ a \emph{GA1 number} if $N$ is composite and $G(N) \ge G(N/p)$ for all prime factors $p$ of
Caveney, Geoffrey, Nicolas, Jean-Louis, Sondow, Jonathan   +2 more
core   +4 more sources

Largest prime factor

Journal of Pure and Applied Algebra, 1993
Let \(P(n)\) be the largest prime factor of an integer \(n\), \(L(n)\) the number of \(k\leq n\) such that \(P(k)
openaire   +2 more sources

Elliott-Halberstam conjecture and values taken by the largest prime factor of shifted primes [PDF]

Journal of Number Theory, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Reciprocal control of viral infection and phosphoinositide dynamics

FEBS Letters, EarlyView.
Phosphoinositides, although scarce, regulate key cellular processes, including membrane dynamics and signaling. Viruses exploit these lipids to support their entry, replication, assembly, and egress. The central role of phosphoinositides in infection highlights phosphoinositide metabolism as a promising antiviral target.
Marie Déborah Bancilhon, Bruno Mesmin
wiley   +1 more source

New Evidence for a Flux-independent Spectral Index of Sgr A* in the Near-infrared

The Astrophysical Journal
In this work, we measure the spectral index of Sagittarius A* (Sgr A*) between the H (1.6 μ m) and $K^{\prime} $ (2.2 μ m) broadband filters in the near-infrared (NIR), sampling over a factor ∼40 in brightness, the largest range probed to date by a ...
Hadrien Paugnat, Tuan Do, Abhimat K. Gautam, Gregory D. Martinez, Andrea M. Ghez, Shoko Sakai, Grant C. Weldon, Matthew W. Hosek Jr., Zoë Haggard, Kelly Kosmo O’Neil, Eric E. Becklin, Gunther Witzel, Jessica R. Lu, Keith Matthews   +13 more
doaj   +1 more source

By dawn or dusk—how circadian timing rewrites bacterial infection outcomes

FEBS Letters, EarlyView.
The circadian clock shapes immune function, yet its influence on infection outcomes is only beginning to be understood. This review highlights how circadian timing alters host responses to the bacterial pathogens Salmonella enterica, Listeria monocytogenes, and Streptococcus pneumoniae revealing that the effectiveness of immune defense depends not only
Devons Mo, Catherine S. Palmer, Jacqueline M. Kimmey   +2 more
wiley   +1 more source

The role and implications of mammalian cellular circadian entrainment

FEBS Letters, EarlyView.
At their most fundamental level, mammalian circadian rhythms occur inside every individual cell. To tell the correct time, cells must align (or ‘entrain’) their circadian rhythm to the external environment. In this review, we highlight how cells entrain to the major circadian cues of light, feeding and temperature, and the implications this has for our
Priya Crosby
wiley   +1 more source