Results 71 to 80 of about 33,489 (278)

Quartic integral polynomial Pell equations

Journal of Number Theory
In this paper we classify all monic, quartic, polynomials $d(x)\in\mathbb{Z}[x]$ for which the Pell equation $$f(x)^2-d(x)g(x)^2=1$$ has a non-trivial solution with $f(x),g(x)\in\mathbb{Z}[x]$.
Scherr, Zachary, Thompson, Katherine
openaire   +2 more sources

Imaging of Biphoton States: Fundamentals and Applications

Advanced Functional Materials, EarlyView.
Quantum states of two photons exhibit a rich polarization and spatial structure, which provides a fundamental resource of strongly correlated and entangled states. This review analyzes the physics of these intriguing properties and explores the various techniques and technologies available to measure them, including the state of the art of their ...
Alessio D'Errico, Ebrahim Karimi
wiley   +1 more source

Quantum integrability of N=2 $$ \mathcal{N}=2 $$ 4d gauge theories

Journal of High Energy Physics, 2018
We provide a description of the quantum integrable structure behind the Thermodynamic Bethe Ansatz (TBA)-like equation derived by Nekrasov and Shatashvili (NS) for N=2 $$ \mathcal{N}=2 $$ 4d Super Yang-Mills (SYM) theories.
Jean-Emile Bourgine, Davide Fioravanti
doaj   +1 more source

Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

, 2007
We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable.
Ablowitz, Ablowitz, Furta, Goriely, Grammaticos, Grammaticos, Guillot, Hietarinta, Hietarinta, Iwasaki, Kowalevski, Kowalevski, Kozlov, Lakshmanan, Lyapunov, Maciejewski, Maciejewski, Maciejewski, Maria Przybylska, Morales-Ruiz, Morales-Ruiz, Morales-Ruiz, Nakagawa, Nowicki, Painlevé, Ramani, Ramani, van der Put, Whittaker, Yoshida, Yoshida, Ziglin, Ziglin   +32 more
core   +2 more sources

Oscillatory integrals with polynomial phase.

MATHEMATICA SCANDINAVICA, 1991
Two theorems on oscillatory integrals are proved. Suppose \(N\) and \(n\) are positive integers, and \({\mathcal P}_ N\) denotes the real polynomials in one variable of degree at most \(N.\) Then there exists a constant \(C(N,n)\) such that for all intervals \([a,b]\) and all \(p\) in \({\mathcal P}_ N,\) \[ |\int_{[a,b]} e^{ip(x)}| p^{(n)}(x)|^{1/ n ...
openaire   +2 more sources

MagPiezo: A Magnetogenetic Platform for Remote Activation of Endogenous Piezo1 Channels in Endothelial Cells

Advanced Functional Materials, EarlyView.
MagPiezo enables wireless activation of endogenous Piezo1 channels without genetic modification using 19 nm magnetic nanoparticles and low‐intensity magnetic fields. It generates torque forces at the piconewton scale to trigger mechanotransduction in endothelial cells, standing as a novel platform to interrogate and manipulate Piezo1 activity in vitro.
Susel Del Sol‐Fernández, Mariarosaria De Simone, Yilian Fernández‐Afonso, Daniel Garcia‐Gonzalez, Pablo Martínez‐Vicente, Thomas van Zanten, Raluca M. Fratila, Maria Moros   +7 more
wiley   +1 more source

Darboux Integrability Of the Biological System

Al-Rafidain Journal of Computer Sciences and Mathematics
In the given paper, we investigate the integrability of a mathematical model of a 3D biological system. Our results show that the system admits a polynomial first integrals for some parameters, an invariant algebraic surface with an exponential factor ...
Zakariya Hashem Ali, Ahmad Muhamad Husien   +1 more
doaj   +1 more source

Some symmetry classifications of hyperbolic vector evolution equations

, 2005
Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered.
Habibullin I T, Sanders J A, Sharpe R W, Sokolov V V   +3 more
core   +3 more sources

Efficient Charge Transport in Zero‐Dimensional Perovskite for Ultrahigh‐Sensitivity X‐Ray Detection

Advanced Functional Materials, EarlyView.
A novel mono‐octahedral 0D Bi‐based Dpy3Bi2I12 perovskite strengthens the internal hydrogen bonds and forms a quasi‐2D lattice, exhibits exceptional charge transport and mobility, achieving high X‐ray sensitivity and ultralow‐dose imaging, and setting a new benchmark for 0D detector performance.
Xin Song, Lijie Wang, Jiayi Wang, Yafeng Xu, Renqian Zhou, Shulin Chen, Partha Maity, Peng Yuan, Yongcao Zhang, Bingyao Shao, Jian‐Xin Wang, Jun Yin, Ren‐Wu Huang, Youyou Yuan, Taimoor Ahmad, Osman M. Bakr, Omar F. Mohammed   +16 more
wiley   +1 more source

Melt Electrowriting High Resolution Poly(ethylene‐co‐vinyl acetate) Scaffolds for Soft Tissue Engineering

Advanced Healthcare Materials, EarlyView.
This work pioneers melt electrowriting (MEW) of polyethylene vinyl acetate (PEVA) to fabricate ultra‐compliant, high‐resolution scaffolds. By integrating microscale precision with soft tissue‐like biomechanics, PEVA overcomes stiffness‐driven limitations of conventional MEW polymers, establishing a mechanically biomimetic platform for soft tissue ...
Finn Snow, Darcy De Rauch, Lilith Mabel Caballero Aguilar, Darcy Millett, Jasley Wilding McBride, David R Nisbet, Magdalena Kita, Elena Pirogova, Robert Michail Ivan Kapsa, Anita Quigley   +9 more
wiley   +1 more source