We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy covering condition. Given contracting potential $\varphi$ (in sense Liverani-Saussol-Vaienti), we prove there exists unique conformal measure $\nu_\varphi$ and equilibrium state $\mu_\varphi$. Further, quasi-compactness associated t...

Although titanium is considered to be a ubiquitous element as it has the 10th-highest Clarke number of all the elements, it is actually classified as a rare metal because the current refinement process for the metal is more environmentally damaging than the processes used to refine iron and aluminum. Furthermore, the principal alloying elements of titanium alloys are very expensive, owing to th...

Spectra of the degenerate two-photon absorption coefficient $\beta(\omega)$, anisotropy parameter $\sigma(\omega)$, and dichroism $\delta(\omega) = \big[\sigma(\omega) + 2\eta(\omega)\big]/2$ crystalline 110-cut GaAs, GaP, Si at 300 K were measured using femtosecond pump-probe modulation spectroscopy over an excitation range in vicinity each material's half-band gap $E_g/2$ (overall $0.62 < \hb...

Fatty liver disease is a common lipid metabolism disorder influenced by the combination of individual genetic makeup, drug exposure, and life-style choices that are frequently associated with metabolic syndrome, which encompasses obesity, dyslipidemia, hypertension, hypertriglyceridemia, and insulin resistant diabetes. Common to obesity related dyslipidemia is the excessive storage of hepatic f...

We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to two-dimensional disc. Our analysis is based on the mean field bounded vortices in microcanonical ensemble. The are specified by inverse temperature $\beta$ and rotation frequency $\omega$, which conjugate variables energy $E$ angular momentum $L$, respectively. formation (azimuthal angle independent) i...

We investigate non-inertial effects induced by a rotating frame on non-relativistic quantum harmonic oscillator as well of the topology associated to screw dislocation, which corresponds distortion vertical line into spiral. To do this, we obtain analytical solutions time-independent Schr\"odinger equation for this potential in background. The expressions energy spectrum are obtained and four s...

Pseudomonas aeruginosa is a gram-negative bacilli frequently encountered in human pathology. This pathogen is involved in a large number of nosocomial infections and chronic diseases. Herein we investigated the effects of polyunsaturated fatty acids (PUFA) in chronic Pseudomonas aeruginosa lung infection. C57BL/6 mice were fed for 5 wk with specifically designed diets with high contents in eith...

This paper deals with the existence and multiplicity of solutions for a class Kirchhoff type elliptic systems involving nonlinearities Trudinger-Moser exponential growth. We first study following system: $$\begin{aligned} \left\{ \begin{array}{ll} -\big (a_1+b_1\Vert u\Vert ^{2(\theta _1-1)}\big )\Delta u= \lambda H_u(x,u,v) &{} \quad \text{ in }\ \ \Omega ,\\ (a_2+b_2\Vert v\Vert _2-1)}\big v=...