Using 3.6- and 5.3-fs pulses, we demonstrated theoretically and experimentally that fringe-resolved autocorrelation (FRAC) traces are distorted by bandwidth limitations of the second-harmonic generation (SHG) in 10-microm-thick, type I ss-BaB2O4 for pulses shorter than sub-5 fs. In addition, detailed numerical analysis of the SHG showed that the optimum crystal angle where the FRAC trace distor...

Nep tu nian dykes were re cently re corded within the Mid dle Mio cene (Up per Badenian and Lower Sarmatian) Medobory reef com plex of the Carpathian Fore land in west ern Ukraine. The Up per Badenian reefs are cut by a reg u lar, semi-per pen dic u lar net work of in ter sect ing fis sures that pen e trate the Badenian reef lime stone down for more than 10 m. The dykes are filled by sev eral g...

PURPOSE Although many models have been proposed to interpret non-Gaussian diffusion MRI data in biological tissues, it is often difficult to see the correlation between the MRI data and the histological changes in the tissue. Among these models, so called statistical models, which assume the diffusion coefficient D is distributed continuously within a voxel, are more suitable for interpreting t...

We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...

Forty years ago Schaer and Wetzel showed that a $\frac{1}{\pi}\times\frac {1}{2\pi}\sqrt{\pi^{2}-4}$ rectangle, whose area is about $0.122\,74,$ is the smallest rectangle that is a cover for the family of all closed unit arcs. More recently F\"{u}redi and Wetzel showed that one corner of this rectangle can be clipped to form a pentagonal cover having area $0.11224$ for this family of curves. He...

for all $a,b>0$, the following two optimal inequalities are presented: $h^{alpha}(a,b)l^{1-alpha}(a,b)geq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ h^{alpha}(a,b)l^{1-alpha}(a,b)leq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. here, $h(a,b)$, $l(a,b)$, and $m_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...