High harmonic generation (HHG) is a versatile technique for probing ultrafast electron dynamics. While HHG sensitive to the electronic properties of target, also depends on waveform laser pulse. As well known, (peak) positions, $\omega$, in high-harmonic spectrum can shift when carrier envelope phase (CEP), $\varphi$ varied. We derive formulae describing corresponding parametric dependencies CE...

Abstract In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is paraconsistent if it rejects laws $\varphi ,\neg \varphi \vdash \psi $ and $\vdash \neg (\varphi \land )$. that paper, author analyzes, among three-valued logics, which them satisfy this property. If we consider multiple-conclusion consequence relations, dual properties ...

The weak commutativity group $\chi(G)$ is generated by two isomorphic groups $G$ and $G^{\varphi }$ subject to the relations $[g,g^{\varphi}]=1$ for all $g \in G$. an extension of $D(G) = [G,G^{\varphi}]$ $G \times We prove that if a finite solvable derived length $d$, then $\exp(D(G))$ divides $\exp(G)^{d}$ $|G|$ odd $2^{d-1}\cdot \exp(G)^{d}$ even. Further, $p$ prime $p$-group class $p-1$, $\...

We extend to Segal–Piatetski-Shapiro sequences previous results on the Luca–Schinzel question. Namely, we prove that for any real c larger than 1, sequence $$(\sum _{m\le n} \varphi (\lfloor m^c \rfloor ) /\lfloor )_{n\ge 1}$$ is dense modulo where $$\varphi $$ denotes Euler’s totient function. The main part of proof consists in showing when R a large integer, residues $$\lfloor contains block ...

We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector fields. This work is motivated the desire to improve complex based either on analytically simplified or data-driven models. derive hierarchy general informa...

Abstract Based on iteration of random-valued functions we study the problem solvability in class continuous and Hölder $$\varphi $$ φ equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ (x)=F(x)+\int ), \end{aligned}$$ <m...

We show that the operator \[ T_{K,s_1,s_2}f(z) := \int_{\mathbb{R}^n} A_{K,s_1,s_2}(z_1,z_2) f(z_2)\, dz_2 \] is a Calderon-Zygmund operator. Here for $K \in L^\infty(\mathbb{R}^n \times \mathbb{R}^n)$, and $s,s_1,s_2 (0,1)$ with $s_1+s_2 = 2s$ we have \frac{K(x,y) \left (|x-z_1|^{s_1-n} -|y-z_1|^{s_1-n} \right )\, (|x-z_2|^{s_2-n} -|y-z_2|^{s_2-n}\right )}{|x-y|^{n+2s}}\, dx\, dy. This motivat...

&lt;abstract&gt;&lt;p&gt;Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (&lt;italic&gt;Appl. Math. Comput.&lt;/italic&gt;, 218 (2011): 3303–3310) proved \r...

Abstract The research determined the resistance to compression and low velocity impact of wood-based sandwich panels, face sheet made high-density fiber board, high pressure laminate, while its auxetic lattice core was by 3D printing using LayWood bio-composite filament. core's property (i.e. exhibiting negative Poisson's ratio) observed within planes parallel facings. ability particular types ...

A bstract We study the near horizon 2d gravity theory which captures extremal thermodynamics of Kerr black holes where a linear combination excess angular momentum δJ and mass δM is held fixed. These correspond to processes both momenta are perturbed leaving them extremal. For AdS 4 we hold $$ \delta J-\mathcal{L}\delta M=0 δJ</m...