In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic algebra valued functions $\mathbb{R}^m$. Being defined as solutions elliptic (generally non-strongly elliptic) partial differential equations, $(\varphi,\psi)$-inframonogenic and $(\varphi,\psi)$-harmonic do not share good structure prop...

Abstract Let $$A_{\varphi }$$ A φ denote the matrix of rotation with angle $$\varphi $$ Euclidean plane, FLOOR function which rounds a real point to nearest lattice down on left and ROUND for rounding off vector node lattice. We prove under natural assumption \not = k\f...

The scalar field theory with potential $V(\ensuremath{\varphi})=\frac{1}{2}{m}^{2}{\ensuremath{\varphi}}^{2}\ensuremath{-}\frac{1}{4}g{\ensuremath{\varphi}}^{4}$ ($g>0$) is ill defined as a Hermitian but in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it well defined, and has positive real energy spectrum for the case of spacetime dimension $D=1$. While methods used literature ...

Abstract In this paper, we study Hankel operators on the doubling Fock spaces for all possible $1\leq p,q&lt;\infty $ 1 ≤ p , q &lt; ∞ . We characterize those symbols f which $H_{f}$ H</mml...

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...