Abstract We generalize the usual Doob maximal operator as well fractional and introduce $$M_{\gamma ,s,\alpha }$$ M γ , s α , a new for martingales. prove that under log-Hölder continuity conditio...

We consider pro-isomorphic zeta functions of the groups $\Gamma (\mathcal {O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb {Z}$ and $K$ varies all number fields. Under certain conditions, we show that these have fine Euler decomposition with factors indexed by primes $\mathfrak {p}$ depending only on structure $\Gamma$, degree $[K:\mathbb {Q}]$, cardinality residue fiel...

We present a phenomenological study of photon--initiated (PI) lepton production at the LHC, as implemented in structure function (SF) approach. provide detailed predictions for multidifferential pair production, and show that impact on observables sensitive to weak mixing angle, ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{W}$, $W$ boson mass, ${M}_{W}$, well PDFs can be non-negligible, particular...

For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

Noticing that some recent variations of descent polynomials are special cases Carlitz and Scoville's four-variable polynomials, which enumerate permutations by the parity ascent positions, we prove a q-analogue Carlitz-Scoville's generating function counting inversion number type B analogue enumerating signed with respect to positions. As by-product our formulas, obtain Chebikin's formula for a...

Charge movement was measured in frog cut twitch fibers with the double Vaseline gap technique. Five manipulations listed below were applied to investigate their effects on the hump component (I gamma) in the ON segments of TEST minus CONTROL current traces. When external Cl-1 was replaced by MeSO3- to eliminate Cl current, I gamma peaked earlier due to a few millivolts shift of the voltage depe...

Abstract Let $N\geq 1$ be squarefree with $(N,6)=1$ . $c\phi _N(n)$ denote the number of N -colored generalized Frobenius partitions n introduced by Andrews in 1984, and $P(n)$ We prove $$ \begin{align*}c\phi_N(n)= \sum_{d \mid N} N/d \cdot P\left( \frac{ N}{d^2}n - \frac{N^2-d^2}{24d^2} \right) + b(n),\end{align*} where $C(z) := (q;q)^N_\infty \sum _{n=1}^{\infty } b(n) q^n$ is a cusp form $S_...

Let $G$ be a finite group and $pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...