We present a search for signatures of neutrino mixing electron anti-neutrinos with additional hypothetical sterile flavors using the Double Chooz experiment. The is based on data from 5 years operation Chooz, including 2 in two-detector configuration. analysis profile likelihood, i.e.\ comparing to model prediction disappearance data-to-data comparison two respective detectors. optimized three ...

Let \(\left( H;\left\langle \cdot ,\cdot \right\rangle \right)\) be a complex Hilbert space and \(f:[0,\infty )\rightarrow \mathbb{R}\) convex (concave) on \([0,\infty )\). If \(x, y\in H\) with \(Re \left\langle x,y\right\rangle \geq 0\), then \begin{align*} f\left( \frac{\left\Vert x\right\Vert ^{2}+Re +\left\Vert y\right\Vert ^{2}}{3}\right) & \leq \left( \right) \int_{0}^{1}f\left( \lef...

The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a super linear upper bound $\widetilde{O}(n\sqrt{m})$ are known, which prompts the question of relaxing the problem: either by asking for $1 \pm \varepsilon$ appro...

Let $(u, v)$ be a solution to semilinear parabolic system $$ \mbox{(P)} \qquad \left\{ \begin{array}{ll} \partial_{t} u = D_1 \Delta u+v^{p} \quad \mbox{in} \mathbf{R}^{N} \times (0, T),\\ v D_2 v+u^{q} u, \geq 0 (u(\cdot, 0), v(\cdot, 0)) (\mu, \nu) \mathbf{R}^N, \end{array} \right. where $N 1$, $T > 0$, $D_1 $D_2 $0 < p \leq q$ with $pq 1$ and $(\mu, \nu)$ is pair of Radon measures or nonnega...

We use machine learning (ML) and non-ML techniques to study optimized $CP$-odd observables, directly maximally sensitive the $i \tilde \kappa \bar t \gamma^5 h$ interaction at LHC prospective future hadron colliders using final state with a Higgs boson top quark pair, $pp\to t\bar h$, followed by semileptonic $t$ decays. perform phase-space optimization of manifestly observables ($\boldsymbol \...

Exploiting the recent work of Tao and Ziegler on a concatenation theorem factors, we find explicit characteristic factors for multiple averages along polynomials systems with commuting transformations, use them to study criteria joint ergodicity sequences form $(T^{p_{1,j}(n)}_{1}\cdot\ldots\cdot T^{p_{d,j}(n)}_{d})_{n\in\mathbb{Z}},$ $1\leq j\leq k$, where $T_{1},\dots,T_{d}$ are measure prese...

The minimal excludant, or “mex” function, on a set S of positive integers is the least integer not in S. In recent paper, Andrews and Newman extended mex-function to partitions found numerous surprising partition identities connected with these functions. Very recently, da Silva Sellers present parity considerations one families functions studied, namely $$p_{t,t}(n)$$ , provide complete charac...

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...

Let $$u(\cdot ,\cdot )$$ be the Caffarelli–Silvestre extension of f. The first goal this article is to establish fractional trace-type inequalities involving In doing so, firstly, we Sobolev/logarithmic Sobolev/Hardy trace in terms $$\nabla _{(x,t)}u(x,t).$$ Then, prove anisotropic $$ {\partial _{t} u(x,t)}$$ or $$(-\varDelta )^{-\gamma /2}u(x,t)$$ only. Moreover, based on an estimate Fourier t...

In the Directed Disjoint Paths problem, we are given a digraph $D$ and set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, task is to find collection pairwise vertex-disjoint paths $\{P_1, P_k\}$ such that each $P_i$ path from $s_i$ $t_i$ in $D$. This problem NP-complete for fixed $k=2$ W[1]-hard with parameter $k$ DAGs. A few positive results known under restrictions on input digraph, as bei...