On a family of nonlinear difference equations of the fifth order solvable in closed form by Stevo Stević, Bratislav Iričanin, Witold Kosmala

“…We present some closed-form formulas for the general solution to the family of difference equations $ x_{n+1} = \Phi^{-1}\left(\Phi(x_{n-1})\frac{{\alpha} \Phi(x_{n-2})+{\beta} \Phi(x_{n-4})}{{\gamma} \Phi(x_{n-2})+{\delta} \Phi(x_{n-4})}\right), $ for $ n\in{\mathbb N}_0 $ where the initial values $ x_{-j} $, $ j = \overline{0, 4} $ and the parameters $ {\alpha}, {\beta}, {\gamma} $ and $ {\delta} $ are real numbers satisfying the conditions $ {\alpha}^2+{\beta}^2\ne 0, $ $ {\gamma}^2+{\delta}^2\ne 0 $ and $ \Phi $ is a function which is a homeomorphism of the real line such that $ \Phi(0) = 0, $ generalizing in a natural way some closed-form formulas to the general solutions to some very special cases of the family of difference equations which have been presented recently in the literature. …”
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On the Laplacian index of tadpole graphs by Braga Rodrigo O., Veloso Bruno S.

“…Using two different approaches, we show that their Laplacian index converges to Δ2Δ−1=92\frac{{\Delta }^{2}}{\Delta -1}=\frac{9}{2} as n,k→∞n,k\to \infty , where Δ=3\Delta =3 is the maximum degree of the graph. …”
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The existence of positive solutions for nonlinear boundary system with $p$-Laplacian operator based on sign-changing nonlinearities by Fuyi Xu

“…In this paper, we study a nonlinear boundary value system with $p$-Laplacian operator $$\left\{\begin{array}{lll} (\phi_{p_1}(u'))'+a_1(t)f(u,v)=0, 0<t<1,\cr (\phi_{p_2}(v'))'+a_2(t)g(u,v)=0, 0<t<1,\cr \alpha_1\phi_{p_1}(u(0))-\beta_1\phi_{p_1}(u'(0))=\gamma_1\phi_{p_1}(u(1))+\delta_1\phi_{p_1}(u'(1))=0, \alpha_2\phi_{p_2}(v(0))-\beta_2\phi_{p_2}(v'(0))=\gamma_2\phi_{p_2}(v(1))+\delta_2\phi_{p_2}(v'(1))=0, \end{array}\right.$$ where $\phi_{p_i}(s)=|s|^{p_i-2}s, p_i>1, i=1,2$. …”
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Atomically synergistic Zn-Cr catalyst for iso-stoichiometric co-conversion of ethane and CO2 to ethylene and CO by Ji Yang, Lu Wang, Jiawei Wan, Farid El Gabaly, Andre L. Fernandes Cauduro, Bernice E. Mills, Jeng-Lung Chen, Liang-Ching Hsu, Daewon Lee, Xiao Zhao, Haimei Zheng, Miquel Salmeron, Caiqi Wang, Zhun Dong, Hongfei Lin, Gabor A. Somorjai, Fabian Rosner, Hanna Breunig, David Prendergast, De-en Jiang, Seema Singh, Ji Su

“…$${{{{{\rm{Zn}}}}}}^{\delta+}$$ Zn δ + ( $$0 \, < \, \delta \, < \, 2$$ 0 < δ < 2 ) sites facilitate β-C-H bond cleavage in ethane and the formation of Zn-H δ- hydride, thereby the enhanced basicity promotes CO2 adsorption/activation and prevents ethane C-C bond scission. …”
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High-dimensional Lehmer problem on Beatty sequences by Xiaoqing Zhao, Yuan Yi

“…. $ $ r_{n}\left(\delta_{1}, \delta_{2}, \cdots, \delta_{k}, \alpha, \beta, c; q\right) $ denotes the number of all $ k $-tuples with positive integer coordinates $ \left(x_{1}, x_{2}, \ldots, x_{k}\right) $ such that $ 1 \leq x_{i} \leq \delta_{i}q, \left(x_{i}, q\right) = 1, x_{1} x_{2} \cdots x_{k} \equiv c(q) $, and $ x_{1}, x_{2}, \cdots, x_{k-1} \in B_{\alpha, \beta} $. …”
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Occupational Therapy in Complex Patients: A Pilot Randomized Controlled Trial by Martina Pellegrini, Debora Formisano, Veronica Bucciarelli, Margherita Schiavi, Stefania Fugazzaro, Stefania Costi

“…The average changes in the Canadian Occupational Performance Measure (COPM) performance score significantly and clinically favored experimental OT [−3,06 (−4.50; −1.61); delta>2 points, resp.]. Similar trends were detected for COPM satisfaction and independence in instrumental activities of daily living (ADL). …”
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Two-distance vertex-distinguishing index of sparse graphs by He Zhengyue, Liang Li, Gao Wei

“…In this article, we used the method of discharging to prove that if GG is a graph with mad(G)<83\left(G)\lt \frac{8}{3}, then χd2′(G)≤max{7,Δ+2}{\chi }_{d2}^{^{\prime} }\left(G)\le \max \left\{7,\Delta +2\right\}, which improves the result that a graph GG of Δ(G)≥4\Delta \left(G)\ge 4 has χd2′(G)≤Δ(G)+2{\chi }_{d2}^{^{\prime} }\left(G)\le \Delta \left(G)+2 if mad(G)<52\left(G)\lt \frac{5}{2}, and χd2′(G)≤Δ(G)+3{\chi }_{d2}^{^{\prime} }\left(G)\le \Delta \left(G)+3 if mad(G)<83\left(G)\lt \frac{8}{3}.…”
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Gestion de l’eau et projet de territoire : vers une gestion intégrée du delta du Rhône by Alain Dervieux, Geneviève Jolly, Aurélien Allouche

“…They are centred on 1/ the Contract of the Camargue delta, 2/ the Executive water commission. They show that one faces this reality not so well integrated in the end : together with the development or rice growing starting fifty years ago and the rise of sea level, water is everywhere in the Camargue all throughout the year and in all places. …”
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Scale Invariance in the Lowest Landau Level by Hofmann, Johannes, Zwerger, Wilhelm

“…Moreover, we show that for contact interactions $\sim g_2 \delta ^{(2)}(\mathbf{x})$, which are scale invariant at the classical level, the non-commutativity of the guiding center coordinates gives rise to a quantum anomaly in the commutator $i [\hat{H}_{\mathrm{LLL}}, \hat{D}_R] = (2 + \ell \partial _\ell ) \hat{H}_{\mathrm{LLL}}$ with the dilatation operator $\hat{D}_R$ in the LLL, which replaces the trace anomaly in the absence of a magnetic field. …”
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One-loop matching of the type-II seesaw model onto the Standard Model effective field theory by Xu Li, Di Zhang, Shun Zhou

“…The Wilson coefficients for 41 dimension-six operators are computed up to O M ∆ − 2 $$ \mathcal{O}\left({M}_{\Delta }^{-2}\right) $$ with M ∆ being the mass scale of the Higgs triplet. …”
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From light edges to strong edge-colouring of 1-planar graphs by Julien Bensmail, François Dross, Hervé Hocquard, Eric Sopena

“…A conjecture of Erd\H{o}s and Ne\v{s}et\v{r}il, stated back in the $80$'s, asserts that every graph with maximum degree $\Delta$ should have strong chromatic index at most roughly $1.25 \Delta^2$. Several works in the last decades have confirmed this conjecture for various graph classes. …”
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Boundary conditions and localization on AdS. Part I by Justin R. David, Edi Gava, Rajesh Kumar Gupta, Kumar Narain

“…We show that if there exists an integer n in the interval D:Δ−12LΔ2L $$ D:\ \left(\frac{\Delta -1}{2L},\frac{\Delta}{2L}\right) $$, where L being the ratio of radius of AdS2 to that of S 1, then the one loop determinants obtained for the two actions differ. …”
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Hypercontractivity of Spherical Averages in Hamming Space by Polyanskiy, Yury

“…It is shown that this operator has a dimension-independent bound on the norm Lp \rightarrow L2 with p = 1 + (1 - 2\delta )2. This result evidently parallels a classical estimate of Bonami and Gross for Lp \rightarrow Lq norms for the operator of convolution with a Bernoulli noise. …”
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Images of absolute retardance L.Deltan, using the rotating polariser method by Geday, M, Kaminsky, W, Lewis, J, Glazer, A

“…Crystallogr. 13, 217), allow one to determine |sin delta|, delta = 2piLDeltan/lambda, Deltan = double refraction, L = light path and lambda = wavelength. …”

Applying periodic and anti-periodic boundary conditions in existence results of fractional differential equations via nonlinear contractive mappings by Sumati Kumari Panda, Velusamy Vijayakumar, Kottakkaran Sooppy Nisar

“…The nonlinear multi-order fractional differential equation L ( D ) θ ( ς ) = σ ( ς , θ ( ς ) ) , ς ∈ J = [ 0 , A ] , A > 0 , $$ \mathcal{L}(\mathcal{D})\theta (\varsigma )=\sigma \bigl(\varsigma , \theta ( \varsigma ) \bigr), \quad \varsigma \in \mathscr{J}=[0,\mathscr{A}], \mathscr{A}>0, $$ where L ( D ) = γ w c D δ w + γ w − 1 c D δ w − 1 + ⋯ + γ 1 c D δ 1 + γ 0 c D δ 0 , γ ♭ ∈ R ( ♭ = 0 , 1 , 2 , 3 , … , w ) , γ w ≠ 0 , 0 ≤ δ 0 < δ 1 < δ 2 < ⋯ < δ w − 1 < δ w < 1 ; $$\begin{aligned} &\mathcal{L}(\mathcal{D})=\gamma _{w} \,{}^{c} \mathcal{D}^{\delta _{w}}+ \gamma _{w-1} \,{}^{c} \mathcal{D}^{\delta _{w-1}}+\cdots+\gamma _{1} \,{}^{c} \mathcal{D}^{\delta _{1}}+\gamma _{0} \,{}^{c} \mathcal{D}^{\delta _{0}},\\ &\gamma _{\flat}\in \mathbb{R}\quad (\flat =0,1,2,3,\ldots,w), \qquad \gamma _{w} \neq 0, \\ &0\leq \delta _{0}< \delta _{1}< \delta _{2}< \cdots< \delta _{w-1}< \delta _{w}< 1; \end{aligned}$$ 2. …”
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Tracking the Genomic Evolution of SARS-CoV-2 for 29 Months in South Korea by Seri Jeong, Jae-Seok Kim, Su Kyung Lee, Eun-Jung Cho, Jungwon Hyun, Wonkeun Song, Hyun Soo Kim

“…Among the sequenced samples, 34 wild-type strains and 75 VOCs, including 4 Alpha, 33 Delta, 2 Epsilon, and 36 Omicron VOCs, were identified. …”
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Phase diagrams for two-component D-wave fermion superfluids with density imbalance by Lei Zhang, Jibiao Wang, Xinle Shang, Yuan Gao

“…While the criteria ∂ ^2 Ω/∂Δ ^2 and $\frac{{\partial }^{2}{\Omega}}{\partial {{\Delta}}^{2}}\frac{{\partial }^{2}{\Omega}}{\partial {q}^{2}}-{\left(\frac{{\partial }^{2}{\Omega}}{\partial {\Delta}\partial q}\right)}^{2}$ against PS in previous studies are equivalent to λ _− only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.…”
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How barrow entropy modifies gravity: with comments on Tsallis entropy by Sofia Di Gennaro, Hao Xu, Yen Chin Ong

“…Abstract Barrow proposed that the area law of the horizon entropy might receive a “fractal correction” $$S\propto A^{1+\Delta /2}$$ S ∝ A 1 + Δ / 2 due to quantum gravitational effects, with $$0\leqslant \Delta \leqslant 1$$ 0 ⩽ Δ ⩽ 1 measures the deviation from the standard area law. …”
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On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially &quot;dominated&quot; nonlinearity and singular weight by Sami Baraket, Safia Mahdaoui, Taieb Ouni

“…We are concerned with the problem \[\Delta^{2} u - H(x,u,D^{k}u) = \rho^{4}\prod_{i=1}^{n}|x-p_{i}|^{4\alpha_{i}}f(x)g(u),\] where the principal term is the bi-Laplacian operator, \(H(x,u,D^{k}u)\) is a functional which grows with respect to \(Du\) at most like \(|Du|^{q}\), \(1\leq q\leq 4\), \(f:\Omega\to [0,+\infty[\) is a smooth function satisfying \(f(p_{i}) \gt 0\) for any \(i = 1,\ldots, n\), \(\alpha_{i}\) are positives numbers and \(g :\mathbb R\to [0,+\infty[\) satisfy \(|g(u)|\leq ce^{u}\). …”
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Electronic inhomogeneity and phase fluctuation in one-unit-cell FeSe films by Dapeng Zhao, Wenqiang Cui, Yaowu Liu, Guanming Gong, Liguo Zhang, Guihao Jia, Yunyi Zang, Xiaopeng Hu, Ding Zhang, Yilin Wang, Wei Li, Shuaihua Ji, Lili Wang, Ke He, Xucun Ma, Qi-Kun Xue

“…We observed two spatially coexisting superconducting phases in domains and on boundaries, characterized by distinct superconducting gaps ( $${\Delta }_{1}$$ Δ 1 ~15 meV vs. $${\Delta }_{2}$$ Δ 2 ~10 meV) and pairing temperatures (T p1~52.0 K vs. …”
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