Correct order on some certain weighted representation functions by Chen, Shi-Qiang, Ding, Yuchen, Lü, Xiaodong, Zhang, Yuhan

“…For any positive integer $k$ and any subset $A$ of nonnegative integers, let $r_{1,k}(A,n)$ be the number of solutions $(a_1,a_2)$ to the equation $n=a_1+ka_2$. In 2016, Qu proved that \[ \liminf _{n\,\rightarrow \,\infty }r_{1,k}(A,n)=\infty \] providing that $r_{1,k}(A,n)=r_{1,k}(\mathbb{N}\setminus A,n)$ for all sufficiently large integers, which answered affirmatively a 2012 problem of Yang and Chen. …”
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Global Behavior of a Higher-Order Difference Equation by Tuo Li, Xiu-Mei Jia

“…This paper is concerned with the global behavior of higher-order difference equation of the form 𝑦𝑛+1=(𝑦𝑛∑exp(𝛽(1−2𝑘𝑖=0𝑎𝑖𝑦𝑛−𝑖)))/(1−𝑦𝑛+𝑦𝑛∑exp(𝛽(1−2𝑘𝑖=0𝑎𝑖𝑦𝑛−𝑖))), 𝑛=0,1,2…, 𝑦−𝑘,𝑦−𝑘+1,…,𝑦0∈(0,1). Under some certain assumptions, it is proved that the positive equilibrium is globally asymptotical stable.…”
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On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations by Paisan Nakmahachalasint

“…Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.…”
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Bioactive Sesquiterpenoids from <i>Santolina chamaecyparissus</i> L. Flowers: Chemical Profiling and Antifungal Activity Against <i>Neocosmospora</i> Species by Eva Sánchez-Hernández, Jesús Martín-Gil, Vicente González-García, José Casanova-Gascón, Pablo Martín-Ramos

“…In vitro tests against <i>N. falciformis</i> and <i>N. keratoplastica</i>, two emerging soil phytopathogens, resulted in effective concentration EC₉₀ values of 984.4 and 728.6 μg·mL⁻¹, respectively. …”
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Impacts of Legacy and Contemporary Nitrogen Inputs on N2O and CO2 Emissions in Miscanthus and Maize Cultivated Soils by Jaejin Lee, Paul Villanueva, Kate Glanville, Andy Vanloocke, Wendy H. Yang, Angela Kent, Marshall McDaniel, Steven J. Hall, Adina Howe

“…A 150‐day soil incubation experiment was conducted using soils from a long‐term M×g and maize fertility experiment with three historic N fertilization rates (0, 112, and 336 kg N ha−1 year−1) and a contemporary amendment (60 mg N kg−1) with negative control (0 mg N kg−1). …”
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Clinical relevance of macromolecular complexes involving integrins, potassium and sodium ion channels and the sodium/proton antiporter in human breast cancer by Elena Lastraioli, Jessica Iorio, Francesco Piazza, Chiara Capitani, Michele Santillo, Claudia Duranti, Simonetta Bianchi, Icro Meattini, Scott P. Fraser, Mustafa B. A. Djamgoz, Andrea Becchetti, Annarosa Arcangeli

“…Moreover, hERG1 and the combination of hERG1 and nNav1.5 had impact on prognosis, contributing to identifying a group of patients with worse prognosis. …”
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Analysis on Bacterial Community of <i>Noctiluca scintillans</i> Algal Blooms Near Pingtan Island, China by Yunguang Liu, Yutong Zhang, Haiyan Yao, Zewen Zheng, Wenbo Zhao, Gang Lin

“…The outbreak of <i>N. scintillans</i> red tide significantly impacted the water quality and bacterial community structure in the affected sea area. …”
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Insights into Enhanced Oil Recovery by Coupling Branched-Preformed Particle Gel and Viscosity Reducer Flooding in Ordinary Heavy Oil Reservoir by Zongyang Li

“…The results show that the oil-water interfacial tensions of the three viscosity reducers S1, S2, and S3 are 0.432 mN·m-1, 0.0112 mN·m-1, and 0.0031 mN·m-1, respectively. …”
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Global Regularity for the ∂-b-Equation on CR Manifolds of Arbitrary Codimension by Shaban Khidr, Osama Abdelkader

“…In this paper, assuming that M satisfies condition Y(s) for some s with 1≤s≤n-l-1, we prove an L2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for (0,s)-forms on M.…”
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Bilayer electrified-membrane with pair-atom tin catalysts for near-complete conversion of low concentration nitrate to dinitrogen by Xuanhao Wu, Xiaoxiong Wang, Yunshuo Wu, Huimin Xu, Zhe Li, Rongrong Hong, Kali Rigby, Zhongbiao Wu, Jae-Hong Kim

“…We further develop a reduced titanium dioxide EM as the anode to generate free chlorines for fully oxidizing the residual ammonia (<1 mg-N L−1) to N2. The sequential cathode-to-anode electrofiltration realizes near-complete removal of 10 mg-N L−1 NO3 − and ~100% N2 selectivity with a water resident time on the order of seconds. …”
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Definition and Properties of the Libera Operator on Mixed Norm Spaces by Miroslav Pavlovic

“…A sufficient, but not necessary, condition is that ∑n=0∞‍|g^(n)|/(n+1)<∞. We identify the indices p, q, α, and ν for which 1∘ℒ is well defined on X, 2∘ℒ acts from X to X, 3∘ the implication g∈X⇒∑n=0∞‍|g^(n)|/(n+1)<∞ holds. …”
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Modified Application of Nitrogen Fertilizer for Increasing Rice Variety Tolerance toward Submergence Stress by Gribaldi Gribaldi, Nurlaili Nurlaili, Nurmala Dewi, Ekawati Danial, Firnawati Sakalena, Rujito A. Suwignyo

“…The submergence was during 7–14 days after planting; N3 = the entire dose of N fertilizer that was given during planting, N4 = 1/2 the dose of N fertilizer that was given during planting, and the rest was given at 42 days after planting. …”
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Relative Efficacy of Liquid Nitrogen Fertilizers in Dryland Spring Wheat by Olga S. Walsh, Robin J. Christiaens

“…In addition to at-seeding urea application at 90 kg N ha−1 to all treatments (except for the unfertilized check plot), the liquid fertilizers were applied utilizing an all-terrain vehicle- (ATV-) mounted stream-bar equipped sprayer at a rate of 45 kg N ha−1 at Feekes 5 growth stage (early tillering). …”
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The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions by Yanping Guo, Xuefei Lv, Yude Ji, Yongchun Liang

“…We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)),  k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where a,b>0 and Δu(k)=u(k+1)-u(k) for k∈{0,1,…,n-1},  f:{0,1,…,n}×[0,+∞)→[0,+∞) is continuous. h(i) is nonnegative i∈{2,3,…,n+2}; g(i) is nonnegative for i∈{0,1,…,n}. …”
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Comparison of Raw Dairy Manure Slurry and Anaerobically Digested Slurry as N Sources for Grass Forage Production by Olivia E. Saunders, Ann-Marie Fortuna, Joe H. Harrison, Elizabeth Whitefield, Craig G. Cogger, Ann C. Kennedy, Andy I. Bary

“…Annual N applications ranged from 600 kg N ha−1 in 2009 to 300 g N ha−1 in 2011. Forage yield and N uptake were similar across slurry treatments. …”
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Microalga <i>Nannochloropsis gaditana</i> as a Sustainable Source of Bioactive Peptides: A Proteomic and In Silico Approach by Samuel Paterson, Laura Alonso-Pintre, Esperanza Morato-López, Sandra González de la Fuente, Pilar Gómez-Cortés, Blanca Hernández-Ledesma

“…This study aimed to characterize <i>N. gaditana</i>’s proteome and evaluate its potential as a source of bioactive peptides by using an in silico approach. …”
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A note on the global attractivity of a discrete model of nicholson's blowflies by B. G. Zhang, H. X. Xu

“…In this paper, we further study the global attractivity of the positive equilibrium of the discrete Nicholson's blowflies model Nn+1−Nn=−δNn+pNn−ke−aNn−k,        n=0,1,2,…. We obtain a new criterion for the positive equilibrium N∗ to be a global attractor, which improve the corresponding results obtained by So and Yu (J. …”
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Divergent sequences satisfying the linear fractional transformations by A. McD. Mercer

“…It is the purpose of this note to examine the limit limN→∞1N∑n=1Nf(xn):f∈C(−∞,∞) in these cases. Except for certain exceptional values of a,b,c,d this value is found for almost all x1.…”
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On Copson Ideal Convergent Sequence Spaces by Mohammad Idrisi, Nazneen Khan, Kavita Saini, Mobeen Ahmad, ‌ Yasmeen, Manal Labadi

“…The present work is an investigation of some new sequence spaces $c^{I}_{0}\left(C\right)$, $c^{I}\left(C\right)$, $\ell^{I}_{\infty}\left(C\right)$ and $\ell_{\infty}\left(C\right)$ as a domain of the triangle Copson matrix via ideal convergence over an admissible ideal of $\mathbb{N}$. Also, I will define some algebraic, topological properties and inclusion relations in these spaces.…”
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Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions by Chengmin Hou, Sui Sun Cheng

“…For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. …”
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