Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Automorphisms of flag systems

We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge–Ampère type equations (2nd order). Next, we describe a prolongation functor operating on the infinitesimal symmetries (automorphisms) of the Darboux flag and extending these, isomorphically, to all the symmetries of any other flag. Hence, flag systems cannot be distinguished by their symmetry algebras and the local classification of these objects is approached by considering higher order isotropies of these algebras as well as the groupoids of k-th order formal equivalences since the differential equations defining the latter provide precious information for the application of flag systems to differential equations (e.g., Cartan's criterion for non-linear Monge equations). In examining the behavior of the isotropy algebras, that can either diminish or remain the same, when passing from a derived system $S_{\nu }$ to the consecutive system $S_{\nu +1}$, we obtain a full set of numerical invariants for the elementary flag systems that moreover specifies the local models.     

Rate coefficients for reactions of OH radicals with CH3D,CH2D2, CHD3, and CD4

Fourier transform infrared (FTIR) smog chamber techniques were used to investigate the atmospheric chemistry of the isotopologues of methane. Relative rate measurements were performed to determine the kinetics of the reaction of the isotopologues of methane with OH radicals in cm³ molecule⁻¹ s⁻¹ units: k(CH₃D + OH) = (5.19 ± 0.90) × 10⁻¹⁵, k(CH₂D₂ + OH) = (4.11 ± 0.74) × 10⁻¹⁵, k(CHD₃ + OH) = (2.14 ± 0.43) × 10⁻¹⁵, and k(CD₄ + OH) = (1.17 ± 0.19) × 10⁻¹⁵ in 700 Torr of air diluent at 296 ± 2 K. Using the determined OH rate coefficients, the atmospheric lifetimes for CH_4–xD_x (x = 1–4) were estimated to be 6.1, 7.7, 14.8, and 27.0 years, respectively. The results are discussed in relation to previous measurements of these rate coefficients.     

Attaching tweezers like ionophore to a proton crane: theoretical design of new tautomeric sensors

ABSTRACT

The tautomeric optical sensors based on 4-(phenyldiazenyl)naphthalen-1-ol exist in their pure enol tautomeric form as free ligands, while the addition of metal ion fully shifts the equilibrium towards the keto tautomer allowing a red shift in the measured absorbance. This effect is achieved when a side ionophore group is connected to a tautomeric backbone by a spacer in a way that stabilizes the enol form via hydrogen boding. When the ionophore captures the metal ion the keto form is stabilized due to C─O tautomeric group participation in the complex. In the current study, we model theoretically the effect of symmetric tweezer like ionophores (RCOXCOR, where X, being CH or N, is the linker to the tautomeric backbone) on the tautomeric state and complexation ability of 4-(phenyldiazenyl)naphthalen-1-ol containing ligands. It was found that enol form stabilisation is achieved when R?=?NMe₂, independing on the linker. Both ligands are unsuitable for capturing alkali metal ions. The calculations predict that the complexation with alkali earth metal ions could lead to a full shift of the tautomeric equilibrium towards keto tautomer.     

Formation of intermediate coupling optical polarons and bipolarons in two-dimensional systems

The formation of the optical polaron and bipolaron in two-dimensional (2D) systems is studied in the intermediate electron–phonon coupling regime. The total energies of the 2D polaron and bipolaron are calculated by using the Buimistrov–Pekar method of canonical transformations. The obtained results are compared with other existing results obtained by using the Feynman path integral method and the modified Lee–Low–Pines unitary transformation method. It is shown that the electron–phonon correlation significantly reduces the total energy of the 2D polaron in comparison with the energy of the strong coupling (adiabatic) polaron. It is found that the polaron formation in 2D systems is possible when the electron–phonon coupling constant α is greater than the critical value ${\alpha }_c?2.94$, which is much lower than a critical value of the electron–phonon coupling constant α in three-dimensional (3D) systems. The critical values of the Fröhlich coupling constant α and the ratio $\eta ={\epsilon }_{\infty }/{\epsilon }_0$ (where ${\epsilon }_{\infty }$ and ${\epsilon }_0$ are the high frequency and static dielectric constants, respectively), which determine the bipolaron stability region in 2D systems, are calculated numerically. It is interesting for application to the layered cuprate superconductors that the (bi)polarons are formed more easily in quasi-2D regions than in the bulk. It is argued that the high-$T_c$ cuprate superconductivity can exist above the bulk superconducting transition temperature $T_c$ as the persisting superfluidity of polaronic (bosonic) Cooper pairs and large bipolarons at quasi-2D grain boundaries or in the CuO₂ layers above $T_c$.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Change of evaporation rate of single monocomponent droplet with temperature using time-resolved phase rainbow refractometry

Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28$\times {10}^{?8}$ m²/s at atmospheric 293 K to a range of (?1.5, ?8)$\times {10}^{?8}$ m²/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions.     

GOSs-稀土配合物紫外增强材料的光谱分析与稳定性研究

氧化石墨烯薄片(GOSs)作为一种新型的二维片状材料,具有较高的比表面积、丰富的表面含氧官能团以及良好的光热稳定性。而稀土配合物通过无机稀土元素与有机配体的结合表现出优异的荧光特性。为了将两类材料具有的物化特性结合起来应用于紫外光谱探测领域。选取了合适的有机配体啉菲罗啉(1,10-邻二氮杂菲,phen)、2’2-联嘧啶(bpm)作为桥联分子,把氧化石墨烯(GOSs)与稀土配合物通过氢键自组装作用进行复合,制备了高效稳定可调的GOSs-稀土配合物复合荧光材料GOSs-Eu(BA)3phen和GOSs-Eu(TTA)3bpm,并且制备了相应的聚乙烯醇(PVA)共混紫外增强薄膜,对其光谱特性与稳定性进行了深入的研究。采用红外光谱、扫描电镜和金相显微镜等方法,对紫外增强材料进行了性能表征。采用吸收光谱,荧光光谱等方法,对紫外增强薄膜进行了性能表征。此外,通过热重测试(TGA)表征了GOSs氢键复合前后紫外增强材料的热稳定性,通过荧光强度-紫外光照次数表征了GOSs氢键复合前后紫外增强薄膜的光稳定性。红外光谱分析发现,进行配位前后有机配体的特征峰产生了频移,表明稀土配合物中Eu 3+与配体之间存在着明显的配位作用。在进行复合之后,桥联配体的特征峰也产生了偏移,表明GOSs与稀土配合物通过桥联分子的氢键作用进行了进行复合。吸收光谱与荧光光谱测定结果表明增强薄膜吸收峰在200~400 nm,荧光主峰在612 nm左右,为Eu 3+特征红色荧光峰,且不同配体可以实现不同范围的吸收产生差异化的荧光表现。扫描电镜和金相显微镜清晰地展示了稀土配合物复合前后的微观形貌,即颗粒状稀土配合物附着在石墨烯薄片上。光稳定性测试表明经过GOSs氢键复合之后,Eu(BA)3phen和Eu(TTA)3bpm稀土配合物荧光材料在进行25次荧光强度测试后光漂白程度分别下降了4.26%和6.41%,提高了其光稳定性。热重测试也表明在经过GOSs氢键复合之后,稀土配合物的热稳定性有了很大提高。总之,得益于GOSs和稀土配合物的特性结合,所制备的紫外增强材料表现出优异的荧光特性与稳定性,必将在紫外探测方面有着广阔的应用前景。     

Development of low concentrated solar photovoltaic system with lead acid battery as storage device

Energy storage system powered by renewable energies is a viable option to meet energy requirement without addition of carbon footprints to the environment. This study involves development of theoretical and computational models for a solar photovoltaic (PV) system coupled with a lead acid battery. The study commenced with selection of most appropriate lead acid battery and PV system for installation in a representative location in Riyadh, Kingdom of Saudi Arabia. Various technical and economic parameters were assessed and calculated by computational approach. The optimized lead acid battery was integrated with low concentration solar PV panels (CPV) followed by a feasibility study. Theoretical model was developed for the integrated system to calculate various parameters of the CPV and lead acid battery. Technical and economic assessment of this coupled unit was calculated using a theoretical approach. The developed model was then subjected to computational approach for verification and validation analysis of the integrated system. The detailed assessment of batteries and integrated system show the applicability of this system in Riyadh region. The research will be extended to develop energy storage systems for remote areas using lead acid batteries.