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1.
In the context of measure spaces equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality, we derive local and global sup bounds of the nonnegative weak subsolutions of
$$\begin{aligned} (u^{q})_t-\nabla \cdot {(|\nabla u|^{p-2}\nabla u)}=0, \quad \mathrm {in} \ U_\tau = U \times (\tau _1, \tau _2] , \quad p>1,\quad q>1 \end{aligned}$$
and of its associated Dirichlet problem, respectively. For particular ranges of the exponents p and q, we show that any locally nonnegative weak subsolution, taken in \(Q (\subset \bar{Q}\subset U_\tau )\), is controlled from above by the \(L^\alpha (\bar{Q}) \)-norm, for \(\alpha = \max \{p, q+1\}\). As for the global setting, under suitable assumptions on the boundary datum g and on the initial datum, we obtain sup bounds for u, in \(U \times \{ t\}\), which depend on the \(\sup g\) and on the \(L^{q+1}(U \times (\tau _1, \tau _1+t])\)-norm of \((u-\sup g)_+\), for all \(t \in (0, \tau _2-\tau _1]\). On the critical ranges of p and q, a priori local and global \(L^\infty \) estimates require extra qualitative information on u.
  相似文献   
2.
The title structures of KScS2 (potassium scandium sulfide), RbScS2 (rubidium scandium sulfide) and KLnS2 [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS2, RbScS2 and KTbS2) or redetermined. All of them belong to the α‐NaFeO2 structure type in agreement with the ratio of the ionic radii r3+/r+. KScS2, the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S—S layers which contain the respective constituent cations, the sulfur fractional coordinates z(S2−) and the bond‐valence sums.  相似文献   
3.
Hirshfeld surfaces and two‐dimensional fingerprint plots are used to analyse the intermolecular interactions in two new phosphorothioic triamide structures, namely N,N′,N′′‐tris(3,4‐dimethylphenyl)phosphorothioic triamide acetonitrile hemisolvate, P(S)[NHC6H3‐3,4‐(CH3)2]3·0.5CH3CN or C24H30N3PS·0.5CH3CN, (I), and N,N′,N′′‐tris(4‐methylphenyl)phosphorothioic triamide–3‐methylpiperidinium chloride (1/1), P(S)[NHC6H4(4‐CH3)]3·[3‐CH3‐C5H9NH2]+·Cl or C21H24N3PS·C6H14N+·Cl, (II). The asymmetric unit of (I) consists of two independent phosphorothioic triamide molecules and one acetonitrile solvent molecule, whereas for (II), the asymmetric unit is composed of three components (molecule, cation and anion). In the structure of (I), the different components are organized into a six‐molecule aggregate through N—H...S and N—H...N hydrogen bonds. The components of (II) are aggregated into a two‐dimensional array through N—H...S and N—H...Cl hydrogen bonds. Moreover, interesting features of packing arise in this structure due to the presence of a double hydrogen‐bond acceptor (the S atom of the phosphorothioic triamide molecule) and of a double hydrogen‐bond donor (the N—H unit of the cation). For both (I) and (II), the full fingerprint plot of each component is asymmetric as a consequence of the presence of three fragments. These analyses reveal that H...H interactions [67.7 and 64.3% for the two symmetry‐independent phosphorothioic triamide molecules of (I), 30.7% for the acetonitrile solvent of (I), 63.8% in the phosphorothioic triamide molecule of (II) and 62.9% in the 3‐methylpiperidinium cation of (II)] outnumber the other contacts for all the components in both structures, except for the chloride anion of (II), which only receives the Cl...H contact. The phosphorothioic triamide molecules of both structures include unsaturated C atoms, thus presenting C...H/H...C interactions: 17.6 and 21% for the two symmetry‐independent phosphorothioic triamide molecules in (I), and 22.7% for the phosphorothioic triamide molecule of (II). Furthermore, the N—H...S hydrogen bonds in both (I) and (II), and the N—H...Cl hydrogen bonds in (II), are the most prominent interactions, appearing as large red spots on the Hirshfeld surface maps. The N...H/H...N contacts in structure (I) are considerable, whereas for (II), they give a negligible contribution to the total interactions in the system.  相似文献   
4.
纤维素酶是一种有效的纤维质类物质水解催化剂,工业应用时可通过固定化纤维素酶来降低其成本。本文将烟曲霉原变种JCF产生的纤维素酶固定在MnO2纳米颗粒上。 MnO2可提高纤维素酶的活性,并充当一个更好的载体。采用扫描电镜表征了所制MnO2纳米粒子及其负载纤维素酶的表面性质,以傅里叶变换红外光谱分析了固定在MnO2纳米粒子上纤维素酶的官能团性质。纤维素酶在MnO2纳米粒子上最大的固定化效率为75%。考察了固定化纤维素酶的活性、操作pH值、温度、热稳定性和重复使用性等性质。结果表明,所制固定化酶的稳定性比游离酶更高。固定于MnO2纳米粒子上的纤维素酶可用于纤维质类物质的水解反应,且能在较宽的温度和pH值范围内使用。表征结果证实了该催化剂具有非常高的催化纤维素类物质水解的活性。  相似文献   
5.
Strontium and calcium (alkaline earth: Ae) olefin complexes stabilised by secondary Ae???F?C and β‐agostic Ae???H?Si interactions are presented. Olefin coordination onto the alkaline earths is plain in the solid state, and it is thermodynamically favoured over the coordination of THF. The existence of the Ae???olefin interactions is corroborated by solution NMR data and DFT computations. The coordination mode of the olefin varies with steric effects and, if enforced, olefin dissociation can be compensated by the other non‐covalent interactions, as supported by DFT computations.  相似文献   
6.
7.
The Cope rearrangement of selectively deuterated isotopomers of 1,5-dimethylsemibullvalene 2 a and 3,7-dicyano-1,5-dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy-atom tunneling. The driving force for the rearrangements is the small difference in the zero-point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b , two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b .  相似文献   
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10.
The study on reactivity of several α-substituted α-sulfonyl malonates toward 1,4-diazabicyclo[2.2.2]octane (DABCO) and Bu3N is described. The reactivity with DABCO revealed the possible competition between decarbalkoxylation and unexpected desulfonylation, depending on the α-substituent, because of sterical hindrance around the electrophilic centers (SO2 and CO2R). The derivatives with crowded α-substituents suffer selective desulfonylation, and a novel and efficient desulfonylation method can be proposed. The dependence of the reactivity of α-sulfonyl malonates on the sterical hindrance around the electrophilic centers is confirmed by conformational analysis (Macromodel/MM2? and Mopac/MP3). The carbanionic mechanism is proved because the corresponding protonated, deuterated, and sulfenylated products were obtained by addition of the corresponding electrophilic agents. Bu3N showed itself to be a novel selective decarbalkoxylation agent for any α-substituted α-sulfonyl malonate.  相似文献   
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