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1.
According to the N-soliton solution derived from Hirota’s bilinear method, higher-order smooth positons and breather positons are obtained efficiently through an ingenious limit approach. This paper takes the Sine-Gordon equation as an example to introduce how to utilize this technique to generate these higher-order smooth positons and breather positons in detail. The dynamical behaviors of smooth positons and breather positons are presented by some figures. During the procedure of deduction, the approach mentioned has the strengths of concision and celerity. In terms of feasibility and practicability, this approach can be exploited widely to study higher-order smooth positons and breather positons of other integrable systems.  相似文献   
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In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results presented here would provide extensions of those given in earlier works.  相似文献   
5.
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by “collapsed” minimal surfaces. We prove here that collapsing only occurs if the mean curvature/pressure of the bulky regions is negative, and that, when this last property holds, the whole soap film lies in the convex hull of its boundary wire frame.  相似文献   
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In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear evolution systems, properties of the resolvent operator and Schauder’s fixed point theorem. Finally, we provide two concrete examples to validate our results.  相似文献   
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An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order n with index λ , denoted by TQS λ ( n ) , is a pair ( X , ? ) , where X is an n ‐set and ? is a set of oriented tetrahedra (blocks) such that every cyclic triple on X is contained in exactly λ members of ? . A TQS λ ( n ) is pure if there do not exist two blocks with the same vertex set. When λ = 1 , the spectrum of a pure TQS ( n ) has been completely determined by Ji. In this paper, we show that there exists a pure TQS 2 ( n ) if and only if n 1 , 2 ( mod 3 ) and n 7 . A corollary is that a simple QS 4 ( n ) also exists if and only if n 1 , 2 ( mod 3 ) and n 7 .  相似文献   
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The present work demonstrates the significant role of ultrasound (US) in intensifying the efficacy of the combination with Fenton reagent and/or ozone for the treatment of real dye industry industrial effluent procured from the local industry. Initial part of the work focused on analysing the literature based on combination approaches of US with different oxidants applied for the treatment of real and simulated effluents focusing on the dyes. The work also provides guidelines for the selection of optimal operating parameters for maximizing the intensification of the degradation. The second part of the work presents an experimental study into combined approaches of ultrasound with ozone (O3) and Fenton’s reagent for treatment of real effluent. Under optimized conditions (100 W, 20 kHz and duty cycle of 70%), maximum COD reductions of 94.79% and 51% were observed using a combined approach of US + Fenton oxidation followed by lime treatment for the treatment of effluent-I and effluent-II respectively at H2O2 loading of 17.5 g/L, H2O2/Fe2+ ratio of 3, pH of 4, CaO dose of 1 g/L and an overall treatment time of 70 min. US + Fenton + O3 followed by lime was also applied for treatment under ozone loading of 1 g/h for the treatment of effluent-I and it was found that maximum COD reduction of 95.12% was obtained within 30 min of treatment time, indicating use of ozone did not result in significant value addition in terms of COD reduction but resulted in faster treatment. HC (inlet pressure: 4 bar) + Fenton + Lime scheme was successfully replicated on a pilot-scale resulting in maximum COD reduction of 57.65% within 70 min of treatment time. Overall, it has been concluded that the hybrid oxidative processes as US + Fenton followed by lime treatment is established as the best approach ensuring effective COD reduction at the same time obtaining final colourless/reusable effluent.  相似文献   
10.
Although recent decades have witnessed the synthesis of 1,3,4-thiadiazoles via phosphorus POCl3-promoted cyclization reaction, simultaneous access to 2-amino-1,3,4-thiadiazole and 2-amino-1,3,4-oxadiazole analogs remains unexpected and elusive. Herein, a detailed regiocontrolled synthesis of 2-amino-1,3,4-thiadiazoles in good to high yields with good regioselectivities from readily available thiosemicarbazides using POCl3 was disclosed. Meantime, to establish a comprehensive structure–activity relationship, 2-amino-1,3,4-oxadiazole derivatives as single regioisomers were prepared via EDCI·HCl-triggered cyclization of the thiosemicarbazide intermediates. The in vitro anti-influenza assays proved that the selected compounds with the pyrazine/pyridine ring exhibited certain inhibitory activities against influenza A virus strains A/HK/68 (H3N2) and A/PR/8/34 (H1N1) in MDCK cells. Among them, N-(adamantan-1-yl)-5-(5-(azepan-1-yl)pyrazin-2-yl)-1,3,4-thiadiazol-2-amine (4j) was the most active compound, and exhibited favorable activity with EC50 values of 3.5 μM and 7.5 μM, respectively. In addition, the molecular docking results explained the reason why compound 4j had dual inhibitory activity and revealed the reasonable binding mode of this compound with the M2-S31N and M2-WT ion channels. This compound had the potential to be further developed as an anti-influenza drug.  相似文献   
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