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Let H \mathbf {H} be the mean curvature vector of an n n -dimensional submanifold M n M^n in a Riemannan manifold. The critical submanifolds of the total mean curvature functional H = ∫ | H | n \mathcal H=\int |\mathbf {H}|^n are called H \mathcal H -submanifolds. In this note, we will prove that compact Legendrian H \mathcal H -surfaces in the unit sphere S 5 \mathbb {S}^{5} are minimal. We also investigate the first eigenvalue of the Schrödinger operator L = − Δ − q L=-\Delta -q on M 2 M^2 and M 3 M^3 , where q q is some potential function, and obtain a sharp estimate for the first eigenvalue of L L .

A micro-packed bed reactor has been developed to demonstrate aerobic oxidation of alcohols to aldehydes, utilizing green oxidant O2 and effective Cu/TEMPO-catalyzed system.

Methods of coating Al2O3 on nickel micro-foam were compared and screened, aiming to overcome the capillary force and prepare the micro-foam monolithic catalyst coatings. The surface of micro-foam substrate was pretreated by a chemical etching method to improve the adhesion of the coatings on the substrate. The results showed that the slurry circulation at 162 ml·min-1 was evaluated as the optimal method. The pore size on the substrate surface can be controlled by changing the pretreatment conditions. An empirical correlation was also proposed, showing an excellent practicality for predicting the pore size. The adhesion of the coatings with substrate pretreatment was significantly better than that without substrate pretreatment. The minimum value of weight loss after ultrasonic vibration was 3.9%. This mainly attributes to the squeezing of Al2O3 particles in the pores of substrate surface. The coatings on nickel micro-foam are hopefully used in micropacked beds for catalytic reactions.

The selective hydrogenation of halogenated nitroaromatic compounds is of great importance in the fine chemical industry. However, the hydrogenation reactions in commonly utilized batch reactors suffer from the undesired dehalogenation, resulting in higher requirement for subsequent separation processes and severe corrosion to industrial fatalities. In this work, a H-flow system with the micropacked bed reactor was developed for the selective hydrogenation of halogenated nitroaromatic compounds and the reduction of 3,4-dichloronitrobenzene was selected as the model reaction. With the optimal hydrogenation conditions, the yield of 3,4-dichloroaniline was obtained as high as 99.8% under mild conditions. With this strategy this flow system was successfully employed to the reduction of other chlorinated nitroaromatics also demonstrating low dehalogenation. The H-flow system enables negligible dehalogenation and remarkable yield of target product with higher efficiency and lower energy cost compared with the batch reactor.

We have carried out a two-layer our own n-layered integrated molecular orbital and molecular mechanics (MM) study on the mechanism of ethanol to propene on H-ZSM-5 and H-FAU zeolites. The entire me...

In this paper, we consider two overdetermined problems for the anisotropic $ p $-Laplacian ($ 1

We have theoretically studied the hydrodesulphurisation (HDS) mechanism of thiophene and its hydrogenated derivatives over sulphided Co–Mo catalysts supported by four zeolites (ZSM-5, FAU, Beta, MCM-22) by a two-layer ONIOM (our Own N-layered Integrated molecular Orbital and molecular Mechanics) method. Due to low energy barriers, the thiophene can be hydrogenated to 2,3-dihydrothiophene (2,3-DHT), 2,5-dihydrothiophene (2,5-DHT) and tetrahydrothiophene (THT). Direct desulphurisation (DDS) and hydrogenolysis desulphurisation (HYD) pathways were investigated in detail. The calculated results show that in DDS mechanism of thiophene, the rate-determining step is the C–S bond cleavage. In HYD mechanisms of 2,5-DHT, 2,3-DHT and THT, the rate-determining step is hydrogen transfer on ZSM-5, FAU and Beta zeolites except MCM-22 zeolite. The HYD of 2,3-DHT and THT should occur by the stepwise pathway. But for the 2,5-DHT, the concerted pathway is probably more favourable than the stepwise pathway. The reduced density gradient (RDG), differential charge density (DCD), and local orbital locator (LOL) maps show that for all transition states (TSs), there are complicated van der Waals (VDW) and electrostatic interactions between the organic fragment and the catalytic centre.

In this paper, we study Lagrangian submanifolds of the homogeneous nearly Kahler 6-dimensional unit sphere S 6 ( 1 ) . As the main result, we derive a Simons’ type integral inequality in terms of the second fundamental form of compact Lagrangian submanifolds of S 6 ( 1 ) . Moreover, we show that this inequality is optimal and the equality sign occurs if and only if the Lagrangian submanifold is either the totally geodesic S 3 ( 1 ) or the Dillen–Verstraelen–Vrancken’s Berger sphere S 3 described in Dillen et al. (1990).

Associated with an immersion φ : S3 → ℂP3, we can define a canonical bundle endomorphism F : TS3 → TS3 by the pull back of the Kahler form of ℂP3. In this article, related to F we study equivariant minimal immersions from S3 into ℂP3 under the additional condition (∇XF)X = 0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ: S3 → ℂP3 satisfying (∇XF)X = 0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.

Aiming at the highly selective production of 2,5-dimethylfuran (DMF) from fructose, a one-pot strategy and bifunctional catalysts with different surface wettability were specially designed. The hyd...

Let $$N^{2n+1}(c)$$ be an $$(2n+1)$$ -dimensional Sasakian space form with Sasakian structure $$(\varphi ,\xi , \eta ,g)$$ and constant $$\varphi $$ -sectional curvature c. An n-dimensional submanifold $$M^n$$ of $$N^{2n+1}(c)$$ is called integral if the contact form $$\eta $$ restricted to $$M^n$$ vanishes. In this paper, we established a general inequality for n-dimensional integral submanifolds in Sasakian space forms involving the norm of the covariant differentiation of both the second fundamental form h and the mean curvature vector field H. Our result is optimal in that we can classify all integral submanifolds realizing the equality case of the inequality. As direct consequence, we give a characterization of the contact Whitney spheres in the Sasakian space forms.

In this short paper, we study compact Lagrangian submanifolds of the homogeneous nearly Kahler 6-dimensional unit sphere $${\mathbb {S}}^6(1)$$. Following a strategy in Hu et al. (J Geom Phys 144:199–208, 2019), we shall establish an optimal pinching theorem in terms of the Ricci curvature so that a new characterization of the totally geodesic $${\mathbb {S}}^3(1)$$ and the Dillen–Verstraelen–Vrancken’s Berger sphere $$S^3$$ (described in J Math Soc Jpn 42:565–584, 1990) in $${\mathbb {S}}^6(1)$$ can be given.

In this paper, we study Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ introduced by Zhang \cite{Zh} in the complex space forms $N(4c)(c=0\ or \ 1)$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$ is the Lagrangian trace-free second fundamental form. We obtain some Simons' type integral inequalities and rigidity theorems for such Lagrangian submanifolds. Moreover we study Lagrangian submanifolds in $\mathbb{C}^n$ satisfying $\nabla^*\nabla^*T=0$ and introduce a flow method related to them., Comment: 18 pages, introduction rearranged and errors corrected.In the last version, we uplodaded a wrong file

The hydrogenation of m-dinitrobenzene to m-phenylenediamine is a significant transformation for the synthesis of dyes and pigments in the fine chemical industry. Owing to the complexity of this reaction mechanism and negative effect of the first amino group on the reduction of the second nitro group, it is difficult to inhibit eminently the generation of side products and obtain m-phenylenediamine efficiently. Hence it is imperative to establish kinetic network and investigate the intrinsic kinetic parameters of this reaction for further optimization. In this study, a continuous flow system based on micro-packed bed reactor was developed and a kinetic model of the hydrogenation of m-dinitrobenzene was established successfully. The activation energies and pre-exponential factors were acquired using the kinetic network and the kinetic model exhibited reasonable fit for the transformation of each substance. Moreover, the influence of pressure was investigated, and the accuracy of kinetic model was validated by the comparison with the values in literature. This kinetic model enabled the accurate determination of kinetic parameters with Pt/C and Ni/SiO2 catalysts, and provided the rate determining steps and characteristics of different catalysts for the process optimization.

Aimed at efficient production of 5-hydroxymethylfurfural (HMF) in a green and sustainable way, dehydrogenation of fructose was enhanced by liquid–liquid extraction in a membrane dispersion microreactor. On account of the high mass-transfer rate resulted from dripping flow, the obtained HMF was readily extracted from the aqueous phase to the organic phase, effectively preventing the sequence side reaction and leading to high HMF selectivity. Enhanced by efficient extraction, the reaction duration decreased from 60 min in a traditional stirred reactor to 4 min in the microreactor, leading to an increase in the space-time yield by 3 orders of magnitude. The effects of total volume flow rate, droplet size, and phase ratio relating to extraction efficiency and HMF yield were systematically investigated. The highest extraction efficiency of nearly 100% coupled with the HMF yield of 93.0% was achieved at the phase ratio of 2 with volume flow rate of 600 mL/h. Overall, this work not only delineates an efficient s...

The equivariant CR minimal immersions from the round 3-sphere $$S^3$$ into the complex projective space $$\mathbb CP^n$$ have been classified by the third author explicitly (Li in J Lond Math Soc 68:223–240, 2003). In this paper, by employing the equivariant condition which implies that the induced metric is left-invariant and that all geometric properties of $$S^3=\mathrm{SU}(2)$$ endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra $$\mathfrak {su}(2)$$ , we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere $$S^3$$ into $$\mathbb CP^n$$ without the assumption of constant sectional curvatures.

A hierarchical NbOx-based catalyst with both Bronsted acid and Lewis acid sites was synthesized in the absence of corrosive hydrofluoric acid, exhibiting high catalytic activity for biobased p-xylene (PX) production from 2,5-dimethylfuran (DMF). The as-prepared composite was composed of Nb2O5 and NbOPO4 crystals, and the densities of Bronsted acid and Lewis acid were determined to be 232.9 and 80.4 μmol/g, respectively. The well-balanced Bronsted/Lewis acidity and the hierarchical structure with small mesopores (3 nm) and large mesopores (48 nm) contributed to the high activity and stability: a conversion of 87.2% with the PX selectivity of 92.7%, and a carbon balance of 94.6% was achieved after 6 h of reaction at 523 K. In comparison with Sn-Beta, NbOx-based catalyst prepared in this work showed obvious advantages in suppressing carbon deposition: 90.9 and 54.7 mmol of PX were obtained over the NbOx-based catalyst and the Sn-Beta, respectively, after 24 h. Spent catalysts were regenerated through calcina...

With the rapid development of computer networks, network management has become more and more complex. In order to improve the operational and intelligence of the management of network equipment and services, we present an improved network topology auto-discovery algorithm based on Simple Network Management Protocol(SNMP), Internet Control Message Protocol(ICMP) and Address Resolution Protocol(ARP). The algorithm based on standard MIB-II and ICMP command, according to TCP/IP protocol addressing relevant principles, to achieve rapid network topology discovery and further reduce the network load. Experimental results show that the algorithm can quickly and accurately find the network topology.

The Network Tomography technology based on RTCP feedback for network monitoring and management is significant. The current RTCP feedback mechanism is defined in RFC3550. In this paper, the RTCP Extended Report (XR) feedback mechanism has been studied. The paper analyses the relationship between the feedback interval and RTCP packet size and the size of the multicast session, points out the shortage of the current feedback mechanism, and puts forward animproved encoding method. Based on the RTCP unicast feedback model, using reasonable encoding XR packets can reduce the feedback bandwidth and promote the feedback rate.