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51.
52.
In this article, we prove the existence and multiplicity of non-trivial solutions for an indefinite fractional elliptic equation with magnetic field and concave–convex nonlinearities. Our multiplicity results are based on studying the decomposition of the Nehari manifold. 相似文献
53.
This paper is concerned with the Langford ODE and PDE systems. For the Langford ODE system, the existence of steady-state solutions is firstly obtained by Lyapunov–Schmidt method, and the stability and bifurcation direction of periodic solutions are established. Then for the Langford PDE system, the steady-state bifurcations from simple and double eigenvalues are intensively studied. The techniques of space decomposition and implicit function theorem are adopted to deal with the case of double eigenvalue. Finally, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomogeneous periodic solutions for the PDE system are investigated. 相似文献
54.
We present measurements of Eulerian longitudinal velocity autocorrelations in homogeneous, isotropic, high-intensity (~9%) free-stream turbulence behind an active grid. Spatial correlations are measured using particle image velocimetry as well as with two-point hot-wire anemometry (HWA), while temporal correlations are measured using HWA. The temporal correlations are transformed into spatial correlations by using Taylor's ‘frozen’ hypothesis with both the mean as well as instantaneous velocities. A model relating Eulerian spatial and temporal autocorrelations is also used for this purpose. The differences from the measured spatial correlation resulting from the use of Taylor's hypothesis on the temporal correlation is quantified; even at this moderately high level of turbulent intensity, the result from the use of the instantaneous velocity as convection velocity is practically indistinguishable from that obtained using the mean velocity. Use of the model produces a good agreement between the estimates of the spatial correlation function. A relation between Eulerian spatial and temporal integral scales is also derived. 相似文献
55.
ZHANG YongBing 《中国科学A辑(英文版)》2009,(8)
We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds. 相似文献
56.
Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps.In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold. 相似文献
57.
In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds. 相似文献
58.
Kazuaki Z. Takahashi 《Journal of computational chemistry》2014,35(11):865-875
In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear‐combination‐based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS‐SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS‐SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water–vapor interfacial systems using the LIPS‐SW method. The results of these simulations show that the LIPS‐SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water–vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS‐SW method. We conclude that the LIPS‐SW method shows great potential for high‐accuracy, high‐performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc. 相似文献
59.
Dr. Muntadar A. H. Al-Yassiri 《ChemistryOpen》2021,10(10):976-985
Off-nucleus isotropic magnetic shielding (σiso(r)) and multi-points nucleus independent chemical shift (NICS(0-2 Å)) index were utilized to find the impacts of the isomerization of gas-phase furfuraldehyde (FD) on bonding and aromaticity of FD. Multidimensional (1D to 3D) grids of ghost atoms (bqs) were used as local magnetic probes to evaluate σiso(r) through gauge-including atomic orbitals (GIAO) at density functional theory (DFT) and B3LYP functional/6-311+G(d,p) basis set level of theory. 1D σiso(r) responses along each bond of FD were examined. Also, a σiso(r) 2D-scan was performed to obtain σiso(r) behavior at vertical heights of 0–1 Å above the FD plane in its cis, transition state (TS) and trans forms. New techniques for evaluating 2D σiso(r) cross-sections are also included. Our findings showed that bonds in cyclic and acyclic parts of FD are dissimilar. Unlike the C−O bond of furanyl, the C=O bond of the formyl group is magnetically different. C−C and C−H bonds in furanyl are found similar to those in aromatic rings. A unique σiso(r) trend was observed for the C2−C6 bond during FD isomerization. Based on NICS(0-2 Å) values, the degree of aromaticity follows the order of cis FD<trans FD<furan<TS FD. 相似文献
60.
We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures. 相似文献