Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY

A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.

Some Inequalities for Submanifolds in Cosymplectic Space Forms

For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.

On Intrinsic Rigidity for Submanifolds with Constant Scalar Curvature in Space Forms

Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.

HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS

Let f: Mn(?)Sn+1 C Rn+2 be an n-dimensional complete oriented Rieman-nian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by S_+~n+1 the upper closed hemisphere. If f(Mn)(?)_+~n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature.

RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS

We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.

Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms

In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.

Study on the Integration and Optimization of Campus Spaces: A Case Study of Yaohu Campus of Jiangxi Normal University

In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, proposed the methods for integrating and optimizing campus spaces, such as establishing artistic conception of campus space, improving campus traffic organization, creating and improving the external communication spaces, on the basis of analyzing evolution history of campus spaces.

Totally Real Sectional Curvature for Submanifolds in Sasakian Space Forms

By using the methods introduced by Chen[Chen Bang-yen,A series of Ka¨hlerian invarianrts and their applications to Khlerian geometry,Beitrge Algebra Geom,2001,42(1):165-178],we establish some inequalities for invariant submanifolds in a Sasakian space form involving totally real sectional curvature and the scalar curvature.Moreover,we consider the case of equalities.

<i>L^pp</i>-Harmonic 1-Forms on <i>δ</i>-Stable Hypersurface in Space Form with Nonnegative Bi-Ricci Curvature

In this paper, we investigate the space of Lp p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface Mm that is immersed in space form with nonnegative BiRic curvature. We prove the nonexistence of Lp p-harmonic 1-forms on Mm. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.

Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms

Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

ON THE INVARIANT SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLD

In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.

Effects of Different Line Spacing and Seedling Belt Width on Yield Formation of Broad-Width Fine Sowing Wheat

In order to explore the interaction effects of line spacing and seedling belt width on wheat yield formation and improve the cultivation techniques of broadwidth and fine seeding of wheat,a high-yielding winter wheat cultivar Shannong 28 was selected as material. Using the split plot design,the main plot was set with line spacing as 20,25 and 30 cm,respectively,and the sub-plot was set with seedling belt width as 3,5,7,9 and 11 cm,respectively. Then,the population dynamics,dry matter accumulation and translocation and yield of wheat were studied under the experimental conditions. The results showed that under the line spacing of 20 cm,the dry matter accumulation and yield of winter wheat were higher with the seedling belt width of 5 cm. When the line spacing was 25 cm,the dry matter accumulation and yield under the seedling belt width of 9 cm reached a high level. Under the line spacing of 30 cm,Shannong 28 achieved higher dry matter accumulation and yield with the seedling belt width of 11 cm. Comprehensive analysis revealed that the suitable treatment for Shannong 28 was 25 cm of line spacing with 9 cm of seedling belt width,which could realize the coordination of the three factors of yield composition and get higher yield. Therefore,the reasonable line spacing and seedling belt width were the important technical ways to realize high yield of wheat.

Perfect Combination of Architectural Functions and Flow Lines: Study on Roof Garden of Frank Gehry's Walt Disney Concert Hall

By exploring the space and the design techniques of roof garden in Frank Gehry's Walt Disney Concert Hall, this paper made further research on the combination of architectural functions and pedestrian fl ow lines, and attempted to summarize the unique design techniques of Frank Gehry by analyzing his works, improve and develop design theories of roof garden, and attract more attention from the public to roof garden design.

C-Totally Real Submanifolds with Parallel Mean Curvature Vector of Sasakian Space Form

We have discussed the C-totally real subrnanifolds with parallel mean curvature vector of Sasakian space form, obtained a formula of J.Simons type, and improved one result of S.Yamaguchi.

Rigidity Theorems for Hypersurfaces in Real Space Form

In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.

2-Harmonic Submanifolds in a Complex Space Form

In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.

On the Mean Absolute Geodesic Curvature of Closed Curves in 2-Dimensional Space Forms

In this paper, we establish some formulas on closed curves in 2-dimensionalspace forms. Mean absolute geodesic curvature is introduced to describe the average curving of aclosed curve. In this sense, a closed curve could be compared with a geodesic circle that is theboundary of a convex geodesic circular disk containing the closed curve. The comparison can be usedto show some properties of space forms only on themselves.

Isometric Spacelike Immersions of Space Forms in Indefinite Space Forms

Let M be a connected n dimensional space form spacelike isometrically immersed in a (2n-1) dimensional indefinite space form. If M is maximal, we prove that either M is totally geodesic or M is a piece of the n dimensional hyperbolic cylinder in the (2n-1) dimensional pseudo hyperbolic space.

A Kinematic Formula for Integral Invariant of Degree 4 in Real Space Form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.