Electric-driven flexible-roller nanoimprint lithography on the stress-sensitive warped wafer

Surface nanopatterning of semiconductor optoelectronic devices is a powerful way to improve their quality and performance.However,photoelectric devices’inherent stress sensitivity and inevitable warpage pose a huge challenge on fabricating nanostructures large-scale.Electric-driven flexible-roller nanoimprint lithography for nanopatterning the optoelectronic wafer is proposed in this study.The flexible nanoimprint template twining around a roller is continuously released and recovered,controlled by the roller’s simple motion.The electric field applied to the template and substrate provides the driving force.The contact line of the template and the substrate gradually moves with the roller to enable scanning and adapting to the entire warped substrate,under the electric field.In addition,the driving force generated from electric field is applied to the surface of substrate,so that the substrate is free from external pressure.Furthermore,liquid resist completely fills in microcavities on the template by powerful electric field force,to ensure the fidelity of the nanostructures.The proposed nanoimprint technology is validated on the prototype.Finally,nano-grating structures are fabricated on a gallium nitride light-emitting diode chip adopting the solution,achieving polarization of the light source.

双warped积流形之间2-调和的积映射(英文)

讨论了积映射Φ2=φ×ψ和2个广义的投影φ和ψ的2-调和性,得到了几个主要结论:Φ2=φ×ψ是恰当2-调和映射的充分必要条件是函数b,f分别为方程-1/f2 Jφ(dφ(grad(lnb)))+n/2grad dφ(grad(lnb))2=0,-1/b2Jψ(dψ(grad(lnf)))+m/2grad dψ(lnf)=0的非常值解;Φ2=φ×ψ是恰当2-调和映射的充分必要条件是φ和ψ都是恰当2-调和映射.

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 ＋ fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler （resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg） manifold are ob- tained, respectively. It is proved that if （M1, F1） and （M2,F2） are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.

IRRIGATING WARPED SOILS——ANTHROPOGENIC SOIL IN ARID AND SEMI-ARID REGIONS OF CHINA

The irrigating warped soils occur in the old irrigation areas of arid and semi-arid re-gions of China, and distributed from Zhangjiakou of Hebei province, through InnerMongolia Autonomous Region, Ningxia Hui Autonomous Region, Gansu province,Qinhai Province, down to Xinjiang Autonomous Region, including the arid subalpine rivervalleys in the western part of Tibet.

f-Harmonic maps of doubly warped product manifolds

In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M ×（μ,λ） N can not be proper f-harmonic maps,we use projection maps and product maps to construct nontrivial f-harmonic maps.Thus we obtain some similar results given in [21],such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps.Furthermore,we investigate non-trivial f-harmonicity of the product of two harmonic maps.

关于warped乘积S^1(a)×_fS^n(b)的迷向曲率

在本文中,我们研究了warped乘积S1(a)×fSn(b)(a2+b2=1,a>0,b>0,n≥3),给出了这类黎曼流形具有正迷向曲率的充分必要条件.

Theory and algorithms for two-dimensional warped discrete Fourier transform

In this paper, the two-dimensional Warped Discrete Fourier Transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.

Estimation of Regression Function for Nonequispaced Samples Based on Warped Wavelets

We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.

Bi-f-harmonic map equations on singly warped product manifolds

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 dimensionM manifolds and some special maps from or into a warped product manifold.

GENERIC WARPED PRODUCT SUBMANIFOLDS OF LOCALLY CONFORMAL KEAHLER MANIFOLDS

Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.

Osserman Conditions in Lightlike Warped Product Geometry

In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings. PART II: The Second Order Contribution

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings

The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .

Conformal Vector Fields on Finsler Warped Product Manifolds

In this paper,we study the conformal vector fields on Finsler warped product manifolds.We obtain a system of equivalent equations that the conformal vector fields on Finsler warped product manifolds satisfy and completely characterize conformal vector fields on such manifolds.Further,by solving the equation,we give the classification.And we also give some examples.

Finsler warped product metrics with special Riemannian curvature properties

One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar)curvature.In this paper,we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature.In particular,we find equations that characterize Finsler warped product metrics of constant flag curvature.Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics.As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature.

S-curvature of Doubly Warped Product of Finsler Manifolds

Doubly warped product of Finsler manifolds is useful in theoretical physics,particularly in general relativity.In this paper,we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or weak isotropic S-curvature.

An intelligent automatic correlation method of oilbearing strata based on pattern constraints:An example of accretionary stratigraphy of Shishen 100 block in Shinan Oilfield of Bohai Bay Basin,East China

Aiming at the problem that the data-driven automatic correlation methods which are difficult to adapt to the automatic correlation of oil-bearing strata with large changes in lateral sedimentary facies and strata thickness,an intelligent automatic correlation method of oil-bearing strata based on pattern constraints is formed.We propose to introduce knowledge-driven in automatic correlation of oil-bearing strata,constraining the correlation process by stratigraphic sedimentary patterns and improving the similarity measuring machine and conditional constraint dynamic time warping algorithm to automate the correlation of marker layers and the interfaces of each stratum.The application in Shishen 100 block in the Shinan Oilfield of the Bohai Bay Basin shows that the coincidence rate of the marker layers identified by this method is over 95.00%,and the average coincidence rate of identified oil-bearing strata reaches 90.02% compared to artificial correlation results,which is about 17 percentage points higher than that of the existing automatic correlation methods.The accuracy of the automatic correlation of oil-bearing strata has been effectively improved.

Isometric Immersions into Warped Product Spaces

This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.

Characterizations of umbilic hypersurfaces in warped product manifolds

We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using an integral formula or Brendle’s Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These results can be viewed as generalizations of the classical Jellet-Liebmann theorem and the Alexandrov theorem in Euclidean space.

Constraint on the warped space from → X_s γ

We analyze the theoretical prediction on the branching ratio of B→Xsγ to order ∧^2EW/∧^2KK in extension of the standard model with a warped extra dimension and the custodial symmetry SU（3）c×SU（2）L×SU（2）R×U（1）××PLR, where AKK denotes the energy scale of low-lying Kaluze-Klein excitations and AEW denotes the electroweak energy scale. Contributions from the infinite series of Kaluze-Klein excitations are summed over through the residue theorem. The numerical result indicates that the present experimental data constrain the parameter space of the concerned model strongly.