On lie algebras of affine vector fields of ideal realizations of holomorphic linear connections

We study the properties of real realizations of holomorphic linear connections over associative commutative algebras \(\mathbb{A}\) _m with unity. The following statements are proved.If a holomorphic linear connection ? on M _n over \(\mathbb{A}\) _m (m ≥ 2) is torsion-free and R ≠ 0, then the dimension over ? of the Lie algebra of all affine vector fields of the space (M _mn ^? , ?^?) is no greater than (mn)² ? 2mn + 5, where m = dim_? \(\mathbb{A}\), \(n = dim_\mathbb{A} \) M _n , and ?^? is the real realization of the connection ?.Let ?^? =¹ ? ײ ? be the real realization of a holomorphic linear connection ? over the algebra of double numbers. If the Weyl tensor W = 0 and the components of the curvature tensor ¹ R ≠ 0, ² R ≠ 0, then the Lie algebra of infinitesimal affine transformations of the space (M _2n ^? , ?^?) is isomorphic to the direct sum of the Lie algebras of infinitesimal affine transformations of the spaces ( ^a M _n , ^a ?) (a = 1, 2).     

Normal connections induced by a framed hypersurface in the conformal space

We find two normal connections induced by the normal framing of a hypersurface V _{n ? 1} in the conformal space C _n , and establish relationship between these connections and a Weyl connection which is also induced by the normal framing of V _{n ? 1}. We study two normal connections induced by a complete framing of a hypersurface V _{n ? 1} in C _n . We establish relationship between geometries of a framed hypersurface V _{n ? 1} of the conformal space C _n and a quadratic hyperband of the projective space P _{n + 1} associated with V _{n ? 1}.     

Higher order PDE's and iterated processes

We introduce a class of stochastic processes based on symmetric -stable processes, for . These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric -stable process. We call them -time processes. They generalize Brownian time processes studied in Allouba and Zheng (2001), Allouba (2002), (2003), and they introduce new interesting examples. We establish the connection of -time processes to some higher order PDE's for rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.

     

容有半对称度量联络的广义复空间中子流形上的Chen-Ricci不等式

本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果.     

On the Riemannian curvature tensor of a real hypersurface in a complex projective space

We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections and classify them when the covariant derivatives associated with both connections, either in the direction of the structure vector field or any direction of the maximal holomorphic distribution, coincide when applying to the Riemannian curvature tensor of the real hypersurface.     

Flat connections and cohomology invariants

The main goal of this article is to construct some geometric invariants for the topology of the set of flat connections on a principal G‐bundle . Although the characteristic classes of principal bundles are trivial when , their classical Chern–Weil construction can still be exploited to define a homomorphism from the set of homology classes of maps to the cohomology group , where S is null‐cobordant ‐manifold, once a G‐invariant polynomial p of degree r on is fixed. For , this gives a homomorphism . The map is shown to be globally gauge invariant and furthermore it descends to the moduli space of flat connections , modulo cohomology with integer coefficients. The construction is also adapted to complex manifolds. In this case, one works with the set of connections with vanishing (0, 2)‐part of the curvature, and the Dolbeault cohomology. Some examples and applications are presented.     

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of where is the strength parameter and is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential such that the density of the system remains unchanged as is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as is varied. Furthermore, using total energies of these systems as a function of , we provide a new perspective into a variety of hybrid functionals.     

Noninvasive quantification of fluid mechanical energy losses in the total cavopulmonary connection with magnetic resonance phase velocity mapping

A major determinant of the success of surgical vascular modifications, such as the total cavopulmonary connection (TCPC), is the energetic efficiency that is assessed by calculating the mechanical energy loss of blood flow through the new connection. Currently, however, to determine the energy loss, invasive pressure measurements are necessary. Therefore, this study evaluated the feasibility of the viscous dissipation (VD) method, which has the potential to provide the energy loss without the need for invasive pressure measurements. Two experimental phantoms, a U-shaped tube and a glass TCPC, were scanned in a magnetic resonance (MR) imaging scanner and the images were used to construct computational models of both geometries. MR phase velocity mapping (PVM) acquisitions of all three spatial components of the fluid velocity were made in both phantoms and the VD was calculated. VD results from MR PVM experiments were compared with VD results from computational fluid dynamics (CFD) simulations on the image-based computational models. The results showed an overall agreement between MR PVM and CFD. There was a similar ascending tendency in the VD values as the image spatial resolution increased. The most accurate computations of the energy loss were achieved for a CFD grid density that was too high for MR to achieve under current MR system capabilities (in-plane pixel size of less than 0.4 mm). Nevertheless, the agreement between the MR PVM and the CFD VD results under the same resolution settings suggests that the VD method implemented with a clinical imaging modality such as MR has good potential to quantify the energy loss in vascular geometries such as the TCPC.     

Q690高性能焊接钢管轴压临界承载力实验研究

为研究国家电网输电塔中Q690高性能钢焊接圆管的临界承载力,取长细比45和60,且考虑径厚比为31.25、37.50和43.75的三种截面,以厚度为8mm的国产Q690高性能钢板设计制作了18根焊接圆管足尺试件并进行轴向受压试验。由试验结果分析表明:试件与普钢圆管发生相同的弹性整体失稳破坏,破坏瞬时突然;而相对普通钢材,Q690高性能钢材料弹性段相对较长,管材环向约束增强,试件失稳相对滞后,临界承载力相应提高。与中国和美国相关行业规范公式计算值对比分析发现:所有规范计算值均不同程度小于试验实测结果,且长细比越大,差异越明显。上述结果进一步验证了将河南省电力勘测设计院"Q690钢管杆塔设计试验研究技术报告"得出的轴压稳定系数取值的相关规范设计公式应用于指导工程设计的可行性。     

In‐situ series connection of an amorphous silicon photovoltaic tandem module

Local shading during thin film deposition monolithically interconnects thin film solar cells into photovoltaic modules. This in‐situ series connection method is, for the first time, applied to an amorphous silicon tandem cell structure. Sequential maskingand mask‐shifting forms the electrical series connection in‐situ, i.e. during the sputtering and plasma depositions of the contact and semiconductor layers of the thin film solar cell structure. The resulting photovoltaic module consists of five amorphous silicon tandem cells with a total module area A_{\rm m} =12.5\mathop {\;{\rm cm}}\nolimits^2. The module exhibits a fill factor {\rm FF}_{\rm m} > 72% and a total area efficiency \eta _{\rm m} =6.2%. Thermographic imaging proves successful patterning by local shading and attributes low shunt resistances of some component cells to single pinhole formation. The dark‐shunt resistance of each cell of the module amounts to R_{{\rm sc}{\rm,dark}{\rm,cell}} > 13\;{\rm k\Omega }\;{\rm cm}^{2} and for the complete module to R_{{\rm sc}{\rm,dark}{\rm,module}} =454\;{\rm k\Omega }\;{\rm cm}^{2}. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)