On Spin Structures and Dirac Operators on the Noncommutative Torus

We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that, similarly as in the classical case, the spectrum of the Dirac operator depends on the spin structure.     

Generalized contact geometry and T-duality

We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant–Dorfman bracket, including T-duality. We define a notion of geometric type for generalized almost contact structures, and study its behavior under T-duality.     

Heterotic non-Kähler geometries via polystable bundles on Calabi-Yau threefolds

In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c₂(X)=c₂(V) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explicit examples of polystable bundles on elliptically fibered Calabi-Yau threefolds where it applies. The polystable bundle is given by a spectral cover bundle, for the visible sector, and a suitably chosen bundle, for the hidden sector. This provides a new class of heterotic flux compactifications via non-Kähler deformation of Calabi-Yau geometries with polystable bundles. As an application, we obtain examples of non-Kähler deformations of some three generation GUT models.     

Study of top and bottom contact resistance in one organic field-effect transistor

This paper reports that the organic field-effect transistors with hybrid contact geometry were fabricated, in which the top electrodes and the bottom electrodes were combined in parallel resistances within one transistor. With the facility of the novel structure, the difference of contact resistance between the top contact geometry and the bottom contact geometry was studied. The hybrid contact devices showed similar characteristics with the top contact configuration devices, which provide helpful evidence on the lower contact resistance of the top contact configuration device. The origin of the different contact resistance between the top contact device and the bottom contact device was discussed.     

Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms

In this paper, we give the explicit construction for isometric immersions of pseudo-Riemannian space forms via loop group actions. As a consequence, we obtain a Ribaucour transformation and its permutability theorem for isometric immersions of pseudo-Riemannian space forms, which is a generalization of the permutability theorem for surfaces in R³$R^3$, and a family of new isometric immersions of the pseudo-Riemannian space forms from a given one via a purely algebraic algorithm.     

On the theory of algebraic invariants of vector spaces of Killing tensors

We employ a hybrid version of the classical Cartan method of moving frames to develop a practical algorithm for the generation of isometry group invariants and covariants for arbitrary vector spaces of Killing tensors defined on any flat pseudo-Riemannian manifold. We then apply our algorithm to construct a set of fundamental covariants for the space of valence-two Killing tensors defined in three-dimensional Euclidean space and use them to invariantly characterize the associated eleven orthogonally separable webs.     

On the integration of Poisson homogeneous spaces

We study a reduction procedure for describing the symplectic groupoid of a Poisson homogeneous space obtained by quotient of a coisotropic subgroup. We perform it as a reduction of the Lu–Weinstein symplectic groupoid integrating Poisson Lie groups, that is suitable even for the non-complete case.     

Transformation to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces

A tractable method is presented for obtaining transformations to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces. The procedure is based on the properties of parallel covector fields. As an illustration, the method is applied to obtain certain transformations that arise in the Hamilton–Jacobi theory of separation of variables.     

The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds

On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution—a class of bivector fields generalizing twisted Poisson structures that we study in detail.     

Graded non-commutative geometries

We present a short exposition of graded finite non-commutative geometries. The theory that serves as an example is based on the algebra of matrices M_n . This non-commutative algebra replaces the algebra of functions on a manifold. Consequently, vector fields (differentiations), forms and connections are constructed. The gauge theory can be introduced without the notion of internal manifold. We discuss some physical application, the similarities with the standard model, and the graded version of this geometry.     

弹性反冲探测分析技术在材料氦行为研究中的应用

弹性反冲探测分析技术（ERDA）对轻元素的测定具有灵敏度高、包含深度信息的优势,因此在材料氦行为研究中发挥着重要作用。镍基哈氏N合金被认为是未来熔盐堆的结构材料,氦脆是其服役性能下降的主要因素之一。利用掠入射模式的ERDA,解析了哈氏N合金样品中的氦原子浓度及其分布,但仅局限于0~175 nm深度范围内。结果表明:在800℃的退火条件下,距离样品辐照表面~33 nm深度区域内,出现了氦原子逃逸现象。更高温度的退火（1 050℃）可加剧氦原子的逃逸,但样品中仍有氦原子滞留。另外,采用透射式的ERDA,极大地扩大了对氦原子分析的深度范围,得到了纯镍薄膜在0~950 nm深度区域内的氦原子浓度分布。这表明将块体材料制备成薄膜样品,利用透射模式的ERDA,将可以得到氦原子在更大范围内的扩散、逃逸行为。Since the elastic recoil detection analysis (ERDA) technique has the advantages of high sensitivity and deep information in analyzing the light elements, it plays an important role in the study of helium behavior in materials. Helium embrittlement is one of the main reasons for the degradation of the Hastelloy N alloy, which has been considered as the promising candidate structural material for the further molten salt reactor. In this work, the profile of helium concentrationin sample of Hastelloy N alloy was analyzed by ERDA experiments applying grazing-incidence geometry. However, the result was limited within the depth range of 0~175 nm, and it shown that helium atoms escaped in the range from the irradiated surface of the sample to the depth of ~33 nm when annealing the sample at 800℃ The annealing at higher temperature (1 050℃) increased the escape of helium atoms, but a small fraction of helium atoms still trapped in the sample. In addition, the profile of helium concentration was obtained in the helium-irradiated pure nickel film in the depth range of 0~950 nm, using the ERDA experiments in transmission geometry. This indicates that the diffusion behavior of helium atoms in bulk samples can be completely obtained using the ERDA experiments in tranmission geometry if the bulk material can be prepared into a thin film sample.     

Renormalizability conditions for almost-commutative geometries

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that classify such geometries. This applies in particular to the Standard Model of particle physics, giving a graph-theoretical argument for its renormalizability. A promising potential application is in the selection of physical (renormalizable) field theories described by almost-commutative geometries, thereby going beyond the Standard Model.     

Geometry and nonlinear evolution equations

We briefly review the nonlinear dynamics of diverse physical systems which can be described in terms of moving curves and surfaces. The interesting connections that exist between the underlying differential geometry of these systems and the corresponding nonlinear partial differential equations are highlighted by considering classic examples such as the motion of a vortex filament in a fluid and the dynamics of a spin chain. The association of the dynamics of a non-stretching curve with a hierarchy of completely integrable soliton-supporting equations is discussed. The application of the surface embeddability approach is shown to be useful in obtaining such connections as well as exact solutions of some nonlinear systems such as the Belavin-Polyakov equation and the inhomogeneous Heisenberg chain.     

More Noncommutative 4-Spheres

New examples of noncommutative 4-spheres are introduced.     

Noncommutat ive Differential Calculus on Discrete Abelian Groups and Its Applications

A new noncommutative differential calculus on function space of discrete Abelian groups is proposed. The derivatives are introduced with respect to the generators of the groups only. It is applied to discrete symplectic geometry and Hamiltonian systems with H(p, q) = T(p) + V(q) as well as the lattice gauge theory on regular lattice.     

Integrable System and Motion of Curves in Projective and Similarity Geometries

Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleration field and governed by endowing an extra space variable in similarity geometry P³ is also studied.