Rhodium-Catalyzed Atroposelective Access to Axially Chiral Olefins via C−H Bond Activation and Directing Group Migration

Axially chiral open-chain olefins represent an underexplored class of chiral platform. In this report, two classes of tetrasubstituted axially chiral acyclic olefins have been accessed in excellent enantioselectivity and regioselectivity via C?H activation of (hetero)arenes assisted by a migratable directing group en route to coupling with sterically hindered alkynes. The coupling of indoles bearing an N-aminocarbonyl directing group afforded C–N axially chiral acrylamides with the assistance of a racemic zinc carboxylate additive. DFT studies suggest a β-nitrogen elimination–reinsertion pathway for the directing group migration. Meanwhile, the employment of N-phenoxycarboxamide delivered C?C axially chiral enamides via migration of the oxidizing directing group. Experiments suggest that in both cases the (hetero)arene substrate adopts a well-defined orientation during the C?H activation, which in turn determines the disposition of the alkyne in migratory insertion. Synthetic applications of representative chiral olefins are demonstrated.     

Global nonlinear stability of longitudinal wave for the planar motion of elastic string with linear Hooke's law

In this paper, we consider the global nonlinear stability of longitudinal wave for the planar motion of elastic string with linear Hooke's law. First, we will give the representation of the traveling wave solution to the recast hyperbolic system. Then, by using the weighted function method, we obtain the global stability of longitudinal wave solution for nonlinear elastic string equation.     

Deformations of the spin currents by topological screw dislocation and cosmic dispiration

We study the spin currents induced by topological screw dislocation and cosmic dispiration. By using the extended Drude model, we find that the spin dependent forces are modified by the nontrivial geometry. For the topological screw dislocation, only the direction of spin current is bent by deforming the spin polarization vector. In contrast, the force induced by cosmic dispiration could affect both the direction and magnitude of the spin current. As a consequence, the spin-Hall conductivity does not receive corrections from screw dislocation.     

Light scalar tetraquarks from a holographic perspective

We discuss how a dominant tetraquark component of the lightest scalar mesons may emerge in AdS/QCD gravity duals. In particular, we show that the exceptionally strong binding required to render the tetraquark ground state lighter than the lowest-lying scalar quark–antiquark nonet can be holographically encoded into bulk-mass corrections for the tetraquark's dual mode. The latter are argued to originate from the anomalous dimension of the corresponding four-quark interpolator. To provide a concrete example, we implement this mechanism into the dilaton soft-wall dual for holographic QCD. Preventing the lowest-lying dual mode from collapsing into the AdS boundary then establishes a rather generic lower bound on the tetraquark mass (which may be overcome in the presence of additional background fields). We further demonstrate that the higher tetraquark excitations can become heavier than their quark–antiquark counterparts and are thus likely to dissolve into the multiparticle continuum.     

From local to global in F-theory model building

When locally engineering F-theory models some D7$D7$-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note, we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally, the possible D7$D7$-branes are not independent from each other and the (compact part of the) D7$D7$-brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension-three loci which are not   intersections of matter curves. We describe these complications specifically in a global SU(5)$SU\left(5\right)$ model and also their impact on the tadpole cancellation condition.     

Instanton partition functions and M-theory

We discuss instanton partition functions in various spacetime dimensions. These partition functions capture some information about the spectrum of the supersymmetric gauge theories and their low-energy dynamics. Some of these theories can be defined microscopically only through string theory. Remarkably, they even know about the M-theory. Our conjectures include the identities between the generalization of the MacMahon formula and the character of M-theory, compactified down to 0 + 1 dimension. This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5, 2008.     

Affine Crystal Graphs And Two-Colored Partitions

We define the cores and the quotients of the elements in the crystal graph of the basic representation of or , and then obtain new combinatorial interpretations of the character and the string function formula. Mathematics Subject Classifications (2000). 17B37, 05A17.     

On cyclic strings avoiding a pattern

We count the number of cyclic strings over an alphabet that avoid a single pattern under two different assumptions. In the first case, we assume that the symbols of the alphabet are on numbered positions on a circle, while in the second case we assume that the symbols can be freely rotated on the circle (i.e., we deal with necklaces). In each case, we provide a generating function, and we explain how these two cases are related. For the situation of avoiding more than one pattern, we formulate a general conjecture for the first case, and a conditional result for the second case. We also explain the differences between our theory and the theory of Edlin and Zeilberger (2000) by emphasizing how we modified the definition of the enumeration of cyclic strings that avoid one or more patterns when their lengths are less than the length of the longest pattern.     

具有模糊目标的多目标双矩阵对策集结与求解

针对不确定性多冲突环境,建立了多个具有模糊目标的多目标双矩阵对策的综合集结模型.在假定局中人各模糊目标的隶属函数为线性函数的情形下,基于总体模糊目标的可达度,给出了纳什均衡解的定义,并应用粒子群优化算法对集结模型求解.最后,给出一个军事例子说明了模型的实用有效性和粒子群优化算法求解的高效性.