Poisson-geometric Analogues of Kitaev Models

We define Poisson-geometric analogues of Kitaev’s lattice models. They are obtained from a Kitaev model on an embedded graph $$\Gamma $$ Γ by replacing its Hopf algebraic data with Poisson data for a Poisson-Lie group G. Each edge is assigned a copy of the Heisenberg double $${\mathcal {H}}(G)$$ H ( G ) . Each vertex (face) of $$\Gamma $$ Γ defines a Poisson action of G (of $$G^*$$ G ∗ ) on the product of these Heisenberg doubles. The actions for a vertex and adjacent face form a Poisson action of the double Poisson-Lie group D(G). We define Poisson counterparts of vertex and face operators and relate them via the Poisson bracket to the vector fields generating the actions of D(G). We construct an isomorphism of Poisson D(G)-spaces between this Poisson-geometrical Kitaev model and Fock and Rosly’s Poisson structure for the graph $$\Gamma $$ Γ and the Poisson-Lie group D(G). This decouples the latter and represents it as a product of Heisenberg doubles. It also relates the Poisson-geometrical Kitaev model to the symplectic structure on the moduli space of flat D(G)-bundles on an oriented surface with boundary constructed from $$\Gamma $$ Γ .

Study on the Law of Fracture Evolution under Repeated Mining of Close-Distance Coal Seams

The western region of China is rich in mineral resources. The vigorous development of mineral resources has exacerbated the environmental and safety problems in the region. One of the important links to solve this problem is to control the development laws and distribution characteristics of the overburdened cracks in the mining of this area. In this paper, the Xiashijie coal mine 3-2 coal seam and 4-2 coal seam are examples of repeated mining, and are examined as the background, through theoretical analysis to optimize the size of the coal pillars in the lower section, using the 3DEC numerical simulation experiment method and the rise of the cracks in the short-distance coal seam. Repeated mining monitoring and analysis of the development law are used to ascertain distribution characteristics of overburdened cracks caused by the repeated mining process of the working face. The results show that: (1) By establishing a mechanical model of the overlying strata structure under short-distance coal seam group mining, and carrying out the force analysis of the double section coal pillar under repeated mining, the reasonable size of a lower section coal pillar was determined to be 70 m. (2) As the development height of a fracture progresses with the working face, its expansion rate undergoes four obvious changes: fluctuations within a certain range, the expansion rate reaches the peak after the rock formation is concentrated and broken, the cyclical change gradually decreases, and the expansion rate is zero after complete mining. (3) The fracture zone height of 222 and 224 face under repeated mining in the 4-2 coal seam was 19.56–22.31 times and 22.38–24.54 times larger, respectively, and the post-mining fracture extension of the face with larger width and deeper burial under repeated mining was higher than that of the adjacent face. This study provides scientific guidance for the rational division of coal pillars and the solution of the problem of water conservation mining under repeated mining in the adjacent face of a short-distance coal seam.

Combined Neural Tuning in Human Ventral Temporal Cortex Resolves the Perceptual Ambiguity of Morphed 2D Images

We have an amazing ability to categorize objects in the world around us. Nevertheless, how cortical regions in human ventral temporal cortex (VTC), which is critical for categorization, support this behavioral ability, is largely unknown. Here, we examined the relationship between neural responses and behavioral performance during the categorization of morphed silhouettes of faces and hands, which are animate categories processed in cortically adjacent regions in VTC. Our results reveal that the combination of neural responses from VTC face- and body-selective regions more accurately explains behavioral categorization than neural responses from either region alone. Furthermore, we built a model that predicts a person’s behavioral performance using estimated parameters of brain–behavior relationships from a different group of people. Moreover, we show that this brain–behavior model generalizes to adjacent face- and body-selective regions in lateral occipitotemporal cortex. Thus, while face- and body-selective regions are located within functionally distinct domain-specific networks, cortically adjacent regions from both networks likely integrate neural responses to resolve competing and perceptually ambiguous information from both categories.

Combined neural tuning in human ventral temporal cortex resolves the perceptual ambiguity of morphed 2-D images

ABSTRACTWe have an amazing ability to categorize objects in the world around us. Nevertheless, how cortical regions in human ventral temporal cortex (VTC), which is critical for categorization, support this behavioral ability, is largely unknown. Here, we examined the relationship between neural responses and behavioral performance during the categorization of morphed silhouettes of faces and hands, which are animate categories processed in cortically adjacent regions in VTC. Our results reveal that the combination of neural responses from VTC face- and body-selective regions more accurately explains behavioral categorization than neural responses from either region alone. Furthermore, we built a model that predicts a person’s behavioral performance using estimated parameters of brain-behavioral relationships from a different group of people. We further show that this brain-behavioral model generalizes to adjacent face- and body-selective regions in lateral occipito-temporal cortex. Thus, while face- and body-selective regions are located within functionally-distinct domain-specific networks, cortically adjacent regions from both networks likely integrate neural responses to resolve competing and perceptually ambiguous information from both categories.

Spindown Polyhedra

Magic: the gathering is a trading card game published by Wizards of the Coast [1]. The aim of most variants of the game is to reduce your opponent's life total from twenty to zero, thus winning the game. As it may take several turns to reduce a player's life total to zero, players need a mechanism to keep track of their current life total. For this purpose, players often use a device called a spindown life counter, shown in Figure 1. A spindown life counter is an icosahedron with a special labelling of the faces, such that − starting with 20 life total − a player can reduce their life total in decrements of one by rolling the icosahedron onto an adjacent face each time. A spindown life counter appears similar to a standard icosahedral die, known in gaming as a d20; however, the labelling of faces is different, as also shown in Figure 1.

Synthesis and crystal structure of new K and Rb selenido/tellurido ferrate cluster compounds

In the course of a systematic study of alkali iron chalcogenido salts containing clusters [Fe4Q8] a series of new mixed-valent potassium and rubidium selenido and tellurido ferrates(II/III) was synthesized by carefully heating the pure elements enclosed in sample tubes under an argon atmosphere up to maximum temperatures of 800–900 °C. Their crystal structures have been determined by means of single crystal X-ray diffraction. The mixed-valent FeII/III tellurido ferrates A7[Fe4Te8] form three different structure types. All structures contain tetramers of four edge sharing [FeTe4] tetrahedra, which are connected by common edges to form only slightly distorted tetrahedral [Fe4Te8]7− anions (‘stella quadrangula’) with a [Fe4Te4] cubane core. In all cases, these anions are surrounded by 26 alkali cations, which are located at the eight corners and the midpoints of the six faces and 12 edges of a cube. The three crystal structures can thus be described by three different packings of cuboid moieties: The monoclinic rubidium compound Rb7[Fe4Te8] (space group C2/c, a = 2000.16(7), b = 897.79(3), c = 1768.12(6) pm, β = 117.4995(10)°, Z = 4, R1 = 0.0296) is isotypic to the known cesium tellurido and sulfido ferrates Cs7[Fe4(S/Te)8]. Depending on the temperature, K7[Fe4Te8] forms two different but closely related new structure types: The tetragonal r.t. modification (space group P42/nmc, a = 1222.25(14), c = 872.1(2) pm, Z = 2, R1 = 0.0583) crystallizes in a supergroup of the orthorhombic l.t. (100 K) form (space group Pbcn, a = 1715.5, b = 866.76(3), c = 1715.50(7) pm, Z = 4, R1 = 0.0160). In all structures, the cluster centered cubes are stacked to form columns along the short (≈870 pm) axis. These columns are themselves densely packed with 4 (both K compounds) and 6 (A = Rb) adjacent face-sharing columns. According to these arrangements of cluster-centered cubes, a relation of the packing of K/Rb cations and cluster anions with the simple cubic packing can be established applying the crystallographic group-subgroup formalism. Attempts to synthesize the corresponding selenium compound K7[Fe4Se8] resulted in the formation of the likewise mixed-valent compound K6[Fe4Se8]. Despite the modified composition, the new orthorhombic structure (space group Pbcn, a = 1632.62(6), b = 821.10(3), c = 1592.75(6) pm, Z = 4, R1 = 0.0540) is almost isotypic to the l.t. form of K7[Fe4Te8], the only difference being a missing K site. K5Fe2Te5 crystallizes in a new structure type (cubic, space group Pa3̅, a = 1709.02(5) pm, Z = 4, R1 = 0.0594). According to K5Fe2Te5=K15[Fe3Te7]2(Te), its structure contains mixed-valent cuboidal trimers [Fe3Te7](6/7)− and isolated telluride ions, which are coordinated by cubes of K+ cations.

Research on Cooperated and Continuous Non-Pillar Mining Technology

This thesis, making research on 4224 Mining District of Zhangcun Mine and combining with the geological features of the good lithological conditions of the roof and floor of the mining district and low gas content，etc, put forward the maintain roadways pattern of gob-side entry retaining, adopt adding anchor cables and erecting monomer pillar and other methods as the means to strengthen support, and effectively prevent the gangue to flow into the roadway by hanging grid on the up-side, and make research on ground behavior regular of gob-side entry retaining. Raise the transporting method that the face support move along the Gob-side Entry to the Open-Off Cut of the next section，which shorten the face moving route and moving time, achieve quick successival of the adjacent face. Meanwhile, continuous mining makes the surface appear continuous sinking, avoid the adverse impact on the surface of the sinking marginal basin, and minimize damage to the environment. Achieve the maximum recovery of coal resources, and minimize damage to the environment.

A Mathematical Solution for Gas-to-Surface Radiative Exchange Area for a Rectangular Parallelepiped Enclosure Containing a Gray Medium

The transfer of heat in a gas filled enclosure can be calculated by the zone method put forward by Hottel and Cohen [1, 2]. For a shape which can be divided into cylindrical or cubic zones, tabulated and graphical data on exchange areas are available, however, insufficient data exist for subdivision into rectangular zones. The present contribution provides a mathematical solution for the gas-to-surface exchange area between a rectangular parallelepiped gas volume and an adjacent face. The rules for manipulating and scaling of exchange areas are reviewed, and their application to the zoning of a rectangular furnace chamber into concentric rectangular volume elements is demonstrated.