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Topological structures based on controllable ferroelectric or ferromagnetic domain configurations offer the opportunity to develop microelectronic devices such as high-density memories. Despite the increasing experimental and theoretical insights into various domain structures (such as polar spirals, polar wave, polar vortex) over the past decade, manipulating the topological transformations of polar structures and comprehensively understanding its underlying mechanism remains lacking. By conducting an in-situ non-contact bias technique, here we systematically investigate the real-time topological transformations of polar structures in PbTiO3/SrTiO3 multilayers at an atomic level. The procedure of vortex pair splitting and the transformation from polar vortex to polar wave and out-of-plane polarization are observed step by step. Furthermore, the redistribution of charge in various topological structures has been demonstrated under an external bias. This provides new insights for the symbiosis of polar and charge and offers an opportunity for a new generation of microelectronic devices. Direct observation of the dynamic evolution of polar domain structures at atomic level remains challenging. Here, the authors report the observation of real-time topological transformations of polar structures in PbTiO3/SrTiO3 multilayers. [ABSTRACT FROM AUTHOR]

The main result is Theorem 1: A flow on a connected open set X ϲ Rd is globally periodic provided (i) periodic points are dense in X, and (ii) at all positive times the flow preserves the partial order defined by a closed convex cone that has nonempty interior and contains no straight line. The proof uses the analog for homeomorphisms due to B. Lemmens et al. [27], a classical theorem of D. Montgomery [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2). [ABSTRACT FROM AUTHOR]

Optoelectronic circuits in 3D shapes with large deformations can offer additional functionalities inaccessible to conventional planar electronics based on 2D geometries constrained by conventional photolithographic patterning processes. A light-sensing focal plane array (FPA) used in imagers is one example of a system that can benefit from fabrication on curved surfaces. By mimicking the hemispherical shape of the retina in the human eye, a hemispherical FPA provides a low-aberration image with a wide field of view. Due to the inherently high value of such applications, intensive efforts have been devoted to solving the problem of transforming a circuit fabricated on a flat wafer surface to an arbitrary shape without loss of performance or distorting the linear layouts that are the natural product of this fabrication paradigm. Here we report a general approach for fabricating electronic circuits and optoelectronic devices on nondevelopable surfaces by introducing shear slip of thin-film circuit components relative to the distorting substrate. In particular, we demonstrate retina-like imagers that allow for a topological transformation from a plane to a hemisphere without changing the relative positions of the pixels from that initially laid out on a planar surface. As a result, the resolution of the imager, particularly in the foveal region, is not compromised by stretching or creasing that inevitably results in transforming a 2D plane into a 3D geometry. The demonstration provides a general strategy for realizing high-density integrated circuits on randomly shaped, nondevelopable surfaces. [ABSTRACT FROM AUTHOR]

Abstract Parallelization of an evolutionary algorithm takes the advantage of modular population division and information exchange among multiple processors. However, existing parallel evolutionary algorithms are rather ad hoc and lack a capability of adapting to diverse problems. To accommodate a wider range of problems and to reduce algorithm design costs, this paper develops a parallel transfer evolution algorithm. It is based on the island-model of parallel evolutionary algorithm and, for improving performance, transfers both the connections and the evolutionary operators from one sub-population pair to another adaptively. Needing no extra upper selection strategy, each sub-population is able to select autonomously evolutionary operators and local search operators as subroutines according to both the sub-population's own and the connected neighbor's ranking boards. The parallel transfer evolution is tested on two typical combinatorial optimization problems in comparison with six existing ad-hoc evolutionary algorithms, and is also applied to a real-world case study in comparison with five typical parallel evolutionary algorithms. The tests show that the proposed scheme and the resultant PEA offer high flexibility in dealing with a wider range of combinatorial optimization problems without algorithmic modification or redesign. Both the topological transfer and the algorithmic transfer are seen applicable not only to combinatorial optimization problems, but also to non-permutated complex problems. Highlights • Topological transfer and algorithmic transfer are proposed to enable a fast and flexible parallel search. • A group of evolutionary states are presented to guide the evolution of multiple sub-populations. • A local search configuration scheme is introduced to enhance the search capability. • Experimental results on two groups of benchmarks and a practical problem show that the proposed algorithm outperforms other ad-hoc parallel evolutionary algorithms without any change. [ABSTRACT FROM AUTHOR]

Highlights • A topology-based rigid spherical quadrilateral mesh method is proposed in this paper. • The nondifferentiable problem of free-form surface is solved based on topological transformation. • The model of feature extraction for free-form surface based on topological transformation is built. • The tangent bundle of smooth free-form surface manifold is analyzed. Abstract Free-form surface reconstruction is the key technology of mathematical modeling of engineering. It is important for accurate reconstruction of the entity model that conforms to the design. In order to improve the measurement accuracy of the workpiece, a method for free-form surface feature recognition based on topological transformation is proposed in this paper. Firstly, the information of scanning points is expressed as the form of topological space. Based on this, a method of surface constructing that selects the natural-quadratic-surface as the manifold of free-form surface is proposed. Then, the free-form surface that is constructed from the original point cloud is transformed into a smooth free-form surface which is homeomorphic to the original free-form surface based on the theory of topological embedding. The features of the transformed free-form surface can be easily analyzed and recognized. Finally, the qualitative description of an arbitrary point on the surface is obtained by analyzing the tangent bundle of smooth free-form surface manifolds. The feature recognition of free-form surface for workpiece is realized. The experimental results on workpiece model are reported in this paper, which validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Given a group Γ acting on a set X , a k -coloring ϕ : X → { 1 , … , k } of X is distinguishing with respect to Γ if the only γ ∈ Γ that fixes ϕ is the identity action. The distinguishing number of the action Γ , denoted D Γ ( X ) , is then the smallest positive integer k such that there is a distinguishing k -coloring of X with respect to Γ . This notion has been studied in a number of settings, but by far the largest body of work has been concerned with finding the distinguishing number of the action of the automorphism group of a graph G upon its vertex set, which is referred to as the distinguishing number of G . The distinguishing number of a group action is a measure of how difficult it is to “break” all of the permutations arising from that action. In this paper, we aim to further differentiate the resilience of group actions with the same distinguishing number. In particular, we introduce a precoloring extension framework to address this issue. A set S ⊆ X is a fixing set for Γ if for every non-identity element γ ∈ Γ there is an element s ∈ S such that γ ( s ) ≠ s . The distinguishing extension number ext D ( X , Γ ; k ) is the minimum number m such that for all fixing sets W ⊆ X with | W | ≥ m , every k -coloring c : X ∖ W → [ k ] can be extended to a k -coloring that distinguishes X . In this paper, we prove that ext D ( R , Aut ( R ) ; 2 ) = 4 , where Aut ( R ) is comprised of compositions of translations and reflections. We also consider the distinguishing extension number of the circle and (finite) cycles, obtaining several exact results and bounds. [ABSTRACT FROM AUTHOR]

The article discusses equivalence relations invariant under group actions along with results about bounded invariant equivalence relations and invariant subgroups of definable groups. It shows w that type-definability and smoothness are equivalent conditions in a wider class of relations including all the cases for which the equivalence was proved before, and amalogous results in topological context.

In this paper, some graph theoretical (topological) transformations are presented for simplifying certain problems involved in structural analysis. For each case, the main problem is stated and the proposed topological transformation is established. Once the required topological analysis is completed, a back transformation results in the solution for the main problem. The transformations studied here employ (i) models drawn on a lower dimensional space, (ii) models embedded on higher dimensional spaces and (iii) interchange models which have simpler connectivity properties than the corresponding original structural models. All these transformations are illustrated utilizing simple examples. [ABSTRACT FROM AUTHOR]

Topological transformation of a zinc-templated trefoil knot, Zn-TK, into a zinc-templated [2]catenane, Zn-[2]C, was studied. The net reaction 2 Zn-TK→3 Zn-[2]C was accomplished in 89% yield by heating a solution of Zn-TK in D2O. Kinetic investigation by 1H NMR spectroscopy and high resolution mass spectrometry revealed that the mechanism is complex, involving a large pool of intermediates that form after imine bond cleavage. Bromide ions, which can occupy the central cavity of Zn-TK, inhibited the reaction. Two similar transformations were also studied, one of a cadmium-containing trefoil knot, Cd-TK, into a cadmium-containing catenane, Cd-[2]C, and the other of Cd-TK into Zn-[2]C. The latter transformation could be achieved in one step at high temperature or in two steps via transmetallation to form Zn-TK at room temperature followed by topological conversion of Zn-TK to Zn-[2]C at high temperature. [ABSTRACT FROM AUTHOR]

Although the topological Berezinskii–Kosterlitz–Thouless transition was for the first time described by 40 years ago, it is still a matter of discussion. It has been used to explain several experiments in the most diverse physical systems. In contrast with the ordinary continuous phase transitions the B K T -transition does not break any symmetry. However, in some contexts it can easily be confused with other continuous transitions, in general due to an insufficient data analysis. The two-dimensional X Y (or sometimes called planar rotator) spin model is the fruit fly model describing the B K T transition. As demonstrated by Bramwell and Holdsworth (1993) the finite-size effects are more important in two-dimensions than in others due to the logarithmic system size dependence of the properties of the system. Closely related is the anisotropic two dimensional Heisenberg model ( A H ). Although they have the same Hamiltonian the spin variable in the former has only two degrees of freedom while the A H has three. Many works treat the A H model as undergoing a transition in the same universality class as the X Y model. However, its characterization as being in the B K T class of universality deserve some investigation. This paper has two goals. First, we describe an analytical evidence showing that the A H model is in the B K T class of universality. Second, we make an extensive simulation, using the numerical Replica Exchange Wang–Landau method that corroborate our analytical calculations. From our simulation we obtain the B K T transition temperature as T B K T = 0 . 6980 ( 10 ) by monitoring the susceptibility, the two point correlation function and the helicity modulus. We discuss the misuse of the fourth order Binder’s cumulant to locate the transition temperature. The specific heat is shown to have a non-critical behavior as expected in the B K T transition. An analysis of the two point correlation function at low temperature, C ( r ) ∝ r − η ( T ) , shows that the exponent, η , is consistent with an exponential law η = η 0 e ζ T , with η 0 = 0 . 025 ( 5 ) and ζ = 3 . 25 ( 10 ) in close agreement with the results of Cardy (1981) for the p -state clock model. [ABSTRACT FROM AUTHOR]

Two electronically delocalized molecules were designed as models to understand how molecular shape impacts the tradeoff between solubility and crystallization tendencies in molecular semiconductors. The more soluble compound TT contains a non-planar bithiophene central fragment, whereas CT has a planar cyclopentadithiophene unit. Calorimetry studies show that CT can crystallize more easily than TT. However, absorption spectroscopy shows that the initially amorphous TT film can eventually form crystals in which the molecular shape is significantly more planar. Two thermally reversible polymorphs for TT were observed by XRD and grazing-incidence wide-angle X-ray scattering (GIWAXS) measurements. These findings are relevant within the context of designing soft semiconductors that exhibit high solubility and a tendency to provide stable organized structures with desirable electronic properties. [ABSTRACT FROM AUTHOR]

We study the dynamics of a localized spin-1/2 driven by a time-periodic magnetic field that undergoes a topological transition. Despite the strongly non-adiabatic effects dominating the spin dynamics, we find that the field's topology appears clearly imprinted in the Floquet spin states through an effective Berry phase emerging in the quasienergy. This has remarkable consequences on the spin resonance condition suggesting a whole new class of experiments to spot topological transitions in the dynamics of spins and other two-level systems, from nuclear magnetic resonance to strongly-driven super-conducting qubits. [ABSTRACT FROM AUTHOR]

There is a countable metrizable group acting continuously on the space of rationals in such a way that the only equivariant compactification of the space is a singleton. This is obtained by a recursive application of a construction due to Megrelishvili, which is a metric fan equipped with a certain group of homeomorphisms. The question of existence of a topological transformation group with the property in the title was asked by Yu.M. Smirnov in the 1980s. [ABSTRACT FROM AUTHOR]

In this note, we study topologically transitive and hypercyclic composition operators on Cp(X) or Ck(X). We prove that if G is a semigroup of continuous self maps of a countable metric space X with the following properties: (1) every element of G is one-to-one on X, (2) the action of G is strongly run-away on X, then the action of Ĝ on Cp(X) is topologically transitive and hypercyclic. If G is the set of all one-to-one and continuous self maps of R \ Z, then the action of Ĝ on Ck(R \ Z) is hypercyclic. We also show that the action of Ĝ on Cp(ω1) is not hypercyclic. [ABSTRACT FROM AUTHOR]

Experiencing power declines when the secondary coil is at the middle position between two primary coils is a serious problem in segmented on-road charging systems with a single energized segmented primary coil. In this paper, the topological transfonnation of a primary circuit and a hierarchical compensation capacitor control are proposed. Firstly, the corresponding compensation capacitors and receiving powers of different primary structures are deduced under the condition of a fixed frequency. Then the receiving power characteristics as a function of the position variations in systems with a single energized segmented primary coil and those with double segmented primary coils are analyzed comparatively. A topological transformation of the primary circuit and hierarchical compensation capacitor control are further introduced to solve the foregoing problem. Finally, an experimental prototype with the proposed topological transfonnation and hierarchical compensation capacitor control is carried out. Measured results show that the receiving power is a lot more stable in the movement of the secondary coil. It is a remarkable fact that the receiving power rises from 10.8W to 19.2W at the middle position between the two primary coils. The experimental are in agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

The interplay between thermal transport properties and topological aspects is investigated in a spin-triplet chiral p-wave superconductor Sr2RuO4 with strong two dimensionality. We show that thermal Hall conductivity is well described by a temperature linear term and an exponential term in the low-temperature region. While the former term is directly proportional to the so-called Chern number, the latter is associated with the superconducting gap amplitude of the γ band. We also demonstrate that the coefficient of the exponential term changes sign around the Lifshitz transition. Our obtained result may enable us to easily access the physical quantities and topological properties of Sr2RuO4 in detail. [ABSTRACT FROM AUTHOR]

Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in category-theoretic terms, where symmetry is expressed as the action of a 2-group G (equivalently, a categorical group) on a category C. It describes the construction of a transformation groupoid in diagrammatic terms, and considers this construction internal to Cat, the category of categories. The result is a double category C//G which describes the local symmetries of C. We define this and describe some of its structure, with the adjoint action of G on itself as a guiding example. [ABSTRACT FROM AUTHOR]

In this work, three-dimensional (3D) Bi 2 WO 6 superstructures assembled by nanosheets were prepared using the topological transformation of BiOCl hierarchical microspheres via a facile one-pot solvothermal method. Interestingly, it was found that the transformation process experienced three stages including BiOCl, BiOCl/Bi 2 WO 6 composites and Bi 2 WO 6 with increasing solvothermal time at 150 °C, which was confirmed by X-Ray Diffraction (XRD), Raman spectrometer and Transmission Electron Microscopy (TEM) results. Importantly, the crystal growth of Bi 2 WO 6 superstructures occurred at the exposed (0 0 1) facets of BiOCl nanosheets with WO 6 6 − units replacing the interlaminar Cl atoms. Also, the growth mechanism was revealed and discussed in the thermodynamic and kinetic dynamic aspects. Compared with BiOCl superstructures, the BiOCl/Bi 2 WO 6 composites and Bi 2 WO 6 superstructures showed better photocatalytic activity in the degradation of benzene gases under visible-light irradiation owing to the existence of visible-light-active Bi 2 WO 6 . This topological transformation by regulating the solvothermal synthetic conditions may provide a new insight into the controllable synthesis of other 3D compounds. [ABSTRACT FROM AUTHOR]

We prove that among the quasi-simple Lie groups only the group SL4(ℝ) occurs as the multiplication group of 3-dimensional connected topological loops L. These loops L are homeomorphic to the sphere S3. Moreover, there does not exist any connected topological loop having an at most 8-dimensional quasi-simple Lie groups as its multiplication group. [ABSTRACT FROM AUTHOR]

Pushed by the availability of large fractional bandwidths, many well-established applications are focusing mm-wave spectrum for product deployment. Generation of broadband power at mm-waves is challenging because a key target such as the efficiency trades with the gain-bandwidth (GBW) product. The major limit is the capacitive parasitics at the interstage between driver and power devices. The latter are designed with a large form factor so as to deliver the desired output power and are commonly biased in class-AB to achieve high drain efficiency, penalizing GBW. In this paper, a design methodology for interstage and output matching networks targeting large fractional bandwidth and high efficiency is proposed. Leveraging inductively coupled resonators, we apply Norton transformations for impedance scaling. In both networks, topological transformations are employed to include a transformer, achieve the desired load impedance and minimize the number of components. A two-stage differential PA with neutralized common source stages has been realized in 28 nm CMOS using low-power devices. The PA delivers 13 dBm saturated output power over the 40–67 GHz bandwidth with a peak power-added efficiency of 16% without power combining. To the best of author's knowledge, the presented PA shows state-of-the-art performances with the largest fractional bandwidth among bulk CMOS mm-wave PAs reported so far. [ABSTRACT FROM AUTHOR]

Suppose that X is a topological space, Dn, n ≥ 0 are its subspaces and a family with fn : Dn → Dn+1 is translated as a nonautonomous discrete system. We introduce two subspaces of D0, the orbits of whose elements carry different kinds of densities. They are invariant under the certain -conjugacies. This fact and some other properties of these subspaces are investigated in the present paper. [ABSTRACT FROM AUTHOR]

In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls toward each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model. [ABSTRACT FROM AUTHOR]

Achieving topological transformation in an inorganic chemical system is an ongoing challenge. We show that such a topological transformation can be achieved in a simple metal-oxide based inorganic system of soft-oxometalates (SOMs). Starting from a dispersion of heptamolybdate-based SOM nanotubes, molybdenum blue SOM nanospheres were synthesised by application of UV-irradiation. This transformation is accompanied by a colour change of the system from colourless to blue. The starting material and product were characterised based on an array of techniques including scanning electron microscopy, dynamic light scattering, horizontal attenuated total reflectance infrared spectroscopy, and UV/Vis spectroscopy. The possibility of using this system as a UV detector is also discussed. [ABSTRACT FROM AUTHOR]

Special operation requirements are needed for repositing broken strands of extra-high-voltage (EHV) power transmission lines before repairing. Metamorphic mechanism is applied to satisfy the requirements and a novel structural synthesis method is proposed, considering the forms and structures of constrained metamorphic joints. Metamorphic cyclogram and equivalent resistance gradient matrix of metamorphic joints are obtained by analyzing the repairing operation. Meanwhile, the source metamorphic mechanism with structure of non-constrained metamorphic joints is selected. Constrained form/structure matrix of metamorphic joints is built according to metamorphic cyclogram and equivalent resistance gradient matrix. The relation between constraint force changes of joints and form/structure of metamorphic joints is then obtained; and all the eight corresponding structures of constrained metamorphic mechanism are synthesized. One of the eight mechanisms is chosen as the broken strands reposition metamorphic mechanism, and its topological transformations of working configuration are analyzed to verify the feasibility and practicality of structural synthesis method proposed in this paper. [ABSTRACT FROM AUTHOR]

As long as 50 years ago theoretical calculations predicted that Möbius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Hückel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Möbius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower degree of strain and precursors can be designed that inherently include the writhe, which, after cyclization, ends up in the Möbius product. With our strategy, triply twisted systems are easier to prepare than their singly twisted counterparts. [ABSTRACT FROM AUTHOR]

The band structure and dependences of the intrinsic concentration in the mercury-cadmium-telluride (MCT) Hg0.32Cd0.68Te/ Hg1-xCdxTe /Hg0.32Cd0.68Te quantum wells in the framework of the 8x8 k.p envelope function method on the well width L and composition x were calculated. Modeling of the energy spectra showed that the intrinsic concentration can vary about an order of magnitude with variation of the well width and chemical composition in the range of x ≤ 0.16 and well width L ≤ 20 nm at the liquid nitrogen temperature. These strong variations of the carrier concentration are caused by the insulator-semimetal topological transition. [ABSTRACT FROM AUTHOR]

This paper introduces both the notions of topological transitivity and topological mixing in the general setting of semigroup actions on topological spaces. A discussion on limit behavior of skew-product transformation semigroups is presented. The main purpose is to characterize the lifts and the projections of recurrent points, attractors and Morse decompositions for transformation semigroups associated to skew-product transformation semigroups. The results play a role to the existence of the finest Morse decomposition for control systems and their control flows. [ABSTRACT FROM AUTHOR]

Abstract: Felix Klein emphasized the intrinsic connection between symmetry groups and geometries in his Erlangen Program. Perhaps motivated by Klein, Gleason [5] posed a very general conjecture on topologizing symmetry groups that he regarded as fundamental for a general study of geometries. Gleason in fact proved his conjecture in a very special case. The purpose of this paper is to show that Gleasonʼs general conjecture is false as originally stated and that it is true only under very strong hypotheses. Along the way new general results in descriptive set theory are proved about a class of functions that behave like but are distinct from functions of Baire class 1. [Copyright &y& Elsevier]

One of the main problems in the topological transformation of submicron VLSIs for the double lithographic mask technology is the decomposition of the initial topological layer into two new ones. Transformation algorithms of the VLSI topology for the double lithographic mask technology, which are oriented towards the application of high-performance computing systems, as well as the results of experimental investigations, which are performed using the developed software, are discussed. The advantages and disadvantages of the suggested approaches are discussed. [ABSTRACT FROM AUTHOR]

Different types of self-similar states are found in quasiperiodic systems characterized by topological invariants--the Chern numbers. We show that the topology introduces a competing length in the self-similar band edge states transforming peaks into doublets of size equal to the Chern number. This length intertwines with quasiperiodicity and introduces an intrinsic scale, producing Chern beats and nested regions where the fractal structure becomes smooth. Chern numbers also influence the zero-energy mode that, for quasiperiodic systems, which exhibit exponential localization, is related to the ghost of the Majorana: the remnant of the edge localized topological state that delocalizes at the onset to a topological transition. In superconducting wires, the exponentially decaying profile of the edge localized Majorana modes also encode fingerprints of the Chern states that reside in close proximity to zero energy. [ABSTRACT FROM AUTHOR]

Abstract: The effects of a special topological transformation on the energy levels, far-infrared spectra and magnetization of one electron inside a semiconductor nanoring under magnetic fields are studied. We have called this transformation as bipartition, and it is defined by a change in ring topological structure, when its shape is changed successively from a single oval-shaped loop up to quasi-two disconnected loops. Our results show that in the course of such transformation the low-lying energies dependencies with multiple crossovers between them, typical for the free electron rotation along an almost circular loop, are converted into a set of non-crossing double plaits related to a sub-barrier electron tunneling along a strongly non-circular loop in a quasi-local state. Also, we find that during the restructuring of the oval-shaped nanostructures the selection rules for the dipole transitions are changed allowing the appearance of additional peaks in the FIR spectrum. [Copyright &y& Elsevier]

We study recurrence and transience for Lévy processes induced by topological transformation groups acting on complete Riemannian manifolds. In particular the transience–recurrence dichotomy in terms of potential measures is established and transience is shown to be equivalent to the potential measure having finite mass on compact sets when the group acts transitively. It is known that all bi-invariant Lévy processes acting in irreducible Riemannian symmetric pairs of noncompact type are transient. We show that we also have ‘harmonic transience’, that is, local integrability of the inverse of the real part of the characteristic exponent which is associated to the process by means of Gangolli’s Lévy–Khinchine formula. [ABSTRACT FROM PUBLISHER]

We study the effects of electron correlations on the topological phase transition in the Bernevig-Hughes-Zhang model using the variational cluster approach, in which the short-range spatial correlations are taken into account exactly. We calculate the spin Chern number and local magnetic moment to show that the topologically nontrivial antiferromagnetic order exists and that the magnetic transition is of the second order. We furthermore demonstrate that under the spin-quantized condition the topological phase transition is caused by the closing of the bulk band gap. [ABSTRACT FROM AUTHOR]

Abstract: Let X be a metric space, and let be a continuous transformation. In this note, a concept indecomposability of f is introduced. We show that transitivity implies indecomposability and that Devaney chaos is equivalent to indecomposability together with dense periodicity. Moreover, we point out that the indecomposability and the dense periodicity are independent of each other even for interval maps (i.e., neither implies the other). [Copyright &y& Elsevier]

We study the dynamical behaviour of composition operators Cϕ defined on spaces (Ω) of real analytic functions on an open subset Ω of ℝd. We characterize when such operators are topologically transitive, i.e. when for every pair of non-empty open sets there is an orbit intersecting both of them. Moreover, under mild assumptions on the composition operator, we investigate when it is sequentially hypercyclic, i.e., when it has a sequentially dense orbit. If ϕ is a self map on a simply connected complex neighbourhood U of ℝ, U ≠ ℂ, then topological transitivity, hypercyclicity and sequential hypercyclicity of Cϕ:(ℝ) → (ℝ) are equivalent. [ABSTRACT FROM PUBLISHER]

Abstract: Shift-compactness has recently been found to be the foundation stone of classical, as well as topological, regular variation; most recently it has come again to prominence in new proofs of the Effros Open Mapping Principle of group action, another ingredient of topological regular variation. Using the real line under the Euclidean and density topologies as a paradigm, we develop group-action versions of shift-compactness theorems for Baire groups acting on Baire spaces under metrizable topologies and under certain refinements of these. One aim is to pursue constructive approaches rather than rely on plain Baire-category methods (so keeping more to the Banach–Mazur strategic approach). Along the way we uncover three new coarse topologies for groups of homeomorphisms. A second purpose is to establish limitations of the shift-compactness methodology. [Copyright &y& Elsevier]

We study the condition for a topological superconductor (TS) phase with end Majorana fermions to appear when a quasiperiodic lattice modulation is applied to a one-dimensional quantum wire with strong spin-orbit interaction situated under a magnetic field and in proximity to a superconductor. By density-matrix renormalization group analysis, we find that multiple topological phases with Majorana end modes are realized in finite ranges of the filling factor, showing a sequence of reentrant transitions as the chemical potential is tuned. The locations of these phases reflect the structure of bands in the noninteracting case, which exhibits a distinct self-similar structure. The stability of the TS in the presence of an on-site interaction or a harmonic trap potential is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we present a scalable rule-based reasoning algorithm for the OWL pD* language. This algorithm uses partial materialization and a syntactic ontology transformation (the extension-based knowledge model) to provide a fast inference. Because the materialized part of the ontology does not contain assertional data, the time consumed by the process, and the number of inferred triples, remain fixed with varying amounts of assertional data. The algorithm uses database reasoning and a query rewriting technique to handle the remaining inference. The extension-based knowledge model and the database reasoning prevent the expected decreases in query performances, which are the natural result of online reasoning during query time. This work also evaluates the efficiency of the proposed method by conducting experiments using LUBM and UOBM benchmarks. [Copyright &y& Elsevier]

We applied a first-principles-based atomistic approach to investigate the formation of dipole patterns in isolated stress-free PbTiO3 nanoparticles of rectangular shape. We found that a sequence of topological transformations takes place as the aspect ratio of the nanostructure changes from elongated nanorods to flat nanoplatelets. Of a particular interest is the formation of a four-vortex state with cores aligned along a closed path. In this way, the vortex structure forms a ring-shaped torus, and a ferroelectric bubble is developed at the center of the ring. The thermal properties of the bubbles indicate that this state is suitable for the development of nanometric ferroelectric devices. Our results cover, for the first time, the gap between the nanodots and wires and between the nanodots and thin films, that is between 0D and 1D as well as between 0D and 2D objects. [ABSTRACT FROM PUBLISHER]