47,462 research outputs found

    Hausdorrf dimension for level sets and k-multiple times

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    We compute the Hausdorff dimension of the zero set of an additive Levy process.Comment: 7 page

    On a theorem in multi-parameter potential theory

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    We prove a theorem on additive Levy processes and give applicationsComment: 9 page

    On a general theorem for additive Levy processes

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    We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.Comment: 10 page

    Cobordism Theory and Poincare Conjecture

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    In this paper, by use of techniques associated to cobordism theory and Morse theory,we give a simple proof of Poincare conjecture, i.e. Every compact smooth simply connected 3-manifold is homeomorphic to 3-sphere.Comment: 20 pages,1 figur

    Ultra-high mechanical stretchability and controllable topological phase transitions in two-dimensional arsenic

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    The mechanical stretchability is the magnitude of strain which a material can suffer before it breaks. Materials with high mechanical stretchability, which can reversibly withstand extreme mechanical deformation and cover arbitrary surfaces and movable parts, are used for stretchable display devices, broadband photonic tuning and aberration-free optical imaging. Strain can be utilised to control the band structures of materials and can even be utilised to induce a topological phase transition, driving the normal insulators to topological non-trivial materials with non-zero Chern number or Z2 number. Here, we propose a new two-dimensional topological material with ultra-high mechanical stretchability - the ditch-like 2D arsenic. This new anisotropic material possesses a large Poisson's ratio 1.049, which is larger than any other reported inorganic materials and has a ultra-high stretchability 44% along the armchair direction, which is unprecedent in inorganic materials as far as we know. Its minimum bend radius of this material can be as low as 0.66 nm, which is comparable to the radius of carbon-nanotube. Such mechanical properties make this new material be a stretchable semiconductor which could be used to construct flexible display devices and stretchable sensors. Axial strain will make a conspicuous affect on the band structure of the system, and a proper strain along the zigzag direction will drive the 2D arsenic into the topological insulator in which the topological edge state can host dissipation-less spin current and spin transfer toque, which are useful in spintronics devices such as dissipation transistor, interconnect channels and spin valve devices

    The d-p band-inversion topological insulator in bismuth-based skutterudites

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    Skutterudites, a class of materials with cage-like crystal structure which have received considerable research interest in recent years, are the breeding ground of several unusual phenomena such as heavy fermion superconductivity, exciton-mediated superconducting state and Weyl fermions. Here, we predict a new topological insulator in bismuth-based skutterudites, in which the bands involved in the topological band-inversion process are d- and p-orbitals, which is distinctive with usual topological insulators, for instance in Bi2Se3 and BiTeI the bands involved in the topological band-inversion process are only p-orbitals. Due to the present of large d-electronic states, the electronic interaction in this topological insulator is much stronger than that in other conventional topological insulators. The stability of the new material is verified by binding energy calculation, phonon modes analysis, and the finite temperature molecular dynamics simulations. This new material can provide nearly zero-resistivity signal current for devices and is expected to be applied in spintronics devices

    A free action of a finite group on 3-sphere equivalent to a linear action

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    In this paper, by use of techniques associated to Cobordism theory and Morse theory, we give a proof of Space-Form-Conjecture, i.e. a free action of a finite group on 3-manifold is equivalent to a linear action.Comment: This paper has been withdrawn by the autho

    The growth of additive processes

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    Let XtX_t be any additive process in Rd.\mathbb{R}^d. There are finite indices δi,βi,i=1,2\delta_i, \beta_i, i=1,2 and a function uu, all of which are defined in terms of the characteristics of XtX_t, such that \liminf_{t\to0}u(t)^{-1/\eta}X_t^*= \cases{0, \quad if η>δ1\eta>\delta_1, \cr\infty, \quad if η<δ2\eta<\delta_2,} \limsup_{t\to0}u(t)^{-1/\eta}X_t^*= \cases{0, \quad if η>β2\eta>\beta_2, \cr\infty, \quad if η<β1\eta<\beta_1,}\qquad {a.s.}, where Xt=sup0stXs.X_t^*=\sup_{0\le s\le t}|X_s|. When XtX_t is a L\'{e}vy process with X0=0X_0=0, δ1=δ2\delta_1=\delta_2, β1=β2\beta_1=\beta_2 and u(t)=t.u(t)=t. This is a special case obtained by Pruitt. When XtX_t is not a L\'{e}vy process, its characteristics are complicated functions of tt. However, there are interesting conditions under which uu becomes sharp to achieve δ1=δ2\delta_1=\delta_2, β1=β2.\beta_1=\beta_2.Comment: Published at http://dx.doi.org/10.1214/009117906000000593 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Data Security Equals Graph Connectivity

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    To protect sensitive information in a cross tabulated table, it is a common practice to suppress some of the cells in the table. This paper investigates four levels of data security of a two-dimensional table concerning the effectiveness of this practice. These four levels of data security protect the information contained in, respectively, individual cells, individual rows and columns, several rows or columns as a whole, and a table as a whole. The paper presents efficient algorithms and NP-completeness results for testing and achieving these four levels of data security. All these complexity results are obtained by means of fundamental equivalences between the four levels of data security of a table and four types of connectivity of a graph constructed from that table

    Total Protection of Analytic Invariant Information in Cross Tabulated Tables

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    To protect sensitive information in a cross tabulated table, it is a common practice to suppress some of the cells in the table. An analytic invariant is a power series in terms of the suppressed cells that has a unique feasible value and a convergence radius equal to +\infty. Intuitively, the information contained in an invariant is not protected even though the values of the suppressed cells are not disclosed. This paper gives an optimal linear-time algorithm for testing whether there exist nontrivial analytic invariants in terms of the suppressed cells in a given set of suppressed cells. This paper also presents NP-completeness results and an almost linear-time algorithm for the problem of suppressing the minimum number of cells in addition to the sensitive ones so that the resulting table does not leak analytic invariant information about a given set of suppressed cells
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