45,726 research outputs found

### Hausdorrf dimension for level sets and k-multiple times

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

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

### On a general theorem for additive Levy processes

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

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

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

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

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

Let $X_t$ be any additive process in $\mathbb{R}^d.$ There are finite indices
$\delta_i, \beta_i, i=1,2$ and a function $u$, all of which are defined in
terms of the characteristics of $X_t$, such that
\liminf_{t\to0}u(t)^{-1/\eta}X_t^*= \cases{0, \quad if $\eta>\delta_1$,
\cr\infty, \quad if $\eta<\delta_2$,}
\limsup_{t\to0}u(t)^{-1/\eta}X_t^*= \cases{0, \quad if $\eta>\beta_2$,
\cr\infty, \quad if $\eta<\beta_1$,}\qquad {a.s.},
where $X_t^*=\sup_{0\le s\le t}|X_s|.$ When $X_t$ is a L\'{e}vy process with
$X_0=0$, $\delta_1=\delta_2$, $\beta_1=\beta_2$ and $u(t)=t.$ This is a special
case obtained by Pruitt. When $X_t$ is not a L\'{e}vy process, its
characteristics are complicated functions of $t$. However, there are
interesting conditions under which $u$ becomes sharp to achieve
$\delta_1=\delta_2$, $\beta_1=\beta_2.$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

### Total Protection of Analytic Invariant Information in Cross Tabulated Tables

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

### Data Security Equals Graph Connectivity

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

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