364 research outputs found
A Spectral Bernstein Theorem
We study the spectrum of the Laplace operator of a complete minimal properly
immersed hypersurface in . (1) Under a volume growth condition on
extrinsic balls and a condition on the unit normal at infinity, we prove that
has only essential spectrum consisting of the half line .
This is the case when , where
is the extrinsic distance to a point of and are the
principal curvatures. (2) If the satisfy the decay conditions
, and strict inequality is achieved at some point
, then there are no eigenvalues. We apply these results to minimal
graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2.
Accepted for publication in the Annali di Matematica Pura ed Applicata, on
the 05/03/201
Certification of Bounds of Non-linear Functions: the Templates Method
The aim of this work is to certify lower bounds for real-valued multivariate
functions, defined by semialgebraic or transcendental expressions. The
certificate must be, eventually, formally provable in a proof system such as
Coq. The application range for such a tool is widespread; for instance Hales'
proof of Kepler's conjecture yields thousands of inequalities. We introduce an
approximation algorithm, which combines ideas of the max-plus basis method (in
optimal control) and of the linear templates method developed by Manna et al.
(in static analysis). This algorithm consists in bounding some of the
constituents of the function by suprema of quadratic forms with a well chosen
curvature. This leads to semialgebraic optimization problems, solved by
sum-of-squares relaxations. Templates limit the blow up of these relaxations at
the price of coarsening the approximation. We illustrate the efficiency of our
framework with various examples from the literature and discuss the interfacing
with Coq.Comment: 16 pages, 3 figures, 2 table
Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators
The aim of the present paper is to study the regularity properties of the
solution of a backward stochastic differential equation with a monotone
generator in infinite dimension. We show some applications to the nonlinear
Kolmogorov equation and to stochastic optimal control
Superconductivity and single crystal growth of Ni0:05TaS2
Superconductivity was discovered in a Ni0:05TaS2 single crystal. A Ni0:05TaS2
single crystal was successfully grown via the NaCl/KCl flux method. The
obtained lattice constant c of Ni0:05TaS2 is 1.1999 nm, which is significantly
smaller than that of 2H-TaS2 (1.208 nm). Electrical resistivity and
magnetization measurements reveal that the superconductivity transition
temperature of Ni0:05TaS2 is enhanced from 0.8 K (2H-TaS2) to 3.9 K. The
charge-density-wave transition of the matrix compound 2H-TaS2 is suppressed in
Ni0:05TaS2. The success of Ni0:05TaS2 single crystal growth via a NaCl/KCl flux
demonstrates that NaCl/KCl flux method will be a feasible method for single
crystal growth of the layered transition metal dichalcogenides.Comment: 13pages, 6 figures, Published in SS
Some flows in shape optimization
Geometric flows related to shape optimization problems of Bernoulli type are
investigated. The evolution law is the sum of a curvature term and a nonlocal
term of Hele-Shaw type. We introduce generalized set solutions, the definition
of which is widely inspired by viscosity solutions. The main result is an
inclusion preservation principle for generalized solutions. As a consequence,
we obtain existence, uniqueness and stability of solutions. Asymptotic behavior
for the flow is discussed: we prove that the solutions converge to a
generalized Bernoulli exterior free boundary problem
Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems
This paper deals with existence and uniqueness, in viscosity sense, of a
solution for a system of m variational partial differential inequalities with
inter-connected obstacles. A particular case of this system is the
deterministic version of the Verification Theorem of the Markovian optimal
m-states switching problem. The switching cost functions are arbitrary. This
problem is connected with the valuation of a power plant in the energy market.
The main tool is the notion of systems of reflected BSDEs with oblique
reflection.Comment: 36 page
On the Existence of Nash Equilibrium for a Two Player Pursuit-Evasion Game with Visibility Constraints
On Sharp Large Deviations for the bridge of a general Diffusion
We provide sharp Large Deviation estimates for the probability of exit from a
domain for the bridge of a -dimensional general diffusion process , as
the conditioning time tends to . This kind of results is motivated by
applications to numerical simulation. In particular we investigate the
influence of the drift of . It turns out that the sharp asymptotics for
the exit time probability are independent of the drift, provided enjoyes a
simple condition that is always satisfied in dimension . On the other hand,
we show that the drift can be influential if this assumption is not satisfied.
Single crystal growth and characterizations of Cu0.03TaS2 superconductors
Single crystal of Cu0.03TaS2 with low copper intercalated content was
successfully grown via chemical iodine-vapor transport. The structural
characterization results show that the copper intercalated 2H-Cu0.03TaS2 single
crystal has the same structure of the CdI2-type structure as the parent 2H-TaS2
crystal. Electrical resistivity and magnetization measurements reveal that
2H-Cu0.03TaS2 becomes a superconductor below 4.2 K. Besides, electrical
resistivity and Hall effects results show that a charge density wave transition
occurs at TCDW = 50 K.Comment: 14 pages, 6 figures,revised versio
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
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