4,012 research outputs found
A remark on a priori estimate for the Navier-Stokes equations with the Coriolis force
The Cauchy problem for the Navier-Stokes equations with the Coriolis force is
considered. It is proved that a similar a priori estimate, which is derived for
the Navier-Stokes equations by Lei and Lin [11], holds under the effect of the
Coriolis force. As an application existence of a unique global solution for
arbitrary speed of rotation is proved, as well as its asymptotic behavior.Comment: 13 page
A new proof of long range scattering for critical nonlinear Schr\"odinger equations
We present a new proof of global existence and long range scattering, from
small initial data, for the one-dimensional cubic gauge invariant nonlinear
Schr\"odinger equation, and for Hartree equations in dimension . The
proof relies on an analysis in Fourier space, related to the recent works of
Germain, Masmoudi and Shatah on space-time resonances. An interesting feature
of our approach is that we are able to identify the long range phase correction
term through a very natural stationary phase argument.Comment: Improved introduction. Corrected typo
Uniqueness of the modified Schroedinger map in H^{3/4+e}(R^2)
We establish local well-posedness of the modified Schroedinger map in H^s,
s>3/4.Comment: 20 page
A One-Factor Conditionally Linear Commodity Pricing Model under Partial Information
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its
state variable is studied under partial information: the mean-reverting level
and the mean-reverting speed parameters are modeled as hidden/unobservable
stochastic variables. No-arbitrage pricing formulas for derivative securities
written on a liquid asset and exponential utility indifference pricing formulas
for derivative securities written on an illiquid asset are presented. Moreover,
a conditionally linear filtering result is introduced to compute the
pricing/hedging formulas and the Bayesian estimators of the hidden variables.Comment: 21 page
Order Estimates for the Exact Lugannani-Rice Expansion
The Lugannani-Rice formula is a saddlepoint approximation method for
estimating the tail probability distribution function, which was originally
studied for the sum of independent identically distributed random variables.
Because of its tractability, the formula is now widely used in practical
financial engineering as an approximation formula for the distribution of a
(single) random variable. In this paper, the Lugannani-Rice approximation
formula is derived for a general, parametrized sequence of random variables and
the order estimates of the approximation are given.Comment: 32 pages, 9 figure
Derived categories of -complexes
We study the homotopy category of -complexes
of an additive category and the derived category
of an abelian category . First we
show that both and have
natural structures of triangulated categories. Then we establish a theory of
projective (resp., injective) resolutions and derived functors. Finally, under
some conditions of an abelian category , we show that
is triangle equivalent to the ordinary derived
category where
is the category of sequential
morphisms of .Comment: 31 page
On t-structures and Torsion Theories Induced by Compact Objects
First, we show that a compact object in a triangulated category, which
satisfies suitable conditions, induces a -structure. Second, in an abelian
category we show that a complex of small projective objects of
term length two, which satisfies suitable conditions, induces a torsion theory.
In the case of module categories, using a torsion theory, we give equivalent
conditions for to be a tilting complex. Finally, in the case
of artin algebras, we give one to one correspondence between tilting complexes
of term length two and torsion theories with certain conditions.Comment: 17 pages, AMSLaTe
Polygon of recollements and -complexes
We study a structure of subcategories which are called a polygon of
recollements in a triangulated category. First, we study a -gon of
recollements in an -Calabi-Yau triangulated category. Second, we show
the homotopy category of
complexes of an additive category of
sequences of split monomorphisms of an additive category has a
-gon of recollments. Third, we show the homotopy category
of -complexes of has also a
-gon of recollments. Finally, we show there is a triangle equivalence
between and
.Comment: 32 page
Recollement of homotopy categories and Cohen-Macaulay modules
We study the homotopy category of unbounded complexes with bounded homologies
and its quotient category by the homotopy category of bounded complexes. We
show the existence of a recollement of the above quotient category and it has
the homotopy category of acyclic complxes as a triangulated subcategory. In the
case of the homotopy category of finitely generated projective modules over an
Iwanaga-Gorenstein ring, we show that the above quotient category are triangle
equivalent to the stable module category of Cohen-Macaulay
\opn{T}_2(R)-modules.Comment: 28 page
The Role of Substrate Roughness in Superfluid Film Flow Velocity
It is known that the apparent film flow rate of superfluid He
increases significantly when the container wall is contaminated by a thin layer
of solid air. However, its microscopic mechanism has not yet been clarified
enough. We have measured under largely different conditions for the
container wall in terms of surface area (0.77-6.15 m) and surface
morphology using silver fine powders (particle size: \mu m) and porous
glass (pore size: 0.5, 1 \mu m). We could increase by more than two
orders of magnitude compared to non-treated smooth glass walls, where liquid
helium flows down from the bottom of container as a continuous stream rather
than discrete drips. By modeling the surface morphology, we estimated the
effective perimeter of container and calculated the flow
rate , where is the apparent perimeter
without considering the microscopic surface structures. The resultant
values for the various containers are constant each other within a factor of
four, suggesting that the enhancement of plays a major role
to change to such a huge extent and that the superfluid critical
velocity, , does not change appreciably. The measured
temperature dependence of revealed that values in our
experiments are determined by the vortex depinning model of Schwarz (Phys. Rev.
B , 5782 (1986)) with several nm size pinning sites
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