780 research outputs found
Estimates for solutions of Burgers type equations and some applications
We obtain precise large time asymptotics for the Cauchy problem for Burgers
type equations satisfying shock profile condition. The proofs are based on the
exact a priori estimates for (local) solutions of these equations and a recent
result of the first and second authors.Comment: to appear in J. Math. Pure et App
New global stability estimates for the Gel'fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse
problem in 3D. For sufficiently regular potentials this result of the present
work is a principal improvement of the result of [G. Alessandrini, Stable
determination of conductivity by boundary measurements, Appl. Anal. 27 (1988),
153-172]
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
New global stability estimates for monochromatic inverse acoustic scattering
We give new global stability estimates for monochromatic inverse acoustic
scattering. These estimates essentially improve estimates of [P. Hahner, T.
Hohage, SIAM J. Math. Anal., 33(3), 2001, 670-685] and can be considered as a
solution of an open problem formulated in the aforementioned work
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems
We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with integrable derivatives
on by an -parametric analytic family better than order
of .
Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of .Comment: 40 page
Approximation of holomorphic mappings on strongly pseudoconvex domains
Let D be a relatively compact strongly pseudoconvex domain in a Stein
manifold, and let Y be a complex manifold. We prove that the set A(D,Y),
consisting of all continuous maps from the closure of D to Y which are
holomorphic in D, is a complex Banach manifold. When D is the unit disc in C
(or any other topologically trivial strongly pseudoconvex domain in a Stein
manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with
n=dim Y. Analogous results hold for maps which are holomorphic in D and of
class C^r up to the boundary for any positive integer r. We also establish the
Oka property for sections of continuous or smooth fiber bundles over the
closure of D which are holomorphic over D and whose fiber enjoys the Convex
approximation property. The main analytic technique used in the paper is a
method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with
control up to the boundary, which was developed in our paper "Holomorphic
curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)
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VASABI: Hierarchical User Profiles for Interactive Visual User Behaviour Analytics
User behaviour analytics (UBA) systems offer sophisticated models that capture users’ behaviour over time with an aim to identify fraudulent activities that do not match their profiles. Making decisions based on such systems; however, requires an in-depth understanding of user behaviour both at an individual and at a group level where a group can consist of users with similar roles. We present a visual analytics approach to help analysts gain a comprehensive, multifaceted understanding of user behaviour at multiple levels. We take a user-centred approach to design a visual analytics framework supporting the analysis of collections of users and the numerous sessions of activities they conduct within digital applications. The framework is centred around the concept of hierarchical user profiles, where the profiles are built based on features derived from sessions they perform and visualised with task-informed designs to facilitate interactive exploration and investigation. We also present techniques to extract user tasks that summarise the behaviour and to cluster users according to these tasks for providing hierarchical overviews of groups of users along with individual users and the sessions they conduct. We externalise a series of analysis goals and tasks, and evaluate our methods through a number of use cases that demonstrate how these tasks are addressed. We observe that with the aid of interactive visual hierarchical user profiles, analysts were able to conduct exploratory and investigative analysis effectively, and able to understand the characteristics of user behaviour to make informed decisions whilst evaluating suspicious users and activities
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
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