Macroscopic limiting dynamics of a class of inhomogeneous mean field quantum systems
Mathematical analysis for the peridynamic nonlocal continuum theory
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical analysis for the peridynamic nonlocal continuum theory*
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical and Computational Models in Tumor Immunology
The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...
Maximal regular boundary value problems in Banach-valued function spaces and applications.
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions
Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights.
Mesures semi-classiques et mesures de défaut
Méthode fonctionnelle en théorie des champs
Méthodes opérationnelles dans l'étude des problèmes aux limites
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
We observe an infinitely dimensional Gaussian random vector x = ξ + v where ξ is a sequence of standard Gaussian variables and v ∈ l2 is an unknown mean. We consider the hypothesis testing problem H0 : v = 0versus alternatives for the sets . The sets Vε are lq-ellipsoids of semi-axes ai = i-s R/ε with lp-ellipsoid of semi-axes bi = i-r pε/ε removed or similar Besov bodies Bq,t;s (R/ε) with Besov bodies Bp,h;r (pε/ε) removed. Here or are the parameters which define the sets Vε for given radii...
Minimizing and maximizing a linear objective function under a fuzzy relational equation and an inequality constraint
This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to fuzzy relational equations and an inequality constraint, where is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy relational equation and an inequality constraint,...
Model selection for regression on a random design
We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small probability....
Model selection for regression on a random design
We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small...
Modeling seasonal time series.
Modular covariance, PCT, spin and statistics
Multiplicative function systems and their application in discrete information processing