Association of Polymorphisms of Serotonin Transporter (5HTTLPR) and 5-HT2C Receptor Genes with Criminal Behavior in Russian Criminal Offenders

Background: Human aggression is a heterogeneous behavior with biological, psychological, and social backgrounds. As the biological mechanisms that regulate aggression are components of both reward-seeking and adversity-fleeing behavior, these phenomena are difficult to disentangle into separate neurochemical processes. Nevertheless, evidence exists linking some forms of ag

A necessary and sufficient condition for existence of measurable flow of a bounded borel vector field

Let b: [0, T] × ℝd → ℝd be a bounded Borel vector field, T > 0 and let µ be a non-negative Radon measure on ℝd. We prove that a µ-measurable flow of b exists if and only if the corresponding continuity equation has a non-negative measure-valued solution with the initial condition µ. © 2018 Independent University of Moscow

On the Definitions of Boundary Values of Generalized Solutions to an Elliptic-Type Equation

An elliptic-type equation with variable coefficients is considered. An overview is given of the definitions of boundary values of generalized solutions to this equation. Conditions for the existence of boundary values as well as conditions for the existence and uniqueness of solutions to the corresponding Dirichlet problem are analyzed. © 2018, Pleiades Publishing, Ltd

A necessary and sufficient condition for existence of measurable flow of a bounded borel vector field

Let b: [0, T] × ℝd → ℝd be a bounded Borel vector field, T > 0 and let µ be a non-negative Radon measure on ℝd. We prove that a µ-measurable flow of b exists if and only if the corresponding continuity equation has a non-negative measure-valued solution with the initial condition µ. © 2018 Independent University of Moscow

On the one-dimensional continuity equation with a nearly incompressible vector field

We consider the Cauchy problem for the continuity equation with a bounded nearly incompressible vector field b : (0; T)×Rd → Rd, T > 0. This class of vector fields arises in the context of hyperbolic conservation laws (in particular, the Keyfitz-Kranzer system, which has applications in nonlinear elasticity theory). It is well known that in the generic multi-dimensional case (d ≥ 1) near incompressibility is sufficient for existence of bounded weak solutions, but uniqueness may fail (even when the vector field is divergence-free), and hence further assumptions on the regularity of b (e.g. Sobolev regularity) are needed in order to obtain uniqueness. We prove that in the one-dimensional case (d = 1) near incompressibility is sufficient for existence and uniqueness of locally integrable weak solutions. We also study compactness properties of the associated Lagrangian ows. © 2019 American Institute of Mathematical Sciences. All Rights Reserved

On the Definitions of Boundary Values of Generalized Solutions to an Elliptic-Type Equation

An elliptic-type equation with variable coefficients is considered. An overview is given of the definitions of boundary values of generalized solutions to this equation. Conditions for the existence of boundary values as well as conditions for the existence and uniqueness of solutions to the corresponding Dirichlet problem are analyzed. © 2018, Pleiades Publishing, Ltd

Superposition principle for the continuity equation in a bounded domain

We consider an initial-boundary value problem for the continuity equation in a class of non-negative measure-valued solutions. We prove that any solution in the considered class can be represented as a superposition of elementary solutions, associated with the solutions of the corresponding ordinary differential equation. © Published under licence by IOP Publishing Ltd

Superposition principle for the continuity equation in a bounded domain

We consider an initial-boundary value problem for the continuity equation in a class of non-negative measure-valued solutions. We prove that any solution in the considered class can be represented as a superposition of elementary solutions, associated with the solutions of the corresponding ordinary differential equation. © Published under licence by IOP Publishing Ltd

Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

We consider the continuity equation partial derivative(t)mu(t) + div(b mu(t)) = 0, where {mu(t)}(t is an element of R) is a measurable family of (possibily signed) Borel measures on R-d and b : R x R-d -> R-d is a bounded Borel vector field (and the equation is understood in the sense of distributions). If the measure-valued solution mu(t) is non-negative, then the following superposition principle holds: mu(t) can be decomposed into a superposition of measures concentrated along the integral curves of b. For smooth b this result follows from the method of characteristics, and in the general case it was established by L. Ambrosio. A partial extension of this result for signed measure-valued solutions mu(t) was obtained in [AB08], where the following problem was proposed: does the superposition principle hold for signed measure-valued solutions in presence of unique flow of homeomorphisms solving the associated ordinary differential equation? We answer to this question in the negative, presenting two counterexamples in which uniqueness of the flow of the vector field holds but one can construct non-trivial signed measure-valued solutions to the continuity equation with zero initial data