相关论文: Observability on lattice points for heat equations…
Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…
We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc) are well-defined. The sign of the latent heat is found to be…
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
We discuss reachable states for the Hermite heat equation on a segment with boundary $L^2$-controls. The Hermite heat equation corresponds to the heat equation to which a quadratic potential is added. We will discuss two situations: when…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
We consider the transport equation $\ppp_t u(x,t) + H(t)\cdot \nabla u(x,t) = 0$ in $\OOO\times(0,T),$ where $T>0$ and $\OOO\subset \R^d $ is a bounded domain with smooth boundary $\ppp\OOO$. First, we prove a Carleman estimate for…
Lattice computations are the only first principle method capable of quantitatively assessing the topological properties of QCD at high temperature, however the numerical determination of the topological properties of QCD, especially in the…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
We consider two degenerate heat equations with a nonlocal space term, studying, in particular, their null controllability property. To this aim, we first consider the associated nonhomogeneous degenerate heat equations: we study their well…
This work is an extention of Shiraishi and Matsumoto [10], and discusses the computational complexity of the long-term average of local observables in one-dimensional lattices with shift-invariant nearest-neighbor interactions for simple…
In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the…
This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the…
In empirical studies, the data usually don't include all the variables of interest in an economic model. This paper shows the identification of unobserved variables in observations at the population level. When the observables are distinct…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
This paper studies the state observation problems for the semilinear heat equation in R^n. We derive observation estimates for the equation using the logarithmic convexity property of the frequency function (see [12]). As an application, we…
We show that the asymmetric inter-particle interactions may induce rapid decay of heat current autocorrelation in one-dimensional momentum conserving lattices. When the asymmetry degree and the temperature are appropriate, the decay is…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…