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Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this…
We give a new and rigorous duality relation between two central notions of weak solutions of nonlinear PDEs: entropy and viscosity solutions. It takes the form of the nonlinear dual inequality: \begin{equation}\int |S_t u_0-S_t v_0|…
The minimum Kullback entropy principle (mKE) is a useful tool to estimate quantum states and operations from incomplete data and prior information. In general, the solution of a mKE problem is analytically challenging and an approximate…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently…
We propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval $(-1,1)$ and possibly have algebraic singularities at the endpoints of the interval. As a space of such…
We find the Euler-Lagrangian equation by maximising the total entropy. Hence we obtain an expression for mass of the spherically symmetric system by solving the Euler-Lagrangian equation where the Homotopy Perturbation Method has been…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space,…
Using methods from Banach space theory, we prove two new structural results on maximal regularity. The first says that there exist positive analytic semigroups on UMD-Banach lattices, namely $\ell_p(\ell_q)$ for $p \neq q \in (1, \infty)$,…
In this note, in particular, we establish the following result: Let $X$ be a real Banach space, $\varphi\in X^*\setminus \{0\}$ and $\psi:X\to {\bf R}$ a Lipschitzian functional with Lipschitz constant equal to $\varphi\|_X^{*}$. Then, we…
In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately…
In this work, we extend the Da Prato-Grisvard theory of maximal regularity estimates for sectorial operators in interpolation spaces. Specifically, for any generator $-A$ of an analytic semigroup on a Banach space $X$, we identify the…
This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the…
We continue the work of \cite{TLNT}. Let $E$ be a non-Blaschke subset of the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$. Fixed $1\leq p\leq \infty$, let $H^p(\mathbb{D})$ be the Hardy space of holomorphic functions in the disk…
We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological…
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the…
We consider the following task: how for a given quantum state $\rho$ to find a grounded Hamiltonian $H$ satisfying the condition $\mathrm{Tr} H\rho\leq E_0<+\infty$ in such a way that the von Neumann entropy of the Gibbs state $\gamma_H(E)$…
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…
We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…