Related papers: On matrix generalization of Robinson's Energy Dela…
A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the…
A theorem on the magnetic energy minimum in a perfect, or ideal, conductor is proved. Contrary to conventional wisdom the theorem provides a classical explanation of the expulsion of a magnetic field from the interior of a conductor that…
In this paper, we introduce various covering number bounds for linear function classes, each subject to different constraints on input and matrix norms. These bounds are contingent on the rank of each class of matrices. We then apply these…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
We consider differential delay equations of the form $\partial_tx(t) = X_{t}(x(t - \tau))$ in $\mathbb{R}^n$, where $(X_t)_{t\in S^1}$ is a time-dependent family of smooth vector fields on $\mathbb{R}^n$ and $\tau$ is a delay parameter. If…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary…
In this paper, we establish bounds for the eigenvalues of matrix polynomials. Specifically, we find different generalizations of the Enestrom-Kakeya Theorem for matrix polynomials.
The Robinson Splitting Theorem states that a c.e. degree $\mathbf{b}$ splits over any low c.e. degree $\mathbf{c}<\mathbf{b}$. We prove that a weaker version of this theorem holds in models of $\mathrm{P}^-+\mathrm{I}\Sigma_1$, with lowness…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
We show that the permanent of a matrix can be written as the expectation value of a function of random variables each with zero mean and unit variance. This result is used to show that Glynn's theorem and a simplified MacMahon theorem…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We prove a theorem for the growth of the energy of bounded, globally minimizing solutions to a class of semilinear elliptic systems of the form $\Delta u=\nabla W(u)$, $x\in \mathbb{R}^n$, $n\geq 2$, with $W:\mathbb{R}^m\to \mathbb{R}$,…
We prove that the Buchweitz-Greuel-Schreyer Conjecture on the minimal rank of a matrix factorization holds for a generic polynomial of given degree and strength. The proof introduces a notion of the secondary strength of a polynomial, and…
We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…
Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power…
Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an…
The equivalence of regularity of a Q-matrix with its bounded perturbations is proved and a integration by parts formula is established for the associated Feller minimal transition functions.