Related papers: Valiron-Titchmarsh Theorem for Positive Temperatur…

We give a new proof of Lucas' Theorem in elementary number theory.

We demonstrate the existence of a thermal analog of Coulomb drag in many-body systems which is driven by thermal photons. We show that this frictional effect can either be positive or negative depending on the separation distances within…

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

We discuss a simple toy model which allows, in a natural way, for deriving central facts from thermodynamics such as its fundamental laws, including Carnot's version of the second principle. Our viewpoint represents thermodynamic systems as…

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.

We study a concrete model of a confined particle in form of a Schr\"odinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any…

We show the pointwise version of the Ste\v{c}kin theorem on approximation by de la Vall\'ee-Poussin means. The result on norm approximation is also derived.

We give an alternative proof for the equivalence of two definitions of the totally positive grassmannian.

We give a counting based proof of the Graham Pollak Theorem

We study the relativistic electron-positron field at positive temperature in the Hartree-Fock-approximation. We consider both the case with and without exchange term, and investigate the existence and properties of minimizers. Our approach…

We are used to measure temperature with a thermometer and we know from everyday life that different types of thermometers measure the same temperature. This experience can be based on equilibrium thermodynamics, which explains the…

The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four…

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

In this paper, we would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem.

We prove that there are energetically stable bimetric theories. These theories satisfies a positive energy theorem. We construct a model example.

We analyse 4-dimensional massive $\vp^4$ theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion. Our main point is to…

This paper gives a proof of the H\"older Inequality by using supersolutions of the Heat Equation. The proof is based on a monotonicity formula for the heat equation presented in Tobias Colding's lectures at MIT.

We prove that the Bergman and the Teichmuller metrics are equivalent on Teichmuller spaces.

We prove a version of Dedekind's Transposition Principle that holds in lattices of equivalence relations.