We prove Pólya’s conjecture of 1943: For a real entire function of order greater than 2 with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity as n → ∞ . We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.

We recently performed a pilot study determining the parameters of the leading order chiral La-grangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. We complement a quick survey of our recent preprint [1] by addressing some points raised during discussions at the conference.

From a distributional-theoretical framework, we make efforts in order to fill a gap in the series of studies which discuss the inheritance of the renormalization behaviour of a finite temperature field theory (FTFT) from the analogous version in quantum field theory (QFT) at T = 0. Renormalization is treated as a distributional extension problem having the mathematical structure disentangled as...

We introduce a novel genotype-phenotype mapping based on the relation between RNA sequence and its secondary structure for the use in evolutionary studies. The inspiration for this particular mapping emerged from the modeling of RNA enzymes within a simulation framework for the evolution of metabolic reaction networks. In our simulation we allow individuals, containing a genome and a metabolism...

Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them. We show that there are 16 equivalence classes of minimal convex imaginary cubes, among whose representatives are a hexagonal bipyramid imaginary cube and a triangular antiprism imag...

The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. An improvement of our previous construction to prove the RH is presented by implementing the Hilbert-Polya proposal and furnishing the Fractal Supersymmetric Quantum Mechanical (SUSY-QM) model whose spectrum reproduces the imaginary parts of the zeta zeros. We model the fr...

This work concerns the low-frequency interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spheres embedded within a homogeneous conductive medium. In such physical applications, where two bodies are placed near one another, the 3D bispherical geometry fits perfectly. Considering two solid impenetrable metallic obsta...

We study a two-level model coupled to the electromagnetic vacuum and to a weak external electric field with fixed frequency. The amplitude of the external electrical field is supposed to vary very slowly in time. The coupling of the two-level system with the environment (vacuum) introduces decreasing exponentials in the probability of the two-level system to be in its upper level. Garrison and ...

Abstract. In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C ), spatial reflection (P) and time reversal (T ) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show tha...

The questions this manuscript addresses arose in the course of an investigation of the imaginary sorts in ultraproducts of p-adic fields. These were shown to be understandable given the imaginary sorts of certain finite-dimensional vector spaces over the residue field. The residue field is pseudo-finite, and the imaginary elements there were previously studied, and shown in fact to be eliminabl...