Related papers: Interactions between function theory and holomorph…
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the…
We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
In this paper, we present a new technique for studying the dynamics of a finitely generated rational semigroup. Such a semigroup can be associated naturally to a certain holomorphic correspondence on $\mathbb{P}^1$. Then, results on the…
An explicit expression is derived for the distribution function of end-to-end vectors and for the mean square end-to-end distance of a flexible chain with excluded-volume interactions. The Hamiltonian for a flexible chain with weak…
We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish the Piunikhin-Salamon-Schwarz isomorphism between the Floer homology and the Morse homology of such a manifold, and then use…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
In connection to a conjecture of W. L\"u. Q. Li and C. Yang we prove a result on small function sharing by a power of a meromorphic function with few poles and its derivative. Our results improve a number of known results.
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…
The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the…
The theory of causal fermion systems is a new physical theory which aims to describe a fundamental level of physical reality. Its mathematical core is the causal action principle. In this thesis, we develop a formalism which connects the…