Related papers: Universal $\alpha$-elasticity of generalized Moufa…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
In this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the…
A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they…
Recently, simple scaling laws concerning the mechanical response and mechanical transition of Kirigami have been revealed through agreement between theory and experiment for kirigami made of paper [M. Isobe and K. Okumura, Sci. Rep. 2016].…
We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating…
The $\alpha$-modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the…
We have derived a universal relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems. The power law exponents of the relaxation function are simply related to a global fractal parameter…
A number of arguments at the interplay of general relativity and quantum theory suggest an operational limit to spatial resolution, conventionally modelled as a generalized uncertainty principle (GUP). Recently, it has been demonstrated…
Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasi-projective surfaces; the…
We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion hold. These conditions are verified, hence bulk spectral universality is proven, for a large class…
We present generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength. The proposed mechanistic contact laws are continuous at the onset of unloading by means of a regularization term, in the spirit of a…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In…
We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincar\'e (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then derive a set of approximate…
We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa $ \beta $-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the $ \beta…
By performing Monte Carlo sampling of $N$-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric and geometrical properties of knotted polymer rings. In…
The character of elastic forces of relativistic membranes and $p$-branes encoded in their nonlinear equations is studied. The toroidal brane equations are reduced to the classical equations of anharmonic elastic media described by monomial…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…