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Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope…
In this work, we demonstrate that quantizing gravity on a null hypersurface leads to the emergence of a CFT associated with each null ray. This result stems from the ultralocal nature of null physics and is derived through a canonical…
Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry…
The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a…
This paper builds on no-go theorems to the effect that quantum theory is inconsistent with observations being absolute; that is, unique and non-relative. Unlike the existing no-go results, the one introduced here is based on a…
The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…
Number theory as a coherent mathematical subject started with the work of Fermat in the decade from 1630 to 1640, but modern number theory, that is, the systematic and mathematically rigorous development of the subject from fundamental…
Abstract upper densities are monotone and subadditive functions from the power set of positive integers into the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper…
This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
We study projections in the bidual of a $C^*$-algebra $B$ that are null with respect to a subalgebra $A$, that is projections $p\in B^{**}$ satisfying $|\phi|(p)=0$ for every $\phi\in B^*$ annihilating $A$. In the separable case, $A$-null…
We consider the dynamics of a spatially flat universe dominated by a self-interacting nonminimally coupled scalar field. The structure of the phase space and complete phase portraits for the conformal coupling case are given. It is shown…
All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit…
Half a century has passed since the foundation of nuclear astrophysics. Since then, this discipline has reached its maturity. Today, nuclear astrophysics constitutes a multidisciplinary crucible of knowledge that combines the achievements…
We propose and develop an approach to study nilsystems and their proximal extensions using cube structures associated with the universal minimal system. We provide alternative proofs for results regarding saturation properties of factor…
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
In this review paper, we comprehensively summarize numerical applications of double-null formalism for studying dynamics within the theory of gravity. By using the double-null coordinates, we can investigate dynamical black holes and…
We "explain", using a Classical approach, how the Universe was created out of "nothing", i.e., with no input of initial energy. This is a Universe with no-initial infinite singularity of energy density.
There is natural association of entropy with gravitational systems on one hand and partition of natural numbers on the other hand. We show that given a partition of natural numbers, it is possible to directly associate a metric with it.…