Related papers: Comment on "Unifying Aspects of Generalized Calcul…
We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality $\mathbf{c}$ of the continuum as the ``cause'' behind motions of material…
An attempt is made to go beyond the standard semi-classical approximation for gravity in the Born-Oppenheimer decomposition of the wave-function in minisuperspace. New terms are included which correspond to quantum gravitational…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The complete axiomatic…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$…
This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…
We discuss various aspects of the calculation of correlation functions in conformal theories coupled to quantized 2-dimensional gravity. The main emphasis lies on the construction of a continuation in the number of insertions of the…
We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement…
Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
$\lambda\upsilon$ is an extension of the $\lambda$-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of $\lambda\upsilon$ focusing on the quantitative aspects of…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
Compactons are solutions of the equations of motion that behave trivially outside a compact region. In general, the operators describing quantum fluctuations above compactons have singularities. However, we show that despite these…