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We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining…
In the paper we apply some of the results from the theory of ball spaces in the semimetric spaces. This allowed us to obtain some fixed point theorems which we believe to be unknown to this day. We also show the limitations of the ball…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
In this paper, we briefly discuss a mathematical concept that can be used in economics.
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…
In this paper we introduce a quotient structure on topological ternary semigroup by defining a congruence suitably. We have found conditions under which this quotient structure becomes a topological ternary semigroup. We have also obtained…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class…