211 research outputs found
A rigorous but gentle introduction for economists
This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.
Fractional Calculus - Theory and Applications
In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications
The Brownian Motion
This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways
q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
We characterise the quantum group gauge symmetries underlying q-deformations
of two-dimensional Yang-Mills theory by studying their relationships with the
matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge
theories, together with their refinements and supersymmetric extensions. We
develop uniqueness results for quantum deformations and refinements of gauge
theories in two dimensions, and describe several potential analytic and
geometric realisations of them. We reconstruct standard q-deformed Yang-Mills
amplitudes via gluing rules in the representation category of the quantum group
associated to the gauge group, whose numerical invariants are the usual
characters in the Grothendieck group of the category. We apply this formalism
to compute refinements of q-deformed amplitudes in terms of generalised
characters, and relate them to refined Chern-Simons matrix models and
generalized unitary matrix integrals in the quantum beta-ensemble which compute
refined topological string amplitudes. We also describe applications of our
results to gauge theories in five and seven dimensions, and to the dual
superconformal field theories in four dimensions which descend from the N=(2,0)
six-dimensional superconformal theory.Comment: 71 pages; v2: references added; final version to be published in
Nuclear Physics
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio
Geometry and field theory in multi-fractional spacetime
We construct a theory of fields living on continuous geometries with
fractional Hausdorff and spectral dimensions, focussing on a flat background
analogous to Minkowski spacetime. After reviewing the properties of fractional
spaces with fixed dimension, presented in a companion paper, we generalize to a
multi-fractional scenario inspired by multi-fractal geometry, where the
dimension changes with the scale. This is related to the renormalization group
properties of fractional field theories, illustrated by the example of a scalar
field. Depending on the symmetries of the Lagrangian, one can define two
models. In one of them, the effective dimension flows from 2 in the ultraviolet
(UV) and geometry constrains the infrared limit to be four-dimensional. At the
UV critical value, the model is rendered power-counting renormalizable.
However, this is not the most fundamental regime. Compelling arguments of
fractal geometry require an extension of the fractional action measure to
complex order. In doing so, we obtain a hierarchy of scales characterizing
different geometric regimes. At very small scales, discrete symmetries emerge
and the notion of a continuous spacetime begins to blur, until one reaches a
fundamental scale and an ultra-microscopic fractal structure. This fine
hierarchy of geometries has implications for non-commutative theories and
discrete quantum gravity. In the latter case, the present model can be viewed
as a top-down realization of a quantum-discrete to classical-continuum
transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and
improved (especially section 4.5), typos corrected, references added; v4:
further typos correcte
Fuzzy EOQ Model with Trapezoidal and Triangular Functions Using Partial Backorder
EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR ̃C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the company's problems in estimating the costs for the next term
ABC of multi-fractal spacetimes and fractional sea turtles
We clarify what it means to have a spacetime fractal geometry in quantum
gravity and show that its properties differ from those of usual fractals. A
weak and a strong definition of multi-scale and multi-fractal spacetimes are
given together with a sketch of the landscape of multi-scale theories of
gravitation. Then, in the context of the fractional theory with
-derivatives, we explore the consequences of living in a multi-fractal
spacetime. To illustrate the behavior of a non-relativistic body, we take the
entertaining example of a sea turtle. We show that, when only the time
direction is fractal, sea turtles swim at a faster speed than in an ordinary
world, while they swim at a slower speed if only the spatial directions are
fractal. The latter type of geometry is the one most commonly found in quantum
gravity. For time-like fractals, relativistic objects can exceed the speed of
light, but strongly so only if their size is smaller than the range of
particle-physics interactions. We also find new results about log-oscillating
measures, the measure presentation and their role in physical observations and
in future extensions to nowhere-differentiable stochastic spacetimes.Comment: 20 pages, 1 figure. v2: typos corrected, minor improvements of the
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