56 research outputs found
Classes of generalized functions with finite type regularities
We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities
Optimization of commodity portfolio management
The problem we consider is introduced by Uljarice Bačka, LLC. The core business activities of the company are trade of agriculture commodities, warehousing and distribution and crops production. The main traded goods are: corn, wheat, barely, sunflower, soybean, soybean meal and raw material for crops production: fertilizers, plant protection products, seeds and other. Since a large part of company’s activities relays on corn, predicting the price of that good is of the main interest. In order to make a reasonable predictions, models which incorporate the crucial factors influencing the corn prices are needed. Of course, the important issue is which data are available. Within the data that we obtained, a correlation analysis is performed to point out the relevant parameters. We introduce different methods for obtaining the predictions and provide some numerical results
Isomorphisms of algebras of Colombeau generalized functions
We show that for smooth manifolds X and Y, any isomorphism between the
special algebra of Colombeau generalized functions on X, resp. Y is given by
composition with a unique Colombeau generalized function from Y to X. We also
identify the multiplicative linear functionals from the special algebra of
Colombeau generalized functions on X to the ring of Colombeau generalized
numbers. Up to multiplication with an idempotent generalized number, they are
given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page
An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms
We offer an axiomatic definition of a differential algebra of generalized
functions over an algebraically closed non-Archimedean field. This algebra is
of Colombeau type in the sense that it contains a copy of the space of Schwartz
distributions. We study the uniqueness of the objects we define and the
consistency of our axioms. Next, we identify an inconsistency in the
conventional Laplace transform theory. As an application we offer a free of
contradictions alternative in the framework of our algebra of generalized
functions. The article is aimed at mathematicians, physicists and engineers who
are interested in the non-linear theory of generalized functions, but who are
not necessarily familiar with the original Colombeau theory. We assume,
however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page
Generalized Fourier Integral Operators on spaces of Colombeau type
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras
are defined. This is based on a theory of generalized oscillatory integrals
(OIs) whose phase functions as well as amplitudes may be generalized functions
of Colombeau type. The mapping properties of these FIOs are studied as the
composition with a generalized pseudodifferential operator. Finally, the
microlocal Colombeau regularity for OIs and the influence of the FIO action on
generalized wave front sets are investigated. This theory of generalized FIOs
is motivated by the need of a general framework for partial differential
operators with non-smooth coefficients and distributional data
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
Does α-Amino-β-methylaminopropionic Acid (BMAA) Play a Role in Neurodegeneration?
The association of α-amino-β-methylaminopropionic acid (BMAA) with elevated incidence of amyotrophic lateral sclerosis/Parkinson’s disease complex (ALS/PDC) was first identified on the island of Guam. BMAA has been shown to be produced across the cyanobacterial order and its detection has been reported in a variety of aquatic and terrestrial environments worldwide, suggesting that it is ubiquitous. Various in vivo studies on rats, mice, chicks and monkeys have shown that it can cause neurodegenerative symptoms such as ataxia and convulsions. Zebrafish research has also shown disruption to neural development after BMAA exposure. In vitro studies on mice, rats and leeches have shown that BMAA acts predominantly on motor neurons. Observed increases in the generation of reactive oxygen species (ROS) and Ca2+ influx, coupled with disruption to mitochondrial activity and general neuronal death, indicate that the main mode of activity is via excitotoxic mechanisms. The current review pertaining to the neurotoxicity of BMAA clearly demonstrates its ability to adversely affect neural tissues, and implicates it as a potentially significant compound in the aetiology of neurodegenerative disease. When considering the potential adverse health effects upon exposure to this compound, further research to better understand the modes of toxicity of BMAA and the environmental exposure limits is essential
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