Algebra Of Functions Research Articles

Compartmentalisation and Hydrogeological Parameters of the Karst Aquifer System in Central Region of Minas Gerais State, Brazil

ABSTRACTThe Environmental Protection Area of Lagoa Santa Karst (EPA) is a critical karst region in Brazil, renowned for its rich biodiversity and archaeological significance, including discoveries by researchers such as Peter W. Lund and the oldest human skeleton in the Americas, Luzia. However, the region faces threats from rapid socioeconomic and industrial development, stressing its vulnerable aquifer systems. This study updates the hydrogeological conceptual model for the EPA using well log data, map algebra and hydrodynamic parameters obtained through the Agarwal (1980) recovery method . It builds on models by De Paula (Conceptual Model in Pelitic‐Carbonate Aquifers in the Lagoa Santa Karst APA Region, MG, 2019) and refined by Dantas et al. (Journal of South American Earth Sciences, 2023, 123, 104219), reassessing the boundaries of various aquifer units. Horizontal compartmentalisation in the karst‐fissured aquifer was achieved by combining transmissivity and porosity data, while vertical separation was determined based on water entry density and productivity, identifying four zones of increased karstification. In the fissured aquifer, vertical limits align with those established by Dantas et al. (Journal of South American Earth Sciences, 2023, 123, 104219), confirming the anisotropy and heterogeneity of the karst‐fissured and fissured aquifers, and the isotropy and productivity of the alluvial aquifers. These findings provide crucial insights for managing aquifer reserves and mitigating water conflicts in the EPA region.

Proposta metodológica para o indicador das áreas potenciais de ocorrência de açaí na região do Baixo Tocantins, Pará

Açaí is highly significant both economically and nutritionally for the communities of the Baixo Tocantins region in the state of Pará, Brazil. However, mapping açaí palm trees has proven to be a challenging task due to their location beneath the forest canopy, which complicates their identification through orbital satellite imagery. To address this challenge, this study aimed to identify potential areas of native açaí occurrence by employing map algebra with Boolean operation rules, integrating land use and land cover data with hydro-topographic data generated using the Height Above the Nearest Drainage algorithm (HAND). The results indicate that approximately 56% of the study area has some potential for native açaí occurrence. To validate the classification, 66 field samples related to fruit production were analyzed, resulting in 70% agreement. Of these, approximately 80% showed high potential for açaí occurrence. These findings provide valuable insights for a broader discussion on regional public policies related to the açaí economy, as the spatialization of this indicator can support local population inclusion while encouraging the conservation of forest resources.

Boson-Fermion Algebraic Mapping in Second Quantization.

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians.

Modelling three fermion generations with S3 family symmetry within ℂℓ(8)

Abstract We present a model of three fermion generations with SU(3) × U(1) gauge symmetry constructed from the complex Clifford algebra ℂℓ(8), within which the discrete group S 3 acts as a family symmetry. ℂℓ(8) corresponds to the algebra of complex linear maps from the (complexification of the) Cayley-Dickson algebra of sedenions, 𝕊, to itself. The automorphism group of 𝕊 is G 2 × S 3. We interpret S 3, suitably embedded into ℂℓ(8), as a family symmetry. The gauge symmetry SU (3) × U (1) is invariant under S 3. First-generation states are represented in terms of two even ℂℓ(8) semi-spinors, obtained from two minimal left ideals, related to each other via the order-two S 3 symmetry. The remaining two generations are obtained by applying the S 3 symmetry of order-three to the first generation, resulting in three linearly independent generations.

Carbon Stocks Estimation Using the Stock Difference Method of Various Land Use Systems Based on Geospatial in Kualan Watershed

Indonesia controls 75%-80% of the world's carbon stocks, so the amount of carbon stocks must be utilized optimally. This study aims to determine carbon stocks, potential emissions, and economic value of carbon stocks in each land use. The method used is secondary data analysis and field checking. The data collected were Sentinel 2A acquisitions in 2020 and 2022, Digital Elevation Model (DEM), and land use land cover in 2020-2023. Data analysis used SNAP and ArcGIS 10.8. The tool used for data analysis is spatial analysis map algebra. The results showed mixed dryland agriculture has the most extensive carbon stock, at 2,614,178 tons/ha, with potential emissions of 9,585,320 tons/ha. The most minor carbon stock is in mining land use, which is 0 tons/ha with potential emissions of 0 tons/ha. The highest C02 value in USD is the forest land use group. In the Secondary Dryland Forest, Secondary Swamp Forest, and Plantation Forest groups, it is 17,517,400.50 USD, while the lowest is mining land use, which is 0 USD. Overall, the CO2 value of land use in the study area is 34,246,314.45 USD. Integrating remote sensing data analysis and field surveys in geospatial technology is one of the new approaches to studying carbon stocks and CO2 emissions in topsoil from various land uses. By utilizing geospatial technology, efforts to estimate carbon stocks on the surface are easier and faster.

Quasi-radial operators on the Fock space and C*-algebras of entire functions

In this article, we consider quasi-radial operators on the Fock space of holomorphic functions on C n that are square integrable with respect to the Gaussian measure on C n . We provide an integral representation for quasi-radial operators. As a consequence, we study several operator theoretic properties of these operators and the Toeplitz operators with quasi-radial defining symbols. In addition to this, we construct various examples of commutative C ∗ -algebras of analytic functions on C n each associated with a particular class of quasi-radial operators.

Differential embeddings into algebras of topological stable rank 1

We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show that group algebras of Abelian groups of unbounded exponent fail to have uniformly open convolution. Finally, we completely characterize in the complex case (uniform) openness of multiplication in algebras of continuous functions in terms of the covering dimension.

Partition Differential Equations and Some Combinatorial Algebraic Structures

Let Λ be the algebra of symmetric functions. We introduce Stirling partitions, factorial partition polynomials, partition differential equations and their corresponding partitions, and partition primitive functions. Most importantly, this investigation provides a new combinatorial coalgebra structure on Λ, and it characterizes the primitive elements in Λ using the Jacobian determinants of partition primitive functions.

On Some Topological Properties of Ch(X) and of the Dual Operator

The hypo-topology on the algebra C(X) of real-valued continuous functions defined on a Tychonoff space 2X f ∈ C(X) with its hypograph, hypof = {(x,t) ∈ X x R:f(x) ≥ t}. This topology is very useful in the calculus of variations and in optimization theory (e.g. Maximization problems). We denote C(X) with the hypo-topology by Ch(X). Our study deals with fundamental properties of these function spaces, and with the linear operators on them and as well as the characterization of the topological properties of Ch(X) in terms of topological properties of the base space X. We are studying the linear operator between the functional algebras Ch(X) and the Ch(Y). We are primarily concerned with the continuity of the evaluation functional, the general evaluation and the continuity of the characters of Ch(X) before the investigation of the properties of the dual operator f* of a continuous function f:X→Y. This operator is defined by f*:Ch (Y)→Ch (X), where f*(g)=gof for all g ∈ C(Y). The continuity of f* enables us to characterize the continuity of an algebra homomorphism of the type φ:Ch (Y)→Ch (X) for a realcompact space Y. For such a space, we present a type of Riesz theorm with states that an algebra homomorphism φ: Ch(Y)→Ch(X) is continuous if and only if there exists a unique hypo-function f: X→Y such that φ = f*. There after, we give the equivalence between the properties of f and those of f*. The study of the continuous linear functional on Ch(X) helps us to compute the topological dual space of this algebra. We show here that this dual space is useful only when the set of isolated points of X is dense.

Fibers and Gleason parts for the maximal ideal space of Au(Bℓp)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}_u(B_{\\ell _p})$$\\end{document}

In the early nineties, R. M. Aron, B. Cole, T. W. Gamelin and W. B. Johnson initiated the study of the maximal ideal space (spectrum) of Banach algebras of holomorphic functions defined on the open unit ball of an infinite dimensional complex Banach space. Within this framework, we investigate the fibers and Gleason parts of the spectrum of the algebra of holomorphic and uniformly continuous functions on the unit ball of ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _p$$\\end{document} (1≤p<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le p<\\infty $$\\end{document}). We show that the inherent geometry of these spaces provides a fundamental ingredient for our results. We prove that whenever p∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\in {\\mathbb {N}}$$\\end{document} (p≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\ge 2$$\\end{document}), the fiber of every z∈Bℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\in B_{\\ell _p}$$\\end{document} contains a set of cardinal 2c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{{\\mathfrak {c}}}$$\\end{document} such that any two elements of this set belong to different Gleason parts. For the case p=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=1$$\\end{document}, we complete the known description of the fibers, showing that, for each z∈B¯ℓ1′′\\Sℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\in \\overline{B}_{\\ell _1''}{\\setminus } S_{\\ell _1}$$\\end{document}, the fiber over z is not a singleton. Also, we establish that different fibers over elements in Sℓ1′′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{\\ell _1''}$$\\end{document} cannot share Gleason parts.

On Lie Homomorphisms of Complex IntuitionisticFuzzy Lie Algebras

In this paper, we investigate the properties of complex intuitionistic fuzzy Lie subalgebras and ideals under Lie algebra homomorphisms, focusing on both images and inverse images. We provide detailed proofs for several new results concerning the preservation of complex intuitionistic fuzzy structures through homomorphisms, and we introduce additional homomorphism-related properties for these structures. This work extends known results to the context of complex intuitionistic fuzzy Lie algebras, contributing new insights into their behavior under algebraic mappings.

Preparation of A Map of Potential Areas For the Installation of A Sanitary Landfill in The Porto Murtinho/MS Region

Objective: The main objective is to prepare a map to identify areas with potential for the installation of a landfill in the region of Porto Murtinho/MS. Theoretical Framework: This study addresses the relevance of the careful selection of locations for the implementation of Sanitary Landfills, with an emphasis on environmental and social aspects, using geotechnologies as fundamental tools for a comprehensive and effective analysis. Method: The mapping was based on the acquisition and processing of geospatial and environmental data. The factors were classified as limiting or not, considering watercourses, areas subject to flooding, roads, land use and occupation, slope, soil and urban proximity. Data integration through map algebra was performed in QGIS software, and WRPLOT View was used for wind analysis. Results and Discussion: The results revealed that the majority of areas with high installation potential are located at a distance of 2 (two) to 5 (five) kilometers from the urban perimeter. The supplementary analysis of Rosa dos Ventos demonstrated that areas located to the east are more suitable for the implementation of sanitary landfills. Research Implications: The multifaceted approach, which includes environmental and operational aspects, makes it possible to identify areas suitable for the implementation of sanitary landfills. Originality/Value: This study demonstrates the relevance of geotechnologies in choosing locations for landfills, where limiting factors exclude unsuitable areas, and non-limiting factors classify the installation potential, being a methodology replicable in other locations for sustainable environmental management.

Algebraic realisation of three fermion generations with S3 family and unbroken gauge symmetry from Cℓ(8)

Building on previous work, we extend an algebraic realisation of three fermion generations within the complex Clifford algebra Cℓ(8) by incorporating a U(1)em gauge symmetry. The algebra Cℓ(8) corresponds to the algebra of complex linear maps from the (complexification of the) Cayley–Dickson algebra of sedenions, S, to itself. Previous work represented three generations of fermions with SU(3)C colour symmetry permuted by an S3 symmetry of order-three, but failed to include a U(1) generator that assigns the correct electric charge to all states. Furthermore, the three generations suffered from a degree of linear dependence between states. By generalising the embedding of the discrete group S3, corresponding to automorphisms of S, into Cℓ(8), we include an S3-invariant U(1) that correctly assigns electric charge. First-generation states are represented in terms of two even Cℓ(8) semi-spinors, obtained from two minimal left ideals, related to each other via the order-two S3 symmetry. The remaining two generations are obtained by applying the S3 symmetry of order-three to the first generation. In this model, the gauge symmetries, SU(3)C×U(1)em, are S3-invariant and preserve the semi-spinors. As a result of the generalised embedding of the S3 automorphisms of S into Cℓ(8), the three generations are now linearly independent.

Book review: “Banach Function Algebras, Arens Regularity, and BSE Norms” by Harold Garth Dales and Ali Ülger

To the memory of Garth Dales.

On monomorphisms of hypergraphic automata

Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects in the category of hypergraphic automata are called universal hypergraphic automata. The semigroups of input symbols of such automata are derivative algebras of mappings for such automata. So their properties are interconnected with properties of the algebraic structures of the automata. This paper describes the structure of monomorphisms of such automata and their semigroups of input signals.

On the classification of function algebras on subvarieties of noncommutative operator balls

We study algebras of bounded noncommutative (nc) functions on unit balls of operator spaces (nc operator balls) and on their subvarieties. Considering the example of the nc unit polydisk we show that these algebras, while having a natural operator algebra structure, might not be the multiplier algebra of any reasonable nc reproducing kernel Hilbert space (RKHS). After examining additional subtleties of the nc RKHS approach, we turn to study the structure and representation theory of these algebras using function theoretic and operator algebraic tools. We show that the underlying nc variety is a complete invariant for the algebra of uniformly continuous nc functions on a homogeneous subvariety, in the sense that two such algebras are completely isometrically isomorphic if and only if the subvarieties are nc biholomorphic. We obtain extension and rigidity results for nc maps between subvarieties of nc operator balls corresponding to injective spaces that imply that a biholomorphism between homogeneous varieties extends to a biholomorphism between the ambient balls, which can be modified to a linear isomorphism. Thus, the algebra of uniformly continuous nc functions on nc operator balls, and even its restriction to certain subvarieties, completely determine the operator space up to completely isometric isomorphism.

Automorphism Groups of Deformations and Quantizations of Kleinian Singularities

AbstractIt is known that, for the algebra of functions on a Kleinian singularity, the parameter space of deformations and the parameter space of quantizations coincide. We prove that, for a Kleinian singularity of type $$\textbf{A}$$ A or $$\textbf{D}$$ D , isomorphisms between the quantizations are essentially the same as Poisson isomorphisms between deformations. In particular, the group of automorphisms of the deformation and the quantization corresponding to the same deformation parameter are isomorphic. We additionally describe the groups of automorphisms as abstract groups: for type $$\textbf{A}$$ A they have an amalgamated free product structure, for type $$\textbf{D}$$ D they are subgroups of the groups of Dynkin diagram automorphisms. For type $$\textbf{D}$$ D we also compute all the possible affine isomorphisms between deformations; this was not known before.

A generalization of prime ideals in MV-algebras

In this paper, we introduce a special type of prime ideals in [Formula: see text]-algebras. We define the concept of a [Formula: see text]-prime ideal, which is a proper ideal [Formula: see text] that preserves the property of being prime with respect to the ideal [Formula: see text]. If [Formula: see text] is not a subset of [Formula: see text], then we call the [Formula: see text]-prime ideal an [Formula: see text]-prime ideal. We investigate the relationships between these ideals and their connections to minimal prime ideals and maximal ideals. Additionally, we explore various properties such as extension, transitivity, meet, join, and annihilator. Finally, we study prime ideals in [Formula: see text]-algebras of continuous functions.

Differential geometry and general relativity with algebraifolds

It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential geometry which eliminate the need for an underlying manifold. While the literature contains various independent approaches to this, we focus on one particular approach that we argue to be the most natural one based on the definition of algebraifold, by which we mean a commutative algebra A for which the module of derivations of A is finitely generated projective. Over R as the base ring, this class of algebras includes the algebra C∞(M) of smooth functions on a manifold M, and similarly for analytic functions. An importantly different example is the Colombeau algebra of generalized functions on M, which makes distributional differential geometry an instance of our formalism. Another instance is a fibred version of smooth differential geometry, since any smooth submersion M→N makes C∞(M) into an algebraifold with C∞(N) as the base ring. Over any field k of characteristic zero, examples include the algebra of regular functions on a smooth affine variety as well as any function field.Our development of differential geometry in terms of algebraifolds comprises tensors, connections, curvature, geodesics and we briefly consider general relativity.

Preparation of a Map of Potential Areas For the Installation of a Sewage Treatment Plant in the Porto Murtinho/MS Region

Objective: The main objective is to prepare a thematic map to identify potential areas for the installation of a Sewage Treatment Station (ETE). Theoretical Framework: This study addresses the importance of selecting locations for the installation of ETEs, which prioritize environmental and social aspects, in which geotechnologies are presented as valuable tools for efficient and integrated analysis. Method: The methodology of this research was based on the acquisition and processing of geospatial and environmental data, complemented by the generation of thematic maps such as watercourses, areas subject to flooding, roads, land use and occupation, slope, soils and distances from the urban perimeter. Data integration through map algebra was performed in the QGIS software, in addition, WRPLOT View was used for the directional analysis of the winds in Porto Murtinho/MS. Results and Discussion: The results of this study indicate that the areas with the greatest potential for installation are mostly located within 1 (one) kilometer of the urban perimeter security strip. The analysis of the prevailing winds revealed that they form a corridor in the north/south direction, suggesting that the regions east of the city are more suitable for the implementation of the treatment system. Research Implications: The multifaceted approach, considering environmental and operational factors, makes it possible to identify suitable areas for ETEs. Originality/Value: This study was developed, highlighting that limiting factors are essential in identifying areas unsuitable for installing the structure, while non-limiting maps are essential for classifying the installation potential.