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DERIVATIONS AND DIFFERENTIALS
Title
DERIVATIONS AND DIFFERENTIALS.
Creator
BASTIDA, VICKI C., Florida Atlantic University, Bastida, Julio R.
Abstract/Description
In this thesis we present a detailed study of the foundations of the general theory of derivations and differentials for commutative algebras over commutative rings. We give a direct and natural proof of the existence of the module of differentials, and then discuss some of its basic properties. A considerable part of the work is devoted to the establishing of the two fundamental exact sequences.
Date Issued
1971
PURL
http://purl.flvc.org/fcla/dt/13447
Subject Headings
Algebra, Abstract
Format
Document (PDF)
LEVEL OF ABSTRACTION AND SELF-UNDERSTANDING
Title
LEVEL OF ABSTRACTION AND SELF-UNDERSTANDING.
Creator
COHEN, JOYCE., Florida Atlantic University
Abstract/Description
The affects of level of abstraction on self-description inventories were investigated in this study. Seventy-five subjects were administered self-description inventories which assessed their overall standing on ten high level, abstract descriptors and ten low level, concrete descriptors. Subjects also indicated how much variability, certainty, and importance they associated with their responses. Results indicated that high level agents make judgments with more certainty than low level agents....
Show moreThe affects of level of abstraction on self-description inventories were investigated in this study. Seventy-five subjects were administered self-description inventories which assessed their overall standing on ten high level, abstract descriptors and ten low level, concrete descriptors. Subjects also indicated how much variability, certainty, and importance they associated with their responses. Results indicated that high level agents make judgments with more certainty than low level agents. Additionally, certainty and importance were unrelated thus indicating different aspects of self-understanding. Variability was negatively correlated with certainty yet positively correlated with the importance measure. This suggests that the notion of the self as a stable entity, as postulated by traditional self-concept theories, may be in error. It was advanced that variability be investigated as a flexible, adaptive aspect of self-understanding.
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Date Issued
1987
PURL
http://purl.flvc.org/fcla/dt/14409
Subject Headings
Abstraction, Self-perception
Format
Document (PDF)
VISUAL CONCEPTS: PROTOTYPE ABSTRACTION AND SPECIFIC REPRESENTATION
Title
VISUAL CONCEPTS: PROTOTYPE ABSTRACTION AND SPECIFIC REPRESENTATION.
Creator
TROMLEY, CHERYL LYNN., Florida Atlantic University
Abstract/Description
Prototype abstraction and specific representations were examined using two acquisition procedures (paired-associate and concept formation) for concept members generated by applying one of two distortion rules (form preserving and form destroying) to eight-dot base patterns. One distortion rule maximized the configurational similarity between concept members and minimized their elemental similarity (form preserving). The other maximized the elemental similarity between concept members and...
Show morePrototype abstraction and specific representations were examined using two acquisition procedures (paired-associate and concept formation) for concept members generated by applying one of two distortion rules (form preserving and form destroying) to eight-dot base patterns. One distortion rule maximized the configurational similarity between concept members and minimized their elemental similarity (form preserving). The other maximized the elemental similarity between concept members and minimized their configurational similarity (form destroying). Either immediately following acquisition or after a two-week delay, subjects were given a classification test which included the concept members learned during acquisition and novel members of the concepts. Evidence for prototype abstraction was found only for form preserving concepts. This result was interpreted as evidence for the configurational nature of a prototypical representation. Evidence for long-term retention of specific representations was found only for form destroying concepts. This result was explained by a model involving a network of partially overlapping features.
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Date Issued
1978
PURL
http://purl.flvc.org/fcla/dt/13941
Subject Headings
Visual perception--Testing, Concepts, Abstraction
Format
Document (PDF)
computation of the Hall coefficient g(q)[('6,4,2)(,42)(,4,2)]
Title
A computation of the Hall coefficient g(q)[('6,4,2)(,42)(,4,2)].
Creator
Anez, Myriam T., Florida Atlantic University, Schmidmeier, Markus
Abstract/Description
Let L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λ-modules which possess a finite composition series. We note that a Λ-module has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λ-modules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = |{U ⊆ B : U ≅ A and B/U ≅ C}|. We show that GBAC = MonoA,B,C Aut A = | S (A, B, C)/∼| = glmn (q),...
Show moreLet L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λ-modules which possess a finite composition series. We note that a Λ-module has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λ-modules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = |{U ⊆ B : U ≅ A and B/U ≅ C}|. We show that GBAC = MonoA,B,C Aut A = | S (A, B, C)/∼| = glmn (q), where |Λ/ r | = q, and the last equality comes from evaluating the Hall polynomial glmn (t) ∈ Z [t] at q, as stated in Hall's Theorem. We note that GBAC make up the coefficients of the Hall algebra. We provide a proof that the Hall algebra is a commutative and associative ring. Using the property of associativity of the Hall algebra and I. G. MacDonald's formula: glb1l =qnl -nb-n 1li≥ 1l'i -b'i,b' i-l'i+1 q-1 we develop a procedure to generate arbitrary Hall polynomials and we compute g6,4,2 4,24,2 (q).
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/13289
Subject Headings
Mathematical statistics, Algebra, Abstract, Abelian groups
Format
Document (PDF)
Algebraic and combinatorial aspects of group factorizations
Title
Algebraic and combinatorial aspects of group factorizations.
Creator
Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
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Date Issued
2008
PURL
http://purl.flvc.org/FAU/107805
Subject Headings
Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
Format
Document (PDF)
Unique decomposition of direct sums of ideals
Title
Unique decomposition of direct sums of ideals.
Creator
Ay, Basak., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one-dimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the Krull-Schmidt property for direct sums of torsion-free rank one modules for a reduced local commutative Noetherian one-dimensional ring R.
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Date Issued
2010
PURL
http://purl.flvc.org/FAU/2683133
Subject Headings
Algebraic number theory, Modules (Algebra), Noetherian rings, Commutative rings, Algebra, Abstract
Format
Document (PDF)
Minimal zero-dimensional extensions
Title
Minimal zero-dimensional extensions.
Creator
Chiorescu, Marcela, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
The structure of minimal zero-dimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a one-to-one correspondence between isomorphism classes of minimal zero-dimensional extensions of R and sets M, where the elements of M are...
Show moreThe structure of minimal zero-dimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a one-to-one correspondence between isomorphism classes of minimal zero-dimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zero-dimensional extensions of general ZPI-rings.
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Date Issued
2009
PURL
http://purl.flvc.org/FAU/210447
Subject Headings
Algebra, Abstract, Noetherian rings, Commutative rings, Modules (Algebra), Algebraic number theory
Format
Document (PDF)
Solace: Intimately Remembered Places
Title
Solace: Intimately Remembered Places.
Creator
Francoeur, Michele, Prusa, Carol, Florida Atlantic University, Dorothy F. Schmidt College of Arts and Letters, Department of Visual Arts and Art History
Abstract/Description
The culmination of my graduate research and investigations is my thesis exhibition Solace; Intimately Remembered Places. This body of paintings is a visual representation of land, water and flora that focuses on my abstraction of nature to extract essential elements that expresses my deep connection to a specific time and place, layered with associated memories. By revisiting a landscape over a sustained period of time, I developed a personal visual vocabulary to communicate the essential...
Show moreThe culmination of my graduate research and investigations is my thesis exhibition Solace; Intimately Remembered Places. This body of paintings is a visual representation of land, water and flora that focuses on my abstraction of nature to extract essential elements that expresses my deep connection to a specific time and place, layered with associated memories. By revisiting a landscape over a sustained period of time, I developed a personal visual vocabulary to communicate the essential abstract forms of nature and record the subtle nuances of color, light, shape, texture, positive and negative space to evoke a particular time and place. I expanded my painting techniques through the addition of a laser cutter. Rooted in a background of graphic design, my thesis also incorporated and included a book form using similar strategies.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004971, http://purl.flvc.org/fau/fd/FA00004961
Subject Headings
Dissertations, Academic -- Florida Atlantic University, Painting--Exhibitions., Art, Abstract., Artists' books., Etching.
Format
Document (PDF)
Modeling multiple abstraction levels in SoC using SystemC
Title
Modeling multiple abstraction levels in SoC using SystemC.
Creator
Jillellamudi, Haritha., Florida Atlantic University, Shankar, Ravi
Abstract/Description
Technological advances are providing us with the capability to integrate more and more functionality into a single chip. This is leading to a new design paradigm, System On a Chip (SoC). SoC design brings with it new challenges and difficulties. Managing these challenges and complexity necessitate modeling of systems at a hierarchy of abstraction levels starting from System Level down to Register Transfer Level. Using a single language across all these levels would ensure that the models are...
Show moreTechnological advances are providing us with the capability to integrate more and more functionality into a single chip. This is leading to a new design paradigm, System On a Chip (SoC). SoC design brings with it new challenges and difficulties. Managing these challenges and complexity necessitate modeling of systems at a hierarchy of abstraction levels starting from System Level down to Register Transfer Level. Using a single language across all these levels would ensure that the models are consistent and error-free. SystemC is one such language that has the infrastructure for specifying the design at System level, Behavioral level and RT levels of abstraction. This thesis showcases the same using two design examples---Simplex Data Protocol and General Purpose Timer (GPT) peripheral. Coding style and level of detailing at different levels are shows. Process of refining from one level to another is illustrated. GPT peripheral module designed in this thesis work can be further reused as a timer library component in system architectures.
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Date Issued
2003
PURL
http://purl.flvc.org/fcla/dt/13064
Subject Headings
Systems on a chip, Abstraction, C++ (Computer program language), System design
Format
Document (PDF)
survey of object-oriented features in SQL3
Title
A survey of object-oriented features in SQL3.
Creator
Wu, Zaiwu., Florida Atlantic University, Solomon, Martin K., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
This thesis, based on (ISO/ANSI) X3H2-93-091 Working Draft Database Language SQL (SQL3) (Melton, 1993, 1994), systematically specifies the characteristics and manipulation of object-oriented techniques in SQL3. An essential difference between SQL3 and the previous SQL standards lies in the fact that the abstract data type (ADT) facility supported in SQL3 causes SQL3 to become an extended relational data model rather than a "pure" relational data model. This master's thesis focuses on the...
Show moreThis thesis, based on (ISO/ANSI) X3H2-93-091 Working Draft Database Language SQL (SQL3) (Melton, 1993, 1994), systematically specifies the characteristics and manipulation of object-oriented techniques in SQL3. An essential difference between SQL3 and the previous SQL standards lies in the fact that the abstract data type (ADT) facility supported in SQL3 causes SQL3 to become an extended relational data model rather than a "pure" relational data model. This master's thesis focuses on the careful examination and explication of ADTs and the corresponding families--type templates as they are used in SQL3. These topics involve four aspects: (1) general concepts and technologies in object-oriented data models, (2) the definition of ADTs and their advantages, (3) the manipulation of ADTs in SQL3, including type templates (e.g., distinct types, explicit ADTs, user-defined type templates, standard type templates) and collection types, (4) "tables of ADTs" (row types with table), and (5) conclusions and challenges.
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Date Issued
1994
PURL
http://purl.flvc.org/fcla/dt/15044
Subject Headings
Abstract data types (Computer science), Object-oriented programming (Computer science), Database management, SQL (Computer program language)
Format
Document (PDF)