Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Keyword
-
- Math (3)
- Coalgebra (2)
- Modal logic (2)
- Algebra (1)
- Calculus (1)
-
- Cauchy transforms (1)
- College freshmen (1)
- Common cyclic vector (1)
- Descriptive general frames (1)
- Educational testing (1)
- Finite Dirichlet integral (1)
- First year students (1)
- Graded rings (1)
- Holomorphic functions (1)
- Kripke polynomial functors (1)
- L_\infty-algebra (1)
- Lie 2-algebra (1)
- Lie algebra cohomology (1)
- Mathematics achievement (1)
- Mathematics education (1)
- Mathematics instruction (1)
- Merrimack College (1)
- Modal expansion (1)
- Neutrosophic algebraic structures (1)
- Neutrosophic logic (1)
- Neutrosophic models (1)
- Norm and weak topologies (1)
- Placement (1)
- Primitive ideals (1)
- Scores (1)
Articles 1 - 10 of 10
Full-Text Articles in Algebra
Primitive Ideals Of Semigroup Graded Rings, Hema Gopalakrishnan
Primitive Ideals Of Semigroup Graded Rings, Hema Gopalakrishnan
Mathematics Faculty Publications
Prime ideals of strong semigroup graded rings have been characterized by Bell, Stalder and Teply for some important classes of semigroups. The prime ideals correspond to certain families of ideals of the component rings called prime families. In this paper, we define the notion of a primitive family and show that primitive ideals of such rings correspond to primitive families of ideals of the component rings.
Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski
Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski
Mathematics Faculty Publications
A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult …
Preface, Thomas Hildebrandt, Alexander Kurz
Preface, Thomas Hildebrandt, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.
Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg
Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg
Department of Math & Statistics Faculty Publications
In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.
Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen
Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen
Department of Math & Statistics Faculty Publications
If μis a finite compactly supported measure on C, then the set Sμ of multiplication operators Mᵩ : L2 (μ) --> L2 (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L2 (μ) In this paper, we explore the question as to whether or not Sμ has a common cyclic vector
The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson
The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson
Department of Math & Statistics Faculty Publications
This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.
Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson
Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson
Engineering Faculty Articles and Research
With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T-coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T, we construct an endofunctor L such that L-algebras provide a sound and complete (algebraic) semantics of the logic. We show that if L is dual to T, then soundness and completeness of the algebraic semantics immediately yield the …
Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano
Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
In this paper we construct a setting in which the question of when a logic supports a classical modal expansion can be made precise. Given a fully selfextensional logic S, we find sufficient conditions under which the Vietoris endofunctor V on S-referential algebras can be defined and we propose to define the modal expansions of S as the logic that arises from the V-coalgebras. As an example, we also show how the Vietoris endofunctor on referential algebras extends the Vietoris endofunctor on Stone spaces. From another point of view, we examine when a category of ‘spaces’ (X,A), ie sets X …
Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy
Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit …
Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans
Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans
Mathematics Faculty Works
The theory of Lie algebras can be categorified starting from a new notion of `2-vector space', which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, `linear functors' as morphisms and `linear natural transformations' as 2-morphisms. We define a `semistrict Lie 2-algebra' to be a 2-vector space L equipped with a skew-symmetric bilinear functor [ . , . ] : L x L -> L satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its …