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Articles 1 - 9 of 9
Full-Text Articles in Mathematics
Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Faculty Publications
No abstract provided.
How To Increase The Ability Of A Student To Learn, Srinivas R. Chakravarthy
How To Increase The Ability Of A Student To Learn, Srinivas R. Chakravarthy
Industrial & Manufacturing Engineering Presentations And Conference Materials
An instructor is always challenged when covering the materials in a course (according to the syllabus) and at the same time making sure that all students have the opportunity to learn and understand the materials presented in the classroom. In this paper we will present some ideas and tools that enable one to try to achieve a balance. These are based on the author’s experience and perspective in teaching deterministic and stochastic operations research courses.
Quantization With Knowledge Base Applied To Geometrical Nesting Problem, Grzegorz Chmaj, Leszek Koszalka
Quantization With Knowledge Base Applied To Geometrical Nesting Problem, Grzegorz Chmaj, Leszek Koszalka
Electrical & Computer Engineering Faculty Research
Nesting algorithms deal with placing two-dimensional shapes on the given canvas. In this paper a binary way of solving the nesting problem is proposed. Geometric shapes are quantized into binary form, which is used to operate on them. After finishing nesting they are converted back into original geometrical form. Investigations showed, that there is a big influence of quantization accuracy for the nesting effect. However, greater accuracy results with longer time of computation. The proposed knowledge base system is able to strongly reduce the computational time.
Preface, Thomas Hildebrandt, Alexander Kurz
Preface, Thomas Hildebrandt, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.
Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford
Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford
Publications
The article focuses on the use of standards-based teaching and learning that has been gaining significant attention in the education world. State and national associations now base their specific subject area or discipline solely on standards, i.e., International Technology Education Association (ITEA), National Council of Teachers of Mathematics (NCTM), National Science Education Association (NSEA). Moreover, at the public school level, state boards of education are holding school districts accountable for teaching standards-based curricula. It is with the latter definition in mind that the authors created a standards-based, integrated technology and mathematics lesson using the design and construction of stair systems.
Advances And Applications Of Dezert-Smarandache Theory (Dsmt), Vol. 1, Florentin Smarandache, Jean Dezert
Advances And Applications Of Dezert-Smarandache Theory (Dsmt), Vol. 1, Florentin Smarandache, Jean Dezert
Branch Mathematics and Statistics Faculty and Staff Publications
The Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning is a natural extension of the classical Dempster-Shafer Theory (DST) but includes fundamental differences with the DST. DSmT allows to formally combine any types of independent sources of information represented in term of belief functions, but is mainly focused on the fusion of uncertain, highly conflicting and imprecise quantitative or qualitative sources of evidence. DSmT is able to solve complex, static or dynamic fusion problems beyond the limits of the DST framework, especially when conflicts between sources become large and when the refinement of the frame of the problem under consideration …
On The Empirical Balanced Truncation For Nonlinear Systems, Marissa Condon, Rossen Ivanov
On The Empirical Balanced Truncation For Nonlinear Systems, Marissa Condon, Rossen Ivanov
Articles
Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.
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 …