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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
The Projectile Inside The Loop, Gabriele U. Varieschi
The Projectile Inside The Loop, Gabriele U. Varieschi
Physics Faculty Works
No abstract provided.
Gravitationally Induced Quantum Superposition Reduction With Large Extra Dimensions, Jonas R. Mureika
Gravitationally Induced Quantum Superposition Reduction With Large Extra Dimensions, Jonas R. Mureika
Physics Faculty Works
A gravity-driven mechanism (``objective reduction'') proposed to explain quantum state reduction is analyzed in light of the possible existence of large extra dimensions in the ADD scenario. By calculating order-of-magnitude estimates for nucleon superpositions, it is shown that if the mechanism at question is correct, constraints may be placed on the number and size of extra dimensions. Hence, measurement of superposition collapse times ({\it e.g.} through diffraction or reflection experiments) could represent a new probe of extra dimensions. The influence of a time-dependent gravitational constant on the gravity-driven collapse scheme with and without the presence of extra dimensions is also …
A Sequence Of Polynomials For Approximating Arctangent, Herbert A. Medina
A Sequence Of Polynomials For Approximating Arctangent, Herbert A. Medina
Mathematics Faculty Works
No abstract provided.
Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor
Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor
Mathematics Faculty Works
We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S3. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S3.
Intersection Graphs For String Links, Blake Mellor
Intersection Graphs For String Links, Blake Mellor
Mathematics Faculty Works
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show that these weight systems are related to the weight systems induced by the Conway and Homfly polynomials.
Tree Diagrams For String Links, Blake Mellor
Tree Diagrams For String Links, Blake Mellor
Mathematics Faculty Works
In previous work, the author defined the intersection graph of a chord diagram associated with string links (as in the theory of finite type invariants). In this paper, we classify the trees which can be obtained as intersection graphs of string link diagrams.
Chord Diagrams And Gauss Codes For Graphs, Thomas Fleming, Blake Mellor
Chord Diagrams And Gauss Codes For Graphs, Thomas Fleming, Blake Mellor
Mathematics Faculty Works
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of planar graphs and their intersection graphs, and prove some basic results. Then, as an application, we will introduce Gauss codes for immersions of graphs in the plane and give algorithms to determine whether a particular crossing sequence is …
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Mathematics Faculty Works
We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.