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- 1)-coloring; Distance two labeling; Graph labeling; Channel assignment; Generalized Petersen graph (1)
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Articles 1 - 21 of 21
Full-Text Articles in Physical Sciences and Mathematics
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Dr Le Chung Tran
Constructions of square, maximum rate complex orthogonal space-time block codes (CO STBCs) are well known, however codes constructed via the known methods include numerous zeros, which impede their practical implementation. By modifying the Williamson and Wallis-Whiteman arrays to apply to complex matrices, we propose two methods of construction of square, order-4n CO STBCs from square, order-n codes which satisfy certain properties. Applying the proposed methods, we construct square, maximum rate, order-8 CO STBCs with no zeros, such that the transmitted symbols are equally dispersed through transmit antennas. Those codes, referred to as the improved square CO STBCs, have the advantages …
Global Existence Of Some Infinite Energy Solutions For A Perfect Incompressible Fluid, Ralph Saxton, Feride Tiğlay
Global Existence Of Some Infinite Energy Solutions For A Perfect Incompressible Fluid, Ralph Saxton, Feride Tiğlay
Ralph Saxton
This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we obtain an initial value problem for a nonlocal equation. We establish local well-posedness in all dimensions and persistence in time of these solutions for three and higher dimensions. We also examine a weaker class of global solutions.
Effects Of Electrostatic Correlations On Electrokinetic Phenomena, Brian Storey, Martin Bazant
Effects Of Electrostatic Correlations On Electrokinetic Phenomena, Brian Storey, Martin Bazant
Brian Storey
The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order modified Poisson equation is developed that captures the essential features in a simple continuum framework. The model is derived as a gradient approximation for nonlocal electrostatics of interacting effective charges, where the permittivity becomes a differential operator, scaled by a correlation length. The theory is able to capture …
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
Sarah Spence Adams
In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)–f(y)|≥ 2 if xand y are adjacent vertices and |f(x)–f(y)|≥1 if xand y are at distance two. The goal is to …
On An Orthogonal Space-Time-Polarization Block Code, Beata Wysocki, Tadeusz Wysocki, Sarah Adams
On An Orthogonal Space-Time-Polarization Block Code, Beata Wysocki, Tadeusz Wysocki, Sarah Adams
Sarah Spence Adams
Over the past several years, diversity methods such as space, time, and polarization diversity have been successfully implemented in wireless communications systems. Orthogonal space-time block codes efficiently combine space and time diversity, and they have been studied in detail. Polarization diversity has also been studied, however it is usually considered in a simple concatenation with other coding methods. In this paper, an efficient method for incorporating polarization diversity with space and time diversity is studied. The simple yet highly efficient technique is based on extending orthogonal space-time block codes into the quaternion domain and utilizing a description of the dual-polarized …
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Sarah Spence Adams
Constructions of square, maximum rate complex orthogonal space-time block codes (CO STBCs) are well known, however codes constructed via the known methods include numerous zeros, which impede their practical implementation. By modifying the Williamson and Wallis-Whiteman arrays to apply to complex matrices, we propose two methods of construction of square, order-4n CO STBCs from square, order-n codes which satisfy certain properties. Applying the proposed methods, we construct square, maximum rate, order-8 CO STBCs with no zeros, such that the transmitted symbols are equally dispersed through transmit antennas. Those codes, referred to as the improved square CO STBCs, have the advantages …
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
Sarah Spence Adams
The channel-assignment problem involves assigning frequencies represented by nonnegative integers to radio transmitters such that transmitters in close proximity receive frequencies that are sufficiently far apart to avoid interference. In one of its variations, the problem is commonly quantified as follows: transmitters separated bythe smallest unit distance must be assigned frequencies that are at least two apart and transmitters separated by twice the smallest unit distance must be assigned frequencies that are at least one apart. Naturally, thischannel-assignment problem can be modeled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the …
Identifying High-Dimension Subspace Subcodes Of Reed-Solomon Codes, Sarah Adams
Identifying High-Dimension Subspace Subcodes Of Reed-Solomon Codes, Sarah Adams
Sarah Spence Adams
Subspace subcodes of Reed-Solomon (SSRS) codes were introduced by Hattori, McEliece, Solomo, and Lin in the mid-1990s. These authors found a complicated dimension formula and a simple, tight lower bound on thedimension of SSRS codes over F2m. We prove a conjecture of Hattori concerning how to identify subspaces that can be used to build SSRS codes whose dimension exceeds this lower bound.
Quaternion Orthogonal Designs From Complex Companion Designs, Sarah Adams, Jennifer Seberry, Nathaniel Karst, Jonathan Pollack, Tadeusz Wysocki
Quaternion Orthogonal Designs From Complex Companion Designs, Sarah Adams, Jennifer Seberry, Nathaniel Karst, Jonathan Pollack, Tadeusz Wysocki
Sarah Spence Adams
The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–time-polarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build quaternion orthogonal designs on complex variables for any even number of columns. A second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries. This second technique is …
The Final Case Of The Decoding Delay Problem For Maximum Rate Complex Orthogonal Designs, Sarah Adams, Nathaniel Karst, Mathav Murugan
The Final Case Of The Decoding Delay Problem For Maximum Rate Complex Orthogonal Designs, Sarah Adams, Nathaniel Karst, Mathav Murugan
Sarah Spence Adams
Complex orthogonal space-time block codes (COSTBCs) based on generalized complex orthogonal designs (CODs) have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas. It has been shown that for a maximum rate COD with 2m-1 or 2m columns, a lower bound on decoding delay is (m-1 2m) and this delay is achievable when the number of columns is congruent to 0, 1 , or 3 modulo 4. In this paper, the final case is addressed, and it is shown that when the number of columns is congruent to 2 modulo 4, the lower …
The Minimum Decoding Delay Of Maximum Rate Complex Orthogonal Space–Time Block Codes, Sarah Adams, Nathaniel Karst, Jonathan Pollack
The Minimum Decoding Delay Of Maximum Rate Complex Orthogonal Space–Time Block Codes, Sarah Adams, Nathaniel Karst, Jonathan Pollack
Sarah Spence Adams
The growing demand for efficient wireless transmissions over fading channels motivated the development ofspace-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decodingalgorithm while achieving full transmit diversity. The two main research problems for these complex orthogonalspace-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate andthe minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on …
Trajectory Generation In High-Speed, High-Precision Micromilling Using Subdivision Surfaces, Athulan Vijayaraghavan, Angela Sodemann, Aaron Hoover, J. Mayor, David Dornfeld
Trajectory Generation In High-Speed, High-Precision Micromilling Using Subdivision Surfaces, Athulan Vijayaraghavan, Angela Sodemann, Aaron Hoover, J. Mayor, David Dornfeld
Aaron M. Hoover
Motion control in high-speed micromilling processes requires fast, accurate following of a specified curvilinear path. The accuracy with which the path can be followed is determined by the speed at which individual trajectories can be generated and sent to the control system. The time required to generate the trajectory is dependent on the representations used for the curvilinear trajectory path. In this study, we introduce the use of subdivision curves as a method for generating high-speed micromilling trajectories. Subdivision curves are discretized curves which are specified as a series of recursive refinements of a coarse mesh. By applying these recursive …
Optimal Synthesis Of Mite Translinear Loops, Shyam Subramanian, David Anderson, Paul Hasler, Bradley Minch
Optimal Synthesis Of Mite Translinear Loops, Shyam Subramanian, David Anderson, Paul Hasler, Bradley Minch
Bradley Minch
A procedure for synthesizing multiple-input translinear element (MITE) networks that implement a given system of translinear-loop equations (STLE) is presented. The minimum number of MITEs required for implementing the STLE, which is equal to the number of current variables in the STLE, is attained. The number of input gates ofthe MITEs is minimal amongst those MITE networks that satisfy the STLE and have the minimum number of MITEs. The synthesized MITE networks have a unique operating point and, in many cases, the network is guaranteed to be stable in a particular sense. This synthesis procedure exploits the relationship between MITEproduct-of-power-law …
Synthesis Of Static And Dynamic Multiple-Input Translinear Element Networks, Bradley Minch
Synthesis Of Static And Dynamic Multiple-Input Translinear Element Networks, Bradley Minch
Bradley Minch
In this paper, we discuss the process of synthesizing static and dynamic multiple-input translinear element (MITE) networks systematically from high-level descriptions given in the time domain, in terms of static polynomial constraints and algebraic differential equations. We provide several examples, illustrating the process for both static and dynamic system constraints. Although our examples will all involve MITE networks, the early steps of the synthesis process are equally applicable to the synthesis of static and dynamic translinear-loop circuits.
Synthesis Of Dynamic Multiple-Input Translinear Element Networks, Bradley Minch
Synthesis Of Dynamic Multiple-Input Translinear Element Networks, Bradley Minch
Bradley Minch
In this paper, the author discusses an approach to the synthesis of dynamic translinear circuits built from multiple-input translation elements (MITEs). In this method, we realize separately the basic static nonlinearities and dynamic signal-processing functions that when cascaded together, form the system that one wishes to construct. The circuit is then simplified systematically through local transformations that do not alter the behavior of the system. The author illustrates the method by synthesizing a simple nonlinear dynamical system, an RMS-DC converter.
On The Issue Of Decoupled Decoding Of Codes Derived From Quaternion Orthogonal Designs, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
On The Issue Of Decoupled Decoding Of Codes Derived From Quaternion Orthogonal Designs, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
Sarah Spence Adams
Quaternion orthogonal designs (QODs) have been previously introduced as a basis for orthogonal space-time polarization block codes (OSTPBCs). This note will serve to correct statements concerning the optimality of a decoupled maximum-likelihood (ML) decoding algorithm. It will be shown that when compared to coupled decoding, the decoupled decoding is only optimal in certain cases. This raises several open problems concerning the decoding of OSTPBCs.
Modeling The Spread Of Fault In Majority-Based Network Systems: Dynamic Monopolies In Triangular Grids, Sarah Spence Adams, Paul Booth, Denise Troxell, Luke Zinnen
Modeling The Spread Of Fault In Majority-Based Network Systems: Dynamic Monopolies In Triangular Grids, Sarah Spence Adams, Paul Booth, Denise Troxell, Luke Zinnen
Sarah Spence Adams
In a graph theoretical model of the spread of fault in distributed computing and communication networks, each element in the network is represented by a vertex of a graph where edges connect pairs of communicating elements, and each colored vertex corresponds to a faulty element at discrete time periods. Majority-based systems have been used to model the spread of fault to a certain vertex by checking for faults within a majority of its neighbors. Our focus is on irreversible majority processes wherein a vertex becomes permanently colored in a certain time period if at least half of its neighbors were …
Multiple Periodic Solutions For A Nonlinear Suspension Bridge Equation, Lisa Humphreys, P. Mckenna
Multiple Periodic Solutions For A Nonlinear Suspension Bridge Equation, Lisa Humphreys, P. Mckenna
Lisa D Humphreys
We investigate nonlinear oscillations in a fourth-order partial differential equation which models a suspension bridge. Previous work establishes multiple periodic solutions when a parameter exceeds a certain eigenvalue. In this paper, we use Leray Schauder degree theory to prove that if the parameter is increased further, beyond a second eigenvalue, then additional solutions are created.
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment f of nonnegative integers to the vertices of G such that if vertices x and y are adjacent, |f(x)−f(y)|≥2, and if x and y are at distance two, |f(x)−f(y)|≥1. The λ-number of Gis the minimum span over all L(2,1)-labelings of G. A generalized Petersen graph (GPG) of order n consists of two disjoint copies of cycles on n vertices together with a perfect matching between the two vertex sets. By …
On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton
On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton
Ralph Saxton
This paper examines the effect of damping on a nonstrictly hyperbolic 2x2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.
On The Strengthening Of Topological Signals In Persistent Homology Through Vector Bundle Based Maps, E. Hanson, F. Motta, C. Peterson, Lori Ziegelmeier
On The Strengthening Of Topological Signals In Persistent Homology Through Vector Bundle Based Maps, E. Hanson, F. Motta, C. Peterson, Lori Ziegelmeier
Lori Beth Ziegelmeier
No abstract provided.