Stochastic Processes Induced By Singular Operators,
2012
Chapman University
Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in …
Interpolating Blaschke Products And Angular Derivatives,
2012
Bucknell University
Interpolating Blaschke Products And Angular Derivatives, Eva A. Gallardo-Gutierrez, Pamela Gorkin
Faculty Journal Articles
We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.
New Topological C-Algebras With Applications In Linear Systems Theory,
2012
Chapman University
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn,
2012
Politecnico di Milano
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn, Fabrizio Colombo, M. E. Luna-Elizarrarás, Irene Sabadini, M. Shapiro, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we develop and extend some techniques introduced in [1] to find integral conditions for the vanishing of the cohomology of open bounded sets in Cn with values in the sheaf of holomorphic functions.
Π/2-Angle Yao Graphs Are Spanners,
2012
Carleton University
Π/2-Angle Yao Graphs Are Spanners, Prosenjit Bose, Mirela Damian, Karim Douïeb, Joseph O'Rourke, Ben Seamone, Michiel Smid, Stefanie Wuhrer
Computer Science: Faculty Publications
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23√ 2). Enroute to this, we also show that the Yao graph Y∞4 in the L∞ metric is a planar spanner with stretch factor 8.
Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves,
2012
Colby College
Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves, Anika Lindemann
Honors Theses
Puzzled by equations in multiple variables for centuries, mathematicians have made relatively few strides in solving these seemingly friendly, but unruly beasts. Currently, there is no systematic method for finding all rational values, that satisfy any equation with degree higher than a quadratic. This is bizarre. Solving these has preoccupied great minds since before the formal notion of an equation existed. Before any sort of mathematical formality, these questions were nested in plucky riddles and folded into folk tales. Because they are so simple to state, these equations are accessible to a very general audience. Yet an astounding amount of …
Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices,
2011
Pomona College
Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Nonparametric Copula Density Estimation In Sensor Networks,
2011
Boise State University
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Mathematics Faculty Publications and Presentations
Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method,
2011
Università del Molise
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza
MPP Published Research
We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …
Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces,
2011
University of Richmond
Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is satisfied in the setting of periodic little-Hölder spaces, provided the coefficients of the differential operator satisfy minimal regularity assumptions.We address parameter-dependent elliptic equations, deriving invertibility and resolvent bounds which lead to results on generation of analytic semigroups. We also demonstrate that the techniques and results of the paper hold for elliptic differential operators with operator-valued coefficients, in the setting of vector-valued functions.
Partial Connectivity In Wireless Sensor Networks,
2011
University of Missouri-St. Louis
Partial Connectivity In Wireless Sensor Networks, Robert Andre Murphy
Dissertations
Given a bounded region of the 2-dimensional plane, a discrete set of nodes is distributed throughout according to a Poisson point process. Given some fixed, finite, real number, two nodes are said to connect and form an edge if their mutual distance is less than this number. Let G be the graph of all such edges over the set of generated nodes and let C be any set of mutually connected nodes. It is shown that there is a critical mutual distance such that at least half of all generated nodes are mutually connected to form a connected cluster. Now, …
Dynamic Appointment Scheduling In Healthcare,
2011
Brigham Young University - Provo
Dynamic Appointment Scheduling In Healthcare, Mckay N. Heasley
Theses and Dissertations
In recent years, healthcare management has become fertile ground for the scheduling theory community. In addition to an extensive academic literature on this subject, there has also been a proliferation of healthcare scheduling software companies in the marketplace. Typical scheduling systems use rule-based analytics that give schedulers advisory information from programmable heuristics such as the Bailey-Welch rule cite{B,BW}, which recommends overbooking early in the day to fill-in potential no-shows later on. We propose a dynamic programming problem formulation to the scheduling problem that maximizes revenue. We formulate the problem and discuss the effectiveness of 3 different algorithms that solve the …
Second-Order Subdifferential Calculus With Applications To Tilt Stability In Optimization,
2011
Wayne State University
Second-Order Subdifferential Calculus With Applications To Tilt Stability In Optimization, Boris S. Mordukhovich, R T. Rockafellar
Mathematics Research Reports
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order sub differential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and …
Bifurcation And Invariant Manifolds Of The Logistic Competition Model,
2011
Trinity University
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi
Mathematics Faculty Research
In this paper we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period doubling bifurcation route to chaos is exhibited via numerical simulations.
Dynamic Server Allocation At Parallel Queues,
2011
Harvey Mudd College
Dynamic Server Allocation At Parallel Queues, Susan E. Martonosi
All HMC Faculty Publications and Research
We explore whether dynamically reassigning servers to parallel queues in response to queue imbalances can reduce average waiting time in those queues. We use approximate dynamic programming methods to determine when servers should be switched, and we compare the performance of such dynamic allocations to that of a pre-scheduled deterministic allocation. Testing our method on both synthetic data and data from airport security checkpoints at Boston Logan International Airport, we find that in situations where the uncertainty in customer arrival rates is significant, dynamically reallocating servers can substantially reduce waiting time. Moreover, we find that intuitive switching strategies that are …
Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students.,
2011
University of Louisville
Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush
Electronic Theses and Dissertations
The purpose of this study was to examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebra-related misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used …
Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method,
2011
University of Haifa
Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
Sequence A054391 in OEIS, which we will denote by an , counts a certain two-pattern avoidance class of the permutations of size n . In this paper, we provide additional combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify six classes of the partitions of size n , all of which have cardinality an and each avoiding two classical patterns. We use both algebraic and combinatorial methods to establish our results. In one apparently more difficult case, to show the result, we make use of the kernel method in solving a system …
The Principle Of Linearized Stability For Size-Structured Population Models,
2011
University of Khartoum
The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma
Applications and Applied Mathematics: An International Journal (AAM)
The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance
Density Dependent Utilities With Transaction Costs,
2011
Louisiana State University
Density Dependent Utilities With Transaction Costs, Eriyoti Chikodza, Julius N Esunge
Communications on Stochastic Analysis
No abstract provided.
Consistent Price Systems For Bounded Processes,
2011
Louisiana State University
Consistent Price Systems For Bounded Processes, Florian Maris, Eric Mbakop, Hasanjan Sayit
Communications on Stochastic Analysis
No abstract provided.
