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Articles 1 - 30 of 113
Full-Text Articles in Physical Sciences and Mathematics
2016 Abstract Book, Undergraduate Creative Activities And Research Forum
2016 Abstract Book, Undergraduate Creative Activities And Research Forum
Undergraduate Creative Activities and Research Forum Abstract Books
This booklet contains all the abstracts from the 2016 forum held at Southern Illinois University Carbondale. Coordinated by the Center for Undergraduate Research and Creative Activities, a unit in the Office of the Vice Chancellor for Research.
Trace Forms Over Finite Fields Of Characteristic 2 With Prescribed Invariants, Robert W. Fitzgerald
Trace Forms Over Finite Fields Of Characteristic 2 With Prescribed Invariants, Robert W. Fitzgerald
Articles and Preprints
No abstract provided.
Stochastic Dynamical Systems In Infinite Dimensions, Salah-Eldin A. Mohammed
Stochastic Dynamical Systems In Infinite Dimensions, Salah-Eldin A. Mohammed
Articles and Preprints
We study the local behavior of infinite-dimensional stochastic semiflows near hyperbolic equilibria. The semiflows are generated by stochastic differential systems with finite memory, stochastic evolution equations and semilinear stochastic partial differential equations.
Factoring Families Of Positive Knots On Lorenz-Like Templates, Michael C. Sullivan
Factoring Families Of Positive Knots On Lorenz-Like Templates, Michael C. Sullivan
Articles and Preprints
We show that for m and n positive, composite closed orbits realized on the Lorenz-like template L(m, n) have two prime factors, each a torus knot; and that composite closed orbits on L(−1,−1) have either two for three prime factors, two of which are torus knots.
Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall
Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall
Miscellaneous (presentations, translations, interviews, etc)
We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow …
Random Dynamics And Memory: Structure Within Chaos? (Maa Invited Address / David Blackwell Lecture), Salah-Eldin A. Mohammed
Random Dynamics And Memory: Structure Within Chaos? (Maa Invited Address / David Blackwell Lecture), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
On Linearizability Of Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
On Linearizability Of Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
In this paper we address the problem of linearizability of systems in strict feedforward form. We provide an algorithm, along with explicit transformations, that linearizes a system by change of coordinates when some easily checkable conditions are met. Those conditions turn out to be necessary and sufficient, that is, if one fails the system is not linearizable. We revisit type I and type II classes of linearizable strict feedforward systems provided by Krstic in [6] and illustrate our algorithm by various examples mostly taken from [5], [6].
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow
Articles and Preprints
We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
Multiplicative Properties Of Integral Binary Quadratic Forms, A. G. Earnest, Robert W. Fitzgerald
Multiplicative Properties Of Integral Binary Quadratic Forms, A. G. Earnest, Robert W. Fitzgerald
Articles and Preprints
In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a k-linear mapping from (Z2)k to Z2. In the case k = 2, this resolves a conjecture of Aicardi and Timorin.
Numerics Of Stochastic Systems With Memory (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed
Numerics Of Stochastic Systems With Memory (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang
The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang
Articles and Preprints
In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …
A Delayed Option Pricing Formula (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed
A Delayed Option Pricing Formula (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
A Delayed Option Pricing Formula (University Of Manchester Probability Seminar), Salah-Eldin A. Mohammed
A Delayed Option Pricing Formula (University Of Manchester Probability Seminar), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Semilinear Spdes As Dynamical Systems (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed
Semilinear Spdes As Dynamical Systems (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Anticipating Semilinear Spdes (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed
Anticipating Semilinear Spdes (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Closed-Neighborhood Anti-Sperner Graphs, John P. Mcsorley, Alison Marr, Thomas D. Porter, Walter D. Wallis
Closed-Neighborhood Anti-Sperner Graphs, John P. Mcsorley, Alison Marr, Thomas D. Porter, Walter D. Wallis
Articles and Preprints
For a simple graph G let NG[u] denote the closed-neighborhood of vertex u ∈ V (G). Then G is closed-neighborhood anti-Sperner (CNAS) if for every u there is a v ∈ V (G)\{u} with NG [u] ⊆ NG [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if NH[u] ≠ NH[v] when u ≠ v, for all u and v ∈ V (H).
In this paper we …
Anticipating Semilinear Spdes (International Conference Stochastic Analysis And Stochastic Geometry), Salah-Eldin A. Mohammed
Anticipating Semilinear Spdes (International Conference Stochastic Analysis And Stochastic Geometry), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Anticipating Semilinear Spdes (International Conference Modern Perpspectives In Real And Stochastic Analysis), Salah-Eldin A. Mohammed
Anticipating Semilinear Spdes (International Conference Modern Perpspectives In Real And Stochastic Analysis), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino
Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino
Articles and Preprints
We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
We show that any symmetry of a smooth strict feedforward system is conjugated to a scaling translation and any 1-parameter family of symmetries to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We deduce, in accordance with our previous work, that a smooth system is feedback equivalent to a strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry whose flow is conjugated to a 1- parameter families of scaling translations and, …
Random Dynamics (Siuc 2006 Outstanding Scholar Public Lecture), Salah-Eldin A. Mohammed
Random Dynamics (Siuc 2006 Outstanding Scholar Public Lecture), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
No abstract provided.
Large Deviations For Stochastic Systems With Memory, Salah-Eldin A. Mohammed, Tusheng Zhang
Large Deviations For Stochastic Systems With Memory, Salah-Eldin A. Mohammed, Tusheng Zhang
Articles and Preprints
We establish a large deviations principle for stochastic delay equations driven by small multiplicative white noise. Both upper and lower large deviations estimates are obtained.
Periodic Prime Knots And Toplogically Transitive Flows On 3-Manifolds, William Basener, Michael C. Sullivan
Periodic Prime Knots And Toplogically Transitive Flows On 3-Manifolds, William Basener, Michael C. Sullivan
Articles and Preprints
Suppose that φ is a nonsingular (fixed point free) C1 flow on a smooth closed 3-dimensional manifold M with H2(M)=0. Suppose that φ has a dense orbit. We show that there exists an open dense set N ⊆ M such that any knotted periodic orbit which intersects N is a nontrivial prime knot.
Bass Series For Small Witt Rings, Robert W. Fitzgerald
Bass Series For Small Witt Rings, Robert W. Fitzgerald
Articles and Preprints
No abstract provided.
The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao
The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao
Articles and Preprints
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2.
In Part 1, we prove general existence and compactness theorems for Ck-cocycles of semilinear see’s and spde’s. Our results cover a large class of semilinear see’s as well as certain semilinear spde’s with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the …
Factoring Positive Braids Via Branched Manifolds, Michael C. Sullivan
Factoring Positive Braids Via Branched Manifolds, Michael C. Sullivan
Articles and Preprints
We show that a positive braid is composite if and only if the factorization is "visually obvious" by placing the braid k in a specially constructed smooth branched 2- manifold B(k) and studying how a would-be cutting sphere meets B(k). This gives an elementary proof of a theorem due to Peter Cromwell.
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
Recently we proved that any smooth (resp. analytic) strict feedforward system can be brought into its normal form via a smooth (resp. analytic) feedback transformation. This will allow us to identify a subclass of strict feedforward systems, called systems in special strict feedforward form, shortly (SSFF), possessing a canonical form which is an analytic counterpart of the formal canonical form. For (SSFF)-systems, the step-by-step normalization procedure of Kang and Krener leads to smooth (resp. convergent analytic) normalizing feedback transformations. We illustrate the class of (SSFF)-systems by a model of an inverted pendulum on a cart.
A Stochastic Calculus For Systems With Memory, Feng Yan, Salah-Eldin A. Mohammed
A Stochastic Calculus For Systems With Memory, Feng Yan, Salah-Eldin A. Mohammed
Articles and Preprints
For a given stochastic process X, its segment Xt at time t represents the "slice" of each path of X over a fixed time-interval [t-r, t], where r is the length of the "memory" of the process. Segment processes are important in the study of stochastic systems with memory (stochastic functional differential equations, SFDEs). The main objective of this paper is to study non-linear transforms of segment processes. Towards this end, we construct a stochastic integral with respect to the Brownian segment process. The difficulty in this construction is the fact that the …
Double Arrays, Triple Arrays And Balanced Grids, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis, Joseph L. Yucas
Double Arrays, Triple Arrays And Balanced Grids, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis, Joseph L. Yucas
Articles and Preprints
Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.
Variable Selection For 1d Regression Models, David J. Olive, Douglas M. Hawkins
Variable Selection For 1d Regression Models, David J. Olive, Douglas M. Hawkins
Articles and Preprints
Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a broad class that includes generalized linear models. We show that existing variable selection algorithms, originally meant for multiple linear regression and based on ordinary least squares and Mallows’ Cp, can also be used for 1D models. Graphical aids for variable selection are also provided.