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Squared Bessel Process With Delay, Harry Randolph Hughes, Pathiranage Lochana Siriwardena

Articles and Preprints

We discuss a generalization of the well known squared Bessel process with real nonnegative parameter $\delta$ by introducing a predictable almost everywhere positive process $\gamma(t,\omega)$ into the drift and diffusion terms. The resulting generalized process is nonnegative with instantaneous reflection at zero when $\delta$ is positive. When $\delta$ is a positive integer, the process can be constructed from $\delta$-dimensional Brownian motion. In particular, we consider $\gamma_t = X_{t-\tau}$ which makes the process a solution of a stochastic delay differential equation with a discrete delay. The solutions of these equations are constructed in successive steps on time intervals of length $\tau$. …

Pac Learning, Vc Dimension, And The Arithmetic Hierarchy, Wesley Calvert

Articles and Preprints

No abstract provided.

Feedback Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall

Articles and Preprints

The problem of feedback linearizability of systems in feedforward form is addressed and an algorithm providing explicit coordinates change and feedback given. At each step, the algorithm replaces the involutive conditions of feedback linearization by some, easily checkable. We also reconsider type II subclass of linearizable strict feedforward systems introduced by Krstic and we show that it constitutes the only linearizable among the class of quasilinear strict feedforward systems. Our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system among others. We illustrate by few examples including the VTOL.

On K-Minimum And M-Minimum Edge-Magic Injections Of Graphs, John P. Mcsorley, John A. Trono

Articles and Preprints

An edge-magic total labelling (EMTL) of a graph G with n vertices and e edges is an injection λ:V(G) ∪ E(G)→[n+e], where, for every edge uv ∈ E(G), we have wt_λ(uv)=k_λ, the magic sum of λ. An edge-magic injection (EMI) μ of G is an injection μ : V(G) ∪ E(G) → N with magic sum k_μ and largest label m_μ. For a graph G we define and study the …

Analytic Normal Forms And Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek

Articles and Preprints

This paper deals with the problem of convergence of normal forms of control systems. We identify a $n$-dimensional subclass of control systems, called \emph{special strict feedforward form}, shortly (SSFF), possessing a normal form which is a smooth (resp. analytic) counterpart of the formal normal form of Kang. We provide a constructive algorithm and illustrate by several examples including the Kapitsa pendulum and the Cart-Pole system. The second part of the paper is concerned about symmetries of single-input control systems. We show that any symmetry of a smooth system in special strict feedforward form is conjugated to a \emph{scaling translation} and …

Descent Construction For Gspin Groups: Main Results And Applications, Joseph Hundley, Eitan Sayag

Articles and Preprints

The purpose of this note is to announce an extension of the descent method of Ginzburg, Rallis, and Soudry to the setting of essentially self dual representations. This extension of the descent construction provides a complement to recent work of Asgari and Shahidi [AS06] on the generic transfer for general Spin groups as well as to the work of Asgari and Raghuram [A-R] on cuspidality of the exterior square lift for representations of GL4. Complete proofs of the results announced in the present note will appear in our forthcoming article(s).

Trace Forms Over Finite Fields Of Characteristic 2 With Prescribed Invariants, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

Norm Principles For Forms Of Higher Degree Permitting Composition, Robert W. Fitzgerald, Susanne Pumplün

Articles and Preprints

Let F be a field of characteristic 0 or greater than d. Scharlau’s norm principle holds for finite field extensions K over F, for certain forms φ of degree d over F which permit composition.

Invariants Of Trace Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

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.

Anomaly Graphs And Champions, John Mcsorley, Walter D. Wallis, Carey E. Priebe

Articles and Preprints

No abstract provided.

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.

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.

Comment On “The Expectation Of Independent Domination Number Over Random Binary Trees”, John Mcsorley, Lane Clark

Articles and Preprints

No abstract provided.

The Adjoint L-Function For Gl5, David Ginzburg, Joseph Hundley

Articles and Preprints

We describe two new Eulerian Rankin-Selberg integrals, using the same Eisenstein series defined on the group E₈, and cuspidal representations from GL₅ and GSpin₁₁, respectively. Connections with past work of Ginzburg, Bump-Ginzburg, Jiang-Rallis and others are described. We give some details of how to relate our two integrals via formal manipulations.

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.

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 …

Highly Degenerate Quadratic Forms Over F2, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

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 N_G[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 N_G [u] ⊆ N_G [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if N_H[u] ≠ N_H[v] when u ≠ v, for all u and v ∈ V (H).

In this paper we …

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 Factorizations Of Cyclotomic And Dickson Polynomials Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

We give, over a finite field F_q, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3·2ⁿ, the Dickson polynomials of the first kind of order 3·2ⁿ and the Dickson polynomials of the second kind of order 3·2ⁿ  − 1.

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

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

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

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 C^k-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 …

A New Tower Of Rankin-Selberg Integrals, David Ginzburg, Joseph Hundley

Articles and Preprints

We recall the notion of a tower of Rankin-Selberg integrals, and two known towers, making observations of how the integrals within a tower may be related to one another via formal manipulations, and offering a heuristic for how the L-functions should be related to one another when the integrals are related in this way. We then describe three new integrals in a tower on the group E₆, and find out which L-functions they represent. The heuristics also predict the existence of a fourth integral.

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.

A Stochastic Calculus For Systems With Memory, Feng Yan, Salah-Eldin A. Mohammed

Articles and Preprints

For a given stochastic process X, its segment X_t 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

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

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’ C_p, can also be used for 1D models. Graphical aids for variable selection are also provided.