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Full-Text Articles in Physical Sciences and Mathematics
A Remark On Conservative Diffeomorphisms, Jairo Bochi, Bassam R. Fayad, Enrique Pujals
A Remark On Conservative Diffeomorphisms, Jairo Bochi, Bassam R. Fayad, Enrique Pujals
Publications and Research
Abstract:
We show that a stably ergodic diffeomorphism can be C1 approximated by a diffeomorphism having stably non-zero Lyapunov exponents.
Résumé:
On montre qu'un difféomorphisme stablement ergodique peut être C1 approché par un difféomorphisme ayant des exposants de Lyapunov stablement non-nuls.
Intersecting Circles And Their Inner Tangent Circle, Max Tran
Intersecting Circles And Their Inner Tangent Circle, Max Tran
Publications and Research
We derive the general equation for the radius of the inner tangent circle that is associated with three pairwise intersecting circles. We then look at three special cases of the equation.
Infinitely Often Dense Bases And Geometric Structure Of Sumsets, Jaewoo Lee
Infinitely Often Dense Bases And Geometric Structure Of Sumsets, Jaewoo Lee
Dissertations, Theses, and Capstone Projects
We'll discuss two problems related to sumsets.
Nathanson constructed bases of integers with prescribed representation functions, then asked how dense bases for integers can be in such cases. Let A(-x, x) be the number of elements of A whose absolute value is less than or equal to x, then it's easy to see that A(-x, x) << x1/2 if its representation function is bounded, giving us a general upper bound. Chen constructed unique representation bases for integers with A(-x, x) ≥ x1/2-epsilon infinitely often. In the first chapter, we'll construct bases for integers with a prescribed representation function with A(-x, x) > x1/2/&phis;(x) infinitely often where &phis;(x) is any nonnegative real-valued function which tends to infinity.
In the second chapter, we'll see how sumsets appear geometrically. Assume A is a finite set of lattice points and h*D=h˙x:x∈conv A is a full dimensional polytope. Then we'll see …
Countable Short Recursively Saturated Models Of Arithmetic, Erez Shochat
Countable Short Recursively Saturated Models Of Arithmetic, Erez Shochat
Dissertations, Theses, and Capstone Projects
Short recursively saturated models of arithmetic are exactly the elementary initial segments of recursively saturated models of arithmetic. Since any countable recursively saturated model of arithmetic has continuum many elementary initial segments which are already recursively saturated, we turn our attention to the (countably many) initial segments which are not recursively saturated. We first look at properties of countable short recursively saturated models of arithmetic and show that although these models cannot be cofinally resplendent (an expandability property slightly weaker than resplendency), these models have non-definable expansions which are still short recursively saturated.