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Continuous reducibility for the real line
, 2012
"... We study Borel subsets of the real line up to continuous reducibility. We firstly show that every quasiorder of size ω1 embeds into the quasiorder of Borel subsets of the real line up to continuous reducibility. We then prove that at least all the types of gaps in P(ω)/fin appear and determine sev ..."
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Cited by 3 (1 self)
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We study Borel subsets of the real line up to continuous reducibility. We firstly show that every quasiorder of size ω1 embeds into the quasiorder of Borel subsets of the real line up to continuous reducibility. We then prove that at least all the types of gaps in P(ω)/fin appear and determine
ON THE ORDERING OF THE NONSTANDARD REAL LINE
"... Abstract. We investigate ordertheoretic properties of the nonstandard real line, by isolating the basic ordertypes involved, and the possible relations among them. We focus on orderisomorphisms between the infinitesimals, the infinites, and the whole hyperreal line. We also compute the main cardi ..."
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Abstract. We investigate ordertheoretic properties of the nonstandard real line, by isolating the basic ordertypes involved, and the possible relations among them. We focus on orderisomorphisms between the infinitesimals, the infinites, and the whole hyperreal line. We also compute the main
Subsets of the real line
 Wydawnictwo Uniwersytetu Lodzkiego, Lodz
, 1995
"... (Communicated by Alan Dow) Abstract. In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpiński. We discuss the number of translations a single subset of the reals may have. Later we discuss almost invarian ..."
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Cited by 3 (0 self)
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(Communicated by Alan Dow) Abstract. In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpiński. We discuss the number of translations a single subset of the reals may have. Later we discuss almost
RealTime Obstacle Avoidance for Manipulators and Mobile Robots
 INT. JOUR OF ROBOTIC RESEARCH
, 1986
"... This paper presents a unique realtime obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, traditionally considered a high level planning problem, can be effectively distributed between different levels of control, al ..."
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Cited by 1345 (28 self)
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This paper presents a unique realtime obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, traditionally considered a high level planning problem, can be effectively distributed between different levels of control, al
On the Subcontinua of a Real Line
, 2003
"... In [11] we showed that the only proper subcontinua of the simple closed curve are arcs and single points. In this article we prove that the only proper subcontinua of the real line are closed intervals. We introduce some auxiliary notions such as]a,b[Q,]a,b[IQ – intervals consisting of rational an ..."
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Cited by 8 (5 self)
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In [11] we showed that the only proper subcontinua of the simple closed curve are arcs and single points. In this article we prove that the only proper subcontinua of the real line are closed intervals. We introduce some auxiliary notions such as]a,b[Q,]a,b[IQ – intervals consisting of rational
Induction And Recursion On The Real Line
"... We characterize the real line by properties similar to the socalled Peano axioms for natural numbers. These properties include an induction principle and a corresponding recursion scheme. The recursion scheme allows us to define functions such as addition, multiplication, exponential, logarithm, s ..."
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Cited by 11 (9 self)
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We characterize the real line by properties similar to the socalled Peano axioms for natural numbers. These properties include an induction principle and a corresponding recursion scheme. The recursion scheme allows us to define functions such as addition, multiplication, exponential, logarithm
Wavelets on Closed Subsets of the Real Line
 in: Topics in the Theory and Applications of Wavelets, L.L. Schumaker and
"... . We construct orthogonal and biorthogonal wavelets on a given closed subset of the real line. We also study wavelets satisfying certain types of boundary conditions. We introduce the concept of "wavelet probing ", which is closely related to our construction of wavelets. This technique al ..."
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Cited by 71 (5 self)
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. We construct orthogonal and biorthogonal wavelets on a given closed subset of the real line. We also study wavelets satisfying certain types of boundary conditions. We introduce the concept of "wavelet probing ", which is closely related to our construction of wavelets. This technique
Betting on the Real Line
"... Abstract. We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mech ..."
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Cited by 11 (8 self)
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Abstract. We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker
Rational Wavelets On The Real Line
, 1998
"... Suppose f k g n k=0 is an orthonormal basis for the function space L n of polynomials or rational functions of degree n with prescribed poles. Suppose n = 2 s and set V s = L n . Then k n (z; w) = P n k=0 k (z) k (w), is a reproducing kernel for V s . For xed w, such reproducing kernels are ..."
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Cited by 3 (2 self)
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;k (z) = l n (z; nk )g n 1 k=0 for an appropriate choice of the parameters f nk g n 1 k=0 where l n = k n+1 k n is the reproducing kernel for W s . These observations form the basic ingredients for a wavelet type of analysis for orthogonal rational functions on the real line with respect
REVERSIBILITY IN THE DIFFEOMORPHISM GROUP OF THE REAL LINE
, 2008
"... An element of a group is said to be reversible if it is conjugate to its inverse. We characterise the reversible elements in the group of diffeomorphisms of the real line, and in the subgroup of order preserving diffeomorphisms. ..."
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Cited by 2 (2 self)
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An element of a group is said to be reversible if it is conjugate to its inverse. We characterise the reversible elements in the group of diffeomorphisms of the real line, and in the subgroup of order preserving diffeomorphisms.
Results 1  10
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