On asymptotic motions of robot-manipulator in homogeneous space

In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group G of motions. Some kinematic subspaces of the Lie algebra (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are ntroduced and by them asymptotic and geodesic motions are described.     

Three-parametric robot manipulators with parallel rotational axes

The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are introduced without explicit use of the Levi-Civita connection.     

USING FINITE GEOMETRIES TO CONSTRUCT 3-PBIB(2) DESIGNS AND 3-DESIGNS

ＵＳＩＮＧＦＩＮＩＴＥＧＥＯＭＥＴＲＩＥＳＴＯＣＯＮＳＴＲＵＣＴ３－ＰＢＩＢ（２）ＤＥＳＩＧＮＳＡＮＤ３－ＤＥＳＩＧＮＳ￥ＹＡＮＧＢＥＮＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｅｎｇｄｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｅｎｇｄｕ...     

Principal Normal Indicatrices of Closed Space Curves

A theorem due to J. Weiner, which is also proven by B. Solomon, implies that a principal normal indicatrix of a closed space curve with nonvanishing curvature has integrated geodesic curvature zero and contains no subarc with integrated geodesic curvature . We prove that the inverse problem always has solutions if one allows zero and negative curvature of space curves and explain why this not is true if nonvanishing curvature is required. This answers affirmatively an open question asked by W. Fenchel in 1950 under the above assumptions but in general this question is found to be answered to the negative.     

CONVERGENCE OF (0,1,2,3) INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

1. IntroductionThis note deals with convergence of (0,1,2,3) illterpolation on an arbitrary system of nodes.Fisrt we illtroduce some definitions and notations.LetGiven a fiXed even integer m, let Ajk 6 Pm.--1 (the set of polynomials of degree at most mn-- 1)satisfyThen the (0,1,...,m--1) Hermite--Fej6r type illterpolation for f 6 C[--1, 1] is defined byand the (0,1,...,m--1) Hernilte interpolation for f e Cd--'[--1, 1] is defined by(of. [6]). We also need a well known fact:where 11' 11 sta…     

An Extremal Class of Three-Dimensional Hyperbolic Affine Spheres

In analogy to an inequality of Chen [2], Scharlach and co-workers [7] have found a new, optimal inequality for (equi-) affine spheres. We classify those three-dimensional hyperbolic affine spheres for which the corresponding equality is assumed. This complements the classification of the elliptic case [3].     

Convexity and the Average Curvature of Plane Curves

The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set.     

Five-Dimensional Contact SU(2)- and SO(3)-Manifolds and Dehn Twists

In the first part of this paper the five-dimensional contact SO(3)-manifolds are classified up to equivariant coorientation preserving contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifolds with singular orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The standard contact structure on such a manifold gives right-handed Dehn twists, and a second contact structure defined in the article gives left-handed twists. In an appendix we also describe the classification of five-dimensional contact SU(2)-manifolds.     

Bounds on the solution of the time-varying linear matrix differential equation P(t) = AH(t) P(t) + P(t) A(t) + Q(t)

^** Email: pagilla{at}ceat.okstate.edu We derive upper and lower bounds for the trace of the solutionof the time-varying linear matrix differential equation (t)= A^H(t) P(t) + P(t) A(t) + Q(t). A practical numerical exampleis given to verify the bounds. The bounds obtained are usefulsince the considered equation is encountered in a number ofapplications in systems and control theory.     

Results on Maximal Partial Spreads in PG(3, p 3) and on Related Minihypers

This article classifies all {(q + 1), 3, q}-minihypers, small, q = p ^h ₀, h 1, for a prime number p ₀ 7, which arise from a maximal partial spread of deficiency . When q is a third power, the minihyper is the disjoint union of projected PG(5, )'s; when q is a square, also Baer subgeometries PG(3, ) can occur. This leads to a discrete spectrum for the small values of the deficiency of the corresponding maximal partial spreads.     

(1/α)-Self similar α-stable processes with stationary increments

In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the α-stable Lévy motion is the only (1/α)-self-similar α-stable process with stationary increments if 0 < α < 1. We also introduce new classes of (1/α)-self-similar α-stable processes with stationary increments for 1 < α < 2.     

Differential structure of the Thompson components of selfadjoint operators

Different equivalence relations are defined in the set of selfadjoint operators of a Hilbert space in order to extend a very well known relation in the cone of positive operators. As in the positive case, for the equivalence class admits a differential structure, which is compatible with a complete metric defined on . This metric coincides with the Thompson metric when is positive.

     

Position vector of a time-like slant helix in Minkowski 3-space

In this paper, position vector of a time-like slant helix with respect to standard frame of Minkowski space E³₁ is studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary time-like slant helix. In terms of solution, we determine the parametric representation of the slant helices from the intrinsic equations. Thereafter, we apply this method to find the representation of a time-like Salkowski and time-like anti-Salkowski curves as examples of a slant helices, by means of intrinsic equations. Moreover, we present some new characterizations of slant helices and illustrate some examples of our main results.     

Quantum and Integral (Co)Bordisms in Partial Differential Equations

Characterizations of quantum bordisms and integral bordisms in PDEs by means of subgroups of usual bordism groups are given. More precisely, it is proved that integral bordism groups can be expressed as extensions of quantum bordism groups and these last are extensions of subgroups of usual bordism groups. Furthermore, a complete cohomological characterization of integral bordism and quantum bordism is given. Applications to particular important classes of PDEs are considered. Finally, we give a complete characterization of integral and quantum singular bordisms by means of some suitable characteristic numbers. Some examples of interesting PDEs which arise in physics are also considered where existence of solutions with change of sectional topology (tunnel effect) is proved. As an application, we relate integral bordism to the spectral term that represents the space of conservation laws for PDEs. This also gives a general method to associate in a natural way a Hopf algebra to any PDE.     

On the Volume Formulas of Cones and Orthogonal Multi-cones in S~n(1) and H~n(-1)

In the study of n-dimensional spherical or hyperbolic geometry, n ≥3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in Sn(l) and Hn(-1).     

Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Liftings of Galois Covers of Smooth Curves

Let (C,G) be a smooth irreducible projective curve of genus g over an algebraically closed field k of chararacteristic p>0 and G be a finite group of automorphisms of C. It is well known that here, contrary to the characteristic 0 case, Hurwitz's bound |G| 84(g-1) doesn't hold in general; in such cases this gives an obstruction to obtaining a smooth galois lifting of (C,G) to characteristic 0. We shall give new obstructions of local nature to the lifting problem, even in the case where G is abelian. In the case where the inertia groups are p ae-cyclic with a 2 and (e,p)=1, we shall prove that smooth galois liftings exist over W(k)[ ].     

On the Volume Formulas of Cones and Orthogonal Multi-cones in S^n（1） and H^n（-1）

Abstract In the study of n-dimensional spherical or hyperbolic geometry, n≥ 3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in Sⁿ(1) and Hⁿ(—1). (Dedicated to the memory of Shiing-Shen Chern)     

Rational Cuspidal Plane Curves of Type (d,d — 3)

In the previous paper [FlZa 2] we classified the rational cuspidal plane curves C with a cusp of multiplicity deg C — 2. In particular, we showed that any such curve can be transformed into a line by Cremona transformations. Here we do the same for rational cuspidal plane curves C with a cusp of multiplicity deg C — 3.     

Geometries of the Group PSL(2,11)

We determine all residually weakly primitive flag-transitive geometries for the groups PSL(2,11) and PGL(2,11). For the first of these we prove the existence by simple constructions while uniqueness, namely the fact that the lists are complete, relies on MAGMA programs. A central role is played by the subgroups Alt(5) in PSL(2,11). The highest rank of a geometry in our lists is four. Our work is related to various atlases of coset geometries.