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This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and orientation of the
Externí odkaz:
http://arxiv.org/abs/2412.18294
Autor:
Henning, Sotirios
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of typical dat
Externí odkaz:
http://arxiv.org/abs/2412.07939
Autor:
Kovács, Zoltán
We give an alternative proof of the statement, by using elimination from algebraic geometry, that the only set $S\subset\mathbb{R}^2$, $\left|S\right|=6$ such that all subsets that form a triangle are isosceles triangles, is the regular pentagon with
Externí odkaz:
http://arxiv.org/abs/2412.05190
Autor:
Hivert, Florent
Publikováno v:
CPP 2025, Proceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs
We present a library of formalized results around symmetric functions and the character theory of symmetric groups. Written in Coq/Rocq and based on the Mathematical Components library, it covers a large part of the contents of a graduate level textb
Externí odkaz:
http://arxiv.org/abs/2412.04864
Autor:
Straton, Jack C.
In a prior paper we found that the Fourier-Legendre series of a Bessel function of the first kind J_{N}\left(kx\right) and of a modified Bessel functions of the first kind I_{N}\left(kx\right) lead to an infinite set of series involving \,_{1}F_{2} h
Externí odkaz:
http://arxiv.org/abs/2412.00019
Autor:
Grimpen, Fritz, Stefanou, Anastasios
Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of $\mathbb Z^n$-graded modules. We consider them in the setting of local graded rings $R$, with grading over an abelian group, and give a criterion f
Externí odkaz:
http://arxiv.org/abs/2410.17667
Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals. Thanks to the functorial properties of
Externí odkaz:
http://arxiv.org/abs/2410.17090
We study the problem of representing multivariate polynomials with rational coefficients, which are nonnegative and strictly positive on finite semialgebraic sets, using rational sums of squares. We focus on the case of finite semialgebraic sets S de
Externí odkaz:
http://arxiv.org/abs/2410.04845
Autor:
Luo, Hengrui, Li, Meng
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising ability to
Externí odkaz:
http://arxiv.org/abs/2410.02623
Autor:
Cox, David A.
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to residues and pa
Externí odkaz:
http://arxiv.org/abs/2410.03745