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We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
In this article we developed a special topic of our pure-mathematics papers concerning the hypergeometric theory. Based upon a Roberts's reduction approach of hyperelliptic integrals to elliptic ones and on the simultaneous multivariable…
We give a Newton type rational interpolation formula (Theorem \ref{theo}). It contains as a special case the original Newton interpolation, as well as the recent interpolation formula of Zhi-Guo Liu, which allows to recover many important…
The design of structures submitted to aerodynamic loads usually requires the development of specific computational models considering fluid-structure interactions. Models using structural frame elements are developed in several relevant…
% context :The precise and accurate modelling of a terrestrial planet like Venus is an exciting and challenging topic, all the more interesting since it can be compared with that of the Earth for which such a modelling has already been…
Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with…
Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…
Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control…
This paper considers the integration of rigid cooperative manipulation with rigidity theory. Motivated by rigid models of cooperative manipulation systems, i.e., where the grasping contacts are rigid, we introduce first the notion of…
Guided by the Jacobi's work published the year before his death about the rotation of a rigid body, the behavior of the rotation matrix describing the dynamics of the free rigid body is studied. To illustrate this dynamics one draws on a…
In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…
We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard…
Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and…
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much…
We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary…
Recent research on mobile robots has focused on increasing their adaptability to unpredictable and unstructured environments using soft materials and structures. However, the determination of key design parameters and control over these…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We study a simple generalization of the rotation (or circular shift) of the binary sequences. In particular, we show each orbit of this generalized rotation has a certain statistical symmetry. This generalized rotation naturally arises when…
One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…