<abstract xmlns="http://www.w3.org/1999/xhtml">

The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand this tendency in modern robotics. Mapping between joint variables in joint-space coordinate and end effector configuration in task-space coordinate are provided by serial manipulator kinematics. A computation of higher-order Jacobian matrix derivatives is required for accurate trajectory tracking. With conventional numerical derivation, only approximate results can be obtained. Still, the computation of high-order derivatives of multi-DoF manipulators with high accuracy requires long time intervals and it is difficult. This paper investigates a novel derivation method for a multilink robot Jacobian. According to this method, an exact value of higher-order acceleration can be obtained using a multidual differentiation transform. Multidual functions for sine and cosine will be used to get the exact value of acceleration, jerk, and hyper-jerk (jounce) expressions, commonly used for accurate trajectory-tracking.
</abstract>

High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

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This paper introduces a novel computational method for analyzing the higher-order acceleration field of spatial kinematics chains. The method is based on vector and quaternionic calculus, as well as dual and multidual algebra. A closed-form coordinate-free solution generated by the morphism between the Lie group of rigid body displacements and the unit multidual quaternions is presented. Presented solution is used for higher-order kinematics investigation of lower-pair serial chains. Additionally, a general method for studying the vector field of arbitrary higher-order accelerations is discribed. The method utilizes the “automatic differentiation” feature of multidual and hyper-multidual functions to obtain the higher-order derivative of a rigid body pose without need in further differentiation of the body pose regarding time. Also is proved that all information regarding the properties of the distribution of higher-order accelerations is contained in the specified unit hyper-multidual quaternion.
</abstract>

Hypercomplex Quaternions and Higher-Order Analysis of Spatial Kinematic Chains

<abstract xmlns="http://www.w3.org/1999/xhtml">

The living brain is physically modeled as a universe, equivalent, in a way, to the physical universe we live in. While in the case of the physical universe the gravitation prevails, in the brain universe, if we may, the electricity prevails, but the mathematical description we provide is essentially the same in both cases. What is imperiously necessary in this approach is, first, a metric description of matter, then, of course, the physical interpretation of this description. These issues were treated, but only in their believed essentials, in the previous three instalments of the present work. The object of the present episode of the work is a classical space image of the matter. This image is worked out here having in the background the idea of a necessary physical connection between the matter of a universe and its fundamental physical structure. The matter can be characterized ‘optically’ as a Maxwell fish-eye, while the fundamental physical structure must be a dipole. Both these concepts are universal.
</abstract>

Physical Principles in Revealing the Working Mechanisms of Brain. Part IV

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Still after the right concept of universe, we extract from the Einstein-de Sitter debate presented previously the physical characteristics of a continuum charge background to serve for the description of brain. This time we settle for the cosmological metric of the universe, which appear to be well suited for the brain, and the content in events of a generic universe serving for the definition of events in the brain. The hologram is also defined as a general characteristic of a universe, in order to serve in describing the process of memory. The idea of coherence is used, in order to define the frequency in an invariant way.
</abstract>

Physical Principles in Revealing the Working Mechanisms of Brain. Part V

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Stokes’ problems for the incompressible generalized Burgers fluids are investigated when magnetic and porous effects are taken into account. Non-dimensional exact expressions are provided for the components of velocity, non-trivial shear stress and Darcy’s resistance. They can immediately be particularized to recover similar solutions for the viscous, second grade, Maxwell, Oldroyd-B and Burgers fluids. For their validation, the solutions are given in two forms whose equivalence has been proved in a graphical manner. The results, which correct previous solutions from the existing literature, can be useful for the experimental researchers who want to know the need time to touch the steady state and to bring to light the influence of porous medium and magnetic field on the flow resistance of the fluid. Finally, by graphical illustrations, it was shown that the flow resistance of fluid enhances through porous media and decreases when a magnetic field is present.
</abstract>

Steady State Solutions of MHD Stokes Problems for Generalized Burgers Fluids Through Porous Media

AHEAD OF PRINT

Volume 70 (2024): Issue 1 (January 2024)

Volume 69 (2023): Issue 1-4 (December 2023)

Volume 68 (2022): Issue 4 (December 2022)

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

Volume 68 (2022): Issue 1 (March 2022)

Volume 67 (2021): Issue 4 (December 2021)

Volume 67 (2021): Issue 3 (September 2021)

Volume 67 (2021): Issue 2 (June 2021)

Volume 67 (2021): Issue 1 (March 2021)

BULLETIN OF THE POLYTECHNIC INSTITUTE FROM IAȘI, Section Mathematics, Theoretical Mechanics, Physics – BIPMF (ISSN-L 1224-7863) is an international journal, with quarterly appearance, for the free publication of research results in theoretical and mathematical physics, mechanics, technical and applied physics, material sciences.  The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes physics, mechanics and mathematics, and given their importance in material sciences, interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, surfaces/interfaces are welcomed if they demonstrate insight into physics, seeking to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.  BIMMF aims to enhance the interdisciplinary research by connecting the fundamental sciences as physics and mathematics with applicative research concerning the relationships between structure, processing, properties, and performance of materials. It also promotes international exchange of scientific activities.  The journal publishes original research, focused review articles that examine the state of the art, book reviews, technical notes, case studies, and preliminary communications, with no restriction on the length of the papers.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. sistemantiplagiat.ro/ 