Branch curves of multiple planes and continuous systems of plane algebraic curves

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

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ANNULAR PLATE DAMPERS ATTACHED TO CONTINUOUS SYSTEMS

Journal of Sound and Vibration ◽

10.1006/jsvi.1996.0155 ◽

1996 ◽

Vol 191 (5) ◽

pp. 781-793 ◽

Cited By ~ 5

Author(s):

A. Arpaci

Keyword(s):

Annular Plate ◽

Continuous Systems

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Hidden Attractors in Discrete Dynamical Systems

Entropy ◽

10.3390/e23050616 ◽

2021 ◽

Vol 23 (5) ◽

pp. 616

Author(s):

Marek Berezowski ◽

Marcin Lawnik

Keyword(s):

Dynamical Systems ◽

Chaos Theory ◽

Scientific Literature ◽

Discrete Systems ◽

Discrete Dynamical Systems ◽

Continuous Systems ◽

Hidden Attractors ◽

Negative Effects ◽

Chemical Reactors ◽

Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

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Generation of Photopolymerized Microparticles Based on PEGDA Using Microfluidic Devices. Part 1. Initial Gelation Time and Mechanical Properties of the Material

Micromachines ◽

10.3390/mi12030293 ◽

2021 ◽

Vol 12 (3) ◽

pp. 293

Author(s):

José M. Acosta-Cuevas ◽

José González-García ◽

Mario García-Ramírez ◽

Víctor H. Pérez-Luna ◽

Erick Omar Cisneros-López ◽

...

Keyword(s):

Mechanical Properties ◽

Gelation Time ◽

Mesh Size ◽

Microfluidic Devices ◽

Future Generation ◽

Mechanical Tests ◽

Continuous Systems ◽

Polyethylene Glycol Diacrylate ◽

Glycol Diacrylate ◽

Close Relationship

Photopolymerized microparticles are made of biocompatible hydrogels like Polyethylene Glycol Diacrylate (PEGDA) by using microfluidic devices are a good option for encapsulation, transport and retention of biological or toxic agents. Due to the different applications of these microparticles, it is important to investigate the formulation and the mechanical properties of the material of which they are made of. Therefore, in the present study, mechanical tests were carried out to determine the swelling, drying, soluble fraction, compression, cross-linking density (Mc) and mesh size (ξ) properties of different hydrogel formulations. Tests provided sufficient data to select the best formulation for the future generation of microparticles using microfluidic devices. The initial gelation times of the hydrogels formulations were estimated for their use in the photopolymerization process inside a microfluidic device. Obtained results showed a close relationship between the amount of PEGDA used in the hydrogel and its mechanical properties as well as its initial gelation time. Consequently, it is of considerable importance to know the mechanical properties of the hydrogels made in this research for their proper manipulation and application. On the other hand, the initial gelation time is crucial in photopolymerizable hydrogels and their use in continuous systems such as microfluidic devices.

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