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1

Formowanie materiałów chitynowych przy zastosowaniu elektroprzędzenia

Biniaś Dorota, Biernat Anna

Polish Journal of Materials and Environmental Engineering

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2021

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Vol. 2 (22)

15--23

EN

As part of the research, chitin materials were obtained using the electrospinning method. For this purpose, chitin solutions were prepared in phosphoric acid and lithium chloride in an am-ide solvent. The coagulation of chitin materials was performed in alkaline water baths and in distilled water. As a result of the method, microspheres and microfibers of chitin were ob-tained. The morphological structure of the obtained materials was analyzed using a scanning electron microscope (SEM) and an optical microscope. The obtained microspheres were characterized by a similar diameter value, amounting to 195 μm. In contrast, chitin microfi-bers from 90 to 150 μm. The obtained materials were subjected to mid-infrared and Raman spectrophotometric tests in order to determine the influence of the solvents used on the chemical structure of native and regenerated chitin. Infrared spectroscopy studies confirmed no changes in the chemical structure of regenerated chitin. Raman spectroscopy studies confirmed no degradation of regenerated chitin. In the spectra obtained, differences were observed in the form of changes in the shape of the bands for oscillators be associated in in-termolecular interactions, which is caused by changes in the supermolecular structure.

2

Examples of non-conformal submersions from spheres with umbilical fibers

Zawadzki T.

Demonstratio Mathematica

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2014

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Vol. 47, nr 3

738--747

EN

We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of Cn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p = 0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way.

3

Differentiable positive definite kernels on spheres

Menegatto V. A., Oliveira C. P., Peron A. P.

Journal of Applied Analysis

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2009

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Vol. 15, nr 1

101-117

EN

We analyze term-by-term differentiability of uniformly convergent series of the form [wzór], where Sm-1 is the unit sphere in Rm, pk ≥ 0, k = 0,1,..., [wzór] Pk > 0 , and {Yk} is a sequence of spherical harmonics or even more general functions. Since this class of kernels includes the continuous positive definite kernels on ,Sm-1, the results in this paper will show that, under certain conditions, the action of convenient differential operators on positive definite (strictly positive definite) kernels on Sm-1 generate positive definite kernels.

4

Rangowa klasyfikacja obiektów za pomocą kul w różnych normach

Topczewska. M.

Zeszyty Naukowe Politechniki Białostockiej. Informatyka

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2008

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Z. 3

145-158

PL

Mając dany zbiór uczący, który zawiera obiekty należące do dwóch lub większej liczby klas, można zbudoważ najmniejsze kule otaczające obiekty z wybranej klasy rozwiązując zadanie programowania kwadratowego. Ze względu na to, że najmniejsze kule są konstruowane oddzielnie dla każdej klasy, problem może być w prosty sposób rozszerzony do przypadków wieloklasowych. W pracy przedstawiamy propozycje klasyfikatorów opartych na kulach w normie euklidesowej oraz w normie l1. Przedstawione eksperymenty zostały przeprowadzone tak na syntetycznych jak i rzeczywistych zbiorach danych.

EN

If a training set containing objects from two or more classes is given, minimum bounding spheres enclosing objects belonging to a marked class can be built by solving a quadratic programming task. Because the minimum spheres are constructed separately for each class the problem can be easily extended to the multi-class cases. In the paper classifiers both in l1 and l2 norms are proposed. Experiments were performed on artificial and on real data sets.

5

Stabilization of nonlinear systems: Radial optimal control approach

Sangelaji Z., Banks S.P.

Systems Science

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2003

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Vol. 29, nr 4

29-41

EN

This paper represents the optimal control of nonlinear systems based upon the associated angular approach. In the latter a general class of nonlinear systems is converted to two associated systems: a nonlinear equation on a sphere (spherical), and a radial differential system. By decoupling the two subsystems and considering only the radial system, a finite-horizon radial optimal control is designed which minimizes the radial cost function. Successive approximation technique is then introduced in which the equations are replaced by a sequence of linear, time-varying approximations. The resulting optimal control is then applied to the original angular system. This control forces the original angular system to the origin.