differential properties
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Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 127
Author(s):  
Jan Kyzioł ◽  
Andrzej Okniński

In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is based on implicit (approximate) amplitude-frequency response equations of the form FΩ,A;c̲=0, where c̲ denotes the parameters. We demonstrate that tools of differential geometry make possible the discovery of the change of differential properties of solutions of the equation FΩ,A;c̲=0. Such qualitative changes of the solutions of the amplitude-frequency response equation, referred to as metamorphoses, lead to qualitative changes of dynamics (bifurcations). We show that the analytical prediction of metamorphoses is of great help in numerical simulation.


Viruses ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 105
Author(s):  
Shuji Hinuma ◽  
Shun’ichi Kuroda

(1) Background: The myristoylated pre-S1 peptide (Myr47) synthesized to mimic pre-S1 domain (2-48) in large (L) surface protein of hepatitis B virus (HBV) prevents HBV infection to hepatocytes by binding to sodium taurocholate cotransporting polypeptide (NTCP). We previously demonstrated that yeast-derived nanoparticles containing L protein (bio-nanocapsules: BNCs) bind scavenger receptor class B type 1 (SR-B1). In this study, we examined the binding of Mry47 to SR-B1. (2) Methods: The binding and endocytosis of fluorescence-labeled Myr47 to SR-B1 (and its mutants)-green fluorescence protein (GFP) fusion proteins expressed in HEK293T cells were analyzed using flow cytometry and laser scanning microscopy (LSM). Various ligand-binding properties were compared between SR-B1-GFP and NTCP-GFP. Furthermore, the binding of biotinylated Myr47 to SR-B1-GFP expressed on HEK293T cells was analyzed via pull-down assays using a crosslinker and streptavidin-conjugated beads. (3) Conclusions: SR-B1 bound not only Myr47 but also its myristoylated analog and BNCs, but failed to bind a peptide without myristoylation. However, NTCP only bound Myr47 among the ligands tested. Studies using SR-B1 mutants suggested that both BNCs and Myr47 bind to similar sites of SR-B1. Crosslinking studies indicated that Myr47 binds preferentially SR-B1 multimer than monomer in both HEK293T and HepG2 cells.


2021 ◽  
pp. 4875-4884
Author(s):  
Khaled Hadi ◽  
Saad Nagy

The question on affine Riesz basis of Walsh affine systems is considered. An affine Riesz basis is constructed, generated by a continuous periodic function that belongs to the space on the real line, which has a derivative almost everywhere; in connection with the construction of this example, we note that the functions of the classical Walsh system suffer a discontinuity and their derivatives almost vanish everywhere. A method of regularization (improvement of differential properties) of the generating function of Walsh affine system is proposed, and a criterion for an affine Riesz basis for a regularized generating function that can be represented as a sum of a series in the Rademacher system is obtained.


Author(s):  
Vladimir Matusevich ◽  
Jurij Sharaban ◽  
Aleksandr Shehov

The mathematical model of estimation of a design mass of the closed planetary mechanism formed from two simple planetary mechanisms of James (mechanism of type ), taking into account their structural diagrams and design constraints, determined by the conditions of contact and bending strengths of external gearing of sun gears and satellites, is offered. A model is a dimensionless function (analogue of mass) of two variables – transmission relations of simple planetary mechanisms, and set of numerical parameters. As parameters of analogue of mass coefficients are chosen, characterizing the models of mass of gear wheels and carriers, structural and strength limitations of the external gearing of simple planetary mechanisms of the type , and also structure of these mechanisms. In the program Mathcad differential properties of the offered model and influence on position of minimum of analogue of mass are investigational depending on the numerical values of his parameters. Documents of the Mathcad program are presented that implement computer modeling of algorithms for parametric optimization of mass closed planetary mechanism, where the function of the analogue of the mass of the given mechanism is used as the objective function. A comparative analysis of minimizing the design mass of two kinematic schemes of planetary mechanisms is considered – closed planetary mechanism and in-line planetary of the type . Keywords: simple planetary mechanism of James, simple planetary mechanism type ; closed planetary mechanism; in-line planetary mechanism; mass of closed planetary mechanism; contact strength of gearing; bending strength of gearing; parametric optimization; parametric optimization of mass of planetary mechanism


2021 ◽  
Author(s):  
Soon-Ho Choi ◽  
Sedong Kim

Abstract It will not be denied that the calculations of the change of state for a gas is highly important in most engineering applications. For determining the gas’s properties such as the pressure (P), the volume (V) and the temperature (T), engineers and scientists uses the Boyle’s, Charles’s and Gay-Lussac’s (B-C-G) law of P1V1/T1=P2V2/T2. Although the B-C-G law provides the accurate property values of a gas, it give no detailed information embedded in the process when a gas changes its state. In this study, the author theoretically carried out the integrations of the partial differentials when differentiating the B-C-G law, which has not been tried by anyone up to now. The integration results of this study were thoroughly compared with the experimentally measured data and it was confirmed that the integration methods suggested in this study accurately provides the differential properties on ΔP, ΔV and ΔT. In addition to it, through the stepwise analysis of the integration of the partial differentials, it revealed that the efficiency in the change of state of a gas inherently exists higher than the Carnot cycle, which is operating between the same conditions. Therefore, the results of this study can be lead to the conclusion that all changes of state of all materials inevitably accompanies an energy loss and it is a natural phenomenon.


2021 ◽  
Vol 100 (4) ◽  
pp. 16-23
Author(s):  
S.Ye. Kondratyuk ◽  
◽  
V.I. Veis ◽  
Z.V. Parkhomchuk ◽  
V.A. Loktyonov-Remyzovskii ◽  
...  

The effect of overheating of the melt over the equilibrium liquidus in the temperature range 1570 °C – 1670 °C and the rate of its cooling during crystallization and structure formation of castings on the formation of the length and morphology of the main macrostructural zones, grain dispersion, characteristics of the fine crystal structure, hardness and intensity of abrasive wear over the section of 25L steel castings with a differentiated cast structure was investigated. Regular changes of these indicators depending on thermokinetic conditions of crystallization are established. The determining influence of the melt cooling rate on the morphology and dispersion of the cast structure due to different degrees of melt supercooling during crystallization of different structural zones of castings is shown. As the distance from the rapidly cooling surface of the castings and taking into account the increase in the temperature of the melt overheat from 1570 ºC to 1670 ºC, the grain size varies from 5… 7 numbers to 1… 2 numbers, respectively. In the case of normal heat removal rate during crystallization, the grain size in the castings varies from 4… 2 to -1… -2 numbers. The determined characteristics of wear resistance of steel in different structural zones correlate with changes in the characteristics of the cast structure and the cross-sectional strength of castings. The research results open the prospect of developing new foundry technologies for the production of cast products with differential properties for special operating conditions. Keywords: gradient structure, structural zones, melt, wear.


Author(s):  
Laura Gonzalez-Blanco ◽  
Enrique Romero ◽  
Paul Marschall ◽  
Séverine Levasseur

AbstractDuring recent decades, argillaceous sedimentary formations have been studied as potential host formations for the geological disposal of long-living and heat-emitting radioactive waste—Boom Clay in Belgium and Opalinus Clay and Brown Dogger in Switzerland. A significant issue in the long-term performance of these potential host rocks concerns the generation and transport of gases. The pressure resulting from the generation of gas in an almost impermeable geological medium in the near field of a repository will increase. Under high gas pressures, the mechanical and hydraulic properties of the host rock are expected to change significantly. Preferential gas pathways may develop which exploit material heterogeneity, anisotropy (bedding planes), rock discontinuities, or interfaces between the different components of the repository, and may eventually lead to the release of the produced gases. Gas flow through these clayey rocks is investigated on the basis of laboratory work. Priority has been given to studying the volume change response of these initially water-saturated materials through relatively fast and controlled volume-rate gas injections. The effect of the gas injection rate, the confining pressure and the bedding orientation on the gas transport properties have been studied with particular attention paid to the coupling with strain behaviour. The results have shown features common to the three formations concerning the gas transfer process through preferential pathways, despite their initially differential properties.


Author(s):  
А.А. Логачева

В статье рассматриваются структурные и семантические особенности предложений с однородными членами на примере поэтических произведений А.С. Пушкина. В исследуемом языковом материале однородные члены осложняют структуру не только самостоятельного простого предложения, но и простого предложения в составе сложного. Типичные дифференциальные свойства однородных компонентов, описанные в работе, указывают на грамматическую однотипность однородных членов предложения. Однако при выделении блока однородных членов учитывается не только данный морфологический признак, но и семантический критерий. В этой связи описываются различные отношения между компонентами однородного ряда: одновременности, последовательности действий, причинной зависимости и другие. Также устанавливается, что однородные члены предложения в лирическом тексте могут являться любым членом предложения, т.е. выполнять различные синтаксические функции. При этом однородный ряд образуют не только отдельные слова, но и целые словосочетания, находящиеся в сочинительных отношениях друг с другом. Язык лирики, отличающийся строгой поэтической формой, стремлением к ритму, рифме, мелодике и т.д., способствует созданию некоторых особенностей функционирования предложений с однородными членами: разнообразная структура, богатая семантика, приём инверсии. Особая поэтическая форма и своеобразие синтаксических конструкций с однородными членами ведут к созданию экспрессии лирического произведения, информативности и передаче авторской субъективности. The article discusses the structural and semantic features of sentences with homogeneous members on the example of the poetic works of A.S. Pushkin. In the studied linguistic material, homogeneous members complicate the structure of not only an independent simple sentence, but also a simple sentence within a complex one. Typical differential properties of homogeneous components described in the work indicate the grammatical uniformity of homogeneous members of the sentence. However, when selecting a block of homogeneous members, not only this morphological feature is taken into account, but also a semantic criterion. In this regard, various relationships between the components of a homogeneous series are described: simultaneity, sequence of actions, causal dependence, and others. It is also established that homogeneous members of a sentence in a lyric text can be any member of a sentence, i.e. perform various syntactic functions. At the same time, a homogeneous series is formed not only by individual words, but also by whole phrases that are in a compositional relationship with each other. The language of lyrics, characterized by a strict poetic form, striving for rhythm, rhyme, melody, etc., contributes to the creation of certain features of the functioning of sentences with homogeneous members: a diverse structure, rich semantics, and the method of inversion. A special poetic form and originality of syntactic constructions with homogeneous members lead to the creation of an expression of a lyric work, information content and the transfer of the author's subjectivity.


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