scholarly journals Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1600
Author(s):  
Francisco José Navarro-González ◽  
Yolanda Villacampa ◽  
Mónica Cortés-Molina ◽  
Salvador Ivorra

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.

1969 ◽  
Vol 62 (4_Suppla) ◽  
pp. S23-S35
Author(s):  
B.-A. Lamberg ◽  
O. P. Heinonen ◽  
K. Liewendahl ◽  
G. Kvist ◽  
M. Viherkoski ◽  
...  

ABSTRACT The distributions of 13 variables based on 10 laboratory tests measuring thyroid function were studied in euthyroid controls and in patients with toxic diffuse or toxic multinodular goitre. Density functions were fitted to the empirical data and the goodness of fit was evaluated by the use of the χ2-test. In a few instances there was a significant difference but the material available was in some respects too small to allow a very accurate estimation. The normal limits for each variable was defined by the 2.5 and 97.5 percentiles. It appears that in some instances these limits are too rigorous from the practical point of view. It is emphasized that the crossing point of the functions for euthyroid controls and hyperthyroid patients may be a better limit to use. In a preliminary analysis of the diagnostic efficiency the variables of total or free hormone concentration in the blood proved clearily superior to all other variables.


2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.


2015 ◽  
Vol 815 ◽  
pp. 49-53
Author(s):  
Nur Fitriah Isa ◽  
Mohd Zulham Affandi Mohd Zahid ◽  
Liyana Ahmad Sofri ◽  
Norrazman Zaiha Zainol ◽  
Muhammad Azizi Azizan ◽  
...  

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to behavior is concerned, it is well known that a key step is to investigate the influence of geometric differences on the non-linear behavior of the panels. One possible approach is to use the validated numerical model based on the non-linear finite element analysis (FEA). The validation of the composite panel’s element using Trim-deck and Span-deck steel sheets under axial load shows that the present results have very good agreement with experimental references. The developed finite element (FE) models are found to reasonably simulate load-displacement response, stress condition, giving percentage of differences below than 15% compared to the experimental values. Trim-deck design provides better axial resistance than Span-deck. More concrete in between due to larger area of contact is the factor that contributes to its resistance.


2016 ◽  
Vol 7 (2) ◽  
pp. 150-166 ◽  
Author(s):  
Péter Ván

Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.


1995 ◽  
Vol 10 ◽  
pp. 201-201
Author(s):  
N. Capitaine ◽  
B. Guinot

In 1991, IAU Resolution A4 introduced General Relativity as the theoretical background for defining celestial space-time reference sytems. It is now essential that units and constants used in dynamical astronomy be defined in the same framework, at least in a manner which is compatible with the minimum degree of approximation of the metrics given in Resolution A4.This resolution states that astronomical constants and quantities should be expressed in SI units, but does not consider the use of astronomical units. We should first evaluate the usefulness of maintaining the system of astronomical units. If this system is kept, it must be defined in the spirit of Resolution A4. According to Huang T.-Y., Han C.-H., Yi Z.-H., Xu B.-X. (What is the astronomical unit of length?, to be published in Asttron. Astrophys.), the astronomical units for time and length are units for proper quantities and are therefore proper quantities. We fully concur with this point of view. Astronomical units are used to establish the system of graduation of coordinates which appear in ephemerides: the graduation units are not, properly speaking astronomical units. Astronomical constants, expressed in SI or astronomical units, are also proper quantities.


2021 ◽  
Vol 46 (1) ◽  
Author(s):  
C. E. Chigbundu ◽  
K. O. Adebowale

Dyes are complex and sensitive organic chemicals which exposes microbial populations, aquatic lives and other living organisms to its toxic effects if their presence in water bodies or industrial effluents are not properly handled. This work therefore, comparatively studied the adsorption efficiencies of natural raw kaolinite (NRK) clay adsorbent and dimethyl sulphoxide (DMSO) faciley intercalated kaolinite clay (DIK) adsorbent for batch adsorption of Basis Red 2 (BR2) dye. The impact of varying the contact time, temperature and other operating variables on adsorption was also considered. The two adsorbents were characterized using SEM images, FTIR and XRD patterns. Linear and non-linear regression analysis of different isotherm and kinetic models were used to describe the appropriate fits to the experimental data. Error analysis equations were also used to measure the goodness-of-fit. Langmuir isotherm model best described the adsorption as being monolayer on homogenous surfaces while Kinetic studies showed that Elovich model provides the best fit to experimental data. The adsorption capacities of NRK and DIK adsorbents for the uptake of BR2 were 16.30 mg/g and 32.81 mg/g, respectively (linear regression) and 19.30 mg/g and 30.81 mg/g, respectively (non-linear regression). The thermodynamic parameter, ∆G showed that BR2 dye adsorption onto the adsorbents were spontaneous. DIK adsorbent was twice efficient compared with NRK for the uptake of BR2 dye.


2019 ◽  
pp. 87-96
Author(s):  
А. Л. Свящук

In the time when the basic formulas and approaches of the aircraft industry are based on the principles of classical science, the nature of the observed phenomena seems non-linear. Such phenomena as turbulence, flutter, buffering, disruption of the air flow can be explained by means of synergetics and system theory in the context of the post-non-classical paradigm. However, a certain contradiction can be observed: non-linear phenomena are explained by linear traditional science. That is why many formulas of aerodynamics and strength have a large empirical part. Therefore, it becomes necessary to revise the philosophical foundations of most approaches and the overall picture of the world as a whole. The use of the concepts of synergetics and system theory allows us to describe more accurately certain phenomena in aviation, which ultimately will lead to the creation of more efficient and safer aircraft. For example, we can design our aircraft not only as a complex system, but also as part of other complex systems, evaluating its effectiveness from the point of view of more ambitious and higher levels, predicting its operation and modernization in the changing conditions of the socio-political system. Moreover, the very nature of engineering creativity based on synergistic approaches will become more efficient and effective by increasing the intensity of aviation thought. Therefore, understanding the role of chance, the effect of emergence will allow us to be prepared for many surprises and black swans and also be wary about our knowledge, assessing their probabilistic nature.


2021 ◽  
Vol 11 (2) ◽  
pp. 83-101
Author(s):  
Mária T. Patakyová

Abstract Digitalisation is a challenge from the regulatory point of view. Competition law, as a special type of regulation, is no exception to this. The article explores the risks of digitalisation, especially the ones related to the enhanced use of pricing algorithms. In theory, pricing algorithms are not easily assessed from the perspective of competition law, let alone its application in practice. The prohibition of anticompetitive agreements (pursuant to Article 101 of the Treaty on Functioning of the European Union (TFEU)) is applied with certain difficulty to agreements created by using pricing algorithms. This is an unfortunate situation, as horizontal agreements represent one of the worst infringements of EU competition law, including price cartels or bid rigging. Apart from presenting a theoretical background, the article dives into the practice of the Antimonopoly Office of the Slovak Republic (AMO) in order to assess which practical issues the AMO might face when applying the theoretical concepts. In sum, the article asks from a theoretical perspective which issues of competition law have been introduced (or deepened) by the enhanced digitalisation, looking in particular to pricing algorithms. On top of that, the article explores the issues which may be encountered in practice, taking the Slovak jurisdiction as the example. The willingness and feasibility of the AMO to enforce digital issues such as pricing algorithms is assessed based on the previous acts of the AMO as well as the new Act on Protection of Competition, adopted by the Slovak parliament on 11 May 2021.


2019 ◽  
Vol 16 (16) ◽  
pp. 158-169
Author(s):  
Olena Stanishevska

Introduction. In scientific literature dedicated to J. Brahms, much attention has been paid to a song genre. The researches note that J. Brahms’s songs can be regarded as a continuation of genre-specific features of Austro-German Lied, which retains the purity of the generic semantics in the composer’s works, without involving typically operatic means of vocal intoning, or approaching the so-called “poem with music”. J. Brahms’s songs do not allow the singer to demonstrate the full range of his/her voice, to reveal his/her artistic temperament, to show the technical skill. Absorption in a special emotional aura of J. Brahms’s songs requires a variety of timbre-intonational resources of a singer, his/her ability not to lose the sense of the whole while detailing the melodious overture. Of particular interest is the issue of music and words correlation in J. Brahms’s songs. As a rule, the composer is considered to be the immediate successor of F. Schubert rather than R. Schuman in his orientation to musical embodiment of a generalized poetic image. At the same time, this issue requires more detailed study, since the composer was very sensitive to the poetic text, in particular, from the point of view of coordinating the intonation-phonetic features of German language and vocal intonation. Theoretical Background. Recent research and publications analysis. Opus 49 by J. Brahms seems to be in the shadow of musicological thought and performing practice. It should be noted that a very famous opus part is “Lullaby”, which is mentioned in the monographs of K. Tsareva (1986), M. Druskin (1959), and K. Geiringer (1965). In the literature being considered the abovementioned opus is not completely covered, thus determining the relevance of our article. There are references to individual songs in different sources, but incidentally, in the context of different issues. Objective is to study J. Brahms’s opus 49 in the aspect of the interaction of poetic word and music, verbal and musical intoning. Methods: 1) historical method, allowing to comprehend the selected material in the perspective of the development of Austro-German song of the XIX century; 2) intonational method, which involves the study of vocal melody in terms of phonetic-tonic links; 3) genre method, caused by the features of chamber vocal lyrics; 4) stylistic method, corresponding to a specific opus consideration in the general context of the composer’s creative work. Results and Discussion. The composer did not have any tendency to the songs cyclization, however, the vocal miniatures, assembled in one opus, appear to be lyrical notes, self-contained but united by poetic motives and nature of the author’s expression. Many researchers see a cyclic organization of his particular vocal opuses. For example, I. Mykhailov (1987: 19) proves the existence of cyclic principles at different compositional levels in composer’s songs: separate “melodious pairs”, a number of songs with the texts by one poet inside the opus, a whole vocal opus with the texts by different authors. According to I. Mikhailov, the cyclic connection of songs is emphasized by several compositional techniques: thematic one, i.e. the unity of the musical material; the continuity of songs alternation, which is sometimes manifested in the absence of a piano introduction of the next song. In opus 49, the author chooses different poetic sources – poems by P. Heyse, L. Hölty, A. F. Schack, and J. Wenzig. The composer refers to one of the samples of the famous collection by Joachim von Arnim and Clemens Brentano “The Magic Horn of a Boy”. Given the anthological principle of poetic texts selection, no transparent storyline in opus 49, such as “A Beautiful Miller” by F. Schubert or “Poet’s Love” by R. Schumann, there is no reason to regard it as a cycle. However, the opus’ songs are arranged in a certain semantic sequence. Owing to the fact that three songs (“Sunday Morning”, “To a Violet”, “Longing for the Sweetheart”) are united by homogeneous poetic motifs, one can regard them as forming a microcycle within the whole. The second micro-cycle of the opus is represented by No. 4 and No. 5 (“Lullaby” and “Twilight”). In interpreting the poetic text, J. Brahms adheres to the principle of emotional and musical generality, once detailing the text, if at all. Here, he succeeds F. Schubert. However, he uses the technique of keywords, distinguishing them in two ways: rhythmically (with syncope) and through intrinsic chants; the composer also uses different types of intoning. Following the tradition of the 19th-century Austro-German song, the composer regards the genre as an alliance of two full members: the vocalist and the pianist, with the part being an instrumental generalization. The intonational image of the whole in vocal music arises at the crossing of two texts – poetic and musical. German has intonation difficulties owing to a large number of consonants. Problems, encountered by the singers in intoning German language, are compensated by the consonants and vowels, which are most favorable for correct sound formation, allowing to achieve the required quality. The soft consonants and vowels should be regarded as the ideal vocal sound, that is, a model for other phonemes in musical-poetic text. While creating vocal melodies of Opus 49 songs, J. Brahms cares the phonetics of a German text in the singing to be comfortable for the performer. Conclusions. J. Brahms uses such principles and techniques of literary original musical embodiment as preservation of the holistic image, created by the author of the poems, on the one hand, and its detailing on the other. In the second case, the composer resorts to all means of musical expression: motive-thematic, texture-register, rhythmic, harmonious, texture ones. The prospects of the research lie in studying the interaction of verbal and musical intonation in other vocal works of J. Brahms, as well as in chamber-vocal music of late romantics.


Author(s):  
Ph. Kamboukos ◽  
K. Mathioudakis

The features of linear performance diagnostic methods are discussed, in comparison to methods based on full non-linear calculation of performance deviations, for the purpose of condition monitoring and diagnostics. First, the theoretical background of linear methods is overviewed to establish a relationship to the principles used by non-linear methods. Then computational procedures are discussed and compared. The effectiveness of determining component performance deviations by the two types of approaches is examined, on different types of diagnostic situations. A way of establishing criteria to define whether non-linear methods have to be employed is presented. An overall assessment of merits or weaknesses of the two types of methods is attempted, based on the results presented in the paper.


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