Rational Transformation Research Articles

On the Algebraic Properties of Quasi-affine Bijective Transformations

A quasi-affine transformation, being the whole part of a rational affine transformation, is the discretized form of an affine transformation. Introduced by Marie-André Jacob-Da Col, it has been the subject of numerous studies. This article is devoted to the study of the algebraic structures of some quasi-affine bijective transformations, in particular the discrete translations of isolated points and Pythagorean rotations.

HESIOD’UN THEOGONY ESERİ: ANTİK YUNAN’DA RASYONEL AKLIN VE ATAERKİLLİĞİN YÜKSELİŞİ

Hesiod’s Theogony is composed of several myths about the origins of gods and men with an emphasize on the turning points in their relations. It is clear that Theogony is a collection of common narrations of oral tradition. What makes it significant is that it is a first attempt to gather all these myths together in a written form. However, writing them down means giving them a stabilized form and content as well. Shaped in accordance with the political and social realities of his time, Hesiod’s narration gains an ideological character which puts the reign of Zeus over all local gods and goddesses while praising a rational understanding and patriarchal order in Greek society. Therefore, this paper aims to give an opinion on how to trace the rational and patriarchal transformation of the Greek society in Hesiod’s text and to observe how ideologies are forced upon texts through writing process.

Necessary and Sufficient Conditions for Expressing Quadratic Rational Bézier Curves

Quadratic rational Bezier curve transformation is widely used in the field of computer geometry. In this paper, we offer several important characteristics of quadratic rational Bezier curve. More precisely, on the basis of proving its monotonicity, the necessary and sufficient conditions for transforming quadratic rational Bezier curve into point, line segment, parabola, elliptic arc, circular arc and hyperbola are proved respectively.

Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule

In this work we introduce new rational transformations which are available for numerical evaluation of weakly singular integrals and Cauchy principal value integrals. The proposed rational transformations include parameters playing an important role in accelerating the accuracy of the Gauss quadrature rule used for the singular integrals. Results of some selected numerical examples show the efficiency of the proposed transformation method compared with some existing transformation methods.

Rational phase transformation and morphology design to optimize oxygen evolution property of cobalt tungstate

In this work, a facile and feasible soft template method with the aid of buffer solution is successfully applied to synthesize high-order mesoporous cobalt tungstate for the first time. Attributing to the regulation of reaction solution’s pH value and the existence of template, the phenomenon of phase transformation occurs, and high-order mesoporous structure is formed. Because of the variation of phase and morphology, only 448 mV can deliver a current density of 10 mA cm−2 with a small Tafel slope (61 mV dec−1) for mesoporous cobalt tungsten oxide hydroxide, while the cobalt tungstate nanoparticles cannot satisfy the basic demand of electrocatalysts. Herein, rational phase transformation and morphology design can significantly affect the property of oxygen evolution, which can provide vast opportunities to turn into candidates for the novel oxygen evolution catalyst.

Solvent exchange as a synthetic handle for controlling molecular crystals

Organic/molecular crystals have been widely applied in medicine, imaging, explosives, and optoelectronics, but there are very limited methods for controlling their size and shape at the micro- or nanoscale. Herein, we develop solvent exchange as a new synthetic handle for creating complex morphologies in molecular crystals. With mitigated driving force in solution phase, solvent loss or exchange in C60 plates does not lead to structural collapse, but leads to crystal transformation to mesh networks. C70 and tetrakis(4-bromophenyl)ethylene crystals show similar transformation upon solvent exchange. We study the co-solvents and uncover their competing roles in the destabilization of the crystal structure and the on-site crystallization towards rods. This unconventional role of co-solvent is of importance not only for understanding the pore formation and crumbling, but also a new step towards regulating the desolvation and recrystallization processes. Rational transformation of organic crystals would open a new synthetic route for designing complex structures and new properties.

Recursive constructions of k-normal polynomials using some rational transformations over finite fields

Some results on the [Formula: see text]-normal elements and [Formula: see text]-normal polynomials over finite fields are given in the recent literature. In this paper, we show that a transformation [Formula: see text] can be used to produce an infinite sequence of irreducible polynomials over a finite field [Formula: see text] of characteristic [Formula: see text]. By iteration of this transformation, we construct the [Formula: see text]-normal polynomials of degree [Formula: see text] in [Formula: see text] starting from a suitable initial [Formula: see text]-normal polynomial of degree [Formula: see text]. We also construct an infinite sequence of [Formula: see text]-normal polynomials using a certain quadratic transformation over [Formula: see text].

Construction of irreducible polynomials through rational transformations

Let Fq be the finite field with q elements, where q is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over Fq of high degree using rational transformations. In particular, given a divisor D>2 of q+1 and an irreducible polynomial f∈Fq[x] of degree n such that n is even or D≢2(mod4), we show how to obtain from f a sequence {fi}i≥0 of irreducible polynomials over Fq with deg⁡(fi)=n⋅Di.

Space-time accurate finite-state dynamic inflow modeling for aeromechanics of rotorcraft

Wake inflow modeling is a crucial issue in the development of efficient and high-fidelity simulation tools for rotorcraft flight dynamics and aeroelasticity. This paper proposes a space-time accurate, finite-state, dynamic wake inflow modeling suitable for conventional and innovative rotor configurations, based on simulations provided by high-fidelity aerodynamic solvers. It relates the coefficients of a rotor-disc, radial-azimuthal wake inflow distribution to the rotor kinematic variables, and is capable to take into account the intrinsic periodicity of aerodynamic responses of rotors in steady forward flight. The proposed inflow modeling consists of a three-step process: (i) numerical evaluation of wake inflow due to perturbations of rotor kinematic variables, (ii) determination of transfer functions of multi-harmonic components of a suitable set of inflow coordinates, followed by (iii) their rational approximation and transformation into time domain to derive the differential operators governing multi-harmonic dynamics. The numerical investigation concerns the derivation of finite-state inflow models for single and coaxial rotors, through application of an aerodynamic boundary-element-method solver for potential flows. These are successfully validated by comparison with inflows directly calculated by the aerodynamic tool for arbitrary rotor perturbations.

Автоматизація процесу розподілу фінансових оборонних ресурсів підчас оборонного планування на основі спроможностей

The article demonstrates an example of automation of the process of allocation of financial defence resources during capability-based defence planning. In the process of solving the problem, a schedule of rational transformation of defence forces within a defined time frame is developed, taking into account scenarios of the use of the defence forces, projected expenditures on defence and the capabilities of the domestic defence industrial complex.

Root polynomials and their role in the theory of matrix polynomials

We develop a complete and rigorous theory of root polynomials of arbitrary matrix polynomials, i.e., either regular or singular, and study how these vector polynomials are related to the spectral properties of matrix polynomials. We pay particular attention to the so-called maximal sets of root polynomials and prove that they carry complete information about the eigenvalues (finite or infinite) of matrix polynomials and that they are related to the matrices that transform any matrix polynomial into its Smith form. In addition, we describe clearly, for the first time in the literature, the extremality properties of such maximal sets and identify some of them whose vectors have minimal grade. Once the main theoretical properties of root polynomials have been established, the interaction of root polynomials with three problems that have attracted considerable attention in the literature is analyzed. More precisely, we study the change of root polynomials under rational transformations, or reparametrizations, of matrix polynomials, the recovery of the root polynomials of a matrix polynomial from those of its most important linearizations, and the relationship between the root polynomials of two dual pencils. We emphasize that for the case of regular matrix polynomials all the results in this paper can be translated into the language of Jordan chains, as a consequence of the well known relationship between root polynomials and Jordan chains. Therefore, a number of open problems are also solved for Jordan chains of regular matrix polynomials. We also briefly discuss how root polynomials can be used to define eigenvectors and eigenspaces for singular matrix polynomials.

THE USE OF SEMIOTIC APPROACH IN THE GRAPHIC TRAINING PROCESS OF INTENDING ENGINEERING TEACHERS OF COMPUTER PROFILE

The article deals with the issues of optimization of the process of graphic concepts formation in the intending specialists who study in “Professional Education. Computer Technologies” specialty based on the experience of the course “Engineering Graphics”. In the context of the educational process, the possibility to build a hierarchical structure of graphic concepts that are required for intending engineering educators for rational perception and transformation of the subject environment, based on the semiotic approach, is analyzed.In the graphic sphere a sign tool is described as an image to be done in accordance with generally accepted instructions. Here a real object, the image one may see on the drawing, is characterized as a sign, while its interpretation is a need for receiving or transferring the definite information.In order to solve the proper assignments, drawing determines its sphere of signs functioning. It proves that strictly regulated structure of lines order with different parameters (sign tools) creates an informational system.Syntactic drawing structure is found as an interconnection of signs, which is conditioned by reactions interconnection. Sign tools are their result or part.Based on the drawing analysis via semiotic interpretation, a dot is found to be its smallest unit. It is impossible to be a sign, since it is a one-sided unit (it has got expressing plan only; it is meaningless). It is a unit for signs structuring and differentiation. A line is a two-sided unit – it has got both expressing and content plan.Semiotic analysis of graphic terms defines their hierarchic scheme. The latter gives the opportunity to provide the levels of the material studying, the list of graphic work types and teaching methods. It may teach students “to observe and understand” contingent graphic image; promote the development and adaptation of natural physiological possibilities into the opportunity to use the drawing language consciously.

Assessment of Traffic Noise Pollution Due to Urban Residential Road Transport

Abstract The problem of combating urban noise is closely linked to the rational transformation of the urban environment, which must go through the elimination or reduction of the number of sources of noise, the localization of the noise emission zone, reducing the level of sound sources and protection against noise for the residential areas. Theoretical and experimental studies of acoustic loading on the territory along the highway for the typical section of the urban territory have been conducted. To estimate the complex noise impact from all sources and from individual sources, as well as to predict the total noise exposure for this site, a noise map was constructed using software. As a measure to combat traffic noise in the territory along the highway, the location of the noise protection screen was justified, taking into account the loss of part of the national income as a result of the continuous impact of noise on a person.The results of the research allow to assess the degree of technogenic impact of noise pollution during the operation of the highway, which allows regulating, by administrative and legislative methods, the nature of the impact on natural objects and human health of certain types of activities, as well as reasonably proposing measures that ensure environmental safety when organizing urban streets traffic.

Möbius-like maps on irreducible polynomials and rational transformations

In the past few years, an action of the group PGL2(Fq) on the set of monic irreducible polynomials over Fq has been introduced and questions on the characterization and number of fixed points were discussed. In this paper we show that, in general, such fixed points arise from rational transformations, extending a work of Mattarei and Pizzato (2017).

The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation

A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ+iℝ under a generalized Boolean transformation, called rational Boolean transformation from ℝ into itself, is derived using Birkhoff’s ergodic theorem. This formula is represented as a computable integral. Using the Cauchy’s integral theorem, values of this integral corresponding to various possible cases are explicitly computed.

Analysis of Sensor Trapped Power Quality Indices Using Empirical Wavelet Transform and Rational Dilation Wavelet Transform to Achieve High Accuracy and Frequency Resolution

Analysis of Sensor Trapped Power Quality Indices Using Empirical Wavelet Transform and Rational Dilation Wavelet Transform to Achieve High Accuracy and Frequency Resolution

Diagnosis of Bearing Outer Race Faults Using a Low-Cost Non-Contact Method with Advanced Wavelet Transforms

This study analyses the vibration of Squirrel Cage Induction Motor (SCIM) with bearing faults using high-frequency signal (Handheld UWB radar) and Software Phase Locked Loop algorithm (SPLL). The contact or non-contact methods perform condition monitoring of the SCIM. The proposed method is a non-contact technique to perform condition monitoring of the SCIM. The contact methods execute via vibration, instantaneous frequency, rotor speed and flux signals analysis; whereas non-contact methods accomplish via acoustic, current and stray flux measurement. The existing techniques suffer from the influence of adjoining electrical machines; require human expertise to mount sensors and analysing the signals. In this paper, a new, non-contact method proposed for bearing fault identification in the SCIM. The proposed method uses a high-frequency signal projected on the motor and the reflected signal captured. The signal obtained is analysed with an advanced signal processing algorithm like Rational Dilation Wavelet Transform (RDWT) to identify the faults in the SCIM. The signal energy at the fault frequency level increases from 4.72 % to 5.82 % with the increase in the number of the faults. The signal energy variation indicates the severity of the faults. From the experimental results, the bearing fault of the motor identified in the beginning stage of the fault.DOI: 10.5755/j01.eie.25.1.22735

Fixed points of rational functions satisfying the Carlitz property

Recent research within the field of cryptography has suggested that S-boxes should be chosen to contain few fixed points, motivating analysis of the fixed points of permutations. This paper presents a novel mean of obtaining fixed points for all functions satisfying a property put forth by Carlitz. We determine particular results concerning the fixed points of rational functions. Such concepts allow the derivation of an algorithm which cyclically generates fixed points for all three classes of functions satisfying the Carlitz property, the most renowned of which are Redei rational functions. Specifically, we present all fixed points for any given Redei function in a single cycle, generated by a particular non-constant rational transformation. For the other two classes of functions, we present their fixed points in cycles consisting of smaller cycles of fixed points. Finally, we provide an explicit expression for the fixed points of all Redei functions over $${\mathbb {F}}_q$$ .

Efficient computational analysis of non-exhaustive service vacation queues: BMAP/R/1/N(∞) under gated-limited discipline

• A finite-buffer vacation queue with batch Markovian arrival process has been analyzed. • The server is subjected to serve under gated-limited service discipline. • Proposed analysis is based on the successive substitution and the supplementary variable method. • The results have been matched with the corresponding infinite-buffer queue. • Numerical results are presented for different service- and vacation-time distributions. This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process ( BMAP ) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N ) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations . The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms.

Wheeze type classification using non-dyadic wavelet transform based optimal energy ratio technique

Background and objectiveWheezes in pulmonary sounds are anomalies which are often associated with obstructive type of lung diseases. The previous works on wheeze-type classification focused mainly on using fixed time-frequency/scale resolution based on Fourier and wavelet transforms. The main contribution of the proposed method, in which the time-scale resolution can be tuned according to the signal of interest, is to discriminate monophonic and polyphonic wheezes with higher accuracy than previously suggested time and time-frequency/scale based methods. MethodsAn optimal Rational Dilation Wavelet Transform (RADWT) based peak energy ratio (PER) parameter selection method is proposed to discriminate wheeze types. Previously suggested Quartile Frequency Ratios, Mean Crossing Irregularity, Multiple Signal Classification, Mel-frequency Cepstrum and Dyadic Discrete Wavelet Transform approaches are also applied and the superiority of the proposed method is demonstrated in leave-one-out (LOO) and leave-one-subject-out (LOSO) cross validation schemes with support vector machine (SVM), k nearest neighbor (k-NN) and extreme learning machine (ELM) classifiers. ResultsThe results show that the proposed RADWT based method outperforms the state-of-the-art time, frequency, time-frequency and time-scale domain approaches for all classifiers in both LOO and LOSO cross validation settings. The highest accuracy values are obtained as 86% and 82.9% in LOO and LOSO respectively when the proposed PER features are fed into SVM. ConclusionsIt is concluded that time and frequency domain characteristics of wheezes are not steady and hence, tunable time-scale representations are more successful in discriminating polyphonic and monophonic wheezes when compared with conventional fixed resolution representations.