Main Formulas Research Articles

Synthesis of expert matrices in inductive system-analytical research based on fuzzy logic algorithm

The object of research is the process of inductive modeling of complex systems. The studies that were conducted related to the application of algorithms of the fuzzy logic theory were to coordinate the conclusions of top-level experts in system information-analytical research (SIAR) in the tasks of innovative design. The possibilities of constructing elements of expert matrices of results, as well as evaluating the effectiveness of such applications, are defined. Thanks to this, obtaining formal expert evaluations in numerical form became possible. Experimental studies have confirmed that the proposed approach to the application of fuzzy logic algorithms to the construction of matrices of expert evaluations of SIAR results is quite effective and simple to implement. In addition, this approach fits well into the general paradigm of the Group Method of Data Handling (GMDH). In particular, it was established that the possibility of «retraining» such a block without significant efforts of professional experts can have a positive result, as well as have a good effect on the economic and time parameters of the research project. The main calculation formulas for the algorithm for building a fuzzy system using a neural network in a system with two rules are given. The construction of a fuzzy information output system trained on expert evaluations in the Matlab system is shown. As a result, a technologically acceptable standard deviation of 0.28268 mg/l was obtained. It has been established that by accumulating a database (knowledge) and/or using an information monitoring system, it is possible to «additionally train» a fuzzy system periodically or according to the established quality criterion in the program mode, without involving experts in this process. Thus, there are reasons to assert the importance of using a fuzzy system as one of the tools in inductive SIAR procedures

Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method

This article discusses methods for calculating the deformations of objects with hyperelastic materials within the framework of the nonlinear elasticity theory. This topic is relevant due to the use of new technological materials in industry, and as a result, the emerging task of preliminary numerical calculations for operational reliability, research and modeling of deformation behavior. The first part provides a brief overview of the main provisions and formulas of the nonlinear elasticity theory. Then the spatial discretization of 3-dimensional objects and the calculation of the deformation gradient using the finite element method are considered. The article provides an algorithm for solving this problem, such as minimizing the functional of stored energy, and also considers the class of permissible deformations. Afterwards, a detailed description is given, along with pseudocode, of the method of implementing and calculating the minimization by Newton’s method. The last part demonstrates an example of the calculations performed, based on the developed software that allows for numerical experiments and computer modeling of deformations of hyperelastic bodies, and one of the capabilities of which is to perform these calculations using Newton’s method.

Relative Effectiveness Of Reading Activities In The Pakistani ESL Context

The quality of reading determines the quality of both content and language learning. Reading plays a key role in developing advanced grammatical skill and academic vocabulary necessary for creating written discourse and thus raising learners’ level of language proficiency. However, a substantial body of ESL college learners in Pakistan are reported to be struggling for attaining a satisfactory level in reading proficiency. Notably, the scrutiny of underachievement reveals that indiscriminate insistence on GTM and consequent failure to actively engage learners for cognitive development are included in major issues. For addressing these problems, a promising alternative is suggested in Task-Based Learning (activities-based learning). A 40-minute task-based class, 3 days a week, was run for four weeks. The sample comprised 111 students of Intermediate Level. The researcher-created videos on reading activities uploaded on his YouTube channel were watched by the learners.[1] Listening to the recorded lecture was followed by a set of activities in which the participants were engaged before they showed their work in the physical classroom. Subsequently, relative effectiveness of ten prevalent reading activities was studied through written tests. Quantitative data analysis was made by SPSS. Furthermore, qualitative data collected through interviews were analyzed by inductive approach thematic analysis. Mathematical nature of activities, such as Main Idea Formula, Students Created Quizzes & Tests and Cause & Effect Grid made them relatively more effective.

Microgravity analysis of periodic oscillations of heat and mass transfer of Darcy-Forchheimer nanofluid along radiating stretching surface with Joule heating effects

Reduced gravity impact on mixed convection flow plays a significant role for designing of electric-generating plants in space, unwanted effects of free convection, thermodynamic stability, space devices, surface tension and movement of nanoparticles. The novelty of present work is to find the impact of reduced gravity, Joule heating and thermal radiations on Darcy Forchheimer magnetized flow of nanofluid along the stretching porous sheet. The variable gravity is assumed as temperature dependent with maximum density and maximum density. The governing model is converted into convenient model to find physical thermo parameters. The primitive steady, real and imaginary equations are formed by using stokes and primitive transformations. To make programming algorithm in FORTRAN Lahey-90/95, the primitively terms are deduced in each equation. For tabular and numerical findings of steady velocity, temperature and concentration, the implicit form of finite difference approach is applied with Gaussian elimination method. The fluctuating skin friction, fluctuating heat transfer and fluctuating mass transfer are displayed by using steady outcomes in main formula. It is found that the magnitude of fluid velocity enhances as magnetic force, reduced gravity and Darcy Forchheimer parameter enhances. It is concluded that temperature distribution decreases as magnetic force enhances. It is noted that oscillating frequency in skin friction and heat transfer enhances as Schmidt number enhances. It is found that the maximum fluctuating layer in heat and mass transfer enhances as Prandtl number enhances.

The Evolutionary Masks of Love: Continuities between Judeo-Christian Religious Love and Modern Secular Love

The aim of this paper is to establish a series of links between some of the main religious formulas that arise in Judaism and Christianism and the romantic and confluent love characteristic of modern societies. To carry it out, firstly, we analyze love in historical Judaism, reflecting on the Ahavah formula, the predominant formula in this religious context. Secondly, to study the Christian drift of love, we first analyze how the emergence of this new religious faith (Christianism) provokes a change in the Jewish way of understanding it (love). Subsequently, we analyze some of the three main formulas in which love materializes in Christianism: Agape, Caritas, and Amor Sui. Regarding modern love, we first carry out a contextualization focused on the processes of secularization and individualization, and their impact on it. Afterwards, we present the main features that define both romantic and confluent love, and finally, we analyze the Judeo-Christian characters inherited for such types of love. The methodology used focused on a literature review and theoretical reflection based on this review. The research carried out allows us to establish sociological continuities between Judeo-Christian religious love and modern secular love in the terms used throughout the paper.

Proofs as stateful programs: A first-order logic with abstract Hoare triples, and an interpretation into an imperative language

We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare logic, and the axioms and rules of the logic ensure that the assertions about the state compose in the correct way. The main result of the paper is a realizability interpretation of our logic that extracts programs into a mixed functional/imperative language. All programs expressible in this language act on the state in a sequential manner, and we make this intuition precise by interpreting them in a semantic metatheory using the state monad. Our basic framework is very general, and our intention is that it can be instantiated and extended in a variety of different ways. We outline in detail one such extension: A monadic version of Heyting arithmetic with a wellfounded while rule, and conclude by outlining several other directions for future work.

Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques

In this study, an optimal L-stable time-efficient hybrid block method with a relative measure of stability is developed for solving stiff systems in ordinary differential equations. The derivation resorts to interpolation and collocation techniques over a single step with two intermediate points, resulting in an efficient one-step method. The optimization of the two off-grid points is achieved by means of the local truncation error (LTE) of the main formula. The theoretical analysis shows that the method is consistent, zero-stable, seventh-order convergent for the main formula, and L-stable. The highly stiff systems solved with the proposed and other algorithms (even of higher-order than the proposed one) proved the efficiency of the former in the context of several types of errors, precision factors, and computational time.

Key Technology of 240°C High-Temperature Drilling Fluid

Hot dry rock (HDR) is a renewable green and clean energy source from the depths of the earth. It has the characteristics of high efficiency, environmental protection, safety, and stability, and is not restricted by seasons and climates. Difficulties in exploration and development include deep burial, formation fragmentation, abnormal pressure, high well temperature gradient, and high hole bottom temperature (usually >200°C), key technical issues such as sticking. This paper analyzes the difficulties of high-temperature resistant drilling fluid in dry hot rock: temperature resistance of treatment agents and systems, foaming, leakage, wellbore instability, and other problems. The optimization and experiment of treatment agents such as loss reducers, high-temperature protective agents, etc., and research on drilling fluid technology resistant to high temperature of 240°C in hot dry rock drilling has been carried out, through the optimization experiment of pulping materials and high temperature treatment agent. The main formula is: 3%-4% Sodium bentonite + 2%-3% HPS + 3%-4% SPNH + 2%-4% GJA + 3%-4% JSJ-1 + 0.5%-1.0% GGDP + 1% GBHJ. The drilling fluid formula has good rheology after hot rolling at 240°C, API filtrate loss<5ml, the viscosity recovery rate is over 90%. It provides effective technical support guarantee for promoting the exploration and development of hot dry rock resources in China.

Методика розрахунку основних характеристик підшипників ковзання систем і агрегатів автомобілів та аналізу їх трибологічної ефективності

A methodology for calculating the main characteristics of sliding bearings of car systems and units is proposed. The specified methodical approach is important when evaluating indicators of tribological efficiency of couplings of parts, nodes, systems and aggregates and operational reliability of cars as a whole. The bearing activation model makes it possible to formulate measures to increase the tribological efficiency of the couplings of parts and the level of operational reliability of nodes, systems and aggregates, and cars as a whole. In addition, the parameters of the actuation model also respond to friction modes. It is shown that it is possible to increase the tribological efficiency of the sliding bearing by means of design, technological and operational methods. The main formulas that make it possible to develop algorithms for calculating a set of bearing characteristics are presented: contact pressure, stress, strength, sliding resistance, wear, resource. For this purpose, the following values are used: compliance coefficients and relative load, contact angle, contact pressures, contact displacements, and the stress state in the contact zone. The geometric and power parameters of the bearing are involved in the developed methodology and algorithm. Modes of friction and the nature and magnitude of the load on the bearing are also taken into account. An algorithm for calculating auxiliary and main characteristics of a sliding bearing has been developed. The conditions of continuity and equilibrium in contact are clarified. The differential-integral equation of the operation of the bearing is obtained and the dependence of the current contact angle on the friction path and other parameters of the sliding bearing operation model is obtained. It is shown that the tribological efficiency of sliding bearings is established by the method of comparative analysis of tribotechnical characteristics determined by the results of tests on friction machines and a stand.

To the 100th anniversary of the main analytical formulas of the decline curves

To the 100th anniversary of the main analytical formulas of the decline curves

Structural Damage Detection Based on Static and Dynamic Flexibility: A Review and Comparative Study

Material damage in structures must be detected in a timely manner to prevent engineering accidents. Damage detection based on structural flexibility has attracted widespread attention in recent years due to its simplicity and practicality. This article provides a detailed overview of damage detection methods based on structural flexibility. Depending on the calculation method and data used, flexibility-based methods can be divided into the following categories: flexibility difference, flexibility derivative index, flexibility sensitivity, flexibility decomposition, static flexibility, and combinations of flexibility with other methods. The basic principles and main calculation formulas of various flexibility methods are explained, and their advantages and disadvantages are analyzed. For the method using flexibility difference, the advantage is that the calculation is very simple and does not require the construction of a finite element model of the structure. The disadvantage is that it requires the measurement of modal data of the intact structure, and this method cannot quantitatively assess the degree of damage. For the method using the flexibility derivative index, the advantage is that it only requires the modal data of the damaged structure to locate the damage, but this method is particularly sensitive to noise in the data and is prone to misjudgment. For methods based on flexibility sensitivity and flexibility decomposition, the advantage is that they can simultaneously obtain the location and degree of damage in the structure, but the disadvantage is that they require the establishment of accurate finite element models in advance. Static flexibility methods can compensate for the shortcomings of dynamic flexibility methods, but they usually affect the normal use of the structure during static testing. Combining flexibility-based methods with advanced intelligent algorithms and other methods can further improve their accuracy and efficiency in identifying structural damage. Finally, this article discusses the challenges that have not yet been solved among damage detection methods based on structural flexibility.

The Performance of a Lip-Sync Imagery Model, New Combinations of Signals, a Supplemental Bond Graph Classifier, and Deep Formula Detection as an Extraction and Root Classifier for Electroencephalograms and Brain–Computer Interfaces

Many current brain–computer interface (BCI) applications depend on the quick processing of brain signals. Most researchers strive to create new methods for future implementation and enhance existing models to discover an optimal feature set that can operate independently. This study focuses on four key concepts that will be used to complete future works. The first concept is related to potential future communication models, whereas the others aim to enhance previous models or methodologies. The four concepts are as follows. First, we suggest a new communication imagery model as a substitute for a speech imager that relies on a mental task approach. As speech imagery is intricate, one cannot imagine the sounds of every character in every language. Our study proposes a new mental task model for lip-sync imagery that can be employed in all languages. Any character in any language can be used with this mental task model. In this study, we utilized two lip-sync movements to indicate two sounds, characters, or letters. Second, we considered innovative hybrid signals. Choosing an unsuitable frequency range can lead to ineffective feature extractions. Therefore, the selection of an appropriate frequency range is crucial for processing. The ultimate goal of this method is to accurately discover distinct frequencies of brain imagery activities. The restricted frequency range combination presents an initial proposal for generating fragmented, continuous frequencies. The first model assesses two 4 Hz intervals as filter banks. The primary objective is to discover new combinations of signals at 8 Hz by selecting filter banks with a 4 Hz scale from the frequency range of 4 Hz to 40 Hz. This approach facilitates the acquisition of efficient and clearly defined features by reducing similar patterns and enhancing distinctive patterns of brain activity. Third, we introduce a new linear bond graph classifier as a supplement to a linear support vector machine (SVM) when handling noisy data. The performance of the linear support vector machine (SVM) significantly declines under high-noise conditions. To complement the linear support vector machine (SVM) in noisy-data situations, we introduce a new linear bond graph classifier. Fourth, this paper presents a deep-learning model for formula recognition that converts the first-layer data into a formula extraction model. The primary goal is to decrease the noise in the formula coefficients of the subsequent layers. The output of the final layer comprises coefficients chosen by different functions at various levels. The classifier then extracts the root interval for each formula, and a diagnosis is established based on these intervals. The final goal of the last idea is to explain the main brain imagery activity formula using a combination formula for similar and distinctive brain imagery activities. The results of implementing all of the proposed methods are reported. The results range between 55% and 98%. The lowest result is 55% for the deep detection formula, and the highest result is 98% for new combinations of signals.

A Unified General Resistance Formula for Uniform Coarse Porous Media

Many authors studied the nonlinear relationship between seepage velocity and hydraulic gradient in coarse granular materials. They managed different approaches and variables to define the resistance formula applicable to that type of granular media. Based on the analysis of the different approaches and experimental data obtained by the corresponding authors, we propose a unified general seepage equation applicable to large-sized granular materials. Such an equation gives unity to the main nonlinear resistance formulas developed to date. Particularly relevant are the conclusions regarding the relationship of the linear (α*) and quadratic (β*) dimensionless coefficients of the resistance formula with the representative size of the particle and the geometrical features of the porous materials.

Optimization of the iot network protocol choozing for monitoring audio information

The subject of research is the choice of a protocol in the Internet of Things (IoT) network for monitoring and analyzing audio information. The purpose of the article is to optimize the process of choosing a protocol for monitoring audio information based on IoT and evaluate the results. The authors have developed an IoT framework for monitoring and analyzing audio and voice information. The IoT network includes a sound sensor (microphone), a unit for analyzing the information received from it and a decision-making module. The description of protocols in the IoT network for assessing the sound level is given: the Wireless USB standard, the narrowband standard of the NB-IoT.The hierarchy analysis method was used to select the best protocol. The methodology and its main formulas for calculating the best option are given. A table of the four selected protocols for the IB network is given. As characteristics of the protocols, the following are considered: downlink speed, latency, device bandwidth, device transmission power. A matrix of paired comparisons of protocol parameter indicators based on expert assessments has been formed. Four matrices of paired comparisons of transmission standards variants in relation to the indicator of speed, delay, bandwidth of devices, transmission power of devices are constructed. Calculations of local vectors and priority vectors of quality indicators were performed for these four matrices. Then the matrix of vectors of global priorities is calculated by calculating the sum of the products of local vectors of matrices of paired comparisons of transmission standards variants on the corresponding priority vectors of quality indicators of the matrix of paired comparisons of protocol parameters. From the results obtained, the best protocol option for the network and sound monitoring was determined by the maximum value.

Screen invariant lightlike hypersurfaces of almost product-like statistical manifolds and locally product-like statistical manifolds

Screen invariant lightlike hypersurfaces of almost product-like statistical manifolds and locally product-like statistical manifolds are introduced. The main formulas and relations are presented for these hypersurfaces. Concurrent and recurrent vector fields are investigated and some characterizations are obtained for screen invariant lightlike hypersurfaces.

The portrait of Jane Austen in chick lit style (“Jane in Love” by R. Givney)

The article studies Rachel Givney’s novel “Jane in Love”, which conjectures the biography of Jane Austen who is considered to be the mother of chick lit. The study proves that Givney uses: 1) the principles and techniques of chick lit, a modern literary genre of the post-feminist era, at the same time revising the matrix of chick lit; 2) a fabulous narrative theme, discovered by V. Propp, which also undergoes some revision. Givney rethinks the happy ending conceptually important for chick lit and for the fairy tale with regard to a psychological novel devoted to an artist who has found his voice and his place in world literature. In her narrative about Jane Austen, a time traveler, the writer conceptualizes her significance for modern English culture and the Englishmen structuring her novel with formulas-codes of Jane Austen’s oeuvre. The main storyline of her novels is devoted to the complexities of love, and their plots assume a certain set of components. A love affair with a happy ending in the spirit of the Cinderella fairy tale is the main formula of Jane Austen’s novels, which is in demand in chick lit. R. Givney reduces this formula and fills it with a new content: her Jane Austen sacrifices a man for the sake of the future.

Counting derangements with signed right-to-left minima and excedances

Recently Alexandersson and Getachew proved some multivariate generalizations of a formula for enumerating signed excedances in derangements. In this paper we first relate their work to a recent continued fraction for permutations and confirm some of their observations. Our second main result is two refinements of their multivariate identities, which clearly explain the meaning of each term in their main formulas. We also explore some similar formulas for permutations of type B.

Anisotropic flow and the valence quark skeleton of hadrons

We study transverse momentum anisotropies, in particular, the elliptic flow v2 due to the interference effect sourced by valence quarks in high-energy hadron-hadron collisions. Our main formula is derived as the high-energy (eikonal) limit of the impact-parameter dependent cross section in quantum field theory, which agrees with that in terms of the impact parameter in the classical picture. As a quantitative assessment of the interference effect, we calculate v2 in the azimuthal distribution of gluons at a comprehensive coverage of the impact parameter and the transverse momentum in high-energy pion-pion collisions. In a broad range of the impact parameter, a sizable amount of v2, comparable with that produced due to saturated dense gluons or final-state interactions, is found to develop. This is in contrast with similar studies in heavy-ion collisions using classical color charge distributions in which such a contribution from geometric correlations was found to be small and has, hence, been ignored in recent studies. In our calculations, the valence sector of the pion wave function is obtained numerically from the Basis Light-Front Quantization, a non-perturbative light-front Hamiltonian approach. And our formalism is generic and can be applied to other small collision systems like proton-proton collisions.

METHOD OF ULTRASONIC PHASE TWO-COORDINATE INFORMATION REGISTRATION FOR AUTOMATED NON-DESTRUCTIVE TESTING SYSTEMS

The article is devoted to the issue of improving the coordinate registration of information in means of automated non-destructive testing. Existing systems of non-contact registration of spatial position sensors of non-destructive testing are mostly focused on the use of signal fields of different physical nature, for example, acoustic or optical, which are created around the position of these sensors and amplitude methods of signal processing. These methods do not provide the necessary accuracy of determining the coordinates in the case of using small-aperture sensors of non-destructive testing.&#x0D; The basis of the proposed technical solution is the trilateration method. The distance between the emitter of ultrasonic vibration, which is structurally connected to the sensor, and the two receivers is determined by the phase method. This method provides increased accuracy in determining the coordinates of the sensor. Eliminating the ambiguity of phase measurements is based on the combination of the multi-frequency method and the numerical system of residual classes. This makes it possible to minimize the probability of incorrect resolution of the ambiguity of the results of phase distance measurements and to ensure high accuracy of coordinate determination (with an absolute error of the order of mm). The idea of the method and the main calculation formulas that make it possible to determine the modules of the numerical system of residual classes and the values of the operating frequencies of ultrasonic oscillations are presented. Matching the discretes for determining the phase shifts of signals with the modules of the numerical system of residual classes at different operating frequencies makes it possible to reduce the resolution of the ambiguity of the results of phase measurements to the task of restoring integers in the positional counting system from their representation by residuals in the numerical system of residual classes. The mechanism of occurrence of gross errors in the recovery of whole numbers is considered. An algorithm for eliminating this error is proposed. In general, the correctness of the algorithm for determining the sensor coordinates is confirmed by the simulation results. The considered method of two-coordinate information registration can be used both in the development of new automated means of non-destructive testing, and for the improvement of existing ones, which involve a manual method of scanning the surface of testing objects.

THE TURKIC “CUCKOO” IN OLONKHO: TRANSFORMATIONS AND RUDIMENTS

The article is devoted to the image of cuckoo in the Yakut Olonkho in comparison with the materials of the Altai, Khakas, Shorian and Tuvan epics. In total, 58 Yakut epic texts, including early records of the Olonkho of the 19th — early 20th centuries were analyzed. It is established that while in Turkic folklore the semantics of the image of the cuckoo was ambivalent on the whole, the epic mostly reflects a favourable or neutral attitude to this bird. In positive connotations, the “cuckoo” is more represented as a harbinger of well-being and prosperity. It was also revealed that the comparison “cuckoo the size of a horse’s head” previously functioned in all five examined epics; the Altai, Khakas, Shorian and Tuvan epics represented the “golden cuckoo” and the Yakut Olonkho — the “sonorously talking cuckoo”. Hence, the Yakut epic Olonkho could separate from the general, pro-Turkic epic before the development of the “gold cult,” and the earliest variant of the image of the Turkic cuckoo was preserved in it. Five main stable formulas containing the image of the cuckoo have been found in the Yakut epic tradition. All of them have positive connotations: the cuckoo appears as a symbol of eternal summer and prosperity; as a symbol of fertility; as a soothsayer preventing misfortune. The structural variants under the general concept of “the cuckoo-udaganka” represent this bird as a translator between the world of people and the supreme protective deity of the Yakuts, Yuryung Aar Toyon, thus the image of the cuckoo is closely associated with the image of a white sounorous-voiced udaganka. Also distinguished is a group of semantically heterogeneous constructions of the later period (post-1932), most of them with negative connotations, influenced by shamanism, folk omens and beliefs. Thus, the key role in the formation of the Yakut version of the cuckoo image was played by the Udagan culture, and at a later stage certain transformations were introduced by shamanism.