Set Of Mathematical Expressions Research Articles

PV Defects Identification through a Synergistic Set of Non-Destructive Testing (NDT) Techniques

A synergistic set of NDT techniques, including I-V analysis, UVF imaging, IR thermography, and EL imaging, supports a diagnostics methodology developed in this work to qualitatively and quantitatively identify a wide range of PV defects. The methodology is based on (a) the deviation of the module electrical parameters at STC from their nominal values, for which a set of mathematical expressions was developed that provide an insight into potential defects and their quantitative impact on the module electrical parameters, and (b) the variation analysis of EL images captured at a sequence of bias voltages for a qualitative investigation on the spatial distribution and strength of the defects. The synergy of these two pillars, supported by UVF imaging, IR thermography, and I-V analysis cross-correlating their findings, makes the diagnostics methodology effective and reliable. It was applied on c-Si and pc-Si modules operating from 0-24 years, exhibiting a diversity of defects of varying severity, either pre-existing or formed by natural ageing or externally induced degradation. Defects such as EVA degradation, browning, corrosion in the busbar/interconnect ribbons, EVA/cell-interface delamination, pn-junction damage, e-+hole recombination regions, breaks, microcracks, finger interruptions, and passivation issues are detected. Degradation factors triggering a cascade of internal degradation processes through cause and effect are analysed and additional models are proposed for the temperature pattern under current mismatch and corrosion along the busbar, further empowering the cross-correlation of NDT results. Power degradation was determined from 1.2% in 2 years of operation to more than 50% in modules with film deposition.

Entropy generation investigation of MHD Ag– and Au–H2O nanofluid above an exponential porous stretchable surface with thermal radiation and stagnation point flow

The current study presents an entropy generation investigation of magnetohydrodynamic Ag - and Au - H 2 O nanofluid flows induced by an exponential stretchable sheet implanted in porous media accompanying suction/injection and heat radiation impact. Moreover, the stagnation point flow and silver and gold nanoparticles are considered. The consequences of ohmic heating and thermal radiation are also included as part of the heat transport examination. A physical process is transformed into a set of mathematical expressions using mathematical concepts, which can then be further simplified by using the necessary variables. Considering numerous physiological factors of interest, exact solutions for velocity and temperature profiles are calculated. Graphs and numerical tables are utilized to examine how different physical entities affect the distribution of velocity, temperature, and entropy. It is noted that enhancing the values of Ω reduces entropy inception. It is observed that the entropy inception field gains due to an increment in Ec rt .

Retrieval and Ranking of Combining Ontology and Content Attributes for Scientific Document.

Traditional mathematical search models retrieve scientific documents only by mathematical expressions and their contexts and do not consider the ontological attributes of scientific documents, which result in gaps between the queries and the retrieval results. To solve this problem, a retrieval and ranking model is constructed that synthesizes the information of mathematical expressions with related texts, and the ontology attributes of scientific documents are extracted to further sort the retrieval results. First, the hesitant fuzzy set of mathematical expressions is constructed by using the characteristics of the hesitant fuzzy set to address the multi-attribute problem of mathematical expression matching; then, the similarity of the mathematical expression context sentence is calculated by using the BiLSTM two-way coding feature, and the retrieval result is obtained by synthesizing the similarity between the mathematical expression and the sentence; finally, considering the ontological attributes of scientific documents, the retrieval results are ranked to obtain the final search results. The MAP_10 value of the mathematical expression retrieval results on the Ntcir-Mathir-Wikipedia-Corpus dataset is 0.815, and the average value of the NDCG@10 of the scientific document ranking results is 0.9; these results prove the effectiveness of the scientific document retrieval and ranking method.

Behaviour of simply supported RC skew slabs stiffened with shallow beams

Skew slab is the most common structural element that finds numerous applications in practice, especially when there is any space constraint that prevents the selection of either square or rectangular slab. Due to its geometry, this type of slab behaves differently in comparison to the rectangular slabs and it is a very time-consuming process to predict the moment field in such type of slabs. It becomes still more complicated when some beam system is used to meet the prescribed serviceability criterion. A set of mathematical expressions is presented in the paper that could be of help to predict the moment field being induced in skew slabs under external loads. The outcome of the proposed expressions is validated experimentally as well as numerically; a good agreement is observed in the results. An illustrative example is also presented in the paper to demonstrate the efficiency of the proposed expressions.

An optimal clear channel assessment in IEEE 802.15.4 medium access control protocol for recurrent data transmission and long acknowledgement wait period

AbstractThe IEEE 802.15.4 standard medium access control (MAC) protocol is widely adopted for short‐range communication in current technologies such as Internet of Things, smart grids, and smart cities. The IEEE 802.15.4 standard adopts the carrier‐sense multiple access with collision avoidance channel access mechanism, which performs two consecutive clear channel assessment (CCA). However, performing two consecutive CCA may not be suitable for all types of network scenarios in a star topology‐enabled wireless sensor networks (WSN). In this article, we develop an optimal CCA channel access mechanism to address the recurrent data transmission and the long acknowledgement wait period which is encountered in two network scenarios considered in a star topology‐enabled WSN. To achieve these requirements, the proposed methodology performs five consecutive CCA for successful data transmission without going into the next backoff stage. Initially, an accurate Markov chain model is developed. Later, a set of mathematical expressions are developed for the proposed method. The model is validated using MATLAB 2017a programming tool. Simulation results show that the proposed methodology outperforms the existing CCA approaches in terms of channel collision time, delay, reliability, probability of collision, packet loss rate, and the probability of successful data transmission.

Detection of DG-islanding employing decision boundary of polarization ellipse parameters

This article presents a mathematical equations-based approach for islanding detection of distributed generations (DGs). To develop the proposed method, first, a set of mathematical expressions, characterizing the dynamics of electrical quantities during islanding situations, are selected; the quantities are: deviation of rotor angle, frequency and rate-of-change-of-frequency (RoCoF). Second, these electrical quantities are transformed into three-dimensional (3D) Polarization Ellipse (PE) domain, which yields five parameters, namely, azimuth, elevation, tilt angles, semi-minor and semi-major axes. Finally, an equation of decision boundary (DB) is developed to classify between the islanding events and non-islanding incidents. An extensive assessment of the proposed method is carried out considering the critical test cases which include surplus or shortage of real/reactive power mismatch situations that may exist during islanding. The presence of different load-types, with various quality factors, is also accounted for the test. A large number of islanding events and non-islanding disturbances, such as, capacitor switching, load switching, temporary faults, etc., are simulated in real-time using the model of a practical distribution network developed in Opal-RT digital platform. The proposed approach is critically assessed using F-measure technique and the assessment emphasize the selection of the method as a potential tool for detection of DG-islanding.

A method for estimating the thermal regime of solar panels when performing angular turns of the Earth observation satellite

The results of modeling the thermal operation of solar panels (PSB) of the Earth observation satellite (EOS) when moving in a circular orbit are presented. Modeling of the thermal regime is carried out for two groups of photovoltaic converters (FEP). FEPs are conventionally divided into groups, depending on the strength of the influence of different heat fluxes characteristic of the movement of the satellite in a circular orbit. Analytical expressions for the heat balance equation of the PSBs and the results of numerical calculations at the end of the active life (SAC) are given. In this work, methods of deduction, induction, analysis, modeling, formalization, experiment, as well as statistical method, system and structural-functional method were used. The presented model for calculating the temperature of the solar panel of the Earth observation satellite is a set of mathematical expressions that allow calculating temperature of any FEP within a particular solar panel and make adjustments to the plan of exploitation.

Analytical Study of Path Loss in Radio Wave Propagation Models of the GSM Cellular Communications Networks in the City of Sana'a

The rapid growth of wireless communication technologies has increased the importance of a proper network planning. Before the actual installation of the network and to ensure that the network is adequately covered, network designers rely heavily on wave propagation models, which are a set of mathematical expressions, and graphs derived from comprehensive field measurements and it is used to represent radio wave properties of a particular environment. The research aims to find a mathematical model to predict the propagation path loss of radio waves in Sana'a city for the appropriate planning of cellular communication systems. In this sense, the researcher applied a practical study to the city of Sana'a by taking three cells (base station) in three different regions (urban and suburban areas and the open area). The research focuses on three stages (the stage of measurements, the stage of analysis and the stage of analysis and comparison). In the results, we obtained three values for path loss constants a and c for the three regions, through which we obtain the logarithmic curves, which in turn has been transformed into mathematical models to be used as a reference for radio planning engineers in the city of Sana'a, the capital of the Republic of Yemen.

Interaction theory of mirror-symmetry soliton pairs in nonlocal nonlinear Schrödinger equation

In this work, we theoretically investigate the evolution of the soliton pairs in strongly nonlocal nonlinear media, which is modeled by the nonlocal nonlinear Schrödinger equation. Taking two pairs of solitons as an example, which initial incident directions have a mirror symmetry, a set of mathematical expressions are derived to describe the soliton pairs’ propagation, the soliton spacing, the area of the optical field. The results demonstrate that the motion state of the soliton pairs is mirror-symmetry. Numerical simulations are carried out to illustrate the quintessential propagation properties.

Weakly diverging to tightly focused Gaussian beams: a single set of analytic expressions.

Analytic expressions describing all vector components of Gaussian beams, linearly polarized as well as radially polarized, are presented. These simple expressions, to high powers in divergence angle, were derived from a single-component vector potential. The vector potential itself, as in the 1979 work of Davis [Phys. Rev. A19, 1177 (1979)PLRAAN1050-294710.1103/PhysRevA.22.1159], was approximated by the first two terms of an infinite series solution of the Helmholtz equation. The expressions presented here were formulated to emphasize the dependence of the amplitude of the various field components on the beam's divergence angle. We show that the amplitude of the axial component of a linearly polarized Gaussian beam scales as the divergence angle squared, whereas the amplitude of the cross-polarized component of a linearly polarized Gaussian beam scales as the divergence angle to the fourth power. Weakly diverging Gaussian beams as well as strongly focused Gaussian beams can be described by exactly the same set of mathematical expressions, up to normalization constant. For a strongly focused linearly polarized Gaussian beam, the ellipticity of the dominant electric field component, typically calculated by the Debye-Wolf integral, is reproduced. For yet higher accuracy, terms with higher powers in divergence angle are presented, but the inclusion of these terms is limited to low divergence angles and short axial distances.

New expressions to determine the water diffusion coefficient in the membrane of PEM fuel cells

A set of mathematical expressions is presented to allow the determination of the water content in a PEMFC membrane, and facilitate the calculation of the water balance under variable conditions of hydration on both sides of it. The study is based on a cooperative model of water diffusion through the membrane, which avoids discontinuities in the calculations, gives a natural path to avoid the Schroeder's paradox, correctly predicting the value limit of ponding of water content, and presents a good behaviour to temperature variation. The model has been tested with Nafion® 117 literature data. Its features are coherent with physical models.

Electromagnetic Field in Air Produced by a Horizontal Magnetic Dipole Immersed in Sea: Theoretical Analysis and Experimental Results

In recent years, data transmission from seawater into air across the sea surface has attracted considerable interest and is essential for undersea sensing and networking applications. In particular, electromagnetic (EM) wave propagation across the sea surface via a seawater-air path has great potential for long-distance transmission, thus providing a possible solution for sensing and networking problems. However, current related theoretical analyses and experimental results are not sufficient to support research and development in the domain. Therefore, based on previous studies, this study theoretically and experimentally investigates EM wave propagation from a horizontal magnetic dipole (HMD), namely, a loop antenna immersed in seawater radiating into the air. A set of mathematical expressions is formulated for a model of three-layered conducting media on the basis of Maxwell's equations. In addition, a proof of concept measurement system was designed and built. A trial was conducted on the sea, and the results were in good agreement with the theoretical analysis. A horizontal transmission distance up to 574 m over the sea surface was achieved using a small loop antenna operated at 19 kHz and with an input power of less than 10 W. Therefore, the approach has been proven to be promising.

Verofocation of Bernoulli Law using the Software Autodesk Simulation CFD

Using Fluid Dynamics Analysis (CFD) provides the opportunity to achieve a faster and more thorough study of fluid flow processes and is an important step to obtain information that cannot be obtained otherwise. The finite element method is generally more accurate than the finite volume method, but finite volume method can achieve more accurate mass balances using the balance sheet continuity per volume control. Finite volume method is more appropriate when fluid transport, while the finite element method is used more in the calculations of tension or conduction, which satisfies local continuity condition, is of less importance. Fluid Dynamics Analysis (CFD) is used in numerical analyzes, based on a set of mathematical expressions on linear complex equations defining fundamental fluid flow and heat transfer. This paper presents the simulation of air flow through a tube of special construction in interpreting the law of Bernoulli energy. Laboratory systems are shown, respectively simulating the actual fluid flow.

Parametric synthesis of amplitude-phase modulators with different variants of connection of a nonlinear element with respect to a resistive two-port

Models of amplitude-phase modulators are obtained by solving parametric synthesis problems. These models have the form of a set of mathematical expressions for determinination of the optimum frequency dependences of the impedances of reactive one-ports and values of their parameters providing formation of high-frequency signals with given frequency dependences of the magnitudes and phases of the ratio between the modulators’ transmission coefficients for two states of two- and three-terminal nonlinear elements.

Effects of temperature on the rupture strength and elastic stiffness of geogrids

ABSTRACT: An automated tensile loading system that can accurately control histories of both loading and temperature was developed. A series of unconventional tensile loading tests were performed on polypropylene (PP), high-density polyethylene (HDPE) and polyester (PET) geogrids using this system. The following was found. The temperature significantly affects the elasto-viscoplastic stress–strain properties of the tested polymer geogrids. The inviscid stress–viscoplastic strain relation changes with temperature. The tensile rupture strength decreases by 9.2%, 26.7% and 4.5% when the temperature rises from 30°C to 50°C with PP, HDPE and PET geogrids, respectively. The elastic stiffness of the geogrid was evaluated by applying small-strain-amplitude unload–reload cycles after a certain period of sustained loading during otherwise monotonic loading at a constant load rate. The value increases with an increase in the tensile load level at a fixed temperature, and decreases with an increase in the temperature at a fixed load level. A set of mathematical expressions are proposed to describe these trends of tensile rupture strength and elastic behaviour.

Domes in the Islamic Architecture of Cairo City: A Mathematical Approach

This work analyzes mathematically and graphically the two methods used historically in the transitional zone between the circular base of the dome and the square top of the cube where the dome is supported. The time frame of this work is the distinguished historical buildings of Islamic Cairo built between the ninth and eighteenth centuries. Ten samples were chosen out of a total of thirty. A set of mathematical expressions has been derived to relate the different parts of the squinches/pendentives to the cube with a side of length l. The equations derived were validated twice, first by generating 3D graphical sequences for both squinches and pendentives for the selected domes using CAD software based on the values obtained from the driven equations, and second by executing physical models using a 3D printer for two examples of squinches and pendentives.

Enhanced Cost231 W.I. Propagation Model in Wireless Network

Implementations of wireless network wave propagation models are necessary to determine propagation characteristic through a medium. Propagation study provides an estimation of signal characteristics. This paper evaluates about propagation models, their path loss behavior, propagation mechanisms, and propagation prediction techniques. A propagation model is a set of mathematical expressions, diagrams, and algorithms used to represent the radio characteristics of a given environment. The accuracy of any particular propagation model in any given condition will depend on the suitability among the constraints required by the model and depend on terrain. This paper proposes new semi deterministic model derived by walficsh and Ikagami, this model simulation results represents the accuracy in terms of through put, end to end delay, average jitter and total packet received with respect to cost 231 Hata model and cost 231 (W.I) models and also shows some limitations, proposed model is unable to calculate multiple reflection loss caused by multi screen.

Experiments and kinetic model regarding the induction period observed during the oxidation by O 2 of adsorbed CO species on Pt/Al 2O 3 catalysts

The present study concerns the characterization, by experiments in the transient regime, at atmospheric pressure, with either a Fourier transform infrared or a mass spectrometer as a detector, of the elementary steps involved in the isothermal oxidation at T O lower than 360 K of the superficial species formed by adsorption of CO on reduced Pt/Al 2O 3 catalysts: linear, bridged, and threefold coordinated CO species. The coverages of the adsorbed species and the rate of the CO 2 production are determined during successive adsorption, desorption, and oxidation reactions for different durations. The evolution of the rate of the CO 2 production with the duration of the oxidation, RCO2( t), presents a variety of profiles, depending on the Pt dispersion of the catalysts. For Pt dispersions higher than 0.6, an induction period is observed and the RCO2( t) profile is characterized by a peak with a maximum defined by t m and RCO2 m. The greater the Pt dispersion is, the longer t m is and the lower RCO2 m is. For Pt dispersions lower than 0.6, the RCO2( t) profile is similar to a decreasing exponential, and its highest value is observed at time 0 of the oxidation. The induction period observed for Pt dispersions higher than 0.6 allows us to characterize the Langmuir–Hinshelwood steps between the adsorbed CO and oxygen species by studying the impacts on t m and RCO2 m of different experimental parameters such as the Pt dispersion, the oxidation temperature, the oxygen partial pressure, and the duration of a desorption stage before oxidation. A kinetic model based on the oxidation of the L CO species by a weakly adsorbed oxygen species formed on the Pt 0 sites liberated by the removal of the bridged CO species provides a set of mathematical expressions that provide a reasonable explanation of the impacts of the various experimental parameters on t m and RCO2 m. As a consequence, this kinetic model reveals how the Pt dispersion affects the elementary step and the turnover frequency of the CO/O 2 reaction. A comparison of the present study with similar literature data on a single Pt crystal shows that the differences in the experimental conditions, material and pressure gaps, may lead to a situation in which the Langmuir–Hinshelwood steps that are studied are not the same.

A DIGITAL METHOD FOR MEASURING THE THERMAL COMFORT OF THE AIR

Opening windows is frequently done to refresh the indoor air for the occupants. To maintain the cleanliness and freshness of the indoor air, more outdoor air is needed. But its high temperature and humidity are harmful to the thermal comfort of the indoor environment. Therefore, determining the amount of outdoor air allowed to enter the room is very important for the optimum conditioning of the indoor air. The ASHRAE comfort charts indicate the percentage of subjects feeling comfortable during various combinations of dry-bulb temperature, humidity, and air movement. A set of mathematical expressions were proposed to model the charts in order to calculate the comfort degree of the outdoor air automatically with its temperature and humidity. In this paper, the measurement of temperature and humidity was completed by a self-developed digital method. Besides, the comfort level of the sampled air was also simultaneously determined by this digital method based on the mathematical model of comfort charts. The system implemented based on our method is portable. This will let us make good use of the outdoor air and controll the ventilation machine more effectively.

Analysis of a DC motor drive in the presence of unbalance

Abstract The increasing presence of harmonics in power system has caused a need for the development of analytical methods of studying harmonic current effects. This paper describes a new method for modeling a six-pulse DC motor drive. One of the main features is that this model is derived from the actual waveform, which can be more accurate than the traditional constant current source model. Computer simulation method is used to analyze the six-pulse DC motor drive system and to compute the steady state responses of the DC load current and the AC line currents. The currents can be presented as a convenient set of mathematical expressions. The harmonic contents of currents can be obtained using fast Fourier transforms (FFT). In this paper, the effect of unbalanced voltage source is also studied. In addition, a full understanding of the sensitivity of the harmonic currents to different operating conditions is introduced.