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Global and regional sea level variations are important indicators of climate change and are derived from accurate sea surface height measurements and precisely determined orbits of altimetry satellites. To validate and improve the quality of these orbits, comparisons with external solutions are important. Since orbit solutions of different institutions are not necessarily provided at the same time instants, interpolation is required for comparison. In this study, we investigate the appropriate interpolation method and its degree to reduce interpolation errors to sub-millimetre levels. We also assess the magnitude of errors occurring at transformations when expressing orbit differences not only in the terrestrial reference frame (Cartesian coordinates), but also in local orbital and ellipsoidal coordinates. The analyses conducted in this study provide good results for Hermite interpolation of degrees 7–11 and Newton interpolation of at least degree 9 with a three-dimensional interpolation error of 0.6 mm and a scattering of 0.2 mm on average for satellite coordinates given with an accuracy of 1 mm in the SP3 format. These interpolation settings limit transformation errors between coordinate systems to ±0.01 mm and incorrect mapping of interpolation errors into certain components in the target system to ±0.02 mm. The spectral analysis of orbit differences is affected up to 0.1 mm in magnitude with appropriate interpolation settings. Extending the number of decimal digits of the satellite position and velocity in SP3 files by one digit benefits the orbit comparisons and reduces the interpolation error by 90% from 0.6 to 0.06 mm. The results are obtained using piece-wise interpolation and a validity interval inside the interpolation interval to minimise the effects of the Runge phenomenon. [ABSTRACT FROM AUTHOR]

Analysis of ECG for detecting different cardiovascular diseases requires real-time ECG signals which are acquired by attaching electrodes to the body. During the ECG signal acquisition, noise gets added to original signal, which might distort the morphological features, like amplitude, segment length and the interval aspects of the ECG leading to a false diagnosis and improper interpretation of cardiovascular disease. Therefore, ECG denoising is imperative. Here, we propose approximation using hermite polynomial interpolation with chebyshev nodes for denoising electrocardiogram signals that consequently compresses them too. Recommended algorithm is applied on twelve ECG signals taken from MIT-BIH arrhythmia database without any additional noise as the signals are already corrupted with noise. Performance of the proposed algorithm is evaluated using various performance metrics. Experimental results prove that the proposed method efficiently denoises electrocardiogram signals and gives quite encouraging results when compared with other existing denoising and compression algorithms. [ABSTRACT FROM AUTHOR]

Abstract Global and regional sea level variations are important indicators of climate change and are derived from accurate sea surface height measurements and precisely determined orbits of altimetry satellites. To validate and improve the quality of these orbits, comparisons with external solutions are important. Since orbit solutions of different institutions are not necessarily provided at the same time instants, interpolation is required for comparison. In this study, we investigate the appropriate interpolation method and its degree to reduce interpolation errors to sub-millimetre levels. We also assess the magnitude of errors occurring at transformations when expressing orbit differences not only in the terrestrial reference frame (Cartesian coordinates), but also in local orbital and ellipsoidal coordinates. The analyses conducted in this study provide good results for Hermite interpolation of degrees 7–11 and Newton interpolation of at least degree 9 with a three-dimensional interpolation error of 0.6 mm and a scattering of 0.2 mm on average for satellite coordinates given with an accuracy of 1 mm in the SP3 format. These interpolation settings limit transformation errors between coordinate systems to ±0.01 mm and incorrect mapping of interpolation errors into certain components in the target system to ±0.02 mm. The spectral analysis of orbit differences is affected up to 0.1 mm in magnitude with appropriate interpolation settings. Extending the number of decimal digits of the satellite position and velocity in SP3 files by one digit benefits the orbit comparisons and reduces the interpolation error by 90% from 0.6 to 0.06 mm. The results are obtained using piece-wise interpolation and a validity interval inside the interpolation interval to minimise the effects of the Runge phenomenon. Graphical Abstract

Using the possibilities of modern science and technology, it can be said that the presented mathematical model has been formulated without significant simplifications, and its (numerical) solution itself will be performed with high accuracy. The main purpose of the work was to create a tool supporting the calculation of the main problem of internal ballistics for barrel propellant systems in order to achieve digital solutions as close as possible to the results obtained using experimental ballistics methods. The scientific hypothesis of the work postulates that the physical model of internal ballistics formulated in Lagrange coordinates will allow to solve the main problem of internal ballistics of barrel systems in a digital way, obtaining such solution results that will satisfactorily reflect the solution results obtained using experimental ballistics methods. The results of digital simulations of physical phenomena of solutions to the main problem of internal ballistics of barrel weapons were compared with the results of experimental tests and the degree of agreement was determined. [ABSTRACT FROM AUTHOR]

Today, most design processes are carried out using specialized tools in the form of advanced computer software, but in the case of designing weapons (especially internal ballistic) it is not generally available or is even classified. On the other hand, there is no analytical system of non-linear differential equations describing the phases of the shot phenomenon in barrel weapons. Therefore, in order to obtain more accurate solutions to the system of equations, it is optimal to use numerical methods. The paper presents a theoretical description of the problem of solving the equations of internal ballistics. Based on this analysis, it was assumed that the solution to the main problem of internal ballistics formulated in Lagrange coordinates gives correct results and enables obtaining more accurate and realistic analytical solutions than using classical solutions. The utilitarian aim was to create a new program to support the design of classic gun tube weapons. [ABSTRACT FROM AUTHOR]

This article mainly analyzes the correlation between the carrier energy in robotic arms, according to enhance its performance. This task is achieved because of the sensors/actuators based on nanostructures properties: short response time and high robustness, which proportionated the possibility to execute intricate instructions by the control subsystem of the robotic arm. Therefore, the instructions executed by the controller are supported by a polynomial design, this algorithm helped to evaluate every response signal as a consequence of the main control system, which was consequently by the short response time from the main sensors "flow (carrier energy) and speed of the robotic arm", moreover, the advantage of the proposed system is given by the extra time obtained also to verify the stability of the robotic arm based in Lyapunov models correlated with Lagrange, as well as every equations were solved and organized by neural network. [ABSTRACT FROM AUTHOR]

Analytical mechanics provides methods for analyzing multibody systems with mathematically equivalent elastic elements. The paper analyzes several of these models, highlighting the advantages and disadvantages offered by each of these methods. The main methods used by the researchers are described in a unitary form, presenting the methods of obtaining the evolution equations in each of these cases, mentioning the strengths and weaknesses of each method. The equations of Lagrange, Gibbs–Appell, Kane, Maggi, and Hamilton are analyzed for the particular case of two-dimensional systems, which present certain particularities that facilitate the analysis. [ABSTRACT FROM AUTHOR]

The author initially describes the general situation within theological thinking prior to the pontificate of Leo XIII, characterized by a skepticism concerning the modern method of Catholic theology, especially Biblical Catholic theology. The approach within Protestant churches, where Biblical studies was much more evolved due to the use of the practice of historical-critical method, was very different. The pioneer in this approach within the Catholic Church was the French Dominican and Biblical theologian Jean-Marie Lagrange. The author of this study explicates how the publication of the encyclical Providentissimus Deus influenced Biblical research in general and opened the Catholic Church up to modernity. [ABSTRACT FROM AUTHOR]

It is undeniable that as vehicle ownership increases; developing countries are constantly dealing with serious issue of traffic accidents. The pavement distress issue is reported as an elementary road entity causing accidents. According to the statistics of the Road Traffic Injury Research and Prevention Centre (RTIR&PC) in Karachi, more than 50% of serious injuries occur due to road faults. This paper aims to develop a mechanism for the exploration of blackspots by inspecting the traffic accidents in Karachi city caused by road distresses. The mathematical analysis involved the Lagrange polynomial method while the screening of blackspots was carried out based on safety inspections. As of lack of technicalities and improved documentation, the paper presented an initiative of complete guidelines for safety audits and investigations specifically for developing countries like Pakistan. According to findings, around 87% locations are pertained with the ranking of blackspots highlighting the pavement problems of the city. [ABSTRACT FROM AUTHOR]

Optimizing the operation of a photovoltaic system involves a precise model. The current–voltage characteristic equation remains the best way to obtain its optimal parameters from the model. However, the transcendence of this equation remains a significant problem in the process of extracting these parameters. This paper presents a hybrid method comprised of the improved social network search algorithm and the Lagrange method for obtaining the best parameters for modeling a photovoltaic panel. The proposed method improves the basic algorithm by randomly adding a control parameter through Gaussian and Cauchy distributions, which aim to boost the search space agents to converge to the best solution. Then, the Lagrange method is used to solve the objective function's transcendental problem and to generate the best-estimated current. The proposed method has been applied to three different systems, viz., a photovoltaic array consisting of 18 modules (GL100), a photovoltaic panel (Photowatt PWP module), and a photovoltaic cell (RTC France). The difference in the results obtained vis-a-vis the other metaheuristic methods and those recently proposed for solving the transcendental of the I–V equation demonstrated the efficiency of the proposed algorithm. For the Photowatt PWP PV panel considered as the test system in the literature, the best parameters obtained are 1.0331 A for the photocurrent, 1.1863 µA for the saturation current, 45.3535 for the diode ideality factor, 1.5002 Ω for the series resistance, and 683.8995 Ω for the parallel resistance. These parameters gave a root mean square error of 1.5410 × 10–3, which converges at the 600th iteration. [ABSTRACT FROM AUTHOR]

In reforming the college physical education curriculum, we can introduce algebraic equations to solve the optimization problem of college physical education curriculum training. The article expounds on the principle of algebraic equations based on consulting many documents. At the same time, we apply it to physical education teaching. This method dramatically improves the numerical behavior of the violation correction method in traditional curriculum education and training. At the same time, the technique is simple, practical, and efficient. Finally, a numerical comparison is made between this method, the traditional augmentation method, and it’s default correction method.

The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a three-dimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context of the experimental benchmark test case examined.

One of the recent advancements in the electrical power systems is the smart-grid technology. For the effective functioning of the smart grid, the process like monitoring and controlling have to be given importance. In this paper, the Wireless Sensor Network (WSN) is utilized for tracking the power in smart grid applications. The smart grid is used to produce the electricity and it is connected with the sensor to transmit or receive the data. The data is transmitted quickly by using the Probabilistic Neural Network (PNN), which aids in identifying the shortest path of the nodes. While transmitting the data from the smart grid to the (Internet of Things) IoT web page, it is secured by introducing the secret keys between the neighbouring nodes through the process of key-management. In this method, the combination of Lagrange's theorem and the Location Based Key (LBK) management is used for better security performance. This approach delivers optimal performance in terms of security, throughput, packet loss and delay, which are comparatively better than the existing methods. [ABSTRACT FROM AUTHOR]

This approach present improved higher-order layer-wise theory for the investigation of flawlessly wedged sandwich-composite beams with general laminate configurations. Our analysis incorporates the continuity assumption of interlaminar shear stresses and in-plane and flexural displacements between interfaces. In addition, interlaminar shear stresses are constrained using the Lagrange multiplier technique by introducing new unknown variables. These unknown variables are expressed with interlaminar strain energy, assuming that the strain energy is continuous throughout the overall thickness of the beam. To govern the newly introduced and other unknown variables, the total potential energy (TPE) is minimised using variational calculus. The numerical analysis results show that our approach provides enhanced accuracy to examine sandwich-composite beams. [ABSTRACT FROM AUTHOR]

Through the art of applying assumptions which restrict the orbital shape and relative inclination of celestial bodies such as the Earth and Moon, trajectory prediction of small bodies of comparatively negligible mass (i.e., a satellite) within a multi-body gravitational system is possible. In this research, Lagrangian analytical methods are applied to formulate succinct derivations of the circular restricted three-body problem (CR3BP), the elliptical restricted three-body problem (ER3BP), and the bicircular restricted four-body problem (BCR4BP). The presence of, or lack thereof, equilibrium points within each dynamical model is discussed and presented in both graphical and tabular form. In terms of application, a form of periodic trajectories within the Earth-Moon system, identified herein as cislunar periodic orbits, is propagated using each of the presented dynamical models. The dynamical variations in these cislunar periodic orbits when transitioning between dynamical models are analyzed and discussed. The methodology behind cislunar periodic orbit generation is also discussed with 33 cislunar periodic orbits presented. Finally, through means of differential correction, it is shown how much error in Δ V ( Δ e V ), the BCR4BP dynamics introduce on the CR3BP solutions for a given number of patchpoints. Results of this analysis show the ER3BP to have a significantly higher perturbative effects than the BCR4BP on cislunar periodic orbits which are closed in the CR3BP. Based on the 33 orbits analyzed, correlation was also observed between the Jacobi constant and the dynamical variations present during the transition of cislunar periodic orbits to higher fidelity models, with larger Jacobi constants being associated with more dynamical variations as an orbit transitions from the CR3BP to both the ER3BP and BCR4BP. [ABSTRACT FROM AUTHOR]

Considering the deployment characteristics of the folding wing, this paper proposed three deployment modes, synchronous deployment, fixed-axis–non-fixed-axis stepwise deployment, and non-fixed-axis–fixed-axis stepwise deployment, to obtain the optimal deployment scheme of the orthogonal biaxial folding wing of Unmanned Aerial Vehicles (UAVs) at different airspeeds. On this basis, combined with the folding wing deployment action, the Lagrange method was used to establish the aerodynamic model of the folding wing, and the Fluent simulation software was used to simulate the aerodynamic simulation of multiple deployment modes of the orthogonal biaxial folding wing, which analyze the influence of the UAV deployment mode and airspeed towards the driving torque of the folding wing. Based on the driving moment of the folding wing, the optimal deployment mode at different airspeeds was obtained. The comparison of simulation results shows that when the airspeed is less than 40 m/s, the optimal deployment mode is synchronous deployment. When the airspeed is greater than or equal to 40 m/s, the optimal deployment mode is non-fixed-axis–fixed-axis stepwise deployment. The accuracy of the folding wing aerodynamics model can be proven according to the comparison of the simulation results with the theoretical results. [ABSTRACT FROM AUTHOR]

Analytical mechanics provides methods for analyzing multibody systems with mathematically equivalent elastic elements. The paper analyzes several of these models, highlighting the advantages and disadvantages offered by each of these methods. The main methods used by the researchers are described in a unitary form, presenting the methods of obtaining the evolution equations in each of these cases, mentioning the strengths and weaknesses of each method. The equations of Lagrange, Gibbs–Appell, Kane, Maggi, and Hamilton are analyzed for the particular case of two-dimensional systems, which present certain particularities that facilitate the analysis.

Aiming at the problems of single movement dimension of traditional vibrating screen, low screening efficiency, short life of key parts, etc. Using the randomness of chaotic vibration and the characteristics of reciprocating non-periodic motion, chaotic vibration is applied to the vibrating screen to improve the screening efficiency. A new type of chaotic vibrating screen with one redundant degree of freedom is developed, the dynamic model of the new chaotic vibrating screen is established, the vibration differential equation of the vibrating screen is obtained by the Lagrange method, and its dynamic characteristic diagram is obtained through simulink simulation analysis. Chaotic identification is performed on the time-frequency diagram, phase diagram, Poincare map and Lyapunov exponent diagram obtained from the simulation results. The simulation shows that the Poincre map of the chaotic vibrating screen is scattered and the maximum Lyapunov exponent is positive. The motion output of the new chaotic vibrating screen is chaos Vibration, the research results of the thesis can provide a theoretical basis for the design and application of chaotic vibrating screens.

Aim: Statistical model comparison has become common in historical biogeography, enabled by the R package BioGeoBEARS, which implements several models in a common framework, allowing models to be compared with standard likelihood‐based methods of statistical model comparison. Ree and Sanmartín (Journal of Biogeography, 45, 741–749, 2018) critiqued the comparison of Dispersal–Extinction–Cladogenesis (DEC) and a modification of it, DEC+J, which adds the process of jump dispersal at speciation. DEC+J provides highly significant improvements in model fit on most (although not all) datasets. They claim that the comparison is statistically invalid for a variety of reasons. I analyse the key claims made by the critique. Location: Simulated data. Taxon: Simulated data. Methods: Likelihood calculations are checked by comparison between programs and by‐hand calculations, and by summing likelihoods across all possible datasets. Model adequacy of DEC versus DEC+J is checked by a simulation/inference experiment. Results: Mistakes in the critique's example likelihood calculations are demonstrated. DEC+J fits better on datasets because the DEC model is statistically inadequate in the common situation when most species have geographical ranges of single areas; the DEC model requires long residence times of multi‐area ranges, and when these are not observed, a model that does produce such data patterns, such as DEC+J, prevails. More fundamentally, statistical comparison of DEC and DEC+J produces identical log‐likelihood differences to statistical comparison of two submodels of ClaSSE where extinction rates are fixed to 0. Main Conclusions: DEC fails a basic model adequacy check for understandable reasons, while DEC+J does not. As Ree and Sanmartín recommend ClaSSE models as valid for comparison, the comparison of DEC and DEC+J is statistically valid according to their own criteria. [ABSTRACT FROM AUTHOR]

The geometry dynamical modeling method for a double pendulum is explored with the Lie group and a double spherical space method. Four types of Lagrange equations are built for relative and absolute motion with the above two geometry methods, which are then used to explore the influence of different expressions for motion on the dynamic modeling and computations. With Legendre transformation, the Lagrange equations are transformed to Hamilton ones which are dynamical models greatly reduced. The models are solved by the same numerical method. The simulation results show that they are better for the relative group than for the absolute one in long time simulation with the same numerical computations. The Lie group based result is better than the double spherical space one. [ABSTRACT FROM AUTHOR]

Detailed knowledge of the thermal behavior of heat storage tanks is necessary for the design and operation of heat supply systems. Storage models enable to simulate the development of the thermal stratification, the thermal losses, the loading and unloading behavior. This article presents a model approach for large‐scale tank stores. It is based on the Lagrange formulation, which is well suited for analyzing variable fill levels. Variable material properties enable the calculation of the thermal expansion of the storage medium. This approach can be used, for example, to model stores with a floating lid. [ABSTRACT FROM AUTHOR]

Aerial manipulators (AM) exhibit particularly challenging, non-linear dynamics; the UAV and its manipulator form a tightly coupled dynamic system, mutually impacting each other. The mathematical model describing these dynamics forms the core of many solutions in non-linear control and deep reinforcement learning. Traditionally, the formulation of the dynamics involves Euler angle parametrization in the Lagrangian framework or quaternion parametrization in the Newton-Euler framework. The former has the disadvantage of giving birth to singularities and the latter being algorithmically complex. This work presents a hybrid solution, combining the benefits of both, namely a quaternion approach leveraging the Lagrangian framework, connecting the singularity-free parameterization with the algorithmic simplicity of the Lagrangian approach. We do so by offering detailed insights into the kinematic modeling process and the formulation of the dynamics of a general aerial manipulator. The obtained dynamics model is validated experimentally against a real-time physics engine. A practical application of the obtained dynamics model is shown in the context of a computed torque feedback controller (feedback linearization), where we analyze its real-time capability with increasingly complex AM models. [ABSTRACT FROM AUTHOR]

Evaporation and seepage are the most important forms of water loss in an open channel. Evaporation loss depends on the area of free surface while, seepage loss is function of channel geometry. The design that achieves minimum water loss is determined for trapezoidal and rectangular cross sections using Lagrangian method with Manning’s equation as a constraint. The water loss function which comprises evaporation and seepage loss was used. Matlab code is created to solve the equations of optimization by trial and error. An approach to determine the bed width and water depth from known discharge, side slope, longitudinal slope, manning’s coefficient, evaporation rate, and soil type is proposed. Design charts which determine bed width and water depth that ensure minimum water loss are presented. Moreover, artificial neural networks are used to get the best design for any value of evaporation rate. Using the created design charts and neural networks optimum design can be determined easily, accurately and quickly. ملخص: ملخصيعد التبخر والتسرب من أهم أشكال فقدان الماء في القنوات المفتوحة. ويعتمد الفقد بالتبخر على مساحة السطح الحر في حين أن فقدان التسرب يعتمد على الشكل الهندسي للقنوات. يتم تحديد التصميم الذي يحقق الحد الأدنى من فقدان المياه للقطاعان شبه المنحرف والمستطيل باستخدام طريقة لاجرانج مع معادلة ماننج كقيد. تم استخدام معادلة لفقد الماء تشتمل على التبخر التسرب. تم كتابة برنامج ماتلاب لحل معادلات تحقيق القيم الدنيا لفقد المياه عن طريق المحاولة والخطأ. تم اقتراح نهج لتحديد عرض القطاع وعمق المياه بمعلومية التصرف والميل الجانبي والميل الطولي ومعامل ماننج وقيمة البخر ونوع التربة. تم تقديم مخططات التصميم التي تحدد عرض القطاع وعمق المياه التي تضمن الحد الأدنى من فقدان المياه. بالاضافة إلى ذلك تم استخدام الشبكات العصبية الاصطناعية لتحديد التصميم الأمثل اياً كانت قيمة البخر. باستخدام مساعدات التصميم والشبكات العصبية الاصطناعية يمكن تحديد التصميم الأمثل بسهولة ودقة وسرعة.

As we know theoretically if we are going to construct a polynomial interpolation function through a mapped base, we create an approximation function. In this study, we try to build an approximation function using all sample data available. The approximation function obtained represents the data whose graph goes through a given set of data points. We determine the value of a function at different points and specific intervals using the interpolation model. The first derivative of the function is obtained to find the growth rate of tweet data. The experimental data is a crawling tweet with the keyword COVID-19. Then we get the amount of data per time duration representing a value of the function at a node. The interpolation includes such as Lagrange, Newton's divided difference, and cubic spline. In this study, we compared polynomial interpolation with cubic splines to obtain optimal results. With the functional approach obtained, a pattern of tweets related to COVID-19 can be seen from its graph that passes through the given data points. The graph and the estimated values obtained show that the cubic spline is the optimal interpolation as an approximation function. [ABSTRACT FROM AUTHOR]

In this paper, we wish to explore the role that textual representations play in the creation of new mathematical objects. We do so by analyzing texts by Joseph-Louis Lagrange (1736–1813) and Évariste Galois (1811–1832), which are seen as central to the historical development of the mathematical concept of groups. In our analysis, we consider how the material features of representations relate to the changes in conceptualization that we see in the texts. Against this backdrop, we discuss the idea that new mathematical concepts, in general, are increasingly abstract in the sense of being detached from material configurations. Our analysis supports the opposite view. We suggest that changes in the material aspects of textual representations (i.e., the actual graphic inscriptions) play an active and crucial role in conceptual change. We employ an analytical framework adapted from Bruno Latour's 1999 account of intertwined material and representational practices in the empirical sciences. This approach facilitates a foregrounding of the interconnection between the conceptual development of mathematics, and the construction, (re-)configuration, and manipulation of the materiality of representations. Our analysis suggests that, in mathematical practice, distinctions between the material and structural features of representations are not permanent and absolute. This problematizes the appropriateness of the distinction between concrete inscriptions and abstract relations in understanding the development of mathematical concepts. [ABSTRACT FROM AUTHOR]

Abstract An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like an empirical process as it is applied and described, is in fact the result of applying variational formulations to the whole considered system, putting together all the finite elements used in modeling and introducing constraints between the elements, which are, in general, nonholonomic. In the paper, we apply the method of Maggi’s equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements. This presents some advantages in the case of mechanical systems with nonholonomic liaisons.

İndüksiyon Motor’lar (IM) farklı yüklerde çalışırken nominal hızın gerisinde kaldıkları bilinmektedir. Bu bağlamda motor sürücüleri önem kazanmaktadır. Bu konu geçmişten günümüze pek çok bilim insanının dikkatini çekmiştir. Bu çalışmada, IM sürücüsü başarımını arttırmak amacıyla gerçekleştirilmiştir. IM sürücüsü de Skaler Denetim (SD) yöntemi kullanılmıştır. SD’de değişken frekanslı kontrol tekniği tercih edilmiştir. Böylece farklı yüklerde çalışan IM’nin nominal hızda çalışabilmesi için frekans değiştirilecektir. Frekans değişimini sağlamak için Gregory-Newton Interpolasyon (GNI) ve Lagrange Interpolasyon (LI) çözüm teknikleri kullanılmıştır. Bu iki farklı çözüm yöntemi, farklı yüklere karşılık nominal hız için gereken frekansı hesaplayarak sürücüye iletmektedir. Çalışma Matlab/Simulink programında test edilmiştir. Testlerden elde edilen sonuçlar iki interpolasyon tekniğinin de başarılı sonuçlar ürettiğini göstermiştir. Benzer sonuçlar üreten bu iki teknikte; GNI tekniğinin farklı yüklere cevap verme süresi yaklaşık 0.041-0.065 s arasında iken, LI tekniğinin cevap verme süresi 0.003 s’dir. Çalışma sonunda Oransal-Integral (PI) denetleyici ile performans incelemesi yapılmıştır. Sonuçlar göstermiştir ki, önerilen teknikler farklı hız ve yük değişimlerine hızlı cevap vermiş, daha hassas ve kararlı bir hız denetimi sağlamıştır.

In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.

Obtaining the equations of motion for an element in finite element analysis (FEA) model in the analysis of a multi-body system (MBS) having component elastic elements represents an important (maybe the main) step to build a soft able to solve such a problem numerically. In use FEA in the study of a MBS with elastic elements, the method of Lagrange's equations is especially used at present. This method presents the advantages of a homogeneous writing and the possibility to follow the operations easier. However, there are also equivalent formulations, developed by analytical mechanics, for approaching such a mechanical system. The earning of these alternative forms will be presented, by comparison.

Considering the deployment characteristics of the folding wing, this paper proposed three deployment modes, synchronous deployment, fixed-axis–non-fixed-axis stepwise deployment, and non-fixed-axis–fixed-axis stepwise deployment, to obtain the optimal deployment scheme of the orthogonal biaxial folding wing of Unmanned Aerial Vehicles (UAVs) at different airspeeds. On this basis, combined with the folding wing deployment action, the Lagrange method was used to establish the aerodynamic model of the folding wing, and the Fluent simulation software was used to simulate the aerodynamic simulation of multiple deployment modes of the orthogonal biaxial folding wing, which analyze the influence of the UAV deployment mode and airspeed towards the driving torque of the folding wing. Based on the driving moment of the folding wing, the optimal deployment mode at different airspeeds was obtained. The comparison of simulation results shows that when the airspeed is less than 40 m/s, the optimal deployment mode is synchronous deployment. When the airspeed is greater than or equal to 40 m/s, the optimal deployment mode is non-fixed-axis–fixed-axis stepwise deployment. The accuracy of the folding wing aerodynamics model can be proven according to the comparison of the simulation results with the theoretical results.

A new perspective for studying Earth processes has been soundly demonstrated by the Deep Space Climate Observatory (DSCOVR) mission. For the past 6 years, the first Earth-observing satellite orbiting at the Lagrange 1 (L1) point, the DSCOVR satellite has been viewing the planet in a fundamentally different way compared to all other satellites. It is providing unique simultaneous observations of nearly the entire sunlit face of the Earth at a relatively high temporal resolution. This capability enables detailed coverage of evolving atmospheric and surface systems over meso- and large-scale domains, both individually and as a whole, from sunrise to sunset, under continuously changing illumination and viewing conditions. DSCOVR’s view also contains polar regions that are only partially seen from geostationary satellites (GEOs). To exploit this unique perspective, DSCOVR instruments provide multispectral imagery and measurements of the Earth’s reflected and emitted radiances from 0.2 to 100 µm. Data from these sensors have been and continue to be utilized for a great variety of research involving retrievals of atmospheric composition, aerosols, clouds, ocean, and vegetation properties; estimates of surface radiation and the top-of-atmosphere radiation budget; and determining exoplanet signatures. DSCOVR’s synoptic and high temporal resolution data encompass the areas observed during the day from low Earth orbiting satellites (LEOs) and GEOs along with occasional views of the Moon. Because the LEO and GEO measurements can be easily matched with simultaneous DSCOVR data, multiangle, multispectral datasets can be developed by integrating DSCOVR, LEO, and GEO data along with surface and airborne observations, when available. Such datasets can open the door for global application of algorithms heretofore limited to specific LEO satellites and development of new scientific tools for Earth sciences. The utility of the integrated datasets relies on accurate intercalibration of the observations, a process that can be facilitated by the DSCOVR views of the Moon, which serves as a stable reference. Because of their full-disc views, observatories at one or more Lagrange points can play a key role in next-generation integrated Earth observing systems.

This document contains a detailed comparison between the initial numerical solution methods of ordinary differential equations, which start from the Euler method approach, which is based on the solution of differential equations by the Taylor method, the others two methods to be compared are improvements of this method, that of Euler, and they are the method of Heun, and the method of the midpoint. It will be observed from the solution of test differential equations its respective error with respect to the analytical solution, obtaining an error index dictated by the mean square error EMC. Through this document we will know the best numerical approximation to the analytical solution of the different PVI (initial value problems) raised, also fixing a solution pattern for certain problems, that is, the appropriate method for each type of problem will be stipulated. [ABSTRACT FROM AUTHOR]

Belt is costliest part of belt conveyor system. Sudden rise in belt tension within transient starting condition, results in belt failure and structure damage. It is difficult to measure these stresses by static calculation method and hence their presence might go undetected. Belt elongation is an evident quantity for these stresses. Dynamic belt stretch is formulated in terms of displacement response of conjugative belt units with respect to time. This paper presents analysis of the event and propagation of dynamic belt stretch for straight horizontal and straight inclined belt conveyor system. Dynamic behavior of belt system is investigated for starting condition of fully stacked conveyor belt. Belt conveyor system is considered as series of vibrating mass and its unit is assumed to be a viscoelastic segment. Equation of motion of belt unit is developed by Lagrange’s approach. Observed transient parameters are more vibrant in inclined belt than the horizontal belt system. Maximum value of dynamic belt stretch for horizontal belt systems founds 1.13% of total belt length and for inclined belt conveyor system, it is 1.16% of belt length. Both values are within range of standard value specified for fabric belt system.

Debido al notable incremento de construcciones de naves industriales en Ecuador, es necesario realizar un análisis técnico-económico para conocer la incidencia del costo de materiales sobre ellas. Para ello, se elaboró una muestra de 40 naves, fijando relación entre luz libre (L), altura del pórtico (H) y distancia entre pórticos (B), con el propósito de determinar una métrica. Para este estudio se estableció el peso de la estructura en kg/m². Con los resultados se aplicó un modelo matemático (interpolación de Lagrange), se obtuvo un polinomio que describe el modelo de cada grupo de naves y su representación gráfica, por consiguiente, se determinó una aproximación del peso de estructuras. Las métricas que se hallaron tienen una repercusión directa en el costo de los materiales de las estructuras, estas se obtuvieron al multiplicarlas por el costo del kg de acero. Se realizó una comprobación con una muestra de 6 naves, en las se halló el peso utilizando el diseño por factores de carga y resistencia y luego con el polinomio; obteniéndose un error: para naves moduladas a 5 m una media de 0,03 % con una desviación de 0,03 y para naves moduladas a 6 m, una media de 0,07 % con una desviación de 0,03

Due to the notable increase in industrial buildings in Ecuador, it is necessary to carry out a technical-economic analysis to know the impact of the cost of materials on them. To do this, a sample of 40 bays was drawn up, establishing the relationship between free span (L), portico height (H) and distance between porticoes (B), in order to determine a metric. For this study, the weight of the structure was established in kg / m². With the results, a mathematical model was applied (Lagrange interpolation), a polynomial was obtained that describes the model of each group of ships and its graphic representation, therefore, an approximation of the weight of structures was determined. The metrics that were found have a direct impact on the cost of the materials of the structures, these were obtained by multiplying them by the cost of the kg of steel. A check was carried out with a sample of 6 ships, in which the weight was found using the design by load and resistance factors and then with the polynomial; obtaining an error: for ships modulated at 5 m an average of 0.03 % with a deviation of 0.03 and for ships modulated at 6 m, an average of 0.07 % with a deviation of 0.03. [ABSTRACT FROM AUTHOR]

Historical biogeography has been characterized by a large diversity of methods and unresolved debates about which processes, such as dispersal or vicariance, are most important for explaining distributions. A new R package, BioGeoBEARS, implements many models in a common likelihood framework, so that standard statistical model selection procedures can be applied to let the data choose the best model. Available models include a likelihood version of DIVA (“DIVALIKE”), LAGRANGE’s DEC model, and BAYAREA, as well as “+J” versions of these models which include founder-event speciation, an important process left out of most inference methods. I use BioGeoBEARS on a large sample of island and non-island clades (including two fossil clades) to show that founder-event speciation is a crucial process in almost every clade, and that most published datasets reject the non-J models currently in widespread use. BioGeoBEARS is open-source and freely available for installation at the Comprehensive R Archive Network at http://CRAN.R-project.org/package=BioGeoBEARS. A step-by-step tutorial is available at http://phylo.wikidot.com/biogeobears.

This paper suggests a new method for solving the cost to go with time penalization. We consider the Lagrange approach in order to incorporate the restrictions of the problem and to solve the convex structured minimization problems. The solution is based on an improved version of the proximal method in which the regularization term that asymptotically disappear involves a penalization time parameter. By assuming that the set of equilibria is non-empty, we show that the proximal algorithm involving time penalization generates a sequence that converges to a saddle point of the Lagrange functional. This method improves the traditional approach of proximal algorithms and its applications. Our approach is implemented using continuous-time Markov chains. We analyze a queueing model with applications to waiting time of customers in the branch of a bank, for showing the effectiveness of the method. [ABSTRACT FROM AUTHOR]

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