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The paper examines the recommendation algorithms of social networks and Internet-platforms in general and assesses the degree of their influence on the promotion of a product or service in particular. For the segmentation of goods and services according to the interests of users, the methods of decomposition of matrixes are considered as a method for determining the optimal solution of the problem aimed at the study of recommendation algorithms. As part of the study, a model with usage of a non-negative matrix factorization was compiled and it was implemented in the RStudio statistical data processing environment. The main segments of interests of Internet-platform users were also highlighted, the economic benefits of using this model for business were analyzed. [ABSTRACT FROM AUTHOR]

In the paper, we present a numerical method for solving fractional delay differential equations with variable coefficients based on the fractional Laplace transform and series Adomian decomposition. We consider the fractional derivative in the Caputo sense. Using the proposed method we get easily solvable iterative algebraic equations for uknown coefficients of power series solutions. Numerical example is included to demonstrate the validity and applicability of this technique. [ABSTRACT FROM AUTHOR]

In this paper, a computational and comparative study of three analytic approximations for a solution of a second order nonlinear convolution type Volterra integro-differential equation containing error function. The study is made by employing three numerical methods assisted by asymptotic approximations with the help of the current literature. The computational methods are Picard's method of successive approximations, Adomian decomposition method and Liao's homotopy decomposition method. The asymptotic approximations are useful for not only to recover the exact solution of the linear part but also to fit the conditions imposed on the solution such as initial conditions, singular boundary condition at x=∞ and so on. [ABSTRACT FROM AUTHOR]

This paper is used to solve the systems of linear Fredholm-Volterra integro-differential equations (SLFVIDEs) and systems of linear Fredholm-Volterra integral equations (SLFVIEs) by means of the combined sumudu transform with Adomian decomposition process. The approximate solution obtained by CST-ADM has been improved by using the Padé approximation (PA) of order[p/q], Trapezoidal rule and Simpson rule. These proposed methods gave excellent results close to the exact solution. By use a comparison of the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the present method is very straightforward and effective. [ABSTRACT FROM AUTHOR]

The paper focuses on the comparison of sequential solvers used for solving quadratic programming problems which have a wide variety of applications including contact modeling. The complex algebraic formulation generated from the contact problems may be reduced in some cases to fairly simple quadratic programming problem using dualization theory and can be effectively solved using different multigrid or domain decomposition based massively parallel solvers. In the paper, selected solvers are applied on benchmark problems and the achieved results are compared. [ABSTRACT FROM AUTHOR]

Cognitive load on the brain is induced by employing cognitive tasks of varying degrees. The load is measured by using the recorded EEG signal while performing the cognitive task. The EEG signals are processed to determine the complexity of the task. The current study looks at different Machine learning Classification techniques to classify 2 tasks. Six pairs of EEG electrodes are arranged in a 10-20 system to capture the EEG signals. The pairs are located on different lobe areas namely pre-frontal, frontal, parietal, temporal, central, occipital. The paper uses the decomposition method like biorthogonal wavelet basis for extracting features from bands. Different Machine Learning classifiers are implemented on two methods like Individual brain lobe areas and Pair-wise electrode combination. Four features like band power, mean, energy and relative energy are extracted and applied as input to classifier for classification of 2 tasks i.e. resting state and mental arithmetic tasks. In Individual brain lobe area method frontal and parietal area have achieved highest classification accuracy of 73.5%. In Pair-wise electrode combination, 3-pair combination (average of all the classifier) i.e., prefrontal, frontal, central have achieved good classification accuracy of 66%. In EEG band ratios indices, band power as feature used to extract different EEG band ratios for pre-frontal and frontal electrodes in L/R (left/right hemisphere), R/L (right/left hemisphere) and (L-R)/(L+R) ratios. The energy in different frequency bands is used to quantify the cognitive load. We conclude from this study that band power ratios of right lobe to left lobe (R/L) perform better in assessing the cognitive load. [ABSTRACT FROM AUTHOR]

This paper propose a new application of the variational iteration method (VIM) by using the Adomian polynomial for solving the nonlinear systems of ordinary differential equations. This is basically a generalisation method. Here, we also discuss the convergence of the presented approach in Banach space. Two scientific problems, including the chaotic Genesio system, are considered to verify the efficacy of the present method. The behaviour of the method is observed for various values of x. This is an efficient technique to solve the several application problems. We compare the proposed approach with the existing Adomian's decomposition method. The outcomes show that our suggested strategy is quite simple and effective. [ABSTRACT FROM AUTHOR]

Robust optimization (RO) assumes that uncertain data has a convex set and a bounded set called uncertainty and seeks a solution that is feasible for all possible data parameters. This paper discusses a decomposition method for solving a robust optimization problem. Benders' decomposition, which is typically used to solve large scale integer programming problems, is investigated in order to crack down on the model's uncertainty. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to apply the Adomian decomposition method and variational iteration methods to approximate and find exact solutions for higher-order Fredholm integro-differential equations. The implementation of these methods showcases their utility in obtaining precise solutions for both linear and nonlinear problems. A comparison is conducted between the exact solutions and the outcomes of approximate methods to validate the accuracy of the results. The comparison reveals that these methods are highly effective and straightforward. [ABSTRACT FROM AUTHOR]

This paper is used to solve the systems of linear Volterra integral equations by means of the combined sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective. Mathematics Subject Classification (2010): 45D05, 34A12, 34C20, 65R10 [ABSTRACT FROM AUTHOR]

In this paper, a new analytical method called the Elzaki Adomian decomposition method (EADM) for solving the nonlinear fractional partial differential equations (FPDEs) is introduced. The proposed analytical method is an elegant combination of Adomian decomposition method (ADM) and the Elzaki transform method (ETM). In this new analytical method, the fractional derivative is computed in Caputo sense (CFD). The approximate solutions of nonlinear biological population model with fractional order are successfully obtained using the new analytical method, and the result is compared with the result of the existing methods. [ABSTRACT FROM AUTHOR]

This paper deals with a Genetic Algorithm for a single machine scheduling to reduce the tardiness with decomposition method, preventive maintenance and its application of steel production system. Also, we have investigated for a setup time, release time and due time in steel plants. In steel production industries, the products are not release within the due time then the fine will occur. The expenses are high when the machine get breakdown. For avoiding this a deterrent maintenance is considered. To reduce the delivery charges the products are grouped into a batch for the completion of the production work. A mixed integer programming model is formulated in this paper. A Genetic Algorithm is used to solve the production work in steel plants. The efficiency metric was examined in order to compare the different types of algorithms. [ABSTRACT FROM AUTHOR]

The nonlinear wave phenomena are described by Partial Differential Equations (PDEs) and the solution of these PDEs plays a significant role in understanding the existence and behaviour of wave propagation under different material media associated with the physical system. This paper presents approximate solution of nonlinear Burgers' equation with linear source term by using Laplace Decomposition Method (LDM).The analysis of the combined effect of source term and initial condition on the wave profiles is presented in this paper. As the solutions of nonlinear PDEs are greatly influenced by the presence of source term under different initial conditions, the results obtained can be readily extended to study the wave profiles of various types of initial value problems describing nonlinear reaction-dissipative phenomena. Moreover, the solutions can be used to study the internal mechanisms of the physical phenomena of more general system with diffusive effects. [ABSTRACT FROM AUTHOR]

In this paper, we propose a combination form of the fuzzy Sumudu transform and Adomain decomposition method to solve nonlinear Volterra-Fredholm fuzzy integro-differential equation (NVFFIDE) of the second kind. The result reveals that the proposed method is very efficient, simple and can be applied to application. Finally, the method is illustrated with example. [ABSTRACT FROM AUTHOR]

In many cases, the order of a differential equation is a natural number. However, in some applications, this order can be in the form of a fractional number, so that the equation is then called a fractional differential equation. In this paper, we study the numerical solution of the fractional logistic differential equation with order α, where 0 < α ≤ 1. The equation can be considered as one of the fractional Riccati differential equations. The numerical methods we use are the Adomian decomposition method (ADM) and the variational iteration method (VIM). We use the Caputo derivative to find the solution. The effect of the fractional-order into the transient solution is studied graphically to find the interpretation in the logistic population growth model. [ABSTRACT FROM AUTHOR]

A big challenge that faces many applications in different fields suffers in dealing with datasets of massive size. Additionally, retrieving and casting this data is somewhat time-consuming. Applications such as government or any institution election, surveys, healthcare ...etc., leverage techniques of data reduction, dimensionality reduction, matrix decomposition, or compression such as the Singular Value Decomposition Technique. Our paper shows the use of this technique as a method in certain circumstances where data is of binary type and can be retrieved, cast, or updated in less time and in a smaller size without losing any information. In other words, we prove practically that the massive size of binary values can be managed in a form of matrices with low rank (low rank is one of the bases used in the Singular Value Decomposition technique) to return the exact matrix of information instead of dealing with the original large matrix of data. The experimental results are implemented on a Lenovo machine, Intel Corei5, CPU 2.5GH with 8GB of RAM, using visual basic, C#, in Visual Studio 2019 environment. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of searching maximum Pareto points which possess special decomposition characteristics, that inherits the properties of the competitive Nash equilibrium. Such point is called market equilibrium. First, the competitive Nash equilibrium is constructed for the auction game of three players and its properties are analyzed. Then the set of Pareto points is described analytically on the basis of convolution method. The main task is to construct a path from the competitive Nash equilibrium to the point of market equilibrium in the Pareto set. This path is generated by the shift algorithm which is based on analytical calculation of the players’ best replies with respect to auction prices. The auction mechanism of the search algorithm is expressed as a system of nonlinear differential equations, precisely they describe formation of auction prices and players’ best replies to these prices. Trajectories of the generated dynamic system are constructed and their properties of convergence to the market equilibrium are examined. The proposed algorithm is applied to the model of the auction game of fast growing economies and its efficiency is shown particularly for the emissions reduction problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the sequence of integers ri, si, ti Ⲉ ℤ of regular continued fraction (RCF) expansions generated from the extended Euclidean algorithm. These sequences always satisfy ri = sia + tib where ri is a remainder whereas si and ti arising from the extended Euclidean algorithm are equal, up to sign, to the convergent of the continued fraction expansion of a/b. We discuss the behavior of these sequences and provide their full proof in detail with their simple calculation of sample. Throughout this work, we deal with the concept of Euclidean algorithm and extended Euclidean algorithm together with continued fraction algorithm. These algorithms are involved in the improvement of computational efficiency of the elliptic curve cryptography (ECC). Henceforth from that, we tend to associate these sequences in ECC. Last but not least, we found that the value of integers (ri, si, ti) satisfy various properties in RCF which then used to solve the shortest vector problem in representing point multiplications in ECC, namely the Gallant, Lambert & Vanstone (GLV) integer decomposition method and the integer sub decomposition (ISD) method. [ABSTRACT FROM AUTHOR]

In this paper, we will study the natural decomposition method (NDM) to obtain exact solution of nonlinear homogeneous and nonhomogeneous advection equation. The Adomian decomposition method is the basis of natural decomposition method. The theoretical analysis of the natural decomposition method is investigated for some equation and calculated with easily computable terms. The results are compared with other method. The evident has illustrated that this method is easy and efficient. [ABSTRACT FROM AUTHOR]

In this paper, we compare two methods for solving Nonlinear Nonhomogeneous Volterra-Integral Equations with known exact algebraic solutions using the "Modified Decomposition Method" and demonstrate the existence and uniqueness of such solutions. Initially, using a numerical technique, a near-exact answer was quickly and easily obtained. Secondly, knowing that a solution to a multi-term Volterra equation always produces a partial combination of the input terms, a combinatory system was then used to find the correct combination representing the exact solution. This method grows exponentially and is only practical for a few terms Volterra equations. Both approaches are detailed with examples using Maple software with performance measurements that show that the numerical system is the winner if a near-exact solution is sufficient enough, which the case for most engineering applications is. For scientific and mathematical applications, the combinatory approach is preferred. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a modification to a model classifying COVID-19 in. Spain given by Faïçal Ndaïrou and Delfim F. M. Torres. It consists of eight fractional differential equations S(t), E(t), I(t), P(t), A(t), H(t), R(t) and F(t), which represent to the susceptible individuals at time t, exposed individuals, symptomatic and infectious individuals, super-spreaders, infectious but asymptomatic individuals, hospitalized individuals, recovery individuals, and fatality class respectively. These fractional differential equations have different orders. The existence and uniqueness of the solution are proved, and the stability of the disease-free equilibrium point is shown. Also, the approximate solution is calculated by using the Sumudu transform and Adomain decomposition method (ADM) and applying the real data. Finding that the model described the disease closely and accurately to the actual data. The reasonable results that get are illustrated by the figures with respect to the values of the fractional derivatives where the symptomatic and infectious individuals I(t) increase rapidly at the beginning to reach the maximum then decrease. Similarly, for super-spreaders P(t) but P(t) grows and decays slower than I(t). All these happen according to the strategies of the governments and the effectiveness of the treatments. [ABSTRACT FROM AUTHOR]

The paper presents the method of assessing the efficiency of technology mapping for logic blocks contained in FPGA. Effective technology mapping is necessary to search for such a decomposition path that will give efficient solutions both in terms of the number of blocks and the number of logic levels. Using non-disjoint decomposition is the key element that makes the solutions more effective. However, it is not always profitable. In an each single stage of decomposition, there is a necessity of assessing the efficiency of mapping in the blocks that have given configurable abilities. Known in literature, the methods of determining this cofactor do not take non-disjoint decomposition into account. In the paper, the authors propose the effective method of determining efficiency cofactor that takes non-disjoint decomposition into account. The effectiveness of the proposed method was confirmed experimentally. [ABSTRACT FROM AUTHOR]

In this paper, we used the modified Adomian Decomposition Method (LADM) joined Padé approximation to solve a system of delay differential equations (DDEs) with initial value problem (IVP). The main objective of the work to solve the Delay differential equations by approximate solutions method. The examples are solved using the presented method and compared the computed result with the exact solution to show the efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

Image processing involves processing the input and extracting the valuable or useful information from the image. Image enhancement is kind of processing technology where the processing is applied to improve the image quality in terms of clarity and quality. In this paper, the image quality is enhanced for the inputs taken from obscure environments by performing multiband fusions techniques. Among the different methods of obtaining dehazed images the proposed model is a combination of model based and fusion based dehazing method strategies along with decomposition methods. The proposed method improves shading and gray scale pictures with no prior data about the image. Further the use of Laplacian module improves the performance mapping between the layers of image and secures the information gradient in the system. The proposed model is efficient enough to enhance the image quality. [ABSTRACT FROM AUTHOR]

In this paper, we find approximate solution of the nonlinear Volterra-Fredholm fuzzy integro-differential equation (NVF-FIDE) by using Adomian decomposition method (ADM). We convert this equation to a nonlinear system of Volterra-Fredholm integro-differential equations in crisp case and find an approximate solution of this system. Hence, we obtain an approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integro-differential equation. A numerical example is given to demonstrate the validity and applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian's decomposition method (ADM) for analytic treatment of nonlinear two-dimensional Volterra-Fredholm fuzzy integral equations (2D-VFFIE) and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations. [ABSTRACT FROM AUTHOR]

The current level of organization in industry, as one of the decisive factors for ensuring their comprehensive efficiency, involves the coverage of technological processes by automated optimal control in stages of completed productions, groups of interconnected productions and production complexes. In these conditions, the use of traditional approaches based on the creation of control systems with a centralized organizational structure is often not effective. One of the most effective and promising in real control tasks is the decomposition method. However, this method is developed and presented in the literature only at the conceptual level, making it difficult to apply it in practice, since specific implementation mechanisms, in particular, algorithms for working interaction between control systems of the upper and lower levels of the hierarchy, have not been worked out. In this paper, this gap is eliminated, giving real opportunities for practical use of the method in decentralized control systems. [ABSTRACT FROM AUTHOR]

The present paper focuses on the convective heat transfer of the boundary layer flow of an incompressible viscous nanofluids over the flat plate surface. Silver and goldnanoparticles have been considered with water as a base fluid. An analytical method called Adomian Decomposition Method is used to study the velocity profile and temperature profile. The thermal physical properties of silver water nanofluid and thermal physical properties of gold water nanofluid have been presented in the table The non-dimensional parameters α1,β1 and Pr are established with graphical representation. [ABSTRACT FROM AUTHOR]

In this paper, a new technique of Adomian decomposition method (NTADM) is proposed for solving fractional order nonlinear differential equations (FONDEs). This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard Adomian decomposition method (ADM). Illustrative examples have been presented, to demonstrate the method and the results obtained are compared with fractional ADM. [ABSTRACT FROM AUTHOR]

Modelling the transport processes in a vadose zone, e.g. modelling contaminant transport or the effect of the soil water regime on changes in soil structure and composition, plays an important role in predicting the reactions of soil biotopes to anthropogenic activity. Water flow is governed by the quasilinear Richards equation. The paper concerns the implementation of a multi-time-step approach for solving a nonlinear Richards equation. When modelling porous media flow with a Richards equation, due to a possible convection dominance and a convergence of a nonlinear solver, a stable finite element approximation requires accurate temporal and spatial integration. The method presented here enables adaptive domain decomposition algorithm together with a multi-time-step treatment of actively changing subdomains. [ABSTRACT FROM AUTHOR]

This paper presents analysis solution for of important type of partial differential equations by suggested new modification of decomposition method to overcome the computational difficulties. Convergence of series solution has been discussed with two illustrated examples, and the method has shown a high-precision, fast approach to solve high order strongly nonlinear of PDEs with initial conditions, there is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials, not requiring any discretization or assumption for a small parameter to be present in the problem. The steps of suggested method are easy implemented, high accuracy and a rapid convergence to the exact solution compared with other methods can be used to solve this type of PDEs. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical method, i.e. homotopy analysis method, is used to find the linear and non-linear Klein–Gordon equation solution. The homotopy analysis method is very effective, easy to calculate. The solution has faster convergence than the traditional Adomian decomposition method and can be applied to other non-linear problems. This method's efficiency with the Klein–Gordon equation has been illustrated via different examples such as homogeneous linear, inhomogeneous linear and non-linear. [ABSTRACT FROM AUTHOR]

Circular cylinder in cross-flow was studied experimentally using time-resolved PIV technique. Reynolds numbers based on the cylinder diameter were in range from 3 850 up to 19 260. Effect of the Reynolds number on wake time-mean topology as well as the dynamical behavior is studied. The wake dynamics is analyzed using the OPD method. The Oscillation Pattern Decomposition method provides unique information on dynamical patterns topology and oscillations in the flow-field. The pseudo-periodical wavy patterns have been detected within the cylinder wake. The parameters of this behavior are Reynolds number dependent, especially their sizes and shapes. Typical flow-field topologies are presented in the paper. The study is of qualitative character as flow boundary conditions are not well defined. [ABSTRACT FROM AUTHOR]

The paper covers the development and research epy computational structure for mathematical modelling of hydrobiological processes in shallow waters – Azov Sea and Gelendzhik Bay, based on the modern information technologies and computational methods to improve the accuracy of predictive modelling the ecological situations in waters during the summer. The models take into account following: the water flow movement; microturbulent diffusion; gravitational settling of pollutants; plankton populations nonlinear interaction; the salinity impact, temperature. The scheme with weights was proposed for discretization of the developed model, that allowed significantly reduce the error and the computational time. Practical significance of the work is that the proposed model was software implemented; the limits and prospects of its use were defined. The experimental software was designed on the basis of a graphics accelerator for mathematical modelling of possible development scenarios of the shallow waters ecosystems, taking into account the environment influence. Parallel implementation was performed using the decomposition methods for computationally labours diffusion-convection problems taking into account the CUDA architecture characteristics. [ABSTRACT FROM AUTHOR]

A modular approach to the development and test of on-board software (OBS) for computing modules (CM) of small spacecrafts is presented, a number of shortcomings are identified in terms of providing functionality, reliability, usability, maintainability and other OBS quality criteria, as well as time and material development costs. The problem of the lack of universality of the methodology and tools regarding the design of OBS as a hardware independent software product is defined in this study as the major. A new OBS decomposition method based on the universal multitasking real time operating system (RT UMTOS) is proposed, which provides OBS structure design optimization by quality criteria in accordance with international standards. The proposed method allows to reduce the costs of OBS development, debugging and verification. The result is a practical algorithm for implementing the new approach in the form of a hierarchical structure of a constantly active server process and client processes launched as necessary with communications in the form of virtual messaging channels. The presented version of OBS design simplifies the process of rewriting and recovery of failed software modules being a part of OBS during the flight, making this mode faster and safer by using the proposed decomposition method. The paper also reflects the advantages of development and test of OBS at the initial stages of the life cycle using a conventional personal computer (PC) as a programmer’s workbench. This programmer’s workbench with the installed RT UMTOS can be used as part of a software-simulation stand for OBS design and verification. Prospects and directions for further research on optimizing the design of OBS, which is not only included in the on-board computing modules (OBCM), but also built into other on-board systems from the on-board control system (OBCS), having computing facilities, are determined. [ABSTRACT FROM AUTHOR]

Prediction of disease spreading represents a challenging and actual topic. We propose in this paper a framework for reduced order modeling and forecasting of non-intrusive data with application to epidemiology. We developed a technique based on randomized dynamic mode decomposition (DMD) as a fast and accurate option in model order reduction (ROM). The key innovation consists in prediction of DMD-ROM dynamics using a forecasting sliding window technique. We illustrate the excellent behavior of the proposed methods by performing a qualitative analysis. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical simulation of features of most popular up today adaptive signal decomposition techniques, which applied to the signals of the ultrasonic gas flowmeter in pipes with intrusive piezo- transducers with vertical wave penetration and frequency modulated continuum waves. The most attention was paid to the case of small pipe diameters in comparison with the piezo-transducer size (when it has to be considered). Among the investigated methods the most accurate results (with respect to the bias error) was obtained for singular signal analysis (SSA). However, in the trade-off of accuracy to computational complexity, the principal component analysis (PCA) method was recommended to the farther researches. [ABSTRACT FROM AUTHOR]

This paper deals with the meteorological applications of wavelets and fuzzy logics and a hybrid of wavelets and fuzzy logics. The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex non-stationary signals. It has been shown that the wavelet transform is a flexible time-frequency decomposition tool which can form the basis of useful time series analysis. It is expected to see an increased amount of research and technology development work in the coming years employing wavelets for various scientific and engineering applications. [ABSTRACT FROM AUTHOR]

The paper presents the methods of searching for non-disjoint decomposition using BDD. Non-disjoint decomposition is a generalization of a classic decomposition model. Its main advantage is the reduction of necessary logic blocks needed to implement bound blocks. The essence of non-disjoint decomposition is based on searching for input variables that may fulfill the role of bound functions. The authors present the methods of searching for these variables in one or multi-root BDD diagrams. DekBDD enables to carry out non-disjoint decomposition on benchmark circuits. In the unit, entitled 'Experimental results', the number of necessary LUT blocks needed to implement multioutput function with the usage and without using non-disjoint decomposition, was determined for selected benchmarks. Moreover, the number of bound functions and the number of found 'switching' variables (non-disjoint decompositions) were given in the table. This attitude enables to determine the degree of optimization of a gained logic structure thanks to non-disjoint decomposition. [ABSTRACT FROM AUTHOR]

In this paper, for a commutative unity ring R and a finite group G, we characterize some submodule properties of RG-module MG introduced in [8]. Our aim is to decompose MG into RG-submodules by defining an idempotent in EndRGMG and to verify the relation between the quotient of group module and the quotient of related module. [ABSTRACT FROM AUTHOR]

This paper presents a novel transformation we call Subspace Supported Rational Transformation (SsSRT). Despite the structure of this transformation seems to be similar to Möbius transformation, SsSRT differs from Möbius transformation due to its enhanced applicability to vectors, matrices and folded matrices. This transformation has been developed during the studies of digital image processing via Tridiagonal Folmat Enhanced Multivariance Products Representation (TFEMPR) in order to increase approximation quality. In this work, Transformational Tridiagonal Folmat Enhanced Multivariance Products Representation (TTFEMPR) enhanced by using SsSRT is taken into consideration as a truncation based approximation method. The SsSRT flexibilities have been determined via an optimization at the constancy level TFEMPR approximation. [ABSTRACT FROM AUTHOR]

The paper presents a method for obtaining nanoparticles of ZnO by thermal decomposition of the Zn-containing compounds. The experiment was based on the thermal decomposition of basic Zinc Acetate dihydrate to zinc oxide. Basic Zinc Acetate dihydrate was analysed by derivatography and then annealed at a selected temperature (500 °C to 700°C) for about 3 h. The precursor was decomposed by heating in air resulting in the formation of Hexagonal structure of zinc oxide. Precursor precipitates were transformed into zinc oxide by Thermal decomposition. The precursor and decomposed products were analyzed using XRD analysis and FTIR analysis techniques. The average size of the particles of ZnO obtained using the thermal decomposition technique was approximately 28.8 nm, 34 nm, 39.5 nm at 500 °C, 600 °C, and 700 °C, respectively. FTIR data shows a strong peak at 430 cm−1, assignable to the Zn-O stretching vibrations mode. [ABSTRACT FROM AUTHOR]

A task of finding for a given Petri net a set of sequential components being able to represent together the behavior of the net arises often in formal analysis of Petri nets and in applications of Petri net to logical control. Such task can be met in two different variants: obtaining a Petri net cover or a decomposition. Petri net cover supposes that a set of the subnets of given net is selected, and the sequential nets forming a decomposition may have additional places, which do not belong to the decomposed net. The paper discusses difference and relations between two mentioned tasks and their results. [ABSTRACT FROM AUTHOR]

In complex analysis, every harmonic function admits a decomposition as a sum of a holomorphic and an antiholomorphic function. However, this fact does not hold for paravector-valued harmonic functions, or so-called A-valued harmonic functions, in quaternion function theory. In previous articles, the authors proved that by taking into account ψ-hyperholomorphic functions, where ψ is a structural set different from the standard one and its conjugation, every A-valued harmonic function can be written as a sum of a monogenic, an anti-monogenic and a ψ-hyperholomorphic function. In this paper, we revisit such a decomposition and apply it to study problems in elasticity. [ABSTRACT FROM AUTHOR]

For the studied average monthly values of the levels of the air pollutant PM10 in Silistra in the period 01.2015 – 12.2019, two modern methods for decomposition were used - X-13ARIMA-SEATS and STL. The trend-cycle and seasonal component of the series were estimated in a total of 24 different ways – 8 models with the X-13ARIMA-SEATS approach with two seasonal adjustment options each – X11 and SEATS and 8 with the STL method. A comparative analysis was made between them, both in terms of estimating the components of the decomposition and in terms of the quality of approximation of the predicted values for the first six months of 2020 to the actually observed ones. In 23 out of 24 assessments of the trend- cycle component, a decreasing trend is observed, followed by a slightly increasing trend in the last year and several months of the period 2015–2019. The STL method yielded better forecast results for the first six months of 2020, using the default settings in the corresponding functions of R programming language. The estimated trend-cycle component by STL method is significantly smoother than that by method X-13ARIMA-SEATS. [ABSTRACT FROM AUTHOR]

The paper presents a combination of the Galerkin-Bubnov decomposition procedure and Optimal Homotopy Asymptotic Method (OHAM) to derive analytical approximate solutions to nonlinear vibration of clamped-clamped micro-electro-mechanical system (MEMS). The nonlinear governing equation of microbeam vibration pre-deformed by an elastic constant field includes both even and odd nonlinearities. The accuracy of the proposed procedure is validates via numerical results. [ABSTRACT FROM AUTHOR]

Application of the traditional centralized approach to construction of automated optimal control systems for complex industrial facilities is often difficult due to the high dimensionality and complexity of the emerging control problems. Such industrial facilities, in particular, can include technological processes of finished products and production complexes of the petrochemical and oil and gas industry. One of the effective ways to eliminate these difficulties can be the use of decentralized control systems with a multi-level hierarchical structural organization. The mathematical basis of decentralized hierarchical control is formed by the methods of optimal control problems decomposition. One of the most effective and promising method for practical use in this class is the feasible decomposition method. This method is distinctive for its obvious operating principle and visual physical interpretation. However, it is developed only at the conceptual level, and it is difficult to apply it in practice, since there are no specific implementation mechanisms, in particular, algorithms for working interaction between the coordinating body and local control systems. In the paper a possible approach to the elimination of this problem is presented. The findings of the experimental study confirm the validity and effectiveness of this approach. [ABSTRACT FROM AUTHOR]

This paper presents the time-series identification a variable-amplitude (VA) strain signal on lower arm suspension component in terms of time-series component analysing and correlate to the fatigue damage properties. The identification technique was used is called classical decomposition method, to classify the strain data into trend, cyclical, seasonal and irregular components. The time history plot of a study case showed the fatigue data contains high and low amplitude events and has resulted the highest amplitude for a pavé, highway and campus are 224 µε, 321 µε and 619 µε, respectively. The trend pattern of a fatigue strain data is a nonstationary series in variance and mean, where a campus data produced highest slope of 31.2Χ10-4 compared to the others. By observing the cyclic movement of the moving average plot, the fatigue strain data contained expansion, contraction and random background. The autocorrelation plot is weak in identifying seasonal pattern, but the autocorrelation coefficient, r1 values are statistically significant and show a positive serial correlation. Based on residual plot in irregular analysis, the residuals pattern is considered random. As to correlate the fatigue characteristic and time-series component, it was found a campus data produced highest value of fatigue damage. This study discovered a slope of a linear trend pattern could be affected to the fatigue damage properties because the fatigue strain data are nonstationary, VA time-series data and have a random background. Thus, the findings of these characteristics are expected for a nonstationary signal. [ABSTRACT FROM AUTHOR]

This work deals with the nonlinear piezoelectric coupling in vibration-based energy harvesting, done by A. Triplett and D.D. Quinn in J. of Intelligent Material Syst. and Structures (2009). In that paper the first order nonlinear fundamental equation has a three dimensional state variable. Introducing both observable and control variables in such a way the controlled system became a SISO system, we can obtain as a corollary that for a particular choice of the observable variable it is possible to present an explicit functional relation between this variable one, and the variable representing the charge harvested. After-by observing that the structure in the Input-Output decomposition essentially changes depending on the relative degree changes, presenting bifurcation branches in its zero dynamics-we are able in to identify this type of bifurcation indicating its close relation with the Hartman - Grobman theorem telling about decomposition into stable and the unstable manifolds for hyperbolic points. [ABSTRACT FROM AUTHOR]

he objective of this paper is to get an approximate solution for Lane-emden and Emden-Fowler initial and boundary value problems. For this, we used the Optimal Homotopy Asymptotic Method (OHAM) which is a semi-analytical method. OHAM Results show the eÂğectiveness and reliability of OHAM for Lane-Emden and Emden-Fowler initial and boundary value problems. The results we obtained are compared to the exact solutions, homotopy perturbation method (HPM), Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). [ABSTRACT FROM AUTHOR]