Search results for: Differential Power Analysis (DPA)
11136 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach
Authors: Lianglin Xiong, Yun Zhao, Tao Jiang
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In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 226011135 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)
Authors: Li Ge
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In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 116111134 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)
Authors: Li Ge
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In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 106611133 An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations
Authors: A. M. Sagir
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In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 145211132 Proposal of Design Method in the Semi-Acausal System Model
Authors: Junji Kaneko, Shigeyuki Haruyama, Ken Kaminishi, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty
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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.
Keywords: System Model, Physical Models, Empirical Models, Conservation Law, Differential Algebraic Equation, Object-Oriented.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 220311131 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability
Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu
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In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 240611130 Availability Analysis of a Power Plant by Computer Simulation
Authors: Mehmet Savsar
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Reliability and availability of power stations are extremely important in order to achieve a required level of power generation. In particular, in the hot desert climate of Kuwait, reliable power generation is extremely important because of cooling requirements at temperatures exceeding 50-centigrade degrees. In this paper, a particular power plant, named Sabiya Power Plant, which has 8 steam turbines and 13 gas turbine stations, has been studied in detail; extensive data are collected; and availability of station units are determined. Furthermore, a simulation model is developed and used to analyze the effects of different maintenance policies on availability of these stations. The results show that significant improvements can be achieved in power plant availabilities if appropriate maintenance policies are implemented.Keywords: Power plants, steam turbines, gas turbines, maintenance, availability, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 146811129 The Differential Transform Method for Advection-Diffusion Problems
Authors: M. F. Patricio, P. M. Rosa
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In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.
Keywords: Method of Lines, Differential Transform Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 171111128 On a Class of Inverse Problems for Degenerate Differential Equations
Authors: Fadi Awawdeh, H.M. Jaradat
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In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 160411127 Compensation of Power Quality Disturbances Using DVR
Authors: R. Rezaeipour
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One of the key aspects of power quality improvement in power system is the mitigation of voltage sags/swells and flicker. Custom power devices have been known as the best tools for voltage disturbances mitigation as well as reactive power compensation. Dynamic Voltage Restorer (DVR) which is the most efficient and effective modern custom power device can provide the most commercial solution to solve several problems of power quality in distribution networks. This paper deals with analysis and simulation technique of DVR based on instantaneous power theory which is a quick control to detect signals. The main purpose of this work is to remove three important disturbances including voltage sags/swells and flicker. Simulation of the proposed method was carried out on two sample systems by using Matlab software environment and the results of simulation show that the proposed method is able to provide desirable power quality in the presence of wide range of disturbances.Keywords: DVR, Power quality, Voltage sags, Voltage swells, Flicker.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 197511126 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations
Authors: A. M. Sagir
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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.
Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 173311125 Representation of Power System for Electromagnetic Transient Calculation
Authors: P. Sowa
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The new idea of analyze of power system failure with use of artificial neural network is proposed. An analysis of the possibility of simulating phenomena accompanying system faults and restitution is described. It was indicated that the universal model for the simulation of phenomena in whole analyzed range does not exist. The main classic method of search of optimal structure and parameter identification are described shortly. The example with results of calculation is shown.Keywords: Dynamic equivalents, Network reduction, Neural networks, Power system analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 186611124 Stable Tending Control of Complex Power Systems: An Example of Localized Design of Power System Stabilizers
Authors: Wenjuan Du
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The phase compensation method was proposed based on the concept of the damping torque analysis (DTA). It is a method for the design of a PSS (power system stabilizer) to suppress local-mode power oscillations in a single-machine infinite-bus power system. This paper presents the application of the phase compensation method for the design of a PSS in a multi-machine power system. The application is achieved by examining the direct damping contribution of the stabilizer to the power oscillations. By using linearized equal area criterion, a theoretical proof to the application for the PSS design is presented. Hence PSS design in the paper is an example of stable tending control by localized method.
Keywords: Phase compensation method, power system small-signal stability, power system stabilizer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 94011123 Elegant: An Intuitive Software Tool for Interactive Learning of Power System Analysis
Authors: Eduardo N. Velloso, Fernando M. N. Dantas, Luciano S. Barros
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A common complaint from power system analysis students lies in the overly complex tools they need to learn and use just to simulate very basic systems or just to check the answers to power system calculations. The most basic power system studies are power-flow solutions and short-circuit calculations. This paper presents a simple tool with an intuitive interface to perform both these studies and assess its performance in comparison with existent commercial solutions. With this in mind, Elegant is a pure Python software tool for learning power system analysis developed for undergraduate and graduate students. It solves the power-flow problem by iterative numerical methods and calculates bolted short-circuit fault currents by modeling the network in the domain of symmetrical components. Elegant can be used with a user-friendly Graphical User Interface (GUI) and automatically generates human-readable reports of the simulation results. The tool is exemplified using a typical Brazilian regional system with 18 buses. This study performs a comparative experiment with 1 undergraduate and 4 graduate students who attempted the same problem using both Elegant and a commercial tool. It was found that Elegant significantly reduces the time and labor involved in basic power system simulations while still providing some insights into real power system designs.
Keywords: Free- and open-source software, power-flow, power system analysis, Python, short-circuit.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 40011122 Position Vector of a Partially Null Curve Derived from a Vector Differential Equation
Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu
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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 113111121 Coupled Lateral-Torsional Free Vibrations Analysis of Laminated Composite Beam using Differential Quadrature Method
Authors: S.H. Mirtalaie, M. Mohammadi, M.A. Hajabasi, F.Hejripour
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In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.
Keywords: Differential Quadrature Method, Free vibration, Laminated composite beam, Material coupling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 208911120 Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay
Authors: Yong Li
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The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.
Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 157111119 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 142711118 Reduction of Differential Column Shortening in Tall Buildings
Authors: Hansoo Kim, Seunghak Shin
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The differential column shortening in tall buildings can be reduced by improving material and structural characteristics of the structural systems. This paper proposes structural methods to reduce differential column shortening in reinforced concrete tall buildings; connecting columns with rigidly jointed horizontal members, using outriggers, and placing additional reinforcement at the columns. The rigidly connected horizontal members including outriggers reduce the differential shortening between adjacent vertical members. The axial stiffness of columns with greater shortening can be effectively increased by placing additional reinforcement at the columns, thus the differential column shortening can be reduced in the design stage. The optimum distribution of additional reinforcement can be determined by applying a gradient based optimization technique.
Keywords: Column shortening, long-term behavior, optimization, tall building.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 395611117 Instability of a Nonlinear Differential Equation of Fifth Order with Variable Delay
Authors: Cemil Tunc
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In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.
Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 142111116 Nodal Load Profiles Estimation for Time Series Load Flow Using Independent Component Analysis
Authors: Mashitah Mohd Hussain, Salleh Serwan, Zuhaina Hj Zakaria
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This paper presents a method to estimate load profile in a multiple power flow solutions for every minutes in 24 hours per day. A method to calculate multiple solutions of non linear profile is introduced. The Power System Simulation/Engineering (PSS®E) and python has been used to solve the load power flow. The result of this power flow solutions has been used to estimate the load profiles for each load at buses using Independent Component Analysis (ICA) without any knowledge of parameter and network topology of the systems. The proposed algorithm is tested with IEEE 69 test bus system represents for distribution part and the method of ICA has been programmed in MATLAB R2012b version. Simulation results and errors of estimations are discussed in this paper.Keywords: Electrical Distribution System, Power Flow Solution, Distribution Network, Independent Component Analysis, Newton Raphson, Power System Simulation for Engineering.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 287311115 Benchmarking Cleaner Production Performance of Coal-fired Power Plants Using Two-stage Super-efficiency Data Envelopment Analysis
Authors: Shao-lun Zeng, Yu-long Ren
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Benchmarking cleaner production performance is an effective way of pollution control and emission reduction in coal-fired power industry. A benchmarking method using two-stage super-efficiency data envelopment analysis for coal-fired power plants is proposed – firstly, to improve the cleaner production performance of DEA-inefficient or weakly DEA-efficient plants, then to select the benchmark from performance-improved power plants. An empirical study is carried out with the survey data of 24 coal-fired power plants. The result shows that in the first stage the performance of 16 plants is DEA-efficient and that of 8 plants is relatively inefficient. The target values for improving DEA-inefficient plants are acquired by projection analysis. The efficient performance of 24 power plants and the benchmarking plant is achieved in the second stage. The two-stage benchmarking method is practical to select the optimal benchmark in the cleaner production of coal-fired power industry and will continuously improve plants- cleaner production performance.Keywords: benchmarking, cleaner production performance, coal-fired power plant, super-efficiency data envelopment analysis
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 239211114 Sensitivity Analysis in Power Systems Reliability Evaluation
Authors: A.R Alesaadi, M. Nafar, A.H. Gheisari
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In this paper sensitivity analysis is performed for reliability evaluation of power systems. When examining the reliability of a system, it is useful to recognize how results change as component parameters are varied. This knowledge helps engineers to understand the impact of poor data, and gives insight on how reliability can be improved. For these reasons, a sensitivity analysis can be performed. Finally, a real network was used for testing the presented method.Keywords: sensitivity analysis, reliability evaluation, powersystems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 223611113 Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design
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In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 176411112 A Novel Design of a Low Cost Wideband Wilkinson Power Divider
Authors: A. Sardi, J. Zbitou, A. Errkik, L. El Abdellaoui, A. Tajmouati, M. Latrach.
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This paper presents analysis and design of a wideband Wilkinson power divider for wireless applications. The design is accomplished by transforming the lengths and impedances of the quarter wavelength sections of the conventional Wilkinson power divider into U-shaped sections. The designed power divider is simulated by using ADS Agilent technologies and CST microwave studio software. It is shown that the proposed power divider has simple topology and good performances in terms of insertion loss, port matching and isolation at all operating frequencies (1.8 GHz, 2.45 GHz and 3.55 GHz).
Keywords: ADS Agilent technologies, CST microwave Studio, Microstrip, Wideband, Wilkinson power divider.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 568911111 Electromagnetic Assessment of Submarine Power Cable Degradation Using Finite Element Method and Sensitivity Analysis
Authors: N. Boutra, N. Ravot, J. Benoit, O. Picon
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Submarine power cables used for offshore wind farms electric energy distribution and transmission are subject to numerous threats. Some of the risks are associated with transport, installation and operating in harsh marine environment. This paper describes the feasibility of an electromagnetic low frequency sensing technique for submarine power cable failure prediction. The impact of a structural damage shape and material variability on the induced electric field is evaluated. The analysis is performed by modeling the cable using the finite element method, we use sensitivity analysis in order to identify the main damage characteristics affecting electric field variation. Lastly, we discuss the results obtained.Keywords: Electromagnetism, defect, finite element method, sensitivity analysis, submarine power cables.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 104911110 Fluid Differential Agitators
Authors: Saeed Asiri
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This research is to design and implement a new kind of agitators called differential agitator. The Differential Agitator is an electro- mechanic set consists of two shafts. The first shaft is the bearing axis while the second shaft is the axis of the quartet upper bearing impellers group and the triple lower group which are called as agitating group. The agitating group is located inside a cylindrical container equipped especially to contain square directors for the liquid entrance and square directors called fixing group for the liquid exit. The fixing group is installed containing the agitating group inside any tank whether from upper or lower position. The agitating process occurs through the agitating group bearing causing a lower pressure over the upper group leading to withdrawing the liquid from the square directors of the liquid entering and consequently the liquid moves to the denser place under the quartet upper group. Then, the liquid moves to the so high pressure area under the agitating group causing the liquid to exit from the square directors in the bottom of the container. For improving efficiency, parametric study and shape optimization has been carried out. A numerical analysis, manufacturing and laboratory experiments were conducted to design and implement the differential agitator. Knowing the material prosperities and the loading conditions, the FEM using ANSYS11 was used to get the optimum design of the geometrical parameters of the differential agitator elements while the experimental test was performed to validate the advantages of the differential agitators to give a high agitation performance of lime in the water as an example. In addition, the experimental work has been done to express the internal container shape in the agitation efficiency. The study ended up with conclusions to maximize agitator performance and optimize the geometrical parameters to be used for manufacturing the differential agitatorKeywords: Differential Agitators, Parametric Optimization, Shape Optimization, Agitation, FEM, ANSYS11.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 367711109 Fractional Delay FIR Filters Design with Enhanced Differential Evolution
Authors: Krzysztof Walczak
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Fractional delay FIR filters design method based on the differential evolution algorithm is presented. Differential evolution is an evolutionary algorithm for solving a global optimization problems in the continuous search space. In the proposed approach, an evolutionary algorithm is used to determine the coefficients of a fractional delay FIR filter based on the Farrow structure. Basic differential evolution is enhanced with a restricted mating technique, which improves the algorithm performance in terms of convergence speed and obtained solution. Evolutionary optimization is carried out by minimizing an objective function which is based on the amplitude response and phase delay errors. Experimental results show that the proposed algorithm leads to a reduction in the amplitude response and phase delay errors relative to those achieved with the Least-Squares method.Keywords: Fractional Delay Filters, Farrow Structure, Evolutionary Computation, Differential Evolution
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 182511108 Physicochemical Characterization of Waste from Vegetal Extracts Industry for Use as Briquettes
Authors: Maíra O. Palm, Cintia Marangoni, Ozair Souza, Noeli Sellin
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Wastes from a vegetal extracts industry (cocoa, oak, Guarana and mate) were characterized by particle size, proximate and ultimate analysis, lignocellulosic fractions, high heating value, thermal analysis (Thermogravimetric analysis – TGA, and Differential thermal analysis - DTA) and energy density to evaluate their potential as biomass in the form of briquettes for power generation. All wastes presented adequate particle sizes to briquettes production. The wastes showed high moisture content, requiring previous drying for use as briquettes. Cocoa and oak wastes had the highest volatile matter contents with maximum mass loss at 310 ºC and 450 ºC, respectively. The solvents used in the aroma extraction process influenced in the moisture content of the wastes, which was higher for mate due to water has been used as solvent. All wastes showed an insignificant loss mass after 565 °C, hence resulting in low ash content. High carbon and hydrogen contents and low sulfur and nitrogen contents were observed ensuring a low generation of sulfur and nitrous oxides. Mate and cocoa exhibited the highest carbon and lignin content, and high heating value. The dried wastes had high heating value, from 17.1 MJ/kg to 20.8 MJ/kg. The results indicate the energy potential of wastes for use as fuel in power generation.
Keywords: Agro-industrial waste, biomass, briquettes, combustion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 99911107 The Analogue of a Property of Pisot Numbers in Fields of Formal Power Series
Authors: Wiem Gadri
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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral characteristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.
Keywords: Pisot numbers, Salem numbers, Formal power series, Minimal polynomial degree.
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