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Relevant bibliographies by topics / Initial problem

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Academic literature on the topic 'Initial problem'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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Journal articles on the topic "Initial problem"

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Solonnikov, V. A. "Initial-boundary value problem for generalized Stokes equations." Mathematica Bohemica 126, no. 2 (2001): 505–19. http://dx.doi.org/10.21136/mb.2001.134018.

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Vibet, C. "The Initial Conditions Problem." International Journal of Electrical Engineering & Education 25, no. 2 (1988): 141–49. http://dx.doi.org/10.1177/002072098802500212.

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Based on control theory, a new method to investigate initial conditions induced by the application of a step command on linear or nonlinear systems is given in this paper. Examples are provided to illustrate the proposed method.

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Shampine, L. F., and Robert M. Corless. "Initial value problems for ODEs in problem solving environments." Journal of Computational and Applied Mathematics 125, no. 1-2 (2000): 31–40. http://dx.doi.org/10.1016/s0377-0427(00)00456-8.

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Prakash, P., JJ Nieto, S. Senthilvelavan, and G. Sudha Priya. "Fuzzy fractional initial value problem." Journal of Intelligent & Fuzzy Systems 28, no. 6 (2015): 2691–704. http://dx.doi.org/10.3233/ifs-151547.

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Adomian, G. "Nonlinear hyperbolic initial value problem." Journal of Mathematical Analysis and Applications 120, no. 2 (1986): 730–33. http://dx.doi.org/10.1016/0022-247x(86)90192-7.

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Wei, Lin, Guo Boling, and Shang Yadong. "The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation." Applicable Analysis 82, no. 8 (2003): 787–808. http://dx.doi.org/10.1080/00036810310001603189.

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Risma Yunita, Septina, and Mohammad Faizal Amir. "ANALOGY PROBLEM POSING FOR ELEMENTARY SCHOOL STUDENTS ON WORD PROBLEMS." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 4, no. 1 (2023): 458–68. http://dx.doi.org/10.46306/lb.v4i1.283.

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This study aims to determine the analogy characteristics of elementary school students in proposing word problems. Analogical reasoning is a complex process that involves retrieving structured knowledge from long-term memory, representing and manipulating role-filling ties in working memory, identifying elements that play appropriate roles, generating new conclusions, and learning abstract schemes. The characteristics of analogy are categorized into four: (1) reformulation, rearrangement of information by changing the order of numbers but still paying attention to the order of mathematical operations. (2) reconstruction, Students rearrange information in the initial problem so that the problem appears different but is identical to the initial problem. (3) reproduction, the resulting product creates a new problem that is different by changing the structure of the initial problem. (4) imitation, changing the structure of the given problem by expanding the goal statement so that the initial problem becomes a step of the solution process of the new problem. Students' failure in making problem posing is included in non-reformulation, where students cannot make problem posing on word problems according to the problem structure

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Amir, Masoud Rahimi, Rajabi Vahid, and Ramezani Khansari Ehsan. "Developing Genetic Algorithm to Solve Vehicle Routing Problem with Simultaneous Pickup and Delivery." Journal of Civil Engineering and Materials Application 4, no. 2 (2020): 103–14. https://doi.org/10.22034/jcema.2020.224281.1019.

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One of the well-known and highly used extensions of vehicle routing problem (VRP) is Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD), in which delivery and pickup for each customer is carried out simultaneously. In this study, it is attempted to present an optimal method for solving VRPSPD using genetic algorithm. In this method, genetic algorithm is improved by modifying genetic parameters and presenting efficient and proper operators. Three Randomized, Nearest neighbor and Cheapest Insertion algorithms are utilized to create the initial population. Given the different structure used in each of these methods, the initial solutions are varied and include all feasible regions. In addition, by making modifications in these methods, the initial population was tried to be created through higher quality solutions to help genetic algorithm reach a better future generation. Also, 4 algorithms were invented for mutation operators, which prevented convergence in local optimums and helped finding better solutions by comparing the results. The proposed algorithm is executed on 40 different standard examples. After comparing the results by this algorithm and the best solutions by other algorithms, improvement is observed in 3 of the examples.

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Kuo, Hung-Wen. "The initial layer for Rayleigh problem." Discrete & Continuous Dynamical Systems - B 15, no. 1 (2011): 137–70. http://dx.doi.org/10.3934/dcdsb.2011.15.137.

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Rybak, Samuil A. "Fuzzy structure, initial problem. Poincare theorem." Journal of the Acoustical Society of America 103, no. 5 (1998): 2979. http://dx.doi.org/10.1121/1.422428.

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Dissertations / Theses on the topic "Initial problem"

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Holt, M. W. "Localised symmetric instability : an initial value problem." Thesis, University of Reading, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253477.

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Webster, Stuart. "The barotropic initial value problem and atmospheric predictability." Thesis, University of Reading, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262485.

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Chihara, Hiroyuki. "The initial value problem for semilinear Schrödinger equations." Kyoto University, 1997. http://hdl.handle.net/2433/157012.

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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(工学)<br>甲第6965号<br>工博第1648号<br>新制||工||1084(附属図書館)<br>UT51-97-L186<br>京都大学大学院工学研究科数理工学専攻<br>(主査)教授大矢勇次郎, 教授曾根良夫, 教授岩井敏洋<br>学位規則第4条第1項該当

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Zhao, Kun. "Initial-boundary value problems in fluid dynamics modeling." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31778.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Hanson-Hart, Zachary Aaron. "A Cauchy Problem with Singularity Along the Initial Hypersurface." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/126171.

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Mathematics<br>Ph.D.<br>We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators.<br>Temple University--Theses

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Forgoston, Eric T. "Initial-Value Problem for Perturbations in Compressible Boundary Layers." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195810.

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An initial-value problem is formulated for a three-dimensional perturbation in a compressible boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.

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Papallo, Giuseppe. "Causality and the initial value problem in Modified Gravity." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/277416.

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Lovelock and Horndeski theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study the Shapiro time delay for gravitons in spherically symmetric spacetimes in Einstein–Gauss–Bonnet gravity (a Lovelock theory). In Lovelock theories, gravitons can propagate faster or slower than light. We show that, thanks to this property, it is possible for them to experience a negative time delay. It was recently argued that this feature could be employed to construct closed causal curves, implying that the theory should be discarded as causally pathological. We show that this construction is unphysical, for it cannot be realised as the evolution of sensible initial data. The second part investigates the local well-posedness of the initial value problem for Lovelock and Horndeski theories. For the initial value problem to be well-posed it is necessary that the equations of motion be strongly hyperbolic. It is known that when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak field background in harmonic and generalised harmonic gauge, respectively. We show that Lovelock theories fail to be strongly hyperbolic in this setting. We also prove that the most general Horndeski theory which is strongly hyperbolic is simply a “k-essence” theory coupled to Einstein gravity and that any more general theory would necessarily fail to be so. Our results imply that the standard methods used to prove the well-posedness of the initial value problem for the Einstein equations cannot be extended to Lovelock or Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields and hence might not constitute a valid alternative to General Relativity.

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Viguria, Jimenez Luis Antidio. "Distributed Task Allocation Methodologies for Solving the Initial Formation Problem." Thesis, Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24731.

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Mobile sensor networks have been shown to be a powerful tool for enabling a number of activities that require recording of environmental parameters at various spatial and temporal distributions. These mobile sensor networks could be implemented using a team of robots, usually called robotic sensor networks. This type of sensor network involves the coordinated control of multiple robots to achieve specific measurements separated by varied distances. In most formation measurement applications, initialization involves identifying a number of interesting sites to which mobility platforms, instrumented with a variety of sensors, are tasked. This process of determining which instrumented robot should be tasked to which location can be viewed as solving the task allocation problem. Unfortunately, a centralized approach does not fit in this type of application due to the fault tolerance requirements. Moreover, as the size of the network grows, limitations in bandwidth severely limits the possibility of conveying and using global information. As such, the utilization of decentralized techniques for forming new sensor topologies and configurations is a highly desired quality of robotic sensor networks. In this thesis, several distributed task allocation algorithms will be explained and compared in different scenarios. They are based on a market approach since our interest is not only to obtain a feasible solution, but also an efficient one. Also, an analysis of the efficiency of those algorithms using probabilistic techniques will be explained. Finally, the task allocation algorithms will be implemented on a real system consisted of a team of six robots and integrated in a complete robotic system that considers obstacle avoidance and path planning. The results will be validated in both simulations and real experiments.

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Thornburg, Jonathan. "Coordinates and boundary conditions for the general relativistic initial data problem." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25060.

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Techniques for numerically constructing initial data in the 3+1 formalism of general relativity (GR) are studied, using the theoretical framework described in Bowen and York (1980), Physical Review D 21(8), 2047-2056. The two main assumptions made are maximal slicing and 3-conformal flatness of the generated spaces. For ease of numerical solution, axisymmetry is also assumed, but all the results should extend without difficulty to the non-axisymmetric case. The numerical code described in this thesis may be used to construct vacuum spaces containing arbitrary numbers of black holes, each with freely specifyable (subject to the axisymmetry assumption) position, mass, linear momentum, and angular momentum. It should be emphasised that the time evolution of these spaces has not yet been attempted. There are two significant innovations in this work: the use of a new boundary condition for the surfaces of the black holes, and the use of multiple coordinate patches in the numerical solution. The new boundary condition studied herein requires the inner boundary of the numerical grid to be a marginally trapped surface. This is in contrast to the approach used in much previous work on this problem area, which requires the constructed spaces to be conformally isometric under a "reflection mapping" which interchanges the interior of a specified black hole with the remainder of the space. The new boundary condition is found to be easy to implement, even for multiple black holes. It may also prove useful in time evolution problems. The coordinate choice scheme introduced in this thesis uses multiple coordinate patches in the numerical solution, each with a coordinate system suited to the local physical symmetries of the region of space it covers. Because each patch need only cover part of the space, the metrics on the individual patches can be kept simple, while the overall patch system still covers a complicated topology. The patches are linked together by interpolation across the interpatch boundaries. Bilinear interpolation suffices to give accuracy comparable with that of common second order difference schemes used in numerical GR. This use of multiple coordinate patches is found to work very well in both one and two black hole models, and should generalise to a wide variety of other numerical GR problems. Patches are also found to be a useful (if somewhat over-general) way of introducing spatially varying grid sizes into the numerical code. However, problems may arise when trying to use multiple patches in time evolution problems, in that the interpatch boundaries must not become spurious generators or reflectors of gravitational radiation, due to the interpolation errors. These problems have not yet been studied. The code described in this thesis is tested against Schwarzschild models and against previously published work using the Bowen and York formalism, reproducing the latter within the limits of error of the codes involved. A number of new spaces containing one and two black holes with linear or angular momentum are also constructed to demonstrate the code, although little analysis of these spaces has yet been done.<br>Science, Faculty of<br>Physics and Astronomy, Department of<br>Graduate

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Fotouhi, A. R. "Longitudinal data analysis : the initial conditions problem in random effects modelling." Thesis, Lancaster University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387647.

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Books on the topic "Initial problem"

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1957-, Jackson Thomas L., Lasseigne D. G, and Langley Research Center, eds. The initial-value problem for viscous channel flows. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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Marciniak, Andrzej. Wybrane metody numeryczne rozwiązywania zagadnienia N ciał. Wydawn. Politechniki Poznańskiej, 1989.

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Lambert, J. D. Numerical methods for ordinary differential systems: The initial value problem. Wiley, 1991.

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Seger, Alexander. The drug problem in the Province of Phongsali: Initial assessment of problems and needs. UNDCP Office in Laos, 1991.

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1953-, Kenig Carlos E., ed. Degenerate diffusions: Initial value problems and local regularity theory. European Mathematical Society, 2007.

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Gawinecki, Jerzy August. Initial-boundary value problem in nonlinear hyperbolic thermoelasticity: Some applications in continuum mechanics. Polska Akademia Nauk, Instytut Matematyczny, 2002.

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Hartley, T. T. Insights into the fractional order initial value problem via semi-infinite systems. National Aeronautics and Space Administration, Lewis Research Center, 1998.

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Graaff, Erik de. Simulation of initial medical problem-solving: Studies on a new measure for the assessment of medical problem-solving ability. Uitgeverij Thesis, 1989.

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K, Davis Paul. Exploratory analysis of "the halt problem": A briefing on methods and initial insights. RAND, 1997.

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Franke, Richard H. The use of observed data for the initial value problem in numerical weather prediction. Naval Postgraduate School, 1987.

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Book chapters on the topic "Initial problem"

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Pava, Jaime. "Initial value problem." In Mathematical Surveys and Monographs. American Mathematical Society, 2009. http://dx.doi.org/10.1090/surv/156/05.

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Gourgoulhon, Éric. "The Initial Data Problem." In 3+1 Formalism in General Relativity. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24525-1_9.

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Fukś, Henryk. "Deterministic Initial Value Problem." In Understanding Complex Systems. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38700-5_2.

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Pedlosky, Joseph. "The Initial Value Problem." In Waves in the Ocean and Atmosphere. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05131-3_5.

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Ibrahimbegovic, Adnan, and Naida Ademovicć. "Initial boundary value problem." In Nonlinear Dynamics of Structures Under Extreme Transient Loads. CRC Press, 2019. http://dx.doi.org/10.1201/9781351052504-1.

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Eriksson, Kenneth, Donald Estep, and Claes Johnson. "The General Initial Value Problem." In Applied Mathematics: Body and Soul. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05798-8_14.

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Schmid, Peter J., and Dan S. Henningson. "The Viscous Initial Value Problem." In Stability and Transition in Shear Flows. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0185-1_4.

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Ghasem, Nayef. "Initial Value Problem Differential Equations." In Numerical Methods in Chemical Engineering Using Python® and Simulink®. CRC Press, 2023. http://dx.doi.org/10.1201/9781003360544-5.

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Leach, J. A., and D. J. Needham. "The Initial-Boundary Value Problem." In Springer Monographs in Mathematics. Springer London, 2004. http://dx.doi.org/10.1007/978-0-85729-396-1_8.

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Bellomo, N., Z. Brzezniak, and L. M. de Socio. "The Random Initial Boundary Value Problem." In Nonlinear Stochastic Evolution Problems in Applied Sciences. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-1820-0_3.

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Conference papers on the topic "Initial problem"

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Arif, Abu Sayeed, Md Ashraful Babu, Aminur Rahman Khan, Mohammad Nazrul Islam, Md Sharif Uddin, and Ramesh Chandra Poonia. "Priority-driven Unbalanced Transportation Problem (PUTP) to obtain better Initial Feasible Solution." In 2024 IEEE International Conference on Contemporary Computing and Communications (InC4). IEEE, 2024. http://dx.doi.org/10.1109/inc460750.2024.10649090.

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Butler, Joseph E. "Initial EMI Shielding Evaluation vs. Corrosion Concerns." In CORROSION 1989. NACE International, 1989. https://doi.org/10.5006/c1989-89050.

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Abstract One of the more significant aspects of galvanic corrosion in mechanical joints of military electronics equipment, other than mechanical integrity, is the resultant loss of electrical conductivity across the joint, and hence a loss of shielding effectiveness. This prevalent problem for EMI shielded electronics equipment which must operate in the marine environment is not effectively addressed during normal system qualification tests. Further, it is typically not properly addressed for fielded systems, even after maintenance, repair or refurbishment of equipment. Evaluations of shielding effectiveness done as a part of system EMI qualification tests are done either independent of the environmental qualification test program or earlier in the test schedule on a given piece of equipment. The qualification test program which is designed to qualify the electronics system in terms of electromagnetic interference and environmental requirements such as a salt fog exposure does so in a mutually exclusive way. While galvanic corrosion in mechanical joints is easily recognized via mechanical inspection when it does occur, the existence of excessive radiated electromagnetic interference coupling into or out of electronic equipment is not normally detected unless a significant operational problem occurs. Loss of electrical conductivity across mechanical joints due to the onset of galvanic corrosion will allow electromagnetic noise to enter the system. Operational upset of equipment or system compatibility problems with co-located equipment can and will occur due to this phenomena. Unfortunately, these upsets are not easily attributed to the galvanic corrosion phenomena. For this reason, a more realistic scenario for qualification testing of equipment must be pursued. The system requirements for electromagnetic interference/electromagnetic compatibility and environmental concerns such as exposure to the marine environment are mutually coupled in the real world. Standards organizations such as the Society of Automotive Engineers (SAE) Committee SAE AE-4G concerned with EMI gaskets and/or the National Association of Corrosion Engineers (NACE) Committee T9E3 should address this oversight in the form of a committee to investigate the feasibility of a practice for proper evaluation of the EMI shielding and galvanic corrosion concerns within mechanical joints of military electronics, prior to system deployment. Specific levels of equipment complexity that could be addressed are at the EMI gasket level per se ; enclosure or rack level; or finally full system level at qualification test or during field maintenance. This paper will define this problem in more detail and offer some suggestions as to its resolution.

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Ozturk, Onur, and Najat Bara. "An initial framework for the less-than-truckload problem: order allocation and planning." In 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2024. http://dx.doi.org/10.1109/codit62066.2024.10708106.

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Hobill, David, and Paul Webster. "Brill wave initial-value problem." In GENERAL RELATIVITY AND RELATIVISTIC ASTROPHYSICS. ASCE, 1999. http://dx.doi.org/10.1063/1.1301602.

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Alvarez, Jose M., Antonio Mastropietro, and Salvatore Ruggieri. "The Initial Screening Order Problem." In WSDM '25: The Eighteenth ACM International Conference on Web Search and Data Mining. ACM, 2025. https://doi.org/10.1145/3701551.3703497.

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Brehm, Christoph, and Hermann Fasel. "An Initial Value Problem Approach to Investigate BiGlobal Stability Problems." In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-184.

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Lu, Bo, and Guanxiu Yuan. "Initial boundary problem of nonlinear dispersion equation." In 2011 International Conference on Electronics, Communications and Control (ICECC). IEEE, 2011. http://dx.doi.org/10.1109/icecc.2011.6066600.

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Barvinsky, A. O., A. Yu Kamenshchik, Vladimir Lebedev, and Mikhail Feigel’man. "The problem of initial conditions in cosmology." In ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference. AIP, 2009. http://dx.doi.org/10.1063/1.3149498.

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Chen, Zhao, She-Sheng Zhang, and Hua-Ling Zhao. "Algorithm of boundary condition problem based on initial condition problem and application." In The 2015 International Conference on Mechanics and Mechanical Engineering (MME 2015). WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813145603_0109.

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Kinsht, N. V., N. N. Petrunko, and Kai Wu. "Partial discharges and the problem of initial conditions." In 2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE, 2017. http://dx.doi.org/10.1109/icieam.2017.8076465.

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Reports on the topic "Initial problem"

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Asmussen, Soeren, Peter W. Glynn, and Hermann Thorisson. Stationarity Detection in the Initial Transient Problem. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada251516.

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Glynn, Peter W. Two Approaches to the Initial Transient Problem. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada295803.

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Glynn, Peter W. Some New Results on the Initial Transient Problem. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada300838.

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Joo, S. W., W. W. Schultz, and A. F. Messiter. Uniformly Valid Solutions to the Initial-Value Wavemaker Problem. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada250958.

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Fernández, Jorge, and Sebastián J. Miller. Carbon Markets in Dynamic Perspective: The Optimal Duration Problem. Inter-American Development Bank, 2012. http://dx.doi.org/10.18235/0008423.

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The effectiveness of carbon markets in the reduction of emissions at minimal cost requires several conditions. In a dynamic context the inter-temporal dimension adds new conditions for the desirable performance of the market, and some tradeoffs. One tradeoff is related to the duration of permits. A long permit allows the private agent to optimize using a longer time horizon, but increases the risk associated with the initial allocation of the permits, for example the risk of generating market power. A short permit generates problems with the private agent's planning horizon but allows the planner to correct initial misallocations, in particular in new markets or those that face important uncertainty. These issues are important in the implementation of these systems, especially in developing countries such as the Latin American ones studied in this paper.

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Kuropiatnyk, D. I. Actuality of the problem of parametric identification of a mathematical model. [б. в.], 2018. http://dx.doi.org/10.31812/123456789/2885.

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The purpose of the article is to study the possibilities of increasing the efficiency of a mathematical model by identifying the parameters of an object. A key factor for parametrization can be called the consideration of properties of the values of the model at a specific time point, which allows a deeper analysis of data dependencies and correlation between them. However, such a technique does not always work, because in advance it is impossible to predict that the parameters can be substantially optimized. In addition, it is necessary to take into account the fact that minimization reduces the values of parameters without taking into account their real physical properties. The correctness of the final values will be based on dynamically selected parameters, which allows you to modify the terms of use of the system in real time. In the development process, the values of experimentally obtained data with the model are compared, which allows you to understand the accuracy of minimization. When choosing the most relevant parameters, various minimization functions are used, which provides an opportunity to cover a wide range of theoretical initial situations. Verification of the correctness of the decision is carried out with the help of a quality function, which can identify the accuracy and correctness of the optimized parameters. It is possible to choose different types of functional quality, depending on the characteristics of the initial data. The presence of such tools during parametrization allows for varied analysis of the model, testing it on various algorithms, data volumes and conditions of guaranteed convergence of functional methods.

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Cetinkaya, Suleyman, and Ali Demir. On the Solution of Bratu’s Initial Value Problem in the Liouville-Caputo Sense by ARA Transform and Decomposition Method. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2021. http://dx.doi.org/10.7546/crabs.2021.12.02.

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Etter, J. Derivation of Kane's equations of motion and the formulation of an initial-value problem for the Polaris A3 missile. Office of Scientific and Technical Information (OSTI), 1986. http://dx.doi.org/10.2172/5809718.

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Baldwin, Richard M. TA-97-4 Black Powder in the Gas Industry - Sources Characteristics and Treatment. Pipeline Research Council International, Inc. (PRCI), 1998. http://dx.doi.org/10.55274/r0011722.

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The original objective of this research was to investigate means of controlling materials ingested into compressors in pipeline, refinery, gathering, and storage services. After an initial industry survey, it was determined that "Black Powder" (various forms of iron sulfide mixed with contaminants) is the least understood and most prominent contamination problem in pipelines and their compression equipment. The information documented in this report was gathered from technical literature, the Internet, researchers, experts, practitioners in the natural gas industry, field experience, and equipment manufacturers' publications. This search has determined that there is much expert knowledge in the technical community concerning many aspects of the iron sulfide problem, however, there is only a limited understanding by those in the gas industry that face the problem. This report discusses information gathered as a part of the research, including a section with references to retrievable literature used.

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Sealza, Lita. Factors affecting the family planning program drop-out rate in Bukidnon, Philippines. Population Council, 1994. http://dx.doi.org/10.31899/rh1994.1002.

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This study has involved interviews with a randomly selected sample of 389 family planning (FP) acceptors from 20 barangays in Bukidnon province, Philippines. Respondents were currently married women who had either continued to use family planning (FP) since their initial acceptance (current users) or who had stopped using FP altogether (dropouts). Findings from the present study are expected to shed light on several aspects of the dropout problem, namely: How extensive is this problem and how accurate are the DOH records in this regard? How do FP acceptors view their local FP clinic and the services offered? What reasons are given by the dropouts for their decision to stop using FP? What are the factors associated with dropping out? As noted in this report, the study was made possible through support provided by the Population Council under its Family Planning Operations Research and Training (FPORT) Program.

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