Relevant bibliographies by topics / Improper fractional integrals

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Improper fractional integrals'

Author: Grafiati
Published: 5 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Improper fractional integrals"

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Chii-Huei, Yu. "Application of Reciprocal Substitution Method in Solving Some Improper Fractional Integrals." International Journal of Mathematics and Physical Sciences Research 11, no. 1 (2023): 1–5. https://doi.org/10.5281/zenodo.7883131.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we use reciprocal substitution method to find two improper fractional integrals. Change of variables for fractional integral and a new multiplication of fractional analytic functions play important roles in this paper. In fact, our results are generalizations of traditional calculus results. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, reciprocal substitution method, improper fractional integrals, change of variables for fractional integral, new multiplication, fractional analytic functions. <strong>Title:</strong> Application of Reciprocal Substitution Method in Solving Some Improper Fractional Integrals <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 11, Issue 1, April 2023 - September 2023</strong> <strong>Page No: 1-5</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 01-May-2023</strong> <strong>DOI: https://doi.org/10.5281/zenodo.7883131</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/application-of-reciprocal-substitution-method-in-solving-some-improper-fractional-integrals</strong>
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Chii-Huei, Yu. "Using Interval Recurrence Formula to Solve Two Improper Fractional Integrals." International Journal of Mathematics and Physical Sciences Research 11, no. 1 (2023): 53–58. https://doi.org/10.5281/zenodo.8076853.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we use interval recurrence formula to solve two improper fractional integrals. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, interval recurrence formula, improper fractional integrals. <strong>Title:</strong> Using Interval Recurrence Formula to Solve Two Improper Fractional Integrals <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 11, Issue 1, April 2023 - September 2023</strong> <strong>Page No: 53-58</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 24-June-2023</strong> <strong>DOI: https://doi.org/10.5281/zenodo.8076853</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/using-interval-recurrence-formula-to-solve-two-improper-fractional-integrals</strong>
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Chii-Huei, Yu. "Application of Differentiation under Fractional Integral Sign." International Journal of Mathematics and Physical Sciences Research 10, no. 2 (2022): 40–46. https://doi.org/10.5281/zenodo.7486538.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we use differentiation under fractional integral sign to evaluate two improper fractional integrals. Integration by parts for fractional calculus and a new multiplication of fractional analytic functions play important roles in this article. In fact, our results are generalizations of the results in ordinary calculus. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, differentiation under fractional integral sign, improper fractional integrals, integration by parts, new multiplication, fractional analytic functions. <strong>Title:</strong> Application of Differentiation under Fractional Integral Sign <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 10, Issue 2, October 2022 - March 2023</strong> <strong>Page No: 40-46</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 27-December-2022</strong> <strong>DOI: https://doi.org/10.5281/zenodo.7486538</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/application-of-differentiation-under-fractional-integral-sign</strong>
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Kalam, B., and G. Vainikko. "About the convergence type of improper integrals defining fractional derivatives." Acta et Commentationes Universitatis Tartuensis de Mathematica 23, no. 1 (2019): 95–102. http://dx.doi.org/10.12697/acutm.2019.23.10.

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This article continues the analysis of the class of fractionally differentiable functions. We complete the main result of [4] that characterises the class of fractionally differentiable functions in terms of the pointwise convergence of certain improper integrals containing these functions. Our aim is to present an example, which shows that in order to obtain all fractionally differentiable functions, one may not replace the conditional convergence of those integrals by their absolute convergence.
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Srivastava, Rekha, Ritu Agarwal, and Sonal Jain. "A family of the incomplete hypergeometric functions and associated integral transform and fractional derivative formulas." Filomat 31, no. 1 (2017): 125–40. http://dx.doi.org/10.2298/fil1701125s.

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Recently, Srivastava et al. [Integral Transforms Spec. Funct. 23 (2012), 659-683] introduced the incomplete Pochhammer symbols that led to a natural generalization and decomposition of a class of hypergeometric and other related functions as well as to certain potentially useful closed-form representations of definite and improper integrals of various special functions of applied mathematics and mathematical physics. In the present paper, our aim is to establish several formulas involving integral transforms and fractional derivatives of this family of incomplete hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results.
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Ghorbani, Hojjat, Yaghoub Mahmoudi, and Farhad Dastmalchi Saei. "Numerical Study of Fractional Mathieu Differential Equation Using Radial Basis Functions." Mathematical Modelling of Engineering Problems 7, no. 4 (2020): 568–76. http://dx.doi.org/10.18280/mmep.070409.

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In this paper, we introduce a method based on Radial Basis Functions (RBFs) for the numerical approximation of Mathieu differential equation with two fractional derivatives in the Caputo sense. For this, we suggest a numerical integration method for approximating the improper integrals with a singularity point at the right end of the integration domain, which appear in the fractional computations. We study numerically the affects of characteristic parameters and damping factor on the behavior of solution for fractional Mathieu differential equation. Some examples are presented to illustrate applicability and accuracy of the proposed method. The fractional derivatives order and the parameters of the Mathieu equation are changed to study the convergency of the numerical solutions.
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Bansal, Manish Kumar, and Devendra Kumar. "On a family of the incomplete H-functions and associated integral transforms." Journal of Applied Analysis 27, no. 1 (2021): 143–52. http://dx.doi.org/10.1515/jaa-2020-2040.

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Abstract Recently, Srivastava, Saxena and Parmar [H. M. Srivastava, R. K. Saxena and R. K. Parmar, Some families of the incomplete H-functions and the incomplete H ¯ {\overline{H}} -functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys. 25 2018, 1, 116–138] suggested incomplete H-functions (IHF) that paved the way to a natural extension and decomposition of H-function and other connected functions as well as to some important closed-form portrayals of definite and improper integrals of different kinds of special functions of physical sciences. In this article, our key aim is to present some new integral transform (Jacobi transform, Gegenbauer transform, Legendre transform and 𝖯 δ {\mathsf{P}_{\delta}} -transform) of this family of incomplete H-functions. Further, we give several interesting new and known results which are special cases our key results.
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Younis, Jihad, Bouchenak Ahmed, Mazin AlJazzazi, Rasha Al Hejaj, and Hassen Aydi. "Existence and Uniqueness Study of the Conformable Laplace Transform." Journal of Mathematics 2022 (April 26, 2022): 1–7. http://dx.doi.org/10.1155/2022/4554065.

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This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, as an application, we use the conformable Laplace transform for solving some fractional differential equations.
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Younis, Jihad, Bouchenak Ahmed, Mazin AlJazzazi, Rasha Al Hejaj, and Hassen Aydi. "Existence and Uniqueness Study of the Conformable Laplace Transform." Journal of Mathematics 2022 (April 26, 2022): 1–7. http://dx.doi.org/10.1155/2022/4554065.

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This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, as an application, we use the conformable Laplace transform for solving some fractional differential equations.
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Chii-Huei, Yu. "Some Type of Improper Fractional Integral." International Journal of Computer Science and Information Technology Research 10, no. 4 (2022): 53–57. https://doi.org/10.5281/zenodo.7476989.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we evaluate some type of improper fractional integral.&nbsp; A new multiplication of fractional analytic functions plays an important role in this paper. The main methods we used are integration by parts for fractional calculus and fractional L&rsquo;Hospital&rsquo;s rule. At the same time, some examples are given to illustrate our result. In fact, our result is a generalization of the classical calculus result. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, improper fractional integral, new multiplication, fractional analytic functions, integration by parts, fractional L&rsquo;Hospital&rsquo;s rule. <strong>Title:</strong> Some Type of Improper Fractional Integral <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Computer Science and Information Technology Research</strong> <strong>ISSN 2348-1196 (print), ISSN 2348-120X (online)</strong> <strong>Vol. 10, Issue 4, October 2022 - December 2022</strong> <strong>Page No: 53-57</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 23-December-2022</strong> <strong>DOI: https://doi.org/10.5281/zenodo.7476989</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/some-type-of-improper-fractional-integral</strong>
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Dissertations / Theses on the topic "Improper fractional integrals"

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Redeby, Theres. "Improved Techniques for Protein Analysis Focusing on Membrane Proteins and Hydrophobic Peptides." Doctoral thesis, Stockholm, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-617.

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Book chapters on the topic "Improper fractional integrals"

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Zhou, Changxiong, Tingqin Yan, Wenlin Tao, and Shufen Lui. "A Study of Images Denoising Based on Two Improved Fractional Integral Marks." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31588-6_50.

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Fochesato, Mattia, and Francesco Bettarini. "A new method of expanding the reconstruction of the occupational structure in Renaissance Florence: A preliminary investigation with insights into the economic impact of political and economic changes." In Datini Studies in Economic History. Firenze University Press, 2025. https://doi.org/10.36253/979-12-215-0667-9.22.

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Previous analyses of occupational structures in the urban centres of Western Europe in the late Middle Ages and Early modern times have attempted to estimate the shares of the labourers employed in different sectors using the information reported in the fiscal censuses. These contributions have often had to deal with the unavoidable limitations of the sources, such as their coverage of almost only the male declarants or that only a fraction of those censed declared their profession. As a result, the reconstruction of the occupational structures and the derived analysis of labour mobility based on these sources presented severe coverage limits of the labour force, for a large part of which, usually 40-50% of the active labourers, it was not possible to know the actual profession. We analyse seven fiscal censuses from Florence, ranging from the second half of the 14th century until the mid-15th century, to reconstruct the urban occupational structure among the male declarants. In addition, for a selected sample of neighbourhoods in one of the fiscal documents, we show a possible new method to integrate the existing information to increase the fraction of known occupations among the urban labour force. We show that our proposed method 1) significantly increases the proportion of the labour force with a known occupation and 2) substantially improves the knowledge of the occupational structure compared to the one obtained from the analysis of the sole declared occupations.
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Dawson, C. Bryan. "Techniques of Integration." In Calculus Set Free. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895592.003.0008.

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“Techniques of Integration” is perhaps the most traditional chapter in the text, with infinitesimals making appearances only for improper integrals. Functional notation is used for integration by parts (instead of differential notation), with the purpose of simplifying exercises involving both parts and substitution. The material on partial fractions is split into two sections, with the first section containing nonrepeated linear factors only. An optional section on “other techniques of integration” calls readers’ attention to the existence of techniques beyond those contained in calculus textbooks. A table of integrals is included, as is a discussion of the use of technology.
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Mazroa, Omnia Reda, and Mohamed Hassan Gadallah. "Branch and Bound Combined Design of Experiment Algorithm." In Practice, Progress, and Proficiency in Sustainability. IGI Global, 2024. https://doi.org/10.4018/979-8-3693-7117-6.ch006.

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The chapter introduces a novel hybrid approach that integrates orthogonal arrays and strong branching rules to solve Mixed Integer Problems using the branch-and-bound technique. For low to medium size problems, full orthogonal arrays are employed without the need to apply the strong branching rule because full-size arrays yield optimum solution consistently. For higher size problems, which return large number of continuous variables, the user uses fractional orthogonal arrays to simplify the solution process of the problem. Fractional arrays result in low number of function evaluations and produce incumbent solutions. Strong branching rule, a widely recognized variable selection rule, is employed and integrated with orthogonal arrays mainly in order to improve the quality of the obtained results from fractional arrays and to minimize the time consumed in solving the problem. The hybrid algorithm has been empirically shown to generate considerably smaller branch-and-bound trees compared to other known rules and the method's effectiveness is validated through several model solutions.
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Li, Bingyu, Jining Guo, and Ying Fu. "Fractional-Order PID and Active Disturbance Rejection Compound Control for Vacuum Induction Furnace." In Advances in Transdisciplinary Engineering. IOS Press, 2022. http://dx.doi.org/10.3233/atde220026.

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This paper proposes a compound control strategy which is generated by the combination of fractional-order proportional-integral-derivative (FOPID) and the active disturbance rejection control (ADRC) to improve temperature control accuracy for melting period of vacuum induction furnace. The method of ADRC does not rely on the accurate mathematical model of the controlled system. Due to the exist of the extended state observer, the ADRC can compensate the influence of the system on the output in a larger range, which is very suitable for the temperature control system of vacuum induction furnace with uncertainty. The method of FOPID control can improve the control quality of the system with the addition of two free variables. The robustness and capacity of resisting disturbance of the proposed method was verified by the simulation results.
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Cong, Xiao, Junwei Lei, and Hong Wang. "Research on Stability of Integral Type Second Order Variable Structure Control for Aircraft Pitch Channel." In Advances in Transdisciplinary Engineering. IOS Press, 2024. http://dx.doi.org/10.3233/atde240219.

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A simplified model for the angle of attack tracking in the pitch channel of unmanned aerial vehicles is proposed. Based on the traditional second-order sliding mode control, the stability problems of the fractional power design of the traditional second-order sliding mode are pointed out, and an improved integral second-order variable structure control method is proposed. At the same time, a softening function design is used to construct the symbol function of the traditional second-order sliding mode. And in the selection of sliding mode surfaces, an integral type sliding mode surface was adopted. Finally, the time-varying Lyapunov function was selected and stability proof was provided under sufficient big gain conditions. After the sliding surface approaches zero, based on the approximate treatment of the simplified model, a proof of Hurwtiz property of the sliding surface is provided, ensuring that the angle of attack tracking error approaches zero and the control of the angle of attack tracking is realized . Finally, the control effect of second-order sliding mode control for unmanned aerial vehicle angle of attack tracking was presented through digital simulation. At the same time, the perturbation problem of control variables in the completely unknown situation of the model was considered, and the control effect was almost unaffected. It can still maintain the stability of the entire system and realize the angle of attack tracking, thus it demonstrates the effectiveness of the design method provided in this paper.
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Chennupati, Janani, Mounika Susarla, Vani K. Suvarna, K. S. Vijaya Lakshmi, and Chennu Nandini Priyanka. "Algorithm-Based Spatio-Temporal Study on Identification of Pure Bamboo Vegetation Using LULC Classification." In Handbook of Research on Advancements in AI and IoT Convergence Technologies. IGI Global, 2023. http://dx.doi.org/10.4018/978-1-6684-6971-2.ch014.

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Bamboo is a natural air purifier that helps to keep the surroundings clean. Bamboo forests, an essential source of socioeconomic life for rural communities and an integral part of the ecosystem, are undergoing substantial changes. In the mapping and identification of natural resources, space technology has been beneficial. The objective of classification is to divide a large subject into fewer, more manageable fractions. For land use and land cover, four supervised learning methods, namely Naive Bayes, random forest, support vector machine, and decision tree, are used. Their overall accuracies will be compared to obtain the best algorithm. Land cover mapping and monitoring were carried out to preserve current natural resources and better understand the causative factors of land use in the study region, i.e., East Garo Hills, a district of Meghalaya, for the 2018 data. The application performance was measured in terms of Accuracy 97.23%, Recall 89.23%, F1 measure 97.23%, and Throughput 96.34%, which were improved and competed with future-level applications.
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Habashneh, Muayad, and Majid Movahedi Rad. "Probabilistic Topology Optimization of Steel I-Beam Web Configurations Under Varied Load Positions." In Advances in Transdisciplinary Engineering. IOS Press, 2024. http://dx.doi.org/10.3233/atde240523.

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This study investigates the impact of uncertain load positions through an innovative optimization technique. It seamlessly integrates reliability-based design into the optimization of the structural topology, with a specific focus on the web portion of steel I-beams and including geometrical imperfection analysis. The study operates under the premise that the applied load is randomly positioned, engaging in a comprehensive probabilistic analysis. This methodology extends its considerations to additional factors, such as material properties, volume fraction, and geometric imperfections. The assumption of a normal distribution for each of these parameters aids in quantifying uncertainties. Moreover, the proposed work leverages the notion of plastic ultimate load multipliers to illustrate how the algorithm can improve the performance of steel beams. To evaluate the algorithm, the results of a benchmark problem were meticulously analyzed. While exploring the probabilistic nature of externally applied force positions, a numerical example was conducted involving a steel I-beam within the context of reliability-based imperfect geometry topology optimization. The outcomes of the proposed method underscore that the integration of probabilistic design significantly influences the topology optimization process.
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Hoffmann, Rainer, and Paolo Colonna. "Evaluation of left ventricular systolic function and mechanics." In The ESC Textbook of Cardiovascular Imaging. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780198703341.003.0023.

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Analysis of left ventricular (LV) systolic function is the most frequent indication to perform echocardiography and an integral part of cardiac magnetic resonance (CMR) or radionuclide studies. Visual estimation of LV function may be supplemented by quantitative analysis of 2D images to obtain parameters of global or regional function. Administration of contrast agents to improve identification of myocardium–blood interface has been demonstrated to improve the reproducibility of 2D-echocardiography-based analysis of LV function and should be applied in cases of insufficient endocardial border definition (more than two LV segments not adequately visualized). 2D-echocardiography-based analysis of LV volumes results in underestimation of end-systolic and end-diastolic LV volumes compared to CMR. 3D-echocardiography results in significantly less volume underestimation and higher accuracy in the analysis of ejection fraction. Analysis of regional wall motion is mainly based on subjective visual assessment, which is limited by significant inter-observer variability. Doppler tissue imaging and speckle tracking echocardiography have become validated methods for quantitative analysis of regional LV function. Similarly, tagging, strain-encoded cardiac magnetic resonance (SENC) and feature tracking are modalities to quantify regional LV function based on CMR. Echocardiography should be used as a primary technique to assess systolic LV function as it is the cheapest, widely available and can be applied without the use of ionizing radiation or nephrotoxic contrast material. CMR has become the clinical gold standard for quantification of LV function and may be applied if other information achievable best by CMR is required. Similarly, nuclear techniques should be applied to assess LV function only if simultaneous assessment of myocardial perfusion is requested.
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Lazzeroni, Davide, and Claudio Stefano Centorbi. "Hypertrophic Cardiomyopathy: Genetics, Pathogenesis, Diagnosis, Clinical Course and Therapy." In Cardiomyopathy - Disease of the Heart Muscle [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.97033.

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Hypertrophic cardiomyopathy (HCM) is a genetic disorder of cardiac myocytes that is characterized by cardiac hypertrophy, unexplained by the loading conditions, a non-dilated left ventricle and a normal or increased left ventricular ejection fraction (LV-EF). Prevalence of HCM has been estimated at 0.16% to 0.29% (≈ 1:625–1:344 individuals) in the general adult population. HCM represents the most common genetic heart disease and represent an archetypical single gene disorder with an autosomal dominant pattern of inheritance and historically termed a “disease of the sarcomere”. The precise mechanisms by which sarcomere variants result in the clinical phenotype have not been fully understood. Mutant sarcomere genes trigger several myocardial changes, leading to hypertrophy and fibrosis, which ultimately result in a small, stiff ventricle with impaired systolic and diastolic performance despite a preserved LV-EF. The most common differential diagnosis challenges in the presence of hypertrophic heart disease are represented by: athlete’s heart, hypertensive heart and other cardiomyopathies mimicking HCM. A multimodality approach using ECG, echocardiography, CMR, cardiac computed tomography (CCT) and cardiac nuclear imaging provides unique information about diagnosis, staging and clinical profiles, anatomical and functional assessment, metabolic evaluation, monitoring of treatment, follow-up, prognosis and risk stratification, as well as preclinical screening and differential diagnosis. HCM may be associated with a normal life expectancy and a very stable clinical course. However, about a third of patients develop heart failure (HF); in addition, 5–15% of cases show progression to either the restrictive or the dilated hypokinetic evolution of HCM, both of which may require evaluation for cardiac transplantation. The clinical course of HCM has been classified into four clinical stages: non-hypertrophic, classic, adverse remodeling and overt dysfunction phenotype. No evidence-based treatments are available for non-hypertrophic HCM patients (pre-hypertrophic stage), on the other hand in classic HCM, adverse remodeling and overt dysfunction phenotype, pharmacological or interventional strategies have the target to improve functional capacity, reduce symptoms, prevent disease progression. Therapeutic approach mainly differs on the basis of the presence or absence of significant obstructive HCM. Adult patients with HCM report an annual incidence for cardiovascular death of 1–2%, with sudden cardiac death (SCD), HF and thromboembolism being the main causes of death; the most commonly recorded fatal arrhythmic event is spontaneous ventricular fibrillation. For this reason, SCD risk estimation is an integral part of clinical management of HCM. International guidelines suggest the evaluation of several risk factor for SCD based on personal and family history, non-invasive testing including echocardiography, ambulatory electrocardiographic 24 hours monitoring and CMR imaging in order to identity those patients most likely to benefit implantable cardioverter-defibrillator (ICD) implantation. The present chapter summarize genetics, pathogenesis, diagnosis, clinical course and therapy of HCM as well as novel therapeutic options.
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Conference papers on the topic "Improper fractional integrals"

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Song, Zeyuan, and Zheyu Jiang. "A Physics-based, Data-driven Numerical Framework for Anomalous Diffusion of Water in Soil." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.163304.

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Precision modeling and forecasting of soil moisture are essential for implementing smart irrigation systems and mitigating agricultural drought. Most agro-hydrological models are based on the standard Richards equation, a highly nonlinear, degenerate elliptic-parabolic partial differential equation (PDE) with first order time derivative. However, research has shown that standard Richards equation is unable to model preferential flow in soil with fractal structure. In such a scenario, the soil exhibits anomalous non-Boltzmann scaling behavior. Incorporating the anomalous non-Boltzmann scaling behavior into the Richards equation leads to a generalized, time-fractional Richards equation based on fractional time derivatives. As expected, solving the time-fractional Richards equation for accurate modeling of water flow dynamics in soil faces extensive computational challenges. To target these challenges, we propose a novel numerical method that integrates finite volume method (FVM), adaptive fixed point iteration scheme, and neural network to solve the time-fractional Richards equation. Specifically, we develop an adaptive fixed point iteration scheme to solve the FVM-discretized equation iteratively, which avoids the stability issues when directly solving a stiff and sparse matrix equation. To improve the solution quality which is influenced by numerical errors and computational constraints during actual implementation, we propose to use neural networks that resemble an encoder-decoder architecture to map soil moisture profiles into a latent space and reconstruct them back. Through 1-D examples, we illustrate the accuracy and computational efficiency of our proposed physics-based, data-driven numerical method. Finally, we present a Markov chain Monte Carlo (MCMC) approach to solve the inverse problem to obtain soil-specific parameters given soil moisture solutions.
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LEPADATU, Daniel, Loredana JUDELE, Ioana ENTUC, Eduard PROASPAT, and Gabriel SANDULACHE. "NANOPARTICLES AND RECYCLABLE WASTE IN CONSTRUCTION MATERIALS. FROM PRACTICAL NECESSITY TO ADVANCED SOLUTIONS." In SGEM International Multidisciplinary Scientific GeoConference. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024v/6.2/s25.29.

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In an increasingly competitive economy, we are facing fierce competition in the construction materials industry, where the use of recyclable waste from demolitions has become more than a necessity. The compensation for the loss of certain properties, which could otherwise lead to a reduction in mechanical characteristics, has been achieved through the addition of nanoparticles with superior qualities. This paper will present the main nanoparticles introduced as subtle additives (ranging from 0.01 percent to a maximum of 1 percent) - currently limited due to manufacturing costs - into the formulations of construction materials such as nanocomposites, nanomortars, nanoconcretes, etc., as well as in sometimes substantial fractions of recycled aggregates, among others. Several types of nanoparticles will be discussed, starting with nanoclay, which improves strength and durability and carbon nanotubes, predominantly used in polymers for construction. In concrete, nano-silica can enhance compressive strength and reduce permeability, graphene oxide can improve mechanical properties and reduce weight and nano-metakaolin, being a pozzolanic material, contributes to long-term strength and durability. At the same time, an analysis will be conducted on some of the recyclable waste from construction, which, under certain conditions, can become integral parts of the formulations for new materials. In this way, we can address two societal issues: the first related to recycling demolition waste and the second to reducing pollution. Furthermore, we can highlight the circular economy, as these materials are reintroduced and repurposed in the creation of new advanced building materials.
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Kiryakova, Virginia. "Use of fractional calculus to evaluate some improper integrals of special functions." In PROCEEDINGS OF THE 43RD INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS: (AMEE’17). Author(s), 2017. http://dx.doi.org/10.1063/1.5013994.

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AbdAlRahman, Alaa, Amr Abdelaty, Ahmed Soltan, and Ahmed G. Radwan. "An Improved Approximation of Grunwald-Letnikov Fractional Integral." In 2021 10th International Conference on Modern Circuits and Systems Technologies (MOCAST). IEEE, 2021. http://dx.doi.org/10.1109/mocast52088.2021.9493399.

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Sun, Jingxue, Chunyang Wang, Xuelian Liu, and Huanhuan Xia. "An improved image denoising algorithm based on adaptive fractional integral." In 2017 29th Chinese Control And Decision Conference (CCDC). IEEE, 2017. http://dx.doi.org/10.1109/ccdc.2017.7978986.

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Wang, Fengping, Weixing Wang, Ting Cao, and Weiwei Chen. "Change detection from remote sensing images based on fractional integral and improved FLICM." In LIDAR Imaging Detection and Target Recognition 2017, edited by Yueguang Lv, Jianzhong Su, Wei Gong, et al. SPIE, 2017. http://dx.doi.org/10.1117/12.2292656.

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Jia, Liangyu, and Zhiyu Zhu. "Improved Fractional-Order Integral Sliding Mode Control for AUV Based on RBF Neural network." In 2019 Chinese Automation Congress (CAC). IEEE, 2019. http://dx.doi.org/10.1109/cac48633.2019.8996977.

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Zolfaghari, Mahdi, Ali Asghar Khodadoost Arani, G. B. Gharehpetian, and Mehrdad Abedi. "A fractional order proportional-integral controller design to improve load sharing between DGs in microgrid." In 2016 Smart Grids Conference (SGC). IEEE, 2016. http://dx.doi.org/10.1109/sgc.2016.7882947.

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Sun, Jihao, Pengchong Chen, and Ying Luo. "A Fractional Order Control and Correction Strategy for EtherCAT Communication Clock Drift." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-70814.

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Abstract Ethernet Control Automation Technology (EtherCAT) applies distributed clock (DC) to realize synchronization among different slaves. Due to the influence of the crystal oscillator manufacturing process and environment, there is still synchronization error between reference clock and non-reference clock. To solve the clock synchronization problem, this paper proposes a clock drift compensation algorithm based on the idea of closed-loop control. By designing integer-order proportional integral (IOPI) and fractional-order proportional integral (FOPI) controllers, the synchronization error between slaves can be minimized. The IOPI and FOPI controllers designed in this paper are used to eliminate the drift error. This method improves the synchronization accuracy without bringing too much computational load. The results show that the proposed FOPI controller can effectively reduce the synchronization error with even better performance over the IOPI controller.
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Jiang, Jianyu, Bin Wu, and Ting Zhou. "Design of a Fractional-Order Controller for the Large Deep Space Observatory Antenna in Wind Disturbance." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-69730.

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Abstract To meet the current and future needs of deep space communication services, some large Deep Space Station antennas had to be built on the existing Deep Space Network sites. The influence of wind disturbance has become a serious problem with the increased size of the antenna. Based on the typical antenna model, a fractional-order controller is designed to improve the pointing accuracy of the antenna in wind disturbance. First, the global stability region of fractional-order proportion integral differential (FOPID) controller for the antenna plant was obtained using the Domain-decomposition (D-decomposition) method, Second, the parameters in the stability region were chosen using a genetic algorithm. Then, the disturbance observer is used to estimate and compensate for the influence of the wind disturbance. Finally, a series of simulations and analyses about this fractional-order control system was conducted, the results show that the fractional-order controller works significantly outperform the traditional proportion integral differential (PID) controller, it achieved a remarkable amelioration in the reduction of overshoot and the capacity of wind disturbance rejection.
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Reports on the topic "Improper fractional integrals"

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Cohen, Shabtai, Melvin Tyree, Amos Naor, Alan N. Lakso, Terence L. Robinson, and Yehezkiel Cohen. Influence of hydraulic properties of rootstocks and the rootstock-scion graft on water use and productivity of apple trees. United States Department of Agriculture, 2001. http://dx.doi.org/10.32747/2001.7587219.bard.

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This one year exploratory project investigated hydraulic architecture of apple dwarfing rootstocks. The hypothesis was that hydraulic conductance is correlated with rootstock vigor. A previous study of trees on three rootstocks in Israel showed that dwarfed trees used less water than un-dwarfed trees. Analysis showed that if the tree maintains leaf water potentials above minimum values, then this implies that the dwarfed trees have lower leaf conductance, which may also be the cause of dwarfing. The current project studied small 2-year old unworked rootstock trees, and full sized trees bearing commercial yields. In both cases hydraulic conductance was determined with two methods - the non-destructive evaporative flux (EF)-leaf water potential (L WP) method, and a destructive method in which water was forced through the plant at known pressure using the "high pressure flow meter" (HPFM). Detailed work allowed measurement of conductance of the rootstock-scion union. This was achieved both with the HPFM and with the EF-LWP methods, the former in the US and the latter in Israel. Direct measurements of leaf conductance were made, and carbon isotope ratios ( d ¹³ C) were determined for leaves sampled at the end of the season. The latter can indicate sustained differences in leaf conductance behavior. HPFM and EF-LWP methods did not give the same results. In the small plants results were similar in magnitude, but not significantly correlated. In large trees, EF- L WP measurements were a fraction of those obtained with the HPFM. The latter indicates that some of the xylem is not normally functional but transports water when pressurized. Additional experimental work targeted this result. Xylem was stained before and after perfusion with water at high pressure. This showed that at least for one rootstock a significant amount of xylem was blocked before perfusion. The "air method" for determining xylem vessel properties was improved and employed. Length, radius and density of xylem vessels of different rootstocks were found to be similar, and significant differences found were not clearly related to rootstock vigor. Measurements in the commercial orchard in Israel showed that the graft union in a dwarfing rootstock was a large obstacle for water transport (i.e. had a high resistance). This apparently led to low leaf conductance to water vapor, as indicated by lower d ¹³ C, which implies low internal CO ₂ concentrations. In the US orchard, d ¹³ C in 2001 was correlated with rootstock vigor, and significant differences were found in leaf conductance. However, the d ¹³ C differences were not observed in 2002, were opposite to those found in the Israeli orchard, and measurements of the graft union with the HPFM did not find large resistances. We speculate that the graft union is not necessarily a large impediment to water transport unless the scion starts to separate from the rootstock. It was concluded that significant differences in hydraulic conductance exist between different dwarfing rootstocks. These differences may be caused by differences in xylem properties and in the degree of cavitation, as well as resistance in the graft union. However, no general relationship to rootstock vigor was found. Therefore, hydraulic conductance alone cannot explain dwarfing, but may be one of two or more factors that lead to dwarfing. Future work should integrate more factors with hydraulic relations, e.g. nutrient and solute transport and production of hormones.
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