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Academic literature on the topic 'Slice Regular Functions'

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Published: 10 March 2023

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Journal articles on the topic "Slice Regular Functions"

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Altavilla, A., and C. de Fabritiis. "$*$-exponential of slice-regular functions." Proceedings of the American Mathematical Society 147, no. 3 (December 6, 2018): 1173–88. http://dx.doi.org/10.1090/proc/14307.

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Sheaves of slice regular functions." Mathematische Nachrichten 285, no. 8-9 (January 18, 2012): 949–58. http://dx.doi.org/10.1002/mana.201000149.

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Stoppato, Caterina. "Singularities of slice regular functions." Mathematische Nachrichten 285, no. 10 (February 21, 2012): 1274–93. http://dx.doi.org/10.1002/mana.201100082.

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Zhenghua, Xu, and Wang Ermin. "Proper slice regular functions over quaternions." SCIENTIA SINICA Mathematica 51, no. 12 (July 16, 2020): 1975. http://dx.doi.org/10.1360/scm-2018-0858.

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Altavilla, Amedeo. "Twistor interpretation of slice regular functions." Journal of Geometry and Physics 123 (January 2018): 184–208. http://dx.doi.org/10.1016/j.geomphys.2017.09.007.

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Ren, Guangbin, and Xieping Wang. "Carathéodory Theorems for Slice Regular Functions." Complex Analysis and Operator Theory 9, no. 5 (December 2, 2014): 1229–43. http://dx.doi.org/10.1007/s11785-014-0432-9.

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Ren, Guangbin, and Xieping Wang. "Julia theory for slice regular functions." Transactions of the American Mathematical Society 369, no. 2 (March 18, 2016): 861–85. http://dx.doi.org/10.1090/tran/6717.

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de Fabritiis, Chiara. "Transcendental operators acting on slice regular functions." Concrete Operators 9, no. 1 (January 1, 2022): 6–18. http://dx.doi.org/10.1515/conop-2022-0002.

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Abstract The aim of this paper is to carry out an analysis of five trascendental operators acting on the space of slice regular functions, namely *-exponential, *-sine and *-cosine and their hyperbolic analogues. The first three of them were introduced by Colombo, Sabadini and Struppa and some features of *-exponential were investigated in a previous paper by Altavilla and the author. We show how exp*(f ), sin*(f ), cos*(f ), sinh*(f ) and cosh*(f ) can be written in terms of the real and the vector part of the function f and we examine the relation between cos* and cosh* when the domain Ω is product and when it is slice. In particular we prove that when Ω is slice, then cos*(f ) = cosh*(f * I) holds if and only if f is ℂ I preserving, while in the case Ω is product there is a much larger family of slice regular functions for which the above relation holds.
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Dou, Xinyuan, Guangbin Ren, Irene Sabadini, and Ting Yang. "Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions." Journal of Geometric Analysis 31, no. 11 (May 12, 2021): 11312–37. http://dx.doi.org/10.1007/s12220-021-00682-5.

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AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.
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Ghiloni, R., and A. Perotti. "Slice regular functions on real alternative algebras." Advances in Mathematics 226, no. 2 (January 2011): 1662–91. http://dx.doi.org/10.1016/j.aim.2010.08.015.

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Dissertations / Theses on the topic "Slice Regular Functions"

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Gabrielli, Andrea. "Defining, calculating and reasoning in Higher-Order Logic: Complex and Hypercomplex Analysis and applications." Doctoral thesis, 2018. http://hdl.handle.net/2158/1160982.

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The occasional ambiguity of traditional mathematical notations, and the increasing complexity of proofs, has led to the situation that the use of a proof-verification system is desirable if not, in some situations, unavoidable. Moreover, by merging calculation techniques and proofs, theorem provers also allow a deep interconnection of the three basic mathematical activities, that is, defining, calculating and reasoning. In this thesis we explore such activities from different points of view, dealing with complex and hypercomplex analysis and computability theory using the HOL Light theorem prover. More precisely, the work is divided into four parts, each independent from the others. In the first we report on a formal development of quaternions and their algebraic structure, and we discuss automatic and certified procedures to perform calculations on them. The second part is dedicated to investigate the formalization of possible applications of our framework about quaternions. They are interesting theories on their own and, at the same time, a test for our work. In particular, we formalize basics definitions and theorems about two of the most recent and stimulating theories based on quaternions, that is, ''Slice regular quaternionic functions'' and ''Pythagorean-Hodograph curves''. Slice regular functions extend, in a suitable way, the notion of complex holomorphic function to the quaternionic case whereas, PH-curves are a class of polynomial functions with many theoretical properties and several significant computational advantages in many fields like computer-aided design (CAD), digital motion control, path planning, robotics applications and animation. The main points of the work presented in the first two parts has been published in proceedings of the 8th International Conference on Interactive Theorem Proving in Brasilia 2017. In part three and four we consider computability as a theory on its own. In particular, we focus on two radically different models of computation (but equally important), namely ''Turing Machines'' and ''quantum computing''. We give the basic definitions and we develop two certified systems to simulate computations in such models. Moreover, by implementing the concepts of Turing machines and quantum circuits in HOL Light, we explore these different approaches formalizing some simple different problems they can solve.
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Books on the topic "Slice Regular Functions"

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. Entire Slice Regular Functions. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49265-0.

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. Entire Slice Regular Functions. Springer, 2016.

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. Entire Slice Regular Functions. Birkhauser Verlag, 2017.

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Sabadini, Irene, and Sorin G. Gal. Quaternionic Approximation: With Application to Slice Regular Functions. Springer International Publishing AG, 2019.

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Book chapters on the topic "Slice Regular Functions"

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Slice Regular Functions: Algebra." In SpringerBriefs in Mathematics, 7–30. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49265-0_2.

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Slice Regular Functions: Analysis." In SpringerBriefs in Mathematics, 31–54. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49265-0_3.

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Growth of Entire Slice Regular Functions." In SpringerBriefs in Mathematics, 77–108. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49265-0_5.

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Vlacci, Fabio. "Regular Composition for Slice-Regular Functions of Quaternionic Variable." In Advances in Hypercomplex Analysis, 141–47. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2445-8_9.

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Gal, Sorin G., and Irene Sabadini. "Approximation of Slice Regular Functions in Compact Sets." In Frontiers in Mathematics, 83–128. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10666-9_4.

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Della Rocchetta, Chiara, Graziano Gentili, and Giulia Sarfatti. "A Bloch-Landau Theorem for Slice Regular Functions." In Advances in Hypercomplex Analysis, 55–74. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2445-8_4.

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Ren, Guangbin, Xieping Wang, and Zhenghua Xu. "Slice Regular Functions on Regular Quadratic Cones of Real Alternative Algebras." In Trends in Mathematics, 227–45. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42529-0_13.

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Colombo, Fabrizio, J. Oscar González-Cervantes, Maria Elena Luna-Elizarrarás, Irene Sabadini, and Michael Shapiro. "On Two Approaches to the Bergman Theory for Slice Regular Functions." In Advances in Hypercomplex Analysis, 39–54. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2445-8_3.

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Gentili, Graziano, and Caterina Stoppato. "The Zero Sets of Slice Regular Functions and the Open Mapping Theorem." In Hypercomplex Analysis and Applications, 95–107. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0246-4_7.

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Hanahan, Donald J. "Introduction to Lipids." In A Guide to Phospholipid Chemistry. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195079814.003.0004.

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Concomitant with the explosive development and progress made in the field of molecular biology, initiated by development and proof of the double helix structure of DNA some 40 years ago, there has been a much more subdued, but equally exciting and important, development in the area of signal transduction (Nishizuka, 1992; Berridge, 1984; Exton, 1990). What makes the latter subject so enchanting to biochemists is the finding that membrane phospholipids are intimately involved in the transduction process. Interestingly, the potential role of phospholipids in the signal transduction pathway was formulated some 40 years ago also. (Perhaps all great discoveries occur in 40 year cycles.) In any event the first hint of any possible involvement of phospholipids in cellular stimulus responses was gained from the work of Hokin and Hokin, which first appeared in 1953. In this classic paper, these investigators reported that treatment of pigeon pancreas slices with acetylcholine or carbamylcholine (cholinergic drugs) resulted not only in the secretion of amylases but also in the turnover of two specific membrane phospholipids, namely, phosphatidylinositol and phosphatidic acid. While the entire process of stimulus response in a mammalian cell is now much more complicated, nevertheless the findings by Hokin and Hokin were of major importance in the maturation of this field. Unfortunately, the impact of the Hokins’ observations was not immmediately felt. At that point in time, phospholipids were viewed mainly as semipermeable membrane structures whose main function was to regulate the ion content of the cell. In addition, another deterrent was the limited information on the chemical structure of the mammalian cell phospholipids. Hence there was a hiatus of many years in which low-profile lipid chemists and biochemists labored to solve the chemical nature of membrane lipids and to deduce their physical arrangement in the cell. Then in 1975, Michell published a key paper (Michell, 1975) in which he noted the importance of the inositol-containing phospholipids in the membrane process known as calcium gating. This paper initiated what can be called the “PI” era, which is still very much alive and well today.
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Conference papers on the topic "Slice Regular Functions"

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Ghiloni, R., and A. Perotti. "Slice regular functions of several Clifford variables." In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4765569.

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Nashold, Karen M., and B. E. A. Saleh. "Generation of bandlimited images from unequally spaced slices." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.mo5.

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It is often desired to generate a 2-D bandlimited function f (x,y), which when thresholded has specified edges. This is the case, for example, in generating binary masks through diffraction-limited systems. It has been shown in the past that bandlimited images can be constructed from slices which are themselves generated using 1-D methods. No emphasis, however, was placed on where the slices should be made. If an exact solution exists, and the slices are produced at distances separated by 1/2B (B being the required bandwidth in the y direction), f(x,y) can be found by simply low pass filtering the slices. If, however, an exact solution does not exist, which is often the case in image construction, such construction only guarantees the exact zero crossings along the slices. Our results indicate that uneven sampling can improve resolution. Samples are taken closer together in a finite region where greater resolution is required and farther apart elsewhere. The desired image is then formed using interpolating functions which are determined, depending on the desired sampling locations, by properly inserting and deleting zeros in a known bandlimited function. The resulting image can thus be forced to have the desired zero crossings at more places than in regular sampling, and hence greater accuracy is achieved.
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Sakaida, Shohei, Ding Zhu, and A. D. Hill. "Development of Comprehensive and Efficient DTS Interpretation Method for Fracture Diagnosis." In 2022 SPWLA 63rd Annual Symposium. Society of Petrophysicists and Well Log Analysts, 2022. http://dx.doi.org/10.30632/spwla-2022-0025.

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Distributed temperature sensing (DTS) by fiber optic technology has been commonly used to evaluate the fracturing treatment efficiency. Once DTS data is quantitively interpreted, we can estimate injected fluid volume distribution along each stimulated stage interval, and it allows us to analyze and optimize completion design such as injection schedule, fluid/proppant types, and perforation design. In general, the DTS data can be interpreted by conducting temperature profile matching. After pumping is stopped, the perforation clusters that take more fluid during injection warm up more slowly. Based on this physical feature, the injected fluid volume can be estimated by reproducing the temperature profile during warm-up using a numerical thermal model as a forward model. The temperature matching technique still contains several uncertainties. One of them is the transient temperature behavior as a function of shut-in time. While the DTS data is continuous with time and space, the temperature profile at one time slice is generally interpreted. However, as presented by several authors, the trend of temperature profile often changes with time during warm-up, which could be caused by the fracture closure or small amount of fluid flow induced by adjacent stage treatments. If degree or locations of cooling spots are different with time, this thermal behavior also needs to be incorporated into the mathematical model to correctly evaluate the fracturing stimulation efficiency. In this study, we extend the existing DTS interpretation method to be able to match the temperature profile at multiple time slices. While the degradation of efficiency is expected due to increase of data to be matched and model parameters to be tuned, we apply high-efficiency inversion techniques which have been established in the regular history matching methods to improve the interpretation procedure. Also, this study explains the connection and conflict between fracture stimulation efficiency and productivity. As previously presented, the estimated injected fluid volume distribution may not be perfectly matched with production inflow distribution. If more reliable injected fluid volume distribution can be estimated by considering the temperature behavior at multiple time slices, we can better diagnose the fracturing treatment performance.
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Luniya, Tanmay, and Geetha Chimata. "Extending the Life of Classic Cars, the Additive Manufacturing Way." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-70355.

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Abstract There has been a steadily increasing global market for Additively Manufactured (AM) products, with a growth forecast of USD 23.75 billion by 2027. Of the various industrial sectors applying AM, the automotive/motor vehicles market takes up approximately 18% share. Saying AM is being widely used in the automotive sector with rapidly growing application avenues is not an overstatement. One such section of the automotive industry is the classic cars. Classic cars are 20 years or more older cars no longer in regular production, preserved and restored for their historical value. Classic cars face a huge problem of spare parts. The non-availability of the spare part leads to the break-down of the car, leaving them as display pieces or eventual scrapping. It is not economically viable to manufacture the spare parts in small volume due to challenges such as high cost of tooling, and indefinite storage time. Additive manufacturing offers attractive solutions to problems precisely such as these as it requires no additional tooling and can produce functional parts in small batches on-demand, provided accurate three-dimensional model data is available. This 3D model data is converted to one of the AM compatible file formats such as STL, AMF, 3MF etc. and then is processed using a Slicer Software. The slicer software converts three-dimensional (3-D) model data to two-dimensional (2-D) layer information that will be printed by the AM machine. Obtaining drawings or 3-D model information for classic car parts is a daunting challenge in itself, often deemed impossible. However, with the advances in imaging and scanning combined with computer aided design technologies, it is shown to be possible to generate the 3-D model data from even partial or broken parts. Now, producing spare parts using AM is not just feasible but has been successfully applied. Few notable examples include restoration of Elvis Presley’s BMW 507, originally released in 1957, which took two years to complete, Jaguar’s XK120 SE restored in 2017, 2019 restorations of Volkswagens iconic 1962 minivan, Bentley’s 1929 Blowers and Bugatti’s 1926 Bugatti Baby. Not just car manufacturers, but hobbyist collectors also found success in producing spare parts for their classic cars. This paper discusses various types of additive manufacturing technologies used to manufacture classic car parts and the strategic impact after implementing them using the examples of famous restored classic cars. The discussion further includes commercialization of these technologies, challenges, material selection and availability. Additionally, the economic implications and, the future are explored.
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Nishimura, Kazuhiko, Yoshiaki Terumichi, Tsutomu Morimura, and Kiyoshi Sogabe. "Development of Vehicle Dynamics Simulation for Safety Analyses of Rail Vehicles on Excited Tracks." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34474.

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Considerable numbers of earthquake disasters have been experienced in Japan. Thus the study and research of earthquake disaster prevention are highly awarded in Japan. In a railway industry, for instance, infrastructures have been reinforced and a new alert system has been employed to regulate the operating system to stop trains immediately if a great earthquake occurs. A railway is organized by a variety of individual technologies, and functions safely and properly as a system, therefore it is beneficial for the system safety to study and examine the individual potential cases of disasters caused by earthquakes from various different viewpoints. Recent reports imply that rail vehicles could derail solely by the ground motions of earthquakes without fatal damages of vehicles and tracks. Therefore, in this paper, the vehicle safety in terms of the dynamic stability and the possibility of derailment directly caused by the track excitations of great earthquakes, is specifically studied. The rail vehicles are supposed to involve severe vehicle body motions, wheel lifts and derailing behaviors. In this study, such extreme responses of the vehicles is focused on, thus at the start, a new vehicle dynamics simulation is developed with unique modeling specifically taking account of internal slide forces between the vehicle body and the bogie resulting from large motions of vehicles. Then, the simulation is employed to assess the safety of vehicles on excited tracks with sinusoidal displacements, and the numerical results are analyzed. Through the assessment and the analyses, four major outcomes are obtained. First, the limit excitation amplitudes for the wheel lift of flange height, defined as safety limits in this paper, are presented in the frequency range of 0.5 to 2.5Hz. Second, two types of critical vehicle motions are captured; one is a rocking motion involving large wheel lift observed in lower frequency excitations and the other is a severe horizontal impact of a wheel to a rail observed in higher frequency excitations. In the latter cases, the vehicles derail with slightly larger excitations than those of the wheel lift of flange height. Third, the roll characteristic of a vehicle body is demonstrated as a dominant factor for the vehicle dynamic motions in terms of large wheel lift and derailment. Finally, the unique modeling in the developed simulation is evaluated and its advantages for precise prediction of the extreme vehicle responses are confirmed.
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