Relevant bibliographies by topics / Functions of hypercomplex variable

Contents

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

Academic literature on the topic 'Functions of hypercomplex variable'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Functions of hypercomplex variable"

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Catoni, Francesco, Roberto Cannata, Enrico Nichelatti, and Paolo Zampetti. "Commutative hypercomplex numbers and functions of hypercomplex variable: a matrix study." Advances in Applied Clifford Algebras 15, no. 2 (October 2005): 183–212. http://dx.doi.org/10.1007/s00006-005-0011-2.

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Gori, Anna, and Fabio Vlacci. "Starlikeness for functions of a hypercomplex variable." Proceedings of the American Mathematical Society 145, no. 2 (August 23, 2016): 791–804. http://dx.doi.org/10.1090/proc/13256.

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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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Ulrych, S. "Conformal relativity with hypercomplex variables." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2168 (August 8, 2014): 20140027. http://dx.doi.org/10.1098/rspa.2014.0027.

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Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a unified theory of general relativity and electroweak interactions. The method is extended to conformal space with the intention to introduce the strong interaction. It is then possible to use the wave equation, operating on representation functions of the conformal group, to describe the dynamics of matter fields. The resulting gauge groups resemble closely the gauge symmetries of Glashow–Salam–Weinberg and the standard model.
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Gryshchuk, S. V. "Hypercomplex monogenic functions of the biharmonic variable in some problems of plane elasticity theory." Reports of the National Academy of Sciences of Ukraine, no. 6 (June 20, 2015): 7–12. http://dx.doi.org/10.15407/dopovidi2015.06.007.

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Yefremov, Alexander P. "Physical theories in hypercomplex geometric description." International Journal of Geometric Methods in Modern Physics 11, no. 06 (July 2014): 1450062. http://dx.doi.org/10.1142/s0219887814500625.

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Compact description is given of algebras of poly-numbers: quaternions, bi-quaternions, double (split-complex) and dual numbers. All units of these (and exceptional) algebras are shown to be represented by direct products of 2D vectors of a local basis defined on a fundamental surface. In this math medium a series of equalities identical or similar to known formulas of physical laws is discovered. In particular, a condition of the algebras' stability with respect to transformations of the 2D-basis turns out equivalent to the spinor (Schrödinger–Pauli and Hamilton–Jacobi) equations of mechanics. It is also demonstrated that isomorphism of SO(3, 1) and SO(3, ℂ) groups leads to formulation of a quaternion relativity theory predicting all effects of special relativity but simplifying solutions of relativistic problems in non-inertial frames. Finely it is shown that the Cauchy–Riemann type equations written for functions of quaternion variable repeat vacuum Maxwell equations of electrodynamics, while a quaternion space with non-metricity comprises main relations of Yang–Mills field theory.
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Park, Su Hyun, and Kwang Ho Shon. "SEDENION FUNCTIONS OF HYPERCOMPLEX VARIABLES IN THE SENSE OF CLIFFORD ANALYSIS." East Asian mathematical journal 29, no. 5 (November 30, 2013): 521–27. http://dx.doi.org/10.7858/eamj.2013.036.

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Zakarya, Mohammed, Mahmoud A. Abd-Rabo, and Ghada AlNemer. "Hypercomplex Systems and Non-Gaussian Stochastic Solutions with Some Numerical Simulation of χ-Wick-Type (2 + 1)-D C-KdV Equations." Axioms 11, no. 11 (November 21, 2022): 658. http://dx.doi.org/10.3390/axioms11110658.

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In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, Hermite transform (HT), and technicality via the F-expansion procedure. By means of the direct connection between the theory of hypercomplex systems (HCS) and white noise analysis (WNA), we establish non-Gaussian white noise (NGWN) by studying stochastic partial differential equations (PDEs) with NG-parameters. So, by using the F-expansion method we present multiples of exact and stochastic families from variable coefficients of travelling wave and stochastic NG-functional solutions of (2 + 1)-D C-KdV equations. These solutions are Jacobi elliptic functions (JEF), trigonometric, and hyperbolic forms, respectively.
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Bin Dehaish, Buthinah A. "Exponentially Convex Functions on Hypercomplex Systems." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/290403.

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A hypercomplex system (h.c.s.)L1(Q,m)is, roughly speaking, a space which is defined by a structure measure(c(A,B,r),(A,B∈ℬ(Q))), such space has been studied by Berezanskii and Krein. Our main result is to define the exponentially convex functions (e.c.f.) on (h.c.s.), and we will study their properties. The definition of such functions is a natural generalization of that defined on semigroup.
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Kim, Ji Eun, Su Jin Lim, and Kwang Ho Shon. "Regularity of Functions on the Reduced Quaternion Field in Clifford Analysis." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/654798.

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We define a new hypercomplex structure ofℝ3and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy-Riemann equations in hypercomplex structures ofℝ3.
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Dissertations / Theses on the topic "Functions of hypercomplex variable"

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Pukhtaievych, Roman. "Periodic and hypercomplex potentials. Properties and applications." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3425759.

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This Dissertation is devoted to the study of boundary value problems and concerns two research areas. The first one is related to the perturbation analysis of boundary value problems in perforated domains and its application to the investigation of effective properties of composite materials. We investigate the dependence of the solutions of transmission boundary value problems upon some parameters and their behavior when the parameter corresponding to the size of the inclusions tends to zero, and the other parameters tend to some fixed values. Then we apply our results to study the effective conductivity of periodic composites. We also investigate the behavior of the solution of the Dirichlet problem for the Poisson equation in the domain in R3 which consists of a periodic array of cylinders upon perturbation of the shape of the cross-section of the cylinders and the periodic structure. Moreover, we apply our results to study the behavior of the longitudinal permeability of a periodic array of cylinders upon such perturbation. The second part of the Dissertation is related to the development of tools for solving boundary value problems for functions taking values in commutative Banach algebras. In particular, we investigate the properties of logarithmic residues of monogenic (continuous and differentiable in the sense of Gateau) functions and the behavior of the certain Cauchy type integral on the boundary of its definition. The Dissertation consists of two parts and is organized as follows. Part I consists of three chapters. In Chapter 1 we investigate the asymptotic behavior of the solutions of singularly perturbed (ideal and nonideal nonlinear) transmission problems in a periodically perforated domain. In Chapter 2 we apply the results of Chapter 1 to study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite. Chapter 3 is devoted to the study of the behavior of the longitudinal permeability of a periodic array of cylinders upon perturbation of the shape of the cross section of the cylinders and of the periodic structure. Part II consists of two chapters. In Chapter 4 we introduce a three-dimensional commutative algebra over C with a one-dimensional radical and study the logarithmic residues of monogenic functions in this algebra. Chapter 5 is devoted to the investigation of a certain analog of Cauchy type integral taking values in the mentioned algebra and its limiting values on the boundary of the domain of definition. At the end of the Dissertation, we have enclosed three appendices with some results which we have exploited in the Dissertation.
Questa Tesi si occupa dello studio di problemi al contorno e analizza due linee di ricerca. La prima riguarda lo studio di perturbazioni di problemi al contorno in domini perforati e la sua applicazione all'analisi delle proprieta efficaci dei materiali compositi. Studiamo la dipendenza delle soluzioni di problemi di trasmissione da alcuni parametri e il loro comportamento quando il parametro corrispondente alla dimensione delle inclusioni tende a zero e gli altri parametri tendono ad alcuni valori fissati. In seguito, applichiamo i nostri risultati allo studio della conduttivita efficace di composti periodici. Analizziamo anche il comportamento della soluzione del problema di Dirichlet per l'equazione di Poisson nell'insieme di R3 che consiste in una serie periodica di cilindri in caso di perturbazione della forma della sezione trasversale dei cilindri e la struttura periodica. Inoltre, applichiamo i nostri risultati per studiare il comportamento della permeabilita longitudinale di una serie periodica di cilindri rispetto a tale perturbazione. La seconda parte della Tesi riguarda lo sviluppo di strumenti per risolvere problemi al contorno per funzioni che assumono valore in algebre di Banach commutative. In particolare, studiamo le proprieta dei residui logaritmici delle funzioni monogeniche (continue e differenziabili nel senso di Gateaux) e il comportamento di certi integrali di tipo Cauchy sulla frontiera dell'insieme di definizione. La Tesi si suddivide in due parti ed è organizzata come segue. La parte I è composta da tre capitoli. Nel capitolo 1 studiamo il comportamento asintotico delle soluzioni di problemi di trasmissione (ideale e nonideale) singolarmente perturbati in un dominio periodicamente perforato. Nel capitolo 2 applichiamo i risultati del capitolo 1 per studiare il comportamento asintotico della conduttivita termica efficace di un composto periodico a due fasi diluito. Il capitolo 3 è dedicato allo studio del comportamento della permeabilita longitudinale di una serie periodica di cilindri quando perturbiamo la forma della sezione trasversale dei cilindri e la struttura periodica. La parte II è composta da due capitoli. Nel capitolo 4 introduciamo un'algebra commutativa tridimensionale su C con un radicale unidimensionale e studiamo i residui logaritmici delle funzioni monogeniche in questa algebra. Il capitolo 5 è dedicato allo studio di un analogo dell'integrale di Cauchy che assume valore nell'algebra menzionata e dei suoi valori limite sulla frontiera del dominio di definizione. Alla fine della Tesi, abbiamo inserito tre appendici con alcuni risultati che abbiamo utilizzato nella Tesi.
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LEITE, LEONARDO DE SOUZA. "CONICS AND GRAPHS OF FUNCTIONS OF ONE VARIABLE." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26149@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O objetivo deste trabalho é apresentar conteúdos necessários para a construção de uma base sólida em Matemática do Ensino Fundamental e Médio, mas que são em geral mal assimilados pelos alunos. Inicialmente apresentaremos o plano cartesiano, equações de uma e duas variáveis, funções de uma variável real e gráfico de funções. Passaremos então ao estudo de curvas simples e bem conhecidas dos alunos em geral, como a circunferência, e chegaremos até as cônicas rotacionadas. A partir daí, procuramos relacionar as duas partes do trabalho, mostrando como as cônicas podem ser vistas como gráficos de função de uma variável. Pretende-se que este trabalho possa ser utilizado por professores do Ensino Fundamental e Médio em sala de aula, pois boa parte do conteúdo apresentado faz parte do currículo mínimo da Secretaria de Educação do Estado do Rio de Janeiro. Propomos atividades teóricas e computacionais, utilizando o software Geogebra para construção de curvas no plano cartesiano.
The objective of this paper is to present content needed to build a solid foundation in mathematics from primary and secondary schools, but are generally poorly assimilated by the students. Initially present the Cartesian plane, equations of one and two variables, functions of a real variable and function graph. Then we pass to the study of simple curves and well known to students in general, as the circumference, and arrive until the conical rotated. From there, we try to relate the two parts of the work, showing how the taper can be seen as a variable function graphs. It is intended that this work can be used by teachers of primary and secondary education in the classroom, because much of the content presented is part of the minimum curriculum of the Department of Education of the State of Rio de Janeiro. We propose theoretical and computational activities, using the Geogebra software to build curves in the Cartesian plane.
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Balli, Umut. "Utility Accrual Real-Time Scheduling Under Variable Cost Functions." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/34358.

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We present a utility accrual real-time scheduling algorithm called CIC-VCUA, for tasks whose execution times are functions of their starting times. We model such variable execution times employing variable cost functions (or VCFs). The algorithm considers application activities that are subject to time/utility function time constraints (or TUFs), execution times de- scribed using VCFs, and concurrent, mutually exclusive sharing of non-CPU resources. We consider the multi-criteria scheduling objective of (1) assuring that the maximum interval between any two consecutive, successful completions of jobs of a task must not exceed a specified upper bound, and (2) maximizing the system's total accrued utility, while satis- fying mutual exclusion resource constraints. Since the scheduling problem is intractable, CIC-VCUA statically computes worst-case sojourn times of tasks, selects tasks for execution based on their potential utility density, and completes them at specific times, in polynomial- time. We establish that CIC-VCUA achieves optimal timeliness during under-loads. Further, we identify the conditions under which timeliness assurances hold. Our simulation experi- ments illustrate CIC-VCUA's effectiveness and superiority.
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Pettersson, Henrik Bengt. "Variable Stability Transfer Function Simulation." Thesis, Virginia Tech, 2002. http://hdl.handle.net/10919/33503.

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Simulation, whether in-flight or ground-based, is an invaluable tool for testing and evaluating aircraft. Classically, a simulation model is specific to a single particular airframe, only able to model those flying characteristics. Vast information can be gained from a simulation that is able to model a wide range of aircraft, through a comparison of the performance of these aircraft. Such a variable stability simulation model was created based on 46 stability parame-ters, including natural frequencies, damping ratios, time constants, and gains. The simula-tion was obtained using transfer functions representing the aircraft state responses to control inputs. These transfer functions were converted into state space systems used to create the linear equations for the model. The model was first developed as a desktop simulation and then converted for use with the Virginia Techâ s 2F122A flight simulator. This conversion required a simple dynamic inversion of the body axis force and moment terms. To reduce the error in these terms, a model following scheme was incorporated. A series of canned inputs and real-time pilot-in-the-loop tests were flown to evaluate the variable stability model. Results in this paper have demonstrated the successful creation of a variable stability simulation model.
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Oliveira, Ana Carolina de. "Quatérnios, operadores de Fueter e relações quaterniônicas transcendentais /." São José do Rio Preto : [s.n.], 2006. http://hdl.handle.net/11449/94269.

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Orientador: Manoel Ferreira Borges Neto
Banca: Gilberto Aparecido Pratavieira
Banca: José Márcio Machado
Resumo: Resumo O objetivo deste trabalho é estabelecer similaridades entre os complexos e os hipercomplexos, motivados em explorar idéias de Murnaghan, que introduziu, pela primeira vez, em uma apresentação elementar, a teoria dos quatérnios baseados no teorema de Moivre. É mostrada em detalhes uma analogia da relação complexa clássica de Moivre para quatérnios, e em brevidade para octônios generalizados, e apresenta-se as conexões com os operadores da teoria de Fueter e as funções transcendentais. A extensão do teorema de Moivre é estudada para quatérnios em definindo-se uma função exponencial quaterniônica.
Abstract: Abstract In this work we establish similarities between the complex and the hipercomplex numbers, motivated in exploring ideas of Murnaghan, that introduced, for the first time, in an elementary presentation, the theory of the quaternions based on the theorem of Moivre. We show an analogy of the classic complex relation of Moivre for quaternions, and briefly discuss generalized octonions, as well as to present connections to operators of the theory of Fueter and transcendental functions. We consider them to study the extension of the theorem of Moivre for quaternions, in defining a exponential function on the quaternions.
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Oliveira, Ana Carolina de [UNESP]. "Quatérnios, operadores de Fueter e relações quaterniônicas transcendentais." Universidade Estadual Paulista (UNESP), 2006. http://hdl.handle.net/11449/94269.

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Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-02-20Bitstream added on 2014-06-13T18:47:50Z : No. of bitstreams: 1 oliveira_ac_me_sjrp.pdf: 346640 bytes, checksum: dfe236f71e5ef2c050420d64d2c48a70 (MD5)
O objetivo deste trabalho é estabelecer similaridades entre os complexos e os hipercomplexos, motivados em explorar idéias de Murnaghan, que introduziu, pela primeira vez, em uma apresentação elementar, a teoria dos quatérnios baseados no teorema de Moivre. É mostrada em detalhes uma analogia da relação complexa clássica de Moivre para quatérnios, e em brevidade para octônios generalizados, e apresenta-se as conexões com os operadores da teoria de Fueter e as funções transcendentais. A extensão do teorema de Moivre é estudada para quatérnios em definindo-se uma função exponencial quaterniônica.
In this work we establish similarities between the complex and the hipercomplex numbers, motivated in exploring ideas of Murnaghan, that introduced, for the first time, in an elementary presentation, the theory of the quaternions based on the theorem of Moivre. We show an analogy of the classic complex relation of Moivre for quaternions, and briefly discuss generalized octonions, as well as to present connections to operators of the theory of Fueter and transcendental functions. We consider them to study the extension of the theorem of Moivre for quaternions, in defining a exponential function on the quaternions.
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Balister, P. N. "Two variable #rho#-adic L-functions for CM elliptic curves with supersingular reduction." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240890.

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Braun, H. T. F. "Model theory of holomorphic functions." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401108.

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This thesis is concerned with a conjecture of Zilber: that the complex field expanded with the exponential function should be `quasi-minimal'; that is, all its definable subsets should be countable or have countable complement. Our purpose is to study the geometry of this structure and other expansions by holomorphic functions of the complex field without having first to settle any number-theoretic problems, by treating all countable sets on an equal footing. We present axioms, modelled on those for a Zariski geometry, defining a non-first-order class of ``quasi-Zariski'' structures endowed with a dimension theory and a topology in which all countable sets are of dimension zero. We derive a quantifier elimination theorem, implying that members of the class are quasi-minimal. We look for analytic structures in this class. To an expansion of the complex field by entire holomorphic functions $\mathcal{R}$ we associate a sheaf $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ of analytic germs which is closed under application of the implicit function theorem. We prove that $\mathcal{O}^{\scriptscriptstyle{\mathcal{R}}}$ is also closed under partial differentiation and that it admits Weierstrass preparation. The sheaf defines a subclass of the analytic sets which we call $\mathcal{R}$-analytic. We develop analytic geometry for this class proving a Nullstellensatz and other classical properties. We isolate a condition on the asymptotes of the varieties of certain functions in $\mathcal{R}$. If this condition is satisfied then the $\mathcal{R}$-analytic sets induce a quasi-Zariski structure under countable union. In the motivating case of the complex exponential we prove a low-dimensional case of the condition, towards the original conjecture.
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Kakehashi, Shoji, Hiroshi Hasegawa, Ken-ichi Sato, Osamu Moriwaki, and Shin Kamei. "Analysis and Development of Fixed and Variable Waveband MUX/DEMUX Utilizing AWG Routing Functions." IEEE, 2009. http://hdl.handle.net/2237/14029.

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Ahmad, Khan Mumtaz, and Bahman Alidad. "Three Variable Analogue of Boas and Buck Type Generating Functions and Its Generalizations to M-Variables." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97282.

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The present papers deals with three variable analogue of Boas and Buck [14] type generating functions forpolynomials of two variables and then the same has been extended for m-variable analogue. The results obtained are extensions of those obtained by us in our earlier paper [14].
El presente artículo trata el anólogo de tres variables de la función generatriz de Boas and Buck [14] para polinomios de dos variables y lo mismo se puede extender para el análogo de m variables. Los resultados obtenidos son extensiones de un artículo previo [14].
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Books on the topic "Functions of hypercomplex variable"

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Gal, Sorin G. Introduction to geometric function theory of hypercomplex variables. New York: Nova Science Publishers, 2002.

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Michael, Shapiro, Sommen Frank, and SpringerLink (Online service), eds. Hypercomplex Analysis. Basel: Birkhäuser Basel, 2009.

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Sabadini, Irene, Swanhild Bernstein, Uwe Kähler, and F. Sommen. Hypercomplex analysis: New perspectives and applications. Cham: Birkhauser, 2014.

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E, Ramírez de Arellano, ed. Operator theory for complex and hypercomplex analysis: Operator theory for complex and hypercomplex analysis, December 12-17, 1994, Mexico City, Mexico. Providence, RI: American Mathematical Society, 1998.

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Abrham, Alena. Variable precision elementary functions. Toronto: University of Toronto, Dept. of Computer Science, 1985.

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Functions of one complex variable. 2nd ed. New York: Springer-Verlag, 1995.

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Deborah, Hughes-Hallett, and Gleason A. M, eds. Calculus: Single variable. 2nd ed. New York: Wiley, 2000.

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Giaquinta, Mariano. Mathematical Analysis: Functions of One Variable. Boston, MA: Birkhäuser Boston, 2003.

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Chuang, Chi Tai, ed. Analytic Functions of One Complex Variable. Providence, Rhode Island: American Mathematical Society, 1985. http://dx.doi.org/10.1090/conm/048.

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Gentili, Graziano, Caterina Stoppato, and Daniele C. Struppa. Regular Functions of a Quaternionic Variable. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-07531-5.

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Book chapters on the topic "Functions of hypercomplex variable"

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Gentili, Graziano, Caterina Stoppato, Daniele C. Struppa, and Fabio Vlacci. "Recent Developments for Regular Functions of a Hypercomplex Variable." In Hypercomplex Analysis, 165–85. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_11.

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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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Imaeda, Mari. "On Regular Functions of a Power-Associative Hypercomplex Variable." In Clifford Algebras and Their Applications in Mathematical Physics, 565–72. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4728-3_50.

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Cho, Ilwoo, and Palle E. T. Jorgensen. "Multi Variable Semicircular Processes From ∗-Homomorphisms and Operators." In New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative, 199–242. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76473-9_7.

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Eriksson, Sirkka-Liisa. "Hypermonogenic functions and their dual functions." In Hypercomplex Analysis, 137–49. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_9.

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Charak, K. S., and D. Rochon. "On Factorization of Bicomplex Meromorphic Functions." In Hypercomplex Analysis, 55–68. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_4.

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Blaya, Ricardo Abreu, and Juan Bory Reyes. "An Extension Theorem for Biregular Functions in Clifford Analysis." In Hypercomplex Analysis, 1–9. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_1.

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Colombo, Fabrizio, and Irene Sabadini. "A Structure Formula for Slice Monogenic Functions and Some of its Consequences." In Hypercomplex Analysis, 101–14. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_6.

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Coulembier, K., H. De Bie, and F. Sommen. "Harmonic and Monogenic Functions in Superspace." In Hypercomplex Analysis and Applications, 29–41. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0246-4_3.

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Luna-Elizarrarás, M. Elena, Marco A. Macías-Cedeño, and Michael Shapiro. "On the Hyperderivatives of Moisil–Théodoresco Hyperholomorphic Functions." In Hypercomplex Analysis and Applications, 181–93. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0246-4_13.

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Conference papers on the topic "Functions of hypercomplex variable"

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Odersky, Martin. "Programming with variable functions." In the third ACM SIGPLAN international conference. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/289423.289433.

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PLAKSA, S. "COMMUTATIVE ALGEBRAS OF HYPERCOMPLEX MONOGENIC FUNCTIONS AND SOLUTIONS OF ELLIPTIC TYPE EQUATIONS DEGENERATING ON AN AXIS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0094.

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Hassan, Hassan. "Image segmentation using variable threshold functions." In Defense and Security, edited by David P. Casasent and Tien-Hsin Chao. SPIE, 2004. http://dx.doi.org/10.1117/12.541603.

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Ivanov, Gennady, Gennady Alferov, and Polina Efimova. "Integrability of nonsmooth one-variable functions." In 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973965.

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Fu, Wen, Rongcai Zhao, Jianmin Pang, and Jingbo Zhang. "Recovering Variable-Argument Functions from Binary Executables." In Seventh IEEE/ACIS International Conference on Computer and Information Science (icis 2008). IEEE, 2008. http://dx.doi.org/10.1109/icis.2008.84.

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Boyle, Elette, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, and Peter Scholl. "Correlated Pseudorandom Functions from Variable-Density LPN." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00103.

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Brunelli, Claudio, Heikki Berg, and David Guevorkian. "Approximating sine functions using variable-precision Taylor polynomials." In 2009 IEEE Workshop on Signal Processing Systems (SiPS). IEEE, 2009. http://dx.doi.org/10.1109/sips.2009.5336225.

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Nagayama, Shinobu, Jon T. Butler, and Tsutomu Sasao. "Programmable Numerical Function Generators for Two-Variable Functions." In 2008 11th EUROMICRO Conference on Digital System Design Architectures, Methods and Tools. IEEE, 2008. http://dx.doi.org/10.1109/dsd.2008.27.

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Zhang, Weiqiang, and Ruihu Li. "Algebraic Immunity of Even Variable Symmetric Boolean Functions." In 2009 Second International Workshop on Knowledge Discovery and Data Mining (WKDD). IEEE, 2009. http://dx.doi.org/10.1109/wkdd.2009.46.

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Sanchez, Tonametl, and Jaime A. Moreno. "Lyapunov functions for Twisting and Terminal controllers." In 2014 13th International Workshop on Variable Structure Systems (VSS). IEEE, 2014. http://dx.doi.org/10.1109/vss.2014.6881136.

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Reports on the topic "Functions of hypercomplex variable"

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Nagayama, Shinobu, Jon T. Butler, and Tsutomu Sasao. Programmable Numerical Function Generators for Two-Variable Functions. Fort Belvoir, VA: Defense Technical Information Center, September 2008. http://dx.doi.org/10.21236/ada608068.

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Borjas, George. The Sensitivity of Labor Demand Functions to Choice of Dependent Variable. Cambridge, MA: National Bureau of Economic Research, June 1985. http://dx.doi.org/10.3386/w1624.

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Blagonravov, A. A. Mechanical continuously variable transmission with oscillatory movement of internal links and adjustable power functions. Ljournal, 2019. http://dx.doi.org/10.18411/b100-22011-t20181205.

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Blagonravov, A. A. Mechanical continuously variable transmission with oscillatory movement of internal links and adjustable power functions. Ljournal, 2019. http://dx.doi.org/10.18411/b10022011t20181205.

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Butler, John T., and Tsutomu Sasao. On the Properties of Multiple-Valued Functions that are Symmetric in Both Variable Values and Labels. Fort Belvoir, VA: Defense Technical Information Center, December 1997. http://dx.doi.org/10.21236/ada335537.

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Jury, William A., and David Russo. Characterization of Field-Scale Solute Transport in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, January 1994. http://dx.doi.org/10.32747/1994.7568772.bard.

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This report describes activity conducted in several lines of research associated with field-scale water and solute processes. A major effort was put forth developing a stochastic continuum analysis for an important class of problems involving flow of reactive and non reactive chemicals under steady unsaturated flow. The field-scale velocity covariance tensor has been derived from local soil properties and their variability, producing a large-scale description of the medium that embodies all of the local variability in a statistical sense. Special cases of anisotropic medium properties not aligned along the flow direction of spatially variable solute sorption were analysed in detail, revealing a dependence of solute spreading on subtle features of the variability of the medium, such as cross-correlations between sorption and conductivity. A novel method was developed and tested for measuring hydraulic conductivity at the scale of observation through the interpretation of a solute transport outflow curve as a stochastic-convective process. This undertaking provided a host of new K(q) relationships for existing solute experiments and also laid the foundation for future work developing a self-consistent description of flow and transport under these conditions. Numerical codes were developed for calculating K(q) functions for a variety of solute pulse outflow shapes, including lognormal, Fickian, Mobile-Immobile water, and bimodal. Testing of this new approach against conventional methodology was mixed, and agreed most closely when the assumptions of the new method were met. We conclude that this procedure offers a valuable alternative to conventional methods of measuring K(q), particularly when the application of the method is at a scale (e.g. and agricultural field) that is large compared to the common scale at which conventional K(q) devices operate. The same problem was approached from a numerical perspective, by studying the feasibility of inverting a solute outflow signal to yield the hydraulic parameters of the medium that housed the experiment. We found that the inverse problem was solvable under certain conditions, depending on the amount of noise in the signal and the degree of heterogeneity in the medium. A realistic three dimensional model of transient water and solute movement in a heterogeneous medium that contains plant roots was developed and tested. The approach taken was to generate a single realization of this complex flow event, and examine the results to see whether features were present that might be overlooked in less sophisticated model efforts. One such feature revealed is transverse dispersion, which is a critically important component in the development of macrodispersion in the longitudinal direction. The lateral mixing that was observed greatly exceeded that predicted from simpler approaches, suggesting that at least part of the important physics of the mixing process is embedded in the complexity of three dimensional flow. Another important finding was the observation that variability can produce a pseudo-kinetic behavior for solute adsorption, even when the local models used are equilibrium.
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Baca Campodónico, Jorge F., and Gerardo Reyes-Tagle. Econometric Estimation of the Capital Stock and the Production Function: The Case of the Bahamas, Barbados, Jamaica, and Suriname. Inter-American Development Bank, February 2023. http://dx.doi.org/10.18235/0004749.

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Most studies of total factor productivity (TFP) and long-term production functions use capital stock time series obtained from ad hoc estimates of the rate of depreciation and the initial capital stock. This paper introduces a methodology that allows the simultaneous econometric estimation of the capital stock, the production function parameters, the rate of depreciation, and the initial capital stock. The proposed methodology, using the underlying cost function to the production function, allows for the incorporation of information about the relative prices of the factors of production and the possibility of having variable depreciation rates over time. The proposed methodology is applied to the case of the Bahamas, Barbados, Jamaica, and Suriname for the period 1989-2019 using national accounts data published by the statistical services of these countries.
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Grumet, Rebecca, and Benjamin Raccah. Identification of Potyviral Domains Controlling Systemic Infection, Host Range and Aphid Transmission. United States Department of Agriculture, July 2000. http://dx.doi.org/10.32747/2000.7695842.bard.

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Potyviruses form one of the largest and most economically important groups of plant viruses. Individual potyviruses and their isolates vary in symptom expression, host range, and ability to overcome host resistance genes. Understanding factors influencing these biological characteristics is of agricultural importance for epidemiology and deployment of resistance strategies. Cucurbit crops are subject to severe losses by several potyviruses including the highly aggressive and variable zucchini yellow mosaic virus (ZYMV). In this project we sought to investigate protein domains in ZYMV that influence systemic infection and host range. Particular emphasis was on coat protein (CP), because of known functions in both cell to cell and long distance movement, and helper component-protease (HC-Pro), which has been implicated to play a role in symptom development and long distance movement. These two genes are also essential for aphid mediated transmission, and domains that influence disease development may also influence transmissibility. The objectives of the approved BARD project were to test roles of specific domains in the CP and HC-Pro by making sequence alterations or switches between different isolates and viruses, and testing for infectivity, host range, and aphid transmissibility. These objectives were largely achieved as described below. Finally, we also initiated new research to identify host factors interacting with potyviral proteins and demonstrated interaction between the ZYMV RNA dependent RNA polymerase and host poly-(A)-binding protein (Wang et al., in press). The focus of the CP studies (MSU) was to investigate the role of the highly variable amino terminus (NT) in host range determination and systemic infection. Hybrid ZYMV infectious clones were produced by substituting the CP-NT of ZYMV with either the CP-NT from watermelon mosaic virus (overlapping, but broader host range) or tobacco etch virus (TEV) (non- overlapping host range) (Grumet et al., 2000; Ullah ct al., in prep). Although both hybrid viruses initially established systemic infection, indicating that even the non-cucurbit adapted TEV CP-NT could facilitate long distance transport in cucurbits, after approximately 4-6, the plants inoculated with the TEV-CPNT hybrid exhibited a distinct recovery of reduced symptoms, virus titer, and virus specific protection against secondary infection. These results suggest that the plant recognizes the presence of the TEV CP-NT, which has not been adapted to infection of cucurbits, and initiates defense responses. The CP-NT also appears to play a role in naturally occurring resistance conferred by the zym locus in the cucumber line 'Dina-1'. Patterns of virus accumulation indicated that expression of resistance is developmentally controlled and is due to a block in virus movement. Switches between the core and NT domains of ZYMV-NAA (does not cause veinal chlorosis on 'Dina-1'), and ZYMV-Ct (causes veinal chlorosis), indicated that the resistance response likely involves interaction with the CP-NT (Ullah and Grumet, submitted). At the Volcani Center the main thrust was to identify domains in the HC-Pro that affect symptom expression or aphid transmissibility. From the data reported in the first and second year report and in the attached publications (Peng et al. 1998; Kadouri et al. 1998; Raccah et al. 2000: it was shown that: 1. The mutation from PTK to PAK resulted in milder symptoms of the virus on squash, 2. Two mutations, PAK and ATK, resulted in total loss of helper activity, 3. It was established for the first time that the PTK domain is involved in binding of the HC-Pro to the potyvirus particle, and 4. Some of these experiments required greater amount of HC-Pro, therefore a simpler and more efficient purification method was developed based on Ni2+ resin.
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Pessino, Carola, Nadir Altinok, and Cristian Chagalj. Allocative Efficiency of Government Spending for Growth in Latin American Countries. Inter-American Development Bank, June 2022. http://dx.doi.org/10.18235/0004310.

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There is scant empirical economic research regarding the way that Latin American governments efficiently allocate their spending across different functions to achieve higher growth. While most papers restrict their analysis to the size of government, much less is known about the composition of spending and its implications for long-term growth. This paper sheds light on how allocating expenditures to investment in quality human and physical capital, and avoiding waste on inefficient expenditures, enhance growth in Latin America. This paper uses a novel dataset on physical and human capital and detailed public spending that includes -for the first time- Latin American countries, which is categorized by a cross-classification that provides the breakdown of government expenditure, both, by economic and by functional heads. The database covers 42 countries of the OECD and LAC between 1985 and 2017. There are five main results. First, the estimated growth equations show significant positive effects of the factors of production on growth and plausible convergence rates (about 2 percent). The estimated effect of the physical investment rate is positive and significant with a long-run elasticity of 1.2. Second, while the addition of years of education as a proxy for human capital tends to have no effect on growth, the addition of a new variable that measures quality-adjusted years of schooling as a proxy for human capital turns out to have a positive and significant effect across all specifications with a long-run elasticity of 1.1. However, if public spending on education (excluding infrastructure spending) is added to the factor specification, growth is not affected. This is mainly because, once quality is considered, spending more on teacher salaries has no effect on student outcomes. Therefore, the key is to increase quality, not just school performance or education spending. Third, both physical and human capital are equally important for growth: the effect of increasing one standard deviation of physical capital or human capital statistically has the same impact on economic growth. Fourth, increasing public investment spending (holding public spending constant) is positive and significant for growth (a 1% increase in public investment would increase the long-term GDP per capita by about 0.3 percent), in addition to the effect of the private investment rate. However, the effect of public spending on payroll, pensions and subsidies does not contribute to economic growth. Fifth, the overall effect of the size of public spending on economic growth is negative in most specifications. An increase in the size of government by about 1 percentage point would decrease 4.1 percent the long-run GDP per capita, but the more effective the government is, the less harmful the size of government is for long-term growth.
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Or, Dani, Shmulik Friedman, and Jeanette Norton. Physical processes affecting microbial habitats and activity in unsaturated agricultural soils. United States Department of Agriculture, October 2002. http://dx.doi.org/10.32747/2002.7587239.bard.

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experimental methods for quantifying effects of water content and other dynamic environmental factors on bacterial growth in partially-saturated soils. Towards this end we reviewed critically the relevant scientific literature and performed theoretical and experimental studies of bacterial growth and activity in modeled, idealized and real unsaturated soils. The natural wetting-drying cycles common to agricultural soils affect water content and liquid organization resulting in fragmentation of aquatic habitats and limit hydraulic connections. Consequently, substrate diffusion pathways to soil microbial communities become limiting and reduce nutrient fluxes, microbial growth, and mobility. Key elements that govern the extent and manifestation of such ubiquitous interactions include characteristics of diffusion pathways and pore space, the timing, duration, and extent of environmental perturbations, the nature of microbiological adjustments (short-term and longterm), and spatial distribution and properties of EPS clusters (microcolonies). Of these key elements we have chosen to focus on a manageable subset namely on modeling microbial growth and coexistence on simple rough surfaces, and experiments on bacterial growth in variably saturated sand samples and columns. Our extensive review paper providing a definitive “snap-shot” of present scientific understanding of microbial behavior in unsaturated soils revealed a lack of modeling tools that are essential for enhanced predictability of microbial processes in soils. We therefore embarked on two pronged approach of development of simple microbial growth models based on diffusion-reaction principles to incorporate key controls for microbial activity in soils such as diffusion coefficients and temporal variations in soil water content (and related substrate diffusion rates), and development of new methodologies in support of experiments on microbial growth in simple and observable porous media under controlled water status conditions. Experimental efforts led to a series of microbial growth experiments in granular media under variable saturation and ambient conditions, and introduction of atomic force microscopy (AFM) and confocal scanning laser microscopy (CSLM) to study cell size, morphology and multi-cell arrangement at a high resolution from growth experiments in various porous media. The modeling efforts elucidated important links between unsaturated conditions and microbial coexistence which is believed to support the unparallel diversity found in soils. We examined the role of spatial and temporal variation in hydration conditions (such as exist in agricultural soils) on local growth rates and on interactions between two competing microbial species. Interestingly, the complexity of soil spaces and aquatic niches are necessary for supporting a rich microbial diversity and the wide array of microbial functions in unsaturated soils. This project supported collaboration between soil physicists and soil microbiologist that is absolutely essential for making progress in both disciplines. It provided a few basic tools (models, parameterization) for guiding future experiments and for gathering key information necessary for prediction of biological processes in agricultural soils. The project sparked a series of ongoing studies (at DTU and EPFL and in the ARO) into effects of soil hydration dynamics on microbial survival strategy under short term and prolonged desiccation (important for general scientific and agricultural applications).
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