Relevant bibliographies by topics / Functions of several complex variables

Contents

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

Academic literature on the topic 'Functions of several complex variables'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Functions of several complex variables"

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Liu, Xiang Yang. "Bloch functions of several complex variables." Pacific Journal of Mathematics 152, no. 2 (February 1, 1992): 347–63. http://dx.doi.org/10.2140/pjm.1992.152.347.

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Hedenmalm, Håkan. "Outer functions of several complex variables." Journal of Functional Analysis 80, no. 1 (September 1988): 9–15. http://dx.doi.org/10.1016/0022-1236(88)90061-4.

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Zhu, Ting, Sheng ao Zhou, and Liu Yang. "On normal functions in several complex variables." Journal of Classical Analysis, no. 1 (2020): 45–58. http://dx.doi.org/10.7153/jca-2020-16-06.

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Backlund, Ulf, Linus Carlsson, Anders Fällström, and Håkan Persson. "Semi-Bloch Functions in Several Complex Variables." Journal of Geometric Analysis 26, no. 1 (January 15, 2015): 463–73. http://dx.doi.org/10.1007/s12220-015-9558-x.

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ALMIRA, J. M., and KH F. ABU-HELAIEL. "On Montel’s theorem in several variables." Carpathian Journal of Mathematics 31, no. 1 (2015): 1–10. http://dx.doi.org/10.37193/cjm.2015.01.01.

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Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and complex functions of several complex variables.
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Sam, Vansak, and Kamthorn Chailuek. "Hardy's Inequality for Functions of Several Complex Variables." Sains Malaysiana 46, no. 9 (September 30, 2017): 1355–59. http://dx.doi.org/10.17576/jsm-2017-4609-01.

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Bavrin, I. I. "Integral representations of functions of several complex variables." Doklady Mathematics 75, no. 3 (June 2007): 395–98. http://dx.doi.org/10.1134/s1064562407030179.

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Mirotin, A. R. "Properties of Bernstein functions of several complex variables." Mathematical Notes 93, no. 1-2 (January 2013): 257–65. http://dx.doi.org/10.1134/s0001434613010288.

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HU, PEI-CHU, and CHUNG-CHUN YANG. "THE TUMURA–CLUNIE THEOREM IN SEVERAL COMPLEX VARIABLES." Bulletin of the Australian Mathematical Society 90, no. 3 (June 13, 2014): 444–56. http://dx.doi.org/10.1017/s0004972714000446.

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AbstractIt is a well-known result that if a nonconstant meromorphic function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f$ on $\mathbb{C}$ and its $l$th derivative $f^{(l)}$ have no zeros for some $l\geq 2$, then $f$ is of the form $f(z)=\exp (Az+B)$ or $f(z)=(Az+B)^{-n}$ for some constants $A$, $B$. We extend this result to meromorphic functions of several variables, by first extending the classic Tumura–Clunie theorem for meromorphic functions of one complex variable to that of meromorphic functions of several complex variables using Nevanlinna theory.
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Grantcharov, Gueo, and Camilo Montoya. "On Functions of Several Split-Quaternionic Variables." Advances in Mathematical Physics 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/3654530.

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Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a specific complex volume form. In this note we show that similar relation holds for functions of several split-quaternionic variables and point to some relations with geometry.
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Dissertations / Theses on the topic "Functions of several complex variables"

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Sadykov, Timour. "Hypergeometric functions in several complex variables." Doctoral thesis, Stockholm : Univ, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-198.

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Mernik, Luka. "Positivity Conditions in Several Complex Variables." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586522855649564.

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McKeown, Jesse. "Functional methods in analysis of several complex variables." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101622.

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Nedic, Mitja. "Integral representations of Herglotz-Nevanlinna functions." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-138962.

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In this thesis, we study integral representations of Herglotz-Nevanlinna functions, that is to say holomorphic functions defined on a product of several copies of the complex upper half-plane having non-negative imaginary part. The manuscript is divided into three parts, beginning with a general introduction followed by two papers. In the general introduction, we familiarize ourselves with the concept of a Herglotz-Nevanlinna function as well as providing a comprehensive introduction into the theory of integral representations for this particular class of functions. Paper I treats exclusively the two-variable case and presents an integral representation of Herglotz-Nevanlinna functions in two complex variables in terms of a real number, two non-negative numbers and a positive Borel measure satisfying two properties. Three properties that hold for the class of measures appearing in such integral representations are also proven. In Paper II, we provide an integral representation for the class of Herglotz-Nevanlinna functions in arbitrarily many complex variables in terms of a real number, a linear term and a positive Borel measure satisfying two properties. Properties of the class of measures appearing in this representation are then discussed in detail as well as alternative descriptions of said class. Finally, a symmetry formula satisfied by Herglotz-Nevanlinna functions is proved at the end.
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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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Lan, Ma. "Abschätzungen von Lösungen der [delta bar]-Gleichung auf streng q-konvexen Mengen mit nicht glattem Rand." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20436892.html.

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Zhang, Yunxin, and 张云鑫. "On the admissible pairs of rational homogeneous manifolds of Picard number 1 and geometric structures defined by their varieties of minimal rational tangents." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206439.

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In a series of works, Jun-Muk Hwang and Ngaiming Mok have developed a geometric theory of uniruled projective manifolds, especially those of Picard Number 1, relying on the study of Varieties of Minimal Rational Tangents (VMRT) from both the algebro-geometric and the G-structure perspectives. Based on this theory, Ngaiming Mok and Jaehyun Hong studied the standard embedding between two Rational Homogeneous Spaces (RHS) associated to long simple roots which are of different dimensions. In this thesis, I consider admissible pairs of RHS (X0, X) of Picard number 1 and locally closed complex submanifolds S ⊂ X inheriting VMRT sub-structures modeled on X0 = G0/P0 ⊂ X = G/P de_ned by taking intersections of VMRT of X with tangent space of S. Moreover, if any such S modeled on (X0, X) is necessarily the image of a standard embedding i : X0 → X, (X0, X) is said to be rigid. In this thesis, it is proved that an admissible pair (X0, X) is rigid whenever X is associated to a long simple root and X0 is non-linear and de_ned by a marked Dynkin sub-diagram. In the case of the pair (S0, S) of compact Hermitian Symmetric Spaces (cHSS), all the admissible pairs (S0, S) are completely classified. Based on this classification, a sufficient condition for the pair (S0, S) to be non-rigid is established through explicitly constructing a submanifold S ⊂ S such that S can never be obtained from the image of any standard embedding i : S0 → S. Besides, the term special pair is coined for those (S0; S) sorted out through classification, and the algebraicity of submanifolds modeled on special pairs is confirmed by checking a modified form of the non-degeneracy condition defined by Hong and Mok is satisfied. However, the question as to whether these special pairs are rigid, as pointed out in this thesis, remains to be investigated. Finally, pairs of hyperquadrics (Q^n, Q^m) are studied separately. Since non-rigidity is trivial, in these cases it is interesting to establish a characterization of the standard embedding i : Q^n→Q^m under some stronger condition. In this thesis, the latter problem is solved in terms of the partial vanishing of second fundamental forms.
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Mathematics
Doctoral
Doctor of Philosophy
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Ravisankar, Sivaguru. "Lipschitz Properties of Harmonic and Holomorphic Functions." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1308299030.

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Hokamp, Samuel A. "Weak*-Closed Unitarily and Moebius Invariant Spaces of Bounded Measurable Functions on a Sphere." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562943150719334.

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Persson, Håkan. "Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables." Doctoral thesis, Uppsala universitet, Analys och sannolikhetsteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-251325.

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This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0<α<1, is hyperconvex. Global estimates of the exhaustion function are given. In Paper IV, it is shown that on the closure of a domain whose boundary locally is the graph of a continuous function, all plurisubharmonic functions with continuous boundary values can be uniformly approximated by smooth plurisubharmonic functions defined in neighbourhoods of the closure of the domain. Paper V studies  Poletsky’s notion of plurisubharmonicity on compact sets. It is shown that a function is plurisubharmonic on a given compact set if, and only if, it can be pointwise approximated by a decreasing sequence of smooth plurisubharmonic functions defined in neighbourhoods of the set. Paper VI introduces the notion of a P-hyperconvex domain. It is shown that in such a domain, both the Dirichlet problem with respect to functions plurisubharmonic on the closure of the domain, and the problem of approximation by smooth plurisubharmoinc functions in neighbourhoods of the closure of the domain have satisfactory answers in terms of plurisubharmonicity on the boundary.
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Books on the topic "Functions of several complex variables"

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Schneider, Michael, 1942 May 18-, Siu Yum-Tong 1943-, Mathematical Sciences Research Institute (Berkeley, Calif.), and Special Year in Several Complex Variables (1995-1996 : Mathematical Sciences Research Institute), eds. Several complex variables. Cambridge, U.K: Cambridge University Press, 1999.

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Hervé, Michel. Several complex variables, local theory. 2nd ed. Oxford: Published for the Tata Institute of Fundamental Research, Bombay [by the] Oxford University Press, 1987.

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Gunning, R. C. Analytic functions of several complex variables. Providence, R.I: AMS Chelsea Pub., 2009.

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Gunning, R. C. Analytic functions of several complex variables. Providence, R.I: AMS Chelsea Pub., 2009.

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Gunning, R. C. Analytic functions of several complex variables. Providence, R.I: AMS Chelsea Pub., 2009.

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Summer Research Institute on Several Complex Variables and Complex Geometry (1989 University of California, Santa Cruz). Several complex variables and complex geometry. Edited by Bedford Eric 1947- and American Mathematical Society. Providence, R.I: American Mathematical Society, 1991.

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Lelong, Pierre, and Lawrence Gruman. Entire Functions of Several Complex Variables. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70344-7.

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1942-, Gruman Lawrence, ed. Entire functions of several complex variables. Berlin: Springer-Verlag, 1986.

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Noguchi, Junjiro. Geometric function theory in several complex variables. Providence, R.I: American Mathematical Society, 1990.

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Krantz, Steven G. Function theory of several complex variables. 2nd ed. Providence, RI: American Mathematical Society, 2001.

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Book chapters on the topic "Functions of several complex variables"

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Ronkin, L. I. "Entire Functions." In Several Complex Variables III, 1–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-61308-1_1.

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Gauthier, Paul M. "Plurisubharmonic Functions." In Lectures on Several Complex Variables, 39–50. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11511-5_8.

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Gauthier, Paul M. "Meromorphic Functions and Subvarieties." In Lectures on Several Complex Variables, 101–5. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11511-5_15.

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Gauthier, Paul M. "Sequences of Holomorphic Functions." In Lectures on Several Complex Variables, 15–17. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11511-5_4.

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Narasimhan, Raghavan, and Yves Nievergelt. "Functions of Several Complex Variables." In Complex Analysis in One Variable, 343–49. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0175-5_21.

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Narasimhan, Raghavan, and Yves Nievergelt. "Functions of Several Complex Variables." In Complex Analysis in One Variable, 151–60. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0175-5_8.

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Narasimhan, Raghavan. "Functions of Several Complex Variables." In Complex Analysis in one Variable, 156–65. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1106-6_8.

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Fischer, Wolfgang, and Ingo Lieb. "Meromorphic functions of several variables." In A Course in Complex Analysis, 193–213. Wiesbaden: Vieweg+Teubner Verlag, 2012. http://dx.doi.org/10.1007/978-3-8348-8661-3_6.

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Baily, Walter L. "Arithmetic Hilbert Modular Functions Ill." In Contributions to Several Complex Variables, 1–40. Wiesbaden: Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-06816-7_1.

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Gauthier, Paul M. "Zero Sets of Holomorphic Functions." In Lectures on Several Complex Variables, 25–29. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11511-5_6.

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Conference papers on the topic "Functions of several complex variables"

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Имомкулов, Севдиёр, and Усмон Собиров. "Some generalization of Hartogs's lemma about analytic extension of functions of several complex variables." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.44.

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Daxberger, Erik, Anastasia Makarova, Matteo Turchetta, and Andreas Krause. "Mixed-Variable Bayesian Optimization." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/365.

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The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases of this problem that consider fully continuous or fully discrete domains have been widely studied. However, few methods exist for mixed-variable domains and none of them can handle discrete constraints that arise in many real-world applications. In this paper, we introduce MiVaBo, a novel BO algorithm for the efficient optimization of mixed-variable functions combining a linear surrogate model based on expressive feature representations with Thompson sampling. We propose an effective method to optimize its acquisition function, a challenging problem for mixed-variable domains, making MiVaBo the first BO method that can handle complex constraints over the discrete variables. Moreover, we provide the first convergence analysis of a mixed-variable BO algorithm. Finally, we show that MiVaBo is significantly more sample efficient than state-of-the-art mixed-variable BO algorithms on several hyperparameter tuning tasks, including the tuning of deep generative models.
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Romero, David A., Cristina H. Amon, and Susan Finger. "A Study of Covariance Functions for Multi-Response Metamodeling for Simulation-Based Design and Optimization." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-50061.

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The optimal design of complex systems in engineering requires the availability of mathematical models of system’s behavior as a function of a set of design variables; such models allow the designer to find the best solution to the design problem. However, system models (e.g. CFD analysis, physical prototypes) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. Approximate models, or metamodels, of system behavior based on a limited set of data allow significant savings by reducing the resources devoted to modeling during the design process. In our work in engineering design based on multiple performance criteria, we propose the use of Multi-response Bayesian Surrogate Models (MRBSM) to model several aspects of system behavior jointly, instead of modeling each individually. By doing so, it is expected that the observed correlation among the response variables can be used to achieve better models with smaller data sets. In this work, we study the approximation capabilities of several covariance functions needed for multi-response metamodeling with MRBSM, performing a simulation study in which we compare MRBSM based on different covariance functions against metamodels built individually for each response. Our preliminary results indicate that MRBSM outperforms individual metamodels in 46% to 67% of the test cases, though the relative performance of the studied covariance functions is highly dependent on the sampling scheme used and the actual correlation among the observed response values.
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Marta, Andre C., Sriram Shankaran, D. Graham Holmes, and Alexander Stein. "Development of Adjoint Solvers for Engineering Gradient-Based Turbomachinery Design Applications." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-59297.

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High-fidelity computational fluid dynamics (CFD) are common practice in turbomachinery design. Typically, several cases are run with manually modified parameters based on designer expertise to fine-tune a machine. Although successful, a more efficient process is desired. Choosing a gradient-based optimization approach, the gradients of the functions of interest need to be estimated. When the number of variables greatly exceeds the number of functions, the adjoint method is the best-suited approach to efficiently estimate gradients. Until recently, the development of CFD adjoint solvers was regarded as complex and difficult, which limited their use mostly to academia. This paper focuses on the problem of developing adjoint solvers for legacy industrial CFD solvers. A discrete adjoint solver is derived with the aid of an automatic differentiation tool that is selectively applied to the CFD code that handles the residual and function evaluations. The adjoint-based gradients are validated against finite-difference and complex-step derivative approximations.
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Folchert, Uwe, Achim Menne, and Heinz Waller. "Experimental Identification of Dynamic Characteristics of Hydrodynamic Torque Converters and Couplings." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-360.

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Hydrodynamic torque converters and couplings can be components of drive systems. The knowledge of their dynamic characteristics is necessary to calculate the dynamic response of the whole system under various time dependent excitations in order to guarantee safe working. The presented mathematical description of the nonlinear behavior consists of several linear models at several operating points. For a special linear “two port” description as used in electro-technique the four state variables are measured: the torques and the rotational speeds. The mathematical models are determined through an application of identification methods. Therefore a computer controlled testing bench has been constructed. High dynamic excitations have been realized with two hydrostatic drives which can be used as motors or brakes. The hydrodynamic component (torque converter or coupling) can be excited harmonically with the aid of the driving machines. By measuring the four state variables it is possible to get the frequency response functions. They are approximated by complex rational functions. The use of an inverse Fourier transformation into the time domain allows to calculate the dynamic behavior under general transient excitations.
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Hu, Chao, and Byeng D. Youn. "Adaptive-Sparse Polynomial Chaos Expansion for Reliability Analysis and Design of Complex Engineering Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87713.

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This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse PCE) method for performing engineering reliability analysis and design. The proposed method leverages three ideas: (i) an adaptive scheme to build sparse PCE with the minimum number of bivariate basis functions, (ii) a new projection method using dimension reduction techniques to effectively compute the expansion coefficients of system responses, and (iii) an integration of copula to handle nonlinear correlation of input random variables. The proposed method thus has three distinct features for reliability analysis and design: (a) no need of response sensitivities, (b) no extra cost to evaluate probabilistic sensitivity for design, and (c) capability to handle a nonlinear correlation. Besides, an error decomposition scheme of the proposed method is presented to help analyze error sources in probability analysis. Several engineering problems are used to demonstrate the effectiveness of the adaptive-sparse PCE method.
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Lee, Sang Hoon, and Wei Chen. "A Comparative Study of Uncertainty Propagation Methods for Black-Box Type Functions." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35533.

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It is an important step in deign under uncertainty to select an appropriate uncertainty propagation (UP) method considering the characteristics of the engineering systems at hand, the required level of UP associated with the probabilistic design scenario, and the required accuracy and efficiency levels. Many uncertainty propagation methods have been developed in various fields, however, there is a lack of good understanding of their relative merits. In this paper, a comparative study on the performances of several UP methods, including a few recent methods that have received growing attention, is performed. The full factorial numerical integration (FFNI), the univariate dimension reduction method (UDR), and the polynomial chaos expansion (PCE) are implemented and applied to several test problems with different settings of the performance nonlinearity, distribution types of input random variables, and the magnitude of input uncertainty. The performances of those methods are compared in moment estimation, tail probability calculation, and the probability density function (PDF) construction. It is found that the FFNI with the moment matching quadrature rule shows good accuracy but the computational cost becomes prohibitive as the number of input random variables increases. The accuracy and efficiency of the UDR method for moment estimations appear to be superior when there is no significant interaction effect in the performance function. Both FFNI and UDR are very robust against the non-normality of input variables. The PCE is implemented in combination with FFNI for coefficients estimation. The PCE method is shown to be a useful approach when a complete PDF description is desired. Inverse Rosenblatt transformation is used to treat non-normal inputs of PCE, however, it is shown that the transformation may result in the degradation of accuracy of PCE. It is also shown that in black-box type of system the performance and convergence of PCE highly depend on the method adopted to estimate its coefficients.
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Yeh, Hsiang Y., and Houshang Masudi. "Reliability Consideration in Plutonium Storage Container." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17176.

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Abstract Plutonium storage container is a very complex structure. There are many variables that affect the structural behavior of container. It is very difficult to obtain an explicit limit state function of this structure to perform the reliability analysis. This study used several techniques for the reliability analysis of container and consequently a suitable and efficient method is recommended for the container reliability study. The reliability of container was calculated using the proposed approach and the effect of random variables in the reliability of container is also assessed.
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Al-Mentheri, Khawla Abdulla, Faisal Salah Al-Jenaibi, Evgenii Gusarov, and Maksim Kuzevanov. "Complex Dynamic Model History Matched through Utilize Smart Workflows." In ADIPEC. SPE, 2022. http://dx.doi.org/10.2118/211351-ms.

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Abstract Reservoir engineers tend to define a simulation model as "complex" when they have several of the following characteristics: Complex fluids schemes loaded with multi PVT's or EOS's data sets associated with lateral and vertical compositional changes that might cause massive fluids mobility and blends, which resulted in unpredictable production trends. Presence of tilted fluid contacts, buffer/tarmat zones, or other feature which increase the number of uncertain parameters and features. Each of which needs to be investigated individually to identify their impacts on field/wells levels history match profiles. Limited sources of data available with high levels of geological heterogeneity with multi-layers and patchy zones, which result in creating many thin layers that would tend to impact dynamic model performance. This paper is going to discuss the implementation steps and procedures utilized to history matching one of Abu Dhabi's complex onshore reservoirs model. This reservoir has high levels of unknown parameters with uncertainty. Our key objective is to achieve acceptable history match profiles which would be used for field development and optimization works. The second objective is to do this "quickly" in a more reasonable timeframe than is usually achieved. In this complex model case study, it would be attractive to use Assisted History Match technologies to create a smart loop which could assess and modify multi-parameters with a linkage between static and dynamic models. This might require several applications to deal with both static and dynamic models in parallel. Using smart workflows all the possible geological parameters subject for uncertainty analysis have been identified and scripted directly in the dynamic model data deck which accelerates parameter adjustment; this allows us to carry out hundreds of runs in a more time efficient and practical ways using one tool. Although this study started with thousands of uncertain parameters, we reduced the unknown parameters into two main groups (A) Global parameters that would influences overall model results, such as shape of Kr's curves per rock types, and (B) Region parameters that would influences only the selected unit and/or region, for example faults transmissibility. After completing the 1st pass runs to optimize global parameters, those parameters were frozen, and the 2nd pass runs were started for the region parameters. This loop is continued for several iterations until most of parameters stabilized. In order to get maximum benefits from the existing CPU's, it was decided to coarsen the dynamic model while adjusting grid cells properties without mislaying geological features to accelerate runs at the beginning of this project. By using smart workflows and a powerful AHM tool, it was easy to rank the converted models and to pick up the fewest representative cases that showed the lowest Objective Function errors. Several development scenarios were created, and these were used to assess multiple options, including: well objectives, configurations, and target locations with a single model. We then replicated that study on the rest of the converted models in order to check overall development risks envelopes (to assess production sustainability, pressure preserving, field max/min ranges of WCT and GOR, etc.….). This paper presents our successful workflows, which have been utilized for the first time to compile static and dynamic models variables under one platform i.e. (introduce both static and dynamic models variables through dynamic data deck file, including to modify oil saturation option around history match problematic wells by redefining their rock types per region(s) while preserving on match quality with Sw_log profiles), as results we have managed to generate several cases that show good outputs while reflecting wide uncertainty ranges.
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Turner, Cameron J. "Metamodels for Planar 3R Workspace Optimization." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/cie-34500.

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Robotic workspace optimization is a central element of robot system design. To formulate the optimization problem, the complex relationships between design variables, tuning parameters, and performance indices need to be accurately and efficiently represented. The nature of the relationships suggests that metamodels, or models of the models, should be used to derive suitable objective functions. A comparison of two metamodeling techniques for robotic workspace optimization problems for several trial cases suggests that non-uniform rational B-spline models, derived from computer graphics and computer-aided design techniques, are as suitable as response surface models to solve planar 3R workspace optimization problems. Promising nonlinear modeling results with B-spline models suggest future work is justified and performance gains can be realized.
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Reports on the topic "Functions of several complex variables"

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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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Usmanova, Z. M., S. P. Balandin, and R. G. Zaynullin. Electronic educational and methodological manual on the sections «Linear algebra and analytical geometry, differential calculus of functions of one and several variables» of the discipline «Mathematics». OFERNIO, September 2021. http://dx.doi.org/10.12731/ofernio.2021.24887.

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Wilson, D., Vladimir Ostashev, and Chris Pettit. Distribution of the two-point product of complex amplitudes in the fully saturated scattering regime. Engineer Research and Development Center (U.S.), November 2020. http://dx.doi.org/10.21079/11681/38701.

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This Letter considers probability density functions (pdfs) involving products of the complex amplitudes observed at two points (which may, in general, involve separations in space, time, or frequency) in conditions of fully saturated scattering. First, the pdf is derived for the product of the complex amplitude at one point with the conjugate of the complex amplitude at another point. It is shown that the real and imaginary parts of this product each have a variance gamma pdf. Second, expressions are derived for several joint pdfs involving complex amplitude products and powers at two points.
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Russo, David, and William A. Jury. Characterization of Preferential Flow in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, October 2001. http://dx.doi.org/10.32747/2001.7580681.bard.

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Preferential flow appears to be the rule rather than the exception in field soils and should be considered in the quantitative description of solute transport in the unsaturated zone of heterogeneous formations on the field scale. This study focused on both experimental monitoring and computer simulations to identify important features of preferential flow in the natural environment. The specific objectives of this research were: (1) To conduct dye tracing and multiple tracer experiments on undisturbed field plots to reveal information about the flow velocity, spatial prevalence, and time evolution of a preferential flow event; (2) To conduct numerical experiments to determine (i) whether preferential flow observations are consistent with the Richards flow equation; and (ii) whether volume averaging over a domain experiencing preferential flow is possible; (3) To develop a stochastic or a transfer function model that incorporates preferential flow. Regarding our field work, we succeeded to develop a new method for detecting flow patterns faithfully representing the movement of water flow paths in structured and non-structured soils. The method which is based on application of ammonium carbonate was tested in a laboratory study. Its use to detect preferential flow was also illustrated in a field experiment. It was shown that ammonium carbonate is a more conservative tracer of the water front than the popular Brilliant Blue. In our detailed field experiments we also succeeded to document the occurrence of preferential flow during soil water redistribution following the cessation of precipitation in several structureless field soils. Symptoms of the unstable flow observed included vertical fingers 20 - 60 cm wide, isolated patches, and highly concentrated areas of the tracers in the transmission zone. Soil moisture and tracer measurements revealed that the redistribution flow became fingered following a reversal of matric potential gradient within the wetted area. Regarding our simulation work, we succeeded to develop, implement and test a finite- difference, numerical scheme for solving the equations governing flow and transport in three-dimensional, heterogeneous, bimodal, flow domains with highly contrasting soil materials. Results of our simulations demonstrated that under steady-state flow conditions, the embedded clay lenses (with very low conductivity) in bimodal formations may induce preferential flow, and, consequently, may enhance considerably both the solute spreading and the skewing of the solute breakthrough curves. On the other hand, under transient flow conditions associated with substantial redistribution periods with diminishing water saturation, the effect of the embedded clay lenses on the flow and the transport might diminish substantially. Regarding our stochastic modeling effort, we succeeded to develop a theoretical framework for flow and transport in bimodal, heterogeneous, unsaturated formations, based on a stochastic continuum presentation of the flow and a general Lagrangian description of the transport. Results of our analysis show that, generally, a bimodal distribution of the formation properties, characterized by a relatively complex spatial correlation structure, contributes to the variability in water velocity and, consequently, may considerably enhance solute spreading. This applies especially in formations in which: (i) the correlation length scales and the variances of the soil properties associated with the embedded soil are much larger than those of the background soil; (ii) the contrast between mean properties of the two subdomains is large; (iii) mean water saturation is relatively small; and (iv) the volume fraction of the flow domain occupied by the embedded soil is relatively large.
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Ronconi, Lucas, Juan Sanguinetti, Maria Victoria Murillo, and Mariano Tommasi. The Economic Effects of Unions in Latin America: Teachers' Unions and Education in Argentina. Inter-American Development Bank, September 2002. http://dx.doi.org/10.18235/0011247.

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This paper considers the effects of trade unions on the education sector in Argentina and the channels of union influence on the performance of this crucial sector. The authors find that those provinces where teacher unionism is fragmented, where union density is higher and where political relations with the governor are more conflictual, have more strikes (fewer class days). Based on estimates of education production functions both in this paper and elsewhere, we expect this to translate into lower student performance. The authors then find a number of weak conclusions related to the impact that unions have on several variables that affect students' performance (i.e., teachers' tenure, job satisfaction, class size, education budget and teachers' salaries). Reviewing these results, we conclude that the impact of unions on students' performance depends on the channel and kind of political market where unions operate, but not on the existence of unions per se.
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Lewin, Alex, Karla Diaz-Ordaz, Chris Bonell, James Hargreaves, and Edoardo Masset. Machine learning for impact evaluation in CEDIL-funded studies: an ex ante lesson learning paper. Centre for Excellence and Development Impact and Learning (CEDIL), April 2023. http://dx.doi.org/10.51744/llp3.

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The Centre of Excellence for Development Impact and Learning (CEDIL) has recently funded several studies that use machine learning methods to enhance the inferences made from impact evaluations. These studies focus on assessing the impact of complex development interventions, which can be expected to have impacts in different domains, possibly over an extended period of time. These studiestherefore involve study participants being followed up at multiple time-points after the intervention, and typically collect large numbers of variables at each follow-up. The hope is that machine learning approaches can uncover new insights into the variation in responses to interventions, and possible causal mechanisms, which in turn can highlight potential areas that policy and planning can focus on. This paper describes these studies using machine learning methods, gives an overview of the common aims and methodological approaches used in impact evaluations, and highlights some lessons and important caveats.
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Goodwin, Peter. Metadata Report for 2022 Matheson Wetland and Vegetation Mapping. Utah Geological Survey, March 2023. http://dx.doi.org/10.34191/ofr-748.

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The Scott and Norma Matheson Wetlands Preserve (the Preserve) occupies nearly 900 acres between the Colorado River and city of Moab, Utah, and encompasses an extensive floodplain-wetland complex that provides several unique functions in the arid west such as recreation, educational opportunities, and crucial aquatic habitats for sensitive wildlife species. The ability of the Preserve to provide these functions is related to water supplies from surrounding groundwater and surface water systems and is likely to be affected by upgradient changes in water use and delivery to the Preserve. The Nature Conservancy (TNC) and the Utah Division of Wildlife Resources (UDWR) jointly manage the Preserve and contracted the Utah Geological Survey (UGS) to conduct a multi-year study that would better inform managers with the baseline data, research, and monitoring necessary to evaluate potential impacts and develop strategies that maintain the ecological health of the Preserve. As part of this multi-year study, the UGS mapped vegetation communities to reflect current habitat and conditions and serve as a baseline for further groundwater studies, remote sensing analyses, or management actions.
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Amengual, Dante, Xinyue Bei, Marine Carrasco, and Enrique Sentana. Score-type tests for normal mixtures. CIRANO, January 2023. http://dx.doi.org/10.54932/uxsg1990.

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Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.
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Dolja, Valerian V., Amit Gal-On, and Victor Gaba. Suppression of Potyvirus Infection by a Closterovirus Protein. United States Department of Agriculture, March 2002. http://dx.doi.org/10.32747/2002.7580682.bard.

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The plant virus family Polyviridae is the largest and most destructive of all plant viruses. Despite the continuous effort to develop resistant plant varieties, there is a desperate need for novel approaches conferring wide-range potyvirus resistance. Based on experiments with the tobacco etch potyvirus (TEV)-derived gene expression vector, we suggested approach for screening of the candidate resistance genes. This approach relies on insertion of the genes into a virus vector and evaluation of the phenotypes of the resulting recombinant viruses. The genes which suppress infection by the recombinant virus are selected as candidates for engineering transgenic resistance. Our analysis of the TEV variants expressing proteins of the beet yellows closterovirus (BYV) revealed that one of those, the leader proteinase (L-Pro), strongly and specifically interfered with the hybrid TEV infection. Since closterovirus L-Pro is evolutionary related to potyviral helper component-proteinase (HC-Pro), we suggested that the L-Pro interfered with HC-Pro function via a trans-dominant inhibitory effect. Based on these findings, we proposed to test two major hypotheses. First, we suggested that L-Pro-mediated suppression of potyvirus infection is a general phenomenon effective against a range of potyviruses. The second hypothesis stated that the suppression effect can be reproduced in transgenic plants expressing L-Pro, and can be utilized for generation of resistance to potyviruses. In accord with these hypotheses, we developed two original objectives of our proposal: A) to determine the range of the closterovirus-derived suppression of potyviral infection, and B) to try and utilize the L-Pro-mediated suppression for the development of transgenic resistance to potyviruses. In the first phase of the project, we have developed all major tools and technologies required for successful completion of the proposed research. These included TEV and ZYMV vectors engineered to express several closteroviral L-Pro variants, and generation of the large collection of transgenic plants. To our satisfaction, characterization of the infection phenotypes exhibited by chimeric TEV and ZYMV variants confirmed our first hypothesis. For instance, similar to TEV-L- Pro(BYV) chimera, ZYMV-L-Pro(LIYV) chimera was debilitated in its systemic spread. In contrast, ZYMV-GUS chimera (positive control) was competent in establishing vigorous systemic infection. These and other results with chimeric viruses indicated that several closteroviral proteinases inhibit long-distance movement of the potyviruses upon co-expression in infected plants. In order to complete the second objective, we have generated ~90 tobacco lines transformed with closteroviral L-Pro variants, as well as ~100 lines transformed with BYV Hsp70-homolog (Hsp70h; a negative control). The presence and expression of the trans gene in each line was initially confirmed using RT-PCR and RNA preparations isolated from plants. However, since detection of the trans gene-specific RNA can not guarantee production of the corresponding protein, we have also generated L-Pro- and Hsp70h-specific antisera using corresponding synthetic peptides. These antisera allowed us to confirm that the transgenic plant lines produced detectable, although highly variable levels of the closterovirus antigens. In a final phase of the project, we tested susceptibility of the transgenic lines to TEV infection. To this end, we determined that the minimal dilution of the TEV inoculum that is still capable of infecting 100% of nontransgenic plants was 1:20, and used 10 plants per line (in total, ~2,000 plants). Unfortunately, none of the lines exhibited statistically significant reduction in susceptibility. Although discouraging, this outcome prompted us to expand our experimental plan and conduct additional experiments. Our aim was to test if closteroviral proteinases are capable of functioning in trans. We have developed agroinfection protocol for BYV, and tested if co- expression of the L-Pro is capable of rescuing corresponding null-mutant. The clear-cut, negative results of these experiments demonstrated that L-Pro acts only in cis, thus explaining the lack of resistance in our transgenic plants. We have also characterized a collection of the L-Pro alanine- scanning mutants and found direct genetic evidence of the requirement for L-Pro in virus systemic spread. To conclude, our research supported by BARD confirmed one but not another of our original hypotheses. Moreover, it provided an important insight into functional specialization of the viral proteinases and generated set of tools and data with which we will be able to address the molecular mechanisms by which these proteins provide a variety of critical functions during virus life cycle.
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Mascagni, Giulia, Roel Dom, and Fabrizio Santoro. The VAT in Practice: Equity, Enforcement and Complexity. Institute of Development Studies (IDS), January 2021. http://dx.doi.org/10.19088/ictd.2021.002.

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The value added tax (VAT) is supposed to be a tax on consumption that achieves greater economic efficiency than alternative indirect taxes. It is also meant to facilitate enforcement through the ‘self-enforcing mechanism’ – based on opposed incentives for buyers and sellers, and because of the paper trail it creates. Being a rather sophisticated tax, however, the VAT is complex to administer and costly to comply with, especially in lower-income countries. This paper takes a closer look at how the VAT system functions in practice in Rwanda. Using a mixed-methods approach, which combines qualitative information from focus group discussions with the analysis of administrative and survey data, we document and explain a number of surprising inconsistencies in the filing behaviour of VAT-remitting firms, which lead to suboptimal usage of electronic billing machines, as well as failure to claim legitimate VAT credits. The consequence of these inconsistencies is twofold. It makes it difficult for the Rwanda Revenue Authority to exploit its VAT data to the fullest, and leads to firms, particularly smaller ones, bearing a higher VAT burden than larger ones. There are several explanations for these inconsistencies. They appear to lie in a combination of taxpayer confusion, fear of audit, and constraints in administrative capacity.
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