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On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation

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Communications on Applied Mathematics and Computation 2022年第3期4卷 1158-1174页

作者： Chacha stephen Chacha Department of Mathematics Physics and InformaticsMkwawa University College of EducationP.O.Box 2513IringaTanzania

In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=*** expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix *** analysis for the derived condition numbers and the proposed algorithm are *** proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line *** condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.

关键词： Mixed condition number Componentwise condition number Iterative algorithm Perturbation analysis Exact line search

Learning Convex Optimization Models

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IEEE/CAA Journal of Automatica Sinica 2021年第8期8卷 1355-1364页

作者： Akshay Agrawal Shane Barratt stephen Boyd Department of Electrical Engineering Stanford UniversityStanfordCA 94305 USA

A convex optimization model predicts an output from an input by solving a convex optimization *** class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic *** propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its *** describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.

关键词： Convex optimization differentiable optimization machine learning

Optimal field development and production design for unconventional reservoirs:A case study from Central Sub-Basin,Permian Basin,New Mexico

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Petroleum Research 2021年第1期6卷 66-76页

作者： Alexander Davis Oladoyin Kolawole marshall Watson Chioma Onwumelu Bob L.Herd Department of Petroleum Engineering Texas Tech University807 Boston AvenueLubbockTXUSA Harold Hamm School of Geology and Geological Engineering University of North DakotaGrand ForksNDUSA

The planning and developmental decisions succeeding the discovery of an unconventional oil and gas field is of utmost importance in attaining successful exploitation and production from these tight *** development and production of hydrocarbon from these unconventional reservoirs require requires adequate planning and execution which could be challenging,due to the sequence of heterogeneous lithologies of these *** this study,we designed and presented a comprehensive field development and production program that is representative of the unconventional oil and gas development in the Central sub-basin of the Permian *** design and achieve optimal field development and production for unconventional reservoirs in the Central sub-basin of the Permian Basin,New Mexico,we utilized field data from an oil and gas well that was drilled to a TVD/MD of 2290 m with a PBTD of 2270 ***,we conducted the petrophysical evaluation of the logs and utilized a decline curve analysis for reservoir evaluation of all the members of the *** also designed and developed comprehensive drilling,completions,and facilities ***,we incorporated an economic analysis of our optimized field development and production *** results provide a valuable plan and critical decision-making insight for optimizing field development and production of unconventional reservoirs in the Permian Basin and across the world.

关键词： Unconventional reservoir Carbonate Permian basin Field development Hydrocarbon production

Characterization of isolated homogeneous hypersurface singularities in C^4

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Science China Mathematics 2006年第11期49卷 1576-1592页

作者： YAU stephen S T Department of Mathematics Statistics and Computer Science University of Illinois at ChicagoChicagoIL 60607-7045USA

Let V be a hypersurface with an isolated singularity at the origin in Cn+1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero.

关键词： homogeneous polynomials, hypersurface singularity, weighted homogeneous polynomial, geometric genus.

A relational database of global U-Pb ages

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Geoscience Frontiers 2018年第3期9卷 877-891页

作者： stephen J.Puetz Progressive Science Institute HonoluluHI 96815USA

Enhanced understanding of how sampling techniques affect estimates of the global U-Pb age-distribution have, in turn, constrained U-Pb database design. Recent studies indicate that each continent has a unique age-distribution, as determined by zircon ages dated by the U-Pb isotope method. Likewise, broad regions within a continent also exhibit diverse age-distributions. To achieve a reliable estimate of the global distribution, the heterogenous composition of the continental crust requires sampling as many regions as feasibly possible. To attain this goal, and to provide a method for calculating age histograms, the records from a recent global U-Pb compilation are supplemented with 281,631 new records. These additions increase the database size to 700,598 records. In addition, the data are now restructured and made available as a relational database. After filtering the records by the six age-models included with the database, the results reveal two problems that might generally be unrecognized. First, an abrupt switch in the best-age at any given point(such as 1000 Ma) from ^(206)Pb/^(238)U ages to ^(207)Pb/^(206)Pb ages artificially depresses the age-distribution at the cutoff point. Second, rejecting analyses based on either absolute discordance or the magnitude of 2σ precision errors artificially depresses the age-distribution between 900 Ma and 2000 Ma. The results indicate that, when estimating the global U-Pb age-distribution, the methods for determining best-age and for rejecting records both require some attention. Possible solutions include using either an Accuracy Model or a Precision Model for estimating best-age, and then including all U-Pb records in the estimate, rather than rejecting any of them.

关键词： U-Pb age-distribution Histogram Global database Sampling Filtering Zircon

Breather Dynamics of the Sine-Gordon Equation

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Communications in Theoretical Physics 2013年第6期59卷 664-670页

作者： stephen Johnson Anjan Biswas stephen Johnson and Anjan Biswas Department of Mathematical Sciences Delaware State University Department of Mathematics Faculty of Science King Abdulaziz University

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.

关键词： solitons phonons conservation laws perturbations numerics

An integrated measurement and modeling methodology for estuarine water quality management

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Water Science and Engineering 2015年第1期8卷 9-19页

作者： Michael Hartnett stephen Nash Department of Civil Engineering National University of Ireland

This paper describes research undertaken by the authors to develop an integrated measurement and modeling methodology for water quality management of estuaries. The approach developed utilizes modeling and measurement results in a synergistic manner. Modeling results were initially used to inform the field campaign of appropriate sampling locations and times, and field data were used to develop accurate models. Remote sensing techniques were used to capture data for both model development and model validation. Field surveys were undertaken to provide model initial conditions through data assimilation and determine nutrient fluxes into the model domain. From field data, salinity re- lationships were developed with various water quality parameters, and relationships between chlorophyll a concentrations, transparency, and light attenuation were also developed. These relationships proved to be invaluable in model development, particularly in modeling the growth and decay of chlorophyll a. Cork Harbour, an estuary that regularly experiences summer algal blooms due to anthropogenic sources of nutrients, was used as a case study to develop the methodology. The integration of remote sensing, conventional fieldwork, and modeling is one of the novel aspects of this research and the approach developed has widespread applicability.

关键词： Estuarine modeling Hydrodynamics Water quality management Nutrients Phytoplankton Field measurements Remote sensing

Suspension Splittings and Self-maps of Flag Manifolds

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Acta Mathematica Sinica,English Series 2019年第4期35卷 445-462页

作者： Shizuo KAJI stephen THERIAULT Institute of Mathematics for Industry Kyushu University Mathematical Sciences University of Southampton

If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.

关键词： Flag manifold self-map stable splitting

Beef and cone-in-cone calcite fibrous cements associated with the end-Permian and end-Triassic mass extinctions： Reassessment of processes of formation

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Journal of Palaeogeography 2016年第1期5卷 28-42页

作者： stephen Kershaw Li Guo Department of Life Sciences Brunel Uniuersity Kingston Lane Uxbridge Middlesex UB8 3PH UK CASP University of Cambridge 181a Huntingdon Road CB3 0DH Cambridge UK

This paper reassesses published interpretation that beef and cone-in-cone （B-CIC） fibrous calcite cements were precipitated contemporaneously just below the sea floor in uncon- solidated sediment, in limestones associated with the end-Permian （P/T） and end-Triassic （T/J） mass extinctions. That interpretation introduced the concept of a sub-seafloor car- bonate factory associated with ocean acidification by raised carbon dioxide driven by volcanic eruption, coinciding with mass extinction. However, our new fieldwork and petrographic analysis, with literature comparison, reveals several problems with this concept. Two key points based on evidence in the T/J transition of the UK are：（I） that B-CIC calcite deposits form thin scattered layers and lenses at several horizons, not a distinct deposit associated with volcanic activity; and （2） B-CIC calcite is more common in Early Jurassic sediments after the extinction and after the end of the Central Atlantic Magmatic Province volcanism proposed to have supplied the carbon dioxide required. Our samples from Late Triassic, Early Jurassic and Early Cretaceous limestones in southern UK show that B-CIC calcite occurs in both marine and non-marine sediments, therefore ocean processes are not mandatory for its formation. There is no proof that fibrous calcite was formed before lithification, but our Early Jurassic samples do prove fibrous calcite formed after compaction, thus interpretation of crystal growth in uncon- solidated sediment is problematic. Furthermore, B-CIC crystals mostly grew both upwards and downwards equally, contradicting the interpretation of the novel carbonate factory that they grew preferentially upwards in soft sediment. Finally, Early Jurassic and Early Cretaceous examples are not associated with mass extinction. Three further key points derived from the literature include：（I） B-CIC calcite is wide- spread geographically and stratigraphically, not clustered around mass extinctions or the Paleocene-E

关键词： End-Permian mass extinction End-Triassic mass extinctionBeefCone-in-cone calciteOcean acidification