scholarly journals Quantification of multiple simultaneously occurring nitrogen flows in the euphotic ocean

2016 ◽  
Author(s):  
Min Nina Xu ◽  
Yanhua Wu ◽  
Li Wei Zheng ◽  
Zhenzhen Zheng ◽  
Huade Zhao ◽  
...  
Keyword(s):  
Matrix Equation ◽  
Ammonia Oxidation ◽  
Mass Conservation ◽  
Quantitative Information ◽  
Nitrite Oxidation ◽  
Dissolved Nitrogen ◽  
Total Dissolved Nitrogen ◽  
Transformation Rates ◽  
The Matrix ◽  
Multiple Transformation

Abstract. The general features of the N cycle in the sunlit ocean are known, but quantitative information about multiple transformation rates among nitrogen pools, i.e., ammonium (NH4+), nitrite (NO2−), nitrate (NO3−) and particulate/dissolved organic nitrogen (PN/DON), are limited due to methodological difficulties. By adding a single 15N-labelled NH4+ tracer into incubators, we monitor ed the changes in concentration and isotopic composition of the total dissolved nitrogen (TDN), PN, NH4+, NO2−, and NO3− pools to trace the 15N and 14N flows. Based on mass conservation and isotope mass balance, we formulate d a matrix equation that allow edus to simultaneously derive the rates of multiple transformation processes in the nitrogen reaction web . We abandoned inhibitors and minimized the alteration of the system by adding a limited amount of tracer. In one single incubation, solution of the matrix equation provided the rates of NH4+, NO2−, and NO3− uptake; ammonia oxidation; nitrite oxidation; nitrite excretion; DON release; and potentially, the remineralization rate. To our knowledge, this is the first and most convenient method designed to quantitatively and simultaneously resolve complicated nitrogen transformation rates, albeit with some uncertainties. Field examples are given, and c omparisons with conventional labeling methods are discussed.

scholarly journals Quantification of multiple simultaneously occurring nitrogen flows in the euphotic ocean

2017 ◽  
Vol 14 (4) ◽  
pp. 1021-1038 ◽  
Author(s):  
Min Nina Xu ◽  
Yanhua Wu ◽  
Li Wei Zheng ◽  
Zhenzhen Zheng ◽  
Huade Zhao ◽  
...  
Keyword(s):  
Ammonia Oxidation ◽  
Isotope Labeling ◽  
Euphotic Zone ◽  
Matrix Inversion ◽  
Analytical Methodology ◽  
Total Dissolved Nitrogen ◽  
In Situ Conditions ◽  
The Matrix ◽  
The Many

Abstract. The general features of the N cycle in the sunlit region of the ocean are well known, but methodological difficulties have previously confounded simultaneous quantification of transformation rates among the many different forms of N, e.g., ammonium (NH4+), nitrite (NO2−), nitrate (NO3−), and particulate/dissolved organic nitrogen (PN/DON). However, recent advances in analytical methodology have made it possible to employ a convenient isotope labeling technique to quantify in situ fluxes among oft-measured nitrogen species within the euphotic zone. Addition of a single 15N-labeled NH4+ tracer and monitoring of the changes in the concentrations and isotopic compositions of the total dissolved nitrogen (TDN), PN, NH4+, NO2−, and NO3− pools allowed us to quantify the 15N and 14N fluxes simultaneously. Constraints expressing the balance of 15N and 14N fluxes between the different N pools were expressed in the form of simultaneous equations, the unique solution of which via matrix inversion yielded the relevant N fluxes, including rates of NH4+, NO2−, and NO3− uptake; ammonia oxidation; nitrite oxidation; DON release; and NH4+ uptake by bacteria. The matrix inversion methodology that we used was designed specifically to analyze the results of incubations under simulated in situ conditions in the euphotic zone. By taking into consideration simultaneous fluxes among multiple N pools, we minimized potential artifacts caused by non-targeted processes in traditional source–product methods. The proposed isotope matrix method facilitates post hoc analysis of data from on-deck incubation experiments and can be used to probe effects of environmental factors (e.g., pH, temperature, and light) on multiple processes under controlled conditions.

scholarly journals Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam ◽  
Wicharn Lewkeeratiyutkul
Keyword(s):  
Spectral Radius ◽  
Matrix Equation ◽  
Iterative Algorithms ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Convergence Factor ◽  
Sylvester Matrix ◽  
Iteration Matrix ◽  
Banach Contraction ◽  
The Matrix

AbstractWe derive an iterative procedure for solving a generalized Sylvester matrix equation $AXB+CXD = E$ A X B + C X D = E , where $A,B,C,D,E$ A , B , C , D , E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation $AXB=C$ A X B = C , the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Solution of the matrix equation AX + XB = C [F4]

1972 ◽  
Vol 15 (9) ◽  
pp. 820-826 ◽  
Author(s):  
R. H. Bartels ◽  
G. W. Stewart
Keyword(s):  
Matrix Equation ◽  
The Matrix

scholarly journals Ranks of Hermitian and skew-Hermitian solutions to the matrix equation AXA∗=B

2009 ◽  
Vol 431 (12) ◽  
pp. 2359-2372 ◽  
Author(s):  
Yonghui Liu ◽  
Yongge Tian ◽  
Yoshio Takane
Keyword(s):  
Matrix Equation ◽  
The Matrix
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