scholarly journals Regularization and error estimates for an inverse heat problem under the conformable derivative

2018 ◽  
Vol 16 (1) ◽  
pp. 999-1011 ◽  
Author(s):  
Ho Vu ◽  
Donal O’Regan ◽  
Ngo Van Hoa
Keyword(s):  
Estimation Error ◽  
The Other ◽  
Time Interval ◽  
Conformable Derivative ◽  
Time Problem ◽  
Regularization Parameters ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Nonhomogeneous Heat ◽  
Inverse Heat Problem

AbstractIn this paper we study an inverse time problem for the nonhomogeneous heat equation under the conformable derivative which is a severely ill-posed problem. Using the quasi-boundary value method with two regularization parameters (one related to the error in a measurement process and the other is related to the regularity of the solution) we regularize this problem and obtain a Hölder-type estimation error for the whole time interval. Numerical results are presented to illustrate the accuracy and efficiency of the method.

scholarly journals Two-Parameter Regularization Method for a Nonlinear Backward Heat Problem with a Conformable Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Donal O’Regan ◽  
Hoa Ngo Van
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
Time Variable ◽  
Conformable Derivative ◽  
Heat Problem ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Parameter Regularization ◽  
Two Parameter ◽  
Backward Heat Problem

In this paper, we consider the nonlinear inverse-time heat problem with a conformable derivative concerning the time variable. This problem is severely ill posed. A new method on the modified integral equation based on two regularization parameters is proposed to regularize this problem. Numerical results are presented to illustrate the efficiency of the proposed method.

scholarly journals Effect of Co-Inoculation of Bacillus sp. Strain with Bacterial Endophytes on Plant Growth and Colonization in Tomato Plant (Solanum lycopersicum)

2021 ◽  
Vol 12 (2) ◽  
pp. 480-490
Author(s):  
Ahsanul Salehin ◽  
Ramesh Raj Puri ◽  
Md Hafizur Rahman Hafiz ◽  
Kazuhito Itoh
Keyword(s):  
Plant Growth ◽  
Solanum Lycopersicum ◽  
Plant Growth Promotion ◽  
Tomato Plant ◽  
Growth Promotion ◽  
Growth Parameters ◽  
The Other ◽  
Time Interval ◽  
Bacillus Sp ◽  
F 33

Colonization of a biofertilizer Bacillus sp. OYK strain, which was isolated from a soil, was compared with three rhizospheric and endophytic Bacillus sp. strains to evaluate the colonization potential of the Bacillus sp. strains with a different origin. Surface-sterilized seeds of tomato (Solanum lycopersicum L. cv. Chika) were sown in the sterilized vermiculite, and four Bacillus sp. strains were each inoculated onto the seed zone. After cultivation in a phytotron, plant growth parameters and populations of the inoculants in the root, shoot, and rhizosphere were determined. In addition, effects of co-inoculation and time interval inoculation of Bacillus sp. F-33 with the other endophytes were examined. All Bacillus sp. strains promoted plant growth except for Bacillus sp. RF-37, and populations of the rhizospheric and endophytic Bacillus sp. strains were 1.4–2.8 orders higher in the tomato plant than that of Bacillus sp. OYK. The plant growth promotion by Bacillus sp. F-33 was reduced by co-inoculation with the other endophytic strains: Klebsiella sp. Sal 1, Enterobacter sp. Sal 3, and Herbaspirillum sp. Sal 6., though the population of Bacillus sp. F-33 maintained or slightly decreased. When Klebsiella sp. Sal 1 was inoculated after Bacillus sp. F-33, the plant growth-promoting effects by Bacillus sp. F-33 were reduced without a reduction of its population, while when Bacillus sp. F-33 was inoculated after Klebsiella sp. Sal 1, the effects were increased in spite of the reduction of its population. Klebsiella sp. Sal 1 colonized dominantly under both conditions. The higher population of rhizospheric and endophytic Bacillus sp. in the plant suggests the importance of the origin of the strains for their colonization. The plant growth promotion and colonization potentials were independently affected by the co-existing microorganisms.

THE EMISSION OF IONIZING RADIATION DURING A SPARK DISCHARGE

1957 ◽  
Vol 35 (3) ◽  
pp. 324-331 ◽  
Author(s):  
W. A. Prowse ◽  
G. R. Bainbridge
Keyword(s):  
Ionizing Radiation ◽  
High Voltage ◽  
Voltage Pulse ◽  
High Voltage Pulse ◽  
Spark Discharge ◽  
The Other ◽  
Time Interval ◽  
Delay Lines

A high voltage pulse lasting 0.35 microsecond is applied to a pair of delay lines, so that two pulses can be picked up from adjustable points of connection on the lines. One is applied to an irradiating gap and the other to a longer test gap, the gaps being so arranged that only mid-gap irradiation occurs. The sparking probability, P, of the test gap is used to indicate the presence of ionizing radiation. Variations of P with the time interval between the two pulses are recorded. They indicate that ionizing radiation is emitted in repeated short flashes. Photographic observations support this view.

scholarly journals Robust Bayesian Joint Inversion of Gravimetric and Muographic Data for the Density Imaging of the Puy de Dôme Volcano (France)

2021 ◽  
Vol 8 ◽  
Author(s):  
Anne Barnoud ◽  
Valérie Cayol ◽  
Peter G. Lelièvre ◽  
Angélie Portal ◽  
Philippe Labazuy ◽  
...  
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Constant Density ◽  
Acquisition Duration ◽  
Regularization Parameters ◽  
Absolute Density ◽  
Gravimetric Data ◽  
Ill Posed ◽  
Leave One Out

Imaging the internal structure of volcanoes helps highlighting magma pathways and monitoring potential structural weaknesses. We jointly invert gravimetric and muographic data to determine the most precise image of the 3D density structure of the Puy de Dôme volcano (Chaîne des Puys, France) ever obtained. With rock thickness of up to 1,600 m along the muon lines of sight, it is, to our knowledge, the largest volcano ever imaged by combining muography and gravimetry. The inversion of gravimetric data is an ill-posed problem with a non-unique solution and a sensitivity rapidly decreasing with depth. Muography has the potential to constrain the absolute density of the studied structures but the use of the method is limited by the possible number of acquisition view points, by the long acquisition duration and by the noise contained in the data. To take advantage of both types of data in a joint inversion scheme, we develop a robust method adapted to the specificities of both the gravimetric and muographic data. Our method is based on a Bayesian formalism. It includes a smoothing relying on two regularization parameters (an a priori density standard deviation and an isotropic correlation length) which are automatically determined using a leave one out criterion. This smoothing overcomes artifacts linked to the data acquisition geometry of each dataset. A possible constant density offset between both datasets is also determined by least-squares. The potential of the method is shown using the Puy de Dôme volcano as case study as high quality gravimetric and muographic data are both available. Our results show that the dome is dry and permeable. Thanks to the muographic data, we better delineate a trachytic dense core surrounded by a less dense talus.

scholarly journals Estimating Subsurface Thermohaline Structure of the Global Ocean Using Surface Remote Sensing Observations

2019 ◽  
Vol 11 (13) ◽  
pp. 1598 ◽  
Author(s):  
Hua Su ◽  
Xin Yang ◽  
Wenfang Lu ◽  
Xiao-Hai Yan
Keyword(s):  
Remote Sensing ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Estimation Error ◽  
Satellite Observations ◽  
The Other ◽  
Global Ocean ◽  
Gradient Boosting ◽  
Mean Square ◽  
Thermohaline Structure

Retrieving multi-temporal and large-scale thermohaline structure information of the interior of the global ocean based on surface satellite observations is important for understanding the complex and multidimensional dynamic processes within the ocean. This study proposes a new ensemble learning algorithm, extreme gradient boosting (XGBoost), for retrieving subsurface thermohaline anomalies, including the subsurface temperature anomaly (STA) and the subsurface salinity anomaly (SSA), in the upper 2000 m of the global ocean. The model combines surface satellite observations and in situ Argo data for estimation, and uses root-mean-square error (RMSE), normalized root-mean-square error (NRMSE), and R2 as accuracy evaluations. The results show that the proposed XGBoost model can easily retrieve subsurface thermohaline anomalies and outperforms the gradient boosting decision tree (GBDT) model. The XGBoost model had good performance with average R2 values of 0.69 and 0.54, and average NRMSE values of 0.035 and 0.042, for STA and SSA estimations, respectively. The thermohaline anomaly patterns presented obvious seasonal variation signals in the upper layers (the upper 500 m); however, these signals became weaker as the depth increased. The model performance fluctuated, with the best performance in October (autumn) for both STA and SSA, and the lowest accuracy occurred in January (winter) for STA and April (spring) for SSA. The STA estimation error mainly occurred in the El Niño-Southern Oscillation (ENSO) region in the upper ocean and the boundary of the ocean basins in the deeper ocean; meanwhile, the SSA estimation error presented a relatively even distribution. The wind speed anomalies, including the u and v components, contributed more to the XGBoost model for both STA and SSA estimations than the other surface parameters; however, its importance at deeper layers decreased and the contributions of the other parameters increased. This study provides an effective remote sensing technique for subsurface thermohaline estimations and further promotes long-term remote sensing reconstructions of internal ocean parameters.

scholarly journals Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method

2018 ◽  
Vol 40 (1) ◽  
pp. 606-627 ◽  
Author(s):  
R Boiger ◽  
A Leitão ◽  
B F Svaiter
Keyword(s):  
Lagrange Multipliers ◽  
Approximate Solutions ◽  
Identification Problem ◽  
Linear Operators ◽  
Type Method ◽  
Geometrical Properties ◽  
Regularization Parameters ◽  
New Strategy ◽  
Parameter Identification Problem ◽  
Ill Posed

Abstract In this article we propose a novel nonstationary iterated Tikhonov (NIT)-type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical properties of the problem are used to derive a new strategy for choosing the sequence of regularization parameters (Lagrange multipliers) for the NIT iteration. Convergence analysis for this new method is provided. Numerical experiments are presented for two distinct applications: (I) a two-dimensional elliptic parameter identification problem (inverse potential problem); and (II) an image-deblurring problem. The results obtained validate the efficiency of our method compared with standard implementations of the NIT method (where a geometrical choice is typically used for the sequence of Lagrange multipliers).

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (4) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval.In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

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