Reliable Mathematical Method Research Articles

Foreword to the Special Issue on Mathematical Methods in Reliability (MMR23)

Foreword to the Special Issue on Mathematical Methods in Reliability (MMR23)

Forecasting of Winter Wheat Yield: A Mathematical Model and Field Experiments

An increase in world population requires growth in food production. Wheat is one of the major food crops, covering 21% of global food needs. The food supply issue necessitates reliable mathematical methods for predicting wheat yields. Crop yield information is necessary for agricultural management and strategic planning. Our mathematical model was developed based on a three-year field experiment in a semi-arid climate zone. Wheat yields ranged from 4310 to 6020 kg/ha. The novelty of this model is the inclusion of some stochastic data (weather and technological). The proposed method for wheat yield modeling is based on the theory of random sequence analysis. The model does not impose any restrictions on the number of production parameters and environmental indicators. A significant advantage of the proposed model is the absence of limits on the yield function. Consideration of the stochastic features of wheat production (technological and weather parameters) allows researchers to achieve the best accuracy. The numerical experiment confirmed the high accuracy of the proposed mathematical model for the prediction of wheat yield. The mean relative error (for the third-order polynomial model) varied from 1.79% to 2.75% depending on the preceding crop.

The (2+1)-dimensional nonlinear evolution equation in dusty plasma and its analytical solutions

In this paper, a (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied from the governing equations of dusty plasma by means of multiscale analysis and reduced perturbation method. We utilize the generalized exponential rational function method to give various forms of analytical solutions with free parameters of the corresponding equation by using Mathematica software calculation. Then, appropriate parameter values are selected to draw the three-dimensional (3D) diagram and contour diagram of the analytic solutions. We also give the influence of these physical parameters on wave amplitude, waves profile, and stability of waves. The results show the generalized method is a reliable mathematical method to solve similar nonlinear equations in mathematical physics and these solutions can enrich the physical behavior of the equation in dusty plasma.

Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime

The generalized Riccati equation mapping method (GREMM) is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of anomalous dispersion. Later, we use the q-homotopy analysis method combined with the Laplace transform (q-HATM) to obtain approximate solutions of the bright and dark optical solitons. The q-HATM illustrates the solutions as a rapid convergent series. In addition, to show the physical behavior of the solutions obtained by the proposed techniques, the graphical representation has been provided with some parameter values. The findings demonstrate that the proposed techniques are useful, efficient and reliable mathematical method for the extraction of soliton solutions.

Special issue on Statistical Models and Methods in Reliability for the 11th international conference on mathematical methods in reliability (MMR 2019)

This special issue of Communications in Statistics – Theory and Methods on “Statistical Models and Methods in Reliability” includes manuscripts of some presentations at The 11th International Confe...

Is reliability a new science? A paper from the panel session held at the 10th International Conference on Mathematical Methods in Reliability

AbstractThe 10th International Conference on Mathematical Methods in Reliability, MMR 2017, held in Grenoble, France during July 3‐7, entailed a panel discussion entitled “Is reliability a new science?” with Mark Brown, Regina Liu, William Meeker, Sheldon Ross, and Nozer Singpurwalla as panelists. Bill Meeker also doubled as a chair and as a moderator of the panel. The panel discussion was spawned by the recent appearance of a book by Professor Paolo Rocchi, Docent Emeritus of IBM, titled “Reliability is a new science: Gnedenko was right” published by Springer in 2017. The panel discussion was well attended and enthusiastically received and could serve as a forerunner to other such panel discussions at future MMR conferences. This paper presents some elements from the lively debate generated by this discussion.

Special issue of ASMBI dedicated to the 10th International Conference on Mathematical Methods in Reliability (MMR 2017)

Special issue of ASMBI dedicated to the 10th International Conference on Mathematical Methods in Reliability (MMR 2017)

Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems

The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.

Analytical predictions for nonlinear optical processes in silicon slot waveguides

Analytical expressions derived for dispersion relations and fields are used to obtain analytical predictions for the performance of modulators fabricated in second-order $$(\upchi ^{2})$$ and third-order $$(\upchi ^{3})$$ nonlinear materials filled into waveguide slot of silicon-on-insulator waveguides. Analytical expressions are used to model the electron-optical modulation and Kerr effect on slot waveguides for the theoretical modeling. The results obtained for slot waveguides with second-order nonlinearities are compared with those obtained under the planar-waveguide approximations reported as in earlier work. Also, exhaustive solutions are obtained for third-order nonlinear slot waveguides. This work employs long standing and reliable mathematical methods to develop the computational modal of photonics integrated devices. Moreover, the present work allows one a new perspective on design of various optical devices based on low-index sub-wavelength nonlinear slot waveguides.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

OPTIMIZATION METHOD AND SOFTWARE FOR FUEL COST REDUCTION IN CASE OF ROAD TRANSPORT ACTIVITY

The transport activity is one of the most expensive processes in the supply chain and the fuel cost is the highest cost among the cost components of transportation. The goal of the research is to optimize the transport costs in case of a given transport task both by the selecting the optimal petrol station and by determining the optimal amount of the refilled fuel. Recently, in practice, these two decisions have not been made centrally at the forwarding company, but they depend on the individual decision of the driver. The aim of this study is to elaborate a precise and reliable mathematical method for selecting the optimal refuelling stations and determining the optimal amount of the refilled fuel to fulfil the transport demands. Based on the elaborated model, new decision-supporting software is developed for the economical fulfilment of transport trips.

Mathematical method to find best suited PV technology for different climatic zones of India

This paper presents a reliable mathematical method to predict the energy generation from grid connected photovoltaic plant of different commercially used technologies in different zones of India. Global horizontal insolation (GHI) and daytime temperature are the two major parameters affecting the output of photovoltaic (PV) plant. Depending on those two major parameters, India is classified into 15 climatic zones. Typical Meteorological Year data were collected from National Renewable Energy Laboratory to classify India in different climatic zones. Energy generation of different commercially used PV technologies in different climatic zones of India is predicted using proposed mathematical method. These results show a decisive study to choose the best PV technology for different climatic zones of India. Results predict that in almost all climatic zones, amorphous silicon (a-Si) is the best suitable PV technology. In very low-temperature zones, irrespective of GHI, the second best suitable PV technology is mono and cadmium telluride (CdTe) as generation from these two technologies is same. Whereas in other climatic zones, after a-Si the best suitable is CdTe PV technology. Predicted energy generation is validated with the 1-year generation of 2014 from 15 working PV plants of different technologies. Predicted generation is in good co-relation with the actual real-time generation from the PV plants.

Mathematical methods for uncertainty quanti cation in nonlin-ear multi-physics systems and their numerical simulations

Nonlinear multi-physics systems and their numerical simulations play an important role in many practical engineering elds, and the development of reliable mathematical methods for uncertainty quanti cation of such multi-physics systems is still facing great challenges. In this paper, taking the multi-physics models from detonation mechanics and their numerical solution, we briefly introduce recently developed mathematical meth-ods for uncertainty quanti cation in both complex multi-physics engineering modeling and associated numerical simulation. Also, the strengths and weaknesses of the methods will be discussed, and open problems as well as mathematical challenges will be underlined.

Foreword: Special Issue on Mathematical Methods in Reliability (MMR13)

Applied Stochastic Models in Business and IndustryVolume 31, Issue 3 p. 283-284 Foreword Foreword: Special Issue on Mathematical Methods in Reliability (MMR13) Maxim Finkelstein, Corresponding Author Maxim Finkelstein Chair of the Program Committee MMR2013 FinkelM@ufs.ac.za Search for more papers by this author Maxim Finkelstein, Corresponding Author Maxim Finkelstein Chair of the Program Committee MMR2013 FinkelM@ufs.ac.za Search for more papers by this author First published: 24 May 2015 https://doi.org/10.1002/asmb.2094Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume31, Issue3Special Issue: Mathematical Methods in Reliability (MMR13)May/June 2015Pages 283-284 RelatedInformation

Stochastic methods in reliability and risk management

This volume focuses on stochastic methods developed for reliability modeling and risk analysis. Reliability theory and risk analysis have been closely related, and stochastic methods that are commonly used in both fields serve as a natural conduit through which useful concepts and best practices can migrate from one field to the other. This special volume highlights this convergence of reliability modeling and risk analysis, that forms the core of the science of analyzing hazards and its applications to various fields. Most of papers appearing in this volume were selected from the presentations given at the 7th International Conference on Mathematical Methods in Reliability (MMR2011), held in Beijing, China, June 20–24, 2011. The conference was co-chaired by Yiming Wei (Beijing Institute of Technology, China), N. Balakrishnan (McMaster, Canada), and N. Limnios (UTC, France). The papers have been significantly extended from the conference presentations and all papers have been refereed according to the standards of Annals of Operations Research. The MMR2011 is the seventh in a series of international conferences on Mathematical Methods in Reliability. Since 1997, when the first of MMR conferences was held in Bucharest, Romania, the MMR has become a major international gathering of researchers from the international reliability community. The MMR conferences intend to serve as a forum for discussing fundamental issues and recent advances in reliability theory and risk analysis methods, as well as their applications, and have attracted an increasing number of participants from every continent in the world. The Beijing conference focused on all aspects

Determination of Interspin Distance Distributions by cw-ESR Is a Single Linear Inverse Problem

Cw-ESR distance measurement method is extremely valuable for studying the dynamics-function relationship of biomolecules. However, extracting distance distributions from experiments has been a highly technique-demanding procedure. It has never been conclusively identified, to our knowledge, that the problems involved in the analysis are ill posed and are best solved using Tikhonov regularization. We treat the problems from a novel point of view. First of all, we identify the equations involved and uncover that they are actually two linear first-kind Fredholm integral equations. They can be combined into one single linear inverse problem and solved in a Tikhonov regularization procedure. The improvement with our new treatment is significant. Our approach is a direct and reliable mathematical method capable of providing an unambiguous solution to the ill-posed problem. It need not perform nonlinear least-squares fitting to infer a solution from noise-contaminated data and, accordingly, substantially reduces the computation time and the difficulty of analysis. Numerical tests and experimental data of polyproline II peptides with variant spin-labeled sites are provided to demonstrate our approach. The high resolution of the distance distributions obtainable with our new approach enables a detailed insight into the flexibility of dynamic structure and the identification of conformational species in solution state.

VI Conference “Mathematical Methods in Reliability” (MMR-2009) Theory. Methods. Applications (Moscow, June 22–27, 2009)

VI Conference “Mathematical Methods in Reliability” (MMR-2009) Theory. Methods. Applications (Moscow, June 22–27, 2009)

Principal component analysis of native ensembles of biomolecular structures (PCA_NEST): insights into functional dynamics

To efficiently analyze the 'native ensemble of conformations' accessible to proteins near their folded state and to extract essential information from observed distributions of conformations, reliable mathematical methods and computational tools are needed. Examination of 24 pairs of structures determined by both NMR and X-ray reveals that the differences in the dynamics of the same protein resolved by the two techniques can be tracked to the most robust low frequency modes elucidated by principal component analysis (PCA) of NMR models. The active sites of enzymes are found to be highly constrained in these PCA modes. Furthermore, the residues predicted to be highly immobile are shown to be evolutionarily conserved, lending support to a PCA-based identification of potential functional sites. An online tool, PCA_NEST, is designed to derive the principal modes of conformational changes from structural ensembles resolved by experiments or generated by computations. http://ignm.ccbb.pitt.edu/oPCA_Online.htm

Determination of the degradation kinetics of anthocyanins in a model juice system using isothermal and non-isothermal methods

The effect of temperature on the degradation of blackcurrant anthocyanins in a model juice system was determined over a temperature range of 4–140 °C. The thermal degradation of anthocyanins followed pseudo first-order kinetics. From 4–100 °C an isothermal method was used to determine the kinetic parameters. In order to mimic the temperature profile in retort systems, a non-isothermal method was applied to determine the kinetic parameters in the model juice over the temperature range 110–140 °C. The results from both isothermal and non-isothermal methods fit well together, indicating that the non-isothermal procedure is a reliable mathematical method to determine the kinetics of anthocyanin degradation. The reaction rate constant ( k) increased from 0.16 (±0.01) × 10 −3 to 9.954 (±0.004) h −1 at 4 and 140 °C, respectively. The temperature dependence of the rate of anthocyanin degradation was modelled by an extension of the Arrhenius equation, which showed a linear increase in the activation energy with temperature.

The settling characteristics and mean settling velocity of granular sludge in upflow anaerobic sludge blanket (UASB)-like reactors

Mean settling velocity of granular sludge in full-scale UASB (upflow anaerobic sludge blanket) and EGSB (expanded granular sludge bed) reactors was evaluated by settling column tests, and a settling velocity model based on the experimental results and available literature data was developed. It is concluded that the settling velocity should be calculated by the Allen formula, because the settling process of the granules is in the category of intermediate flow regime rather than in the laminar flow one. The comparison between calculated and measured values of the settling velocity shows an excellent agreement, with an average relative error of 4.04%. A simple but reliable mathematical method to determine the settling velocity is therefore proposed.