Improved techniques for parametric and nonparametric evaluations of the first‐passage time for degradation processes

For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results.     

An approach for solving an inverse spherical two‐phase Stefan problem arising in modeling of electric contact phenomena

In this paper, a model problem that can be used for mathematical modeling and investigation of arc phenomena in electrical contacts is considered. An analytical approach for the solution of a two‐phase inverse spherical Stefan problem where along with unknown temperature functions heat flux function has to be determined is presented. The suggested solution method is obtained from a new form of integral error function and its properties that are represented in the form of series whose coefficients have to be determined. Using integral error function and collocation method, the solution of a test problem is obtained in exact form and approximately.     

The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line

The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier‐Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented.     

Birnbaum‐Saunders distribution: A review of models,analysis, and applications

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.     

A further study on value distribution of the Riemann zeta‐function

The paper concerns the uniqueness problem of Riemann zeta‐function. It is showed that the Riemann zeta‐function is uniquely determined in terms of the preimages of three complex values except possibly a set G with , where G is called an exceptional set.     

Skew‐selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations

In this paper we study direct and inverse problems for discrete and continuous skew‐selfadjoint Dirac systems with rectangular (possibly non‐square) pseudo‐exponential potentials. For such a system the Weyl function is a strictly proper rational matrix function and any strictly proper rational matrix function appears in this way. In fact, extending earlier results, given a strictly proper rational matrix function we present an explicit procedure to recover the corresponding potential using techniques from mathematical system and control theory. We also introduce and study a nonlinear generalized discrete Heisenberg magnet model, extending earlier results for the isotropic case. A large part of the paper is devoted to the related discrete systems of which the pseudo‐exponential potential depends on an additional continuous time parameter. Our technique allows us to obtain explicit solutions for the generalized discrete Heisenberg magnet model and evolution of the Weyl functions.     

Multifunctional land‐use value mapping and space type classification: A case study of Puge County,China

Land exhibits diverse functions under the combined influence of natural and human forces. A production–living–ecology functional classification system was constructed by integrating land, ecosystem, and landscape functions. The land functional value was calculated by systematically integrating ecosystem service value assessments. The primary and secondary functions, as well as combinations of different land‐use types, were determined using vertical and horizontal comparison methods. The production–living–ecology ranges were then delineated in Puge County, which is a typical mountain county in China. The production–living–ecology functions identified were well connected with the current land‐use types. The “production–living–ecology” space in Puge County showed obvious multifunctionality and agglomeration. The function identification system proposed in this paper integrated multiple methods, overcame the difficulty of direct quantitative identification of land functions. The methods used to map and quantify land function will enhance our ability to understand and model land system changes and adequately inform policies and planning. Summary for Managers

• The function valuation method constructed in this paper could be used to reflect the multifunctionality and importance of land use and provide guidance and a quantitative basis for regional development planning.
• The spatial classification results provided in this paper could offer a valuable reference for the land management department to scientifically formulate land use planning.
• Under the goal of creating a group‐type urban development pattern and constructing an ecological protection pattern in Puge County, the hotspot analysis results of this paper can provide decision‐making tools and alternative spatial plans.

     

The impact of network structure on innovation efficiency: An agent‐based study in the context of innovation networks

This article investigates the impact of network structure on innovation efficiency by establishing a simulation model of innovation process in the context of innovation networks. The results indicate that short path lengths between vertices are conductive to high efficiency of explorative innovations, dense clusters are conductive to high efficiency of exploitative innovations, and high small‐worldness is conductive to high efficiency of the hybrid of these two innovations. Moreover, we discussed the reason of the results and give some suggestions to innovators and innovation policy makers. © 2014 Wiley Periodicals, Inc. Complexity 21: 111–122, 2015     

A method based on meshless approach for the numerical solution of the two‐space dimensional hyperbolic telegraph equation

In the current article, we investigate the RBF solution of second‐order two‐space dimensional linear hyperbolic telegraph equation. For this purpose, we use a combination of boundary knot method (BKM) and analog equation method (AEM). The BKM is a meshfree, boundary‐only and integration‐free technique. The BKM is an alternative to the method of fundamental solution to avoid the fictitious boundary and to deal with low accuracy, singular integration and mesh generation. Also, on the basis of the AEM, the governing operator is substituted by an equivalent nonhomogeneous linear one with known fundamental solution under the same boundary conditions. Finally, several numerical results and discussions are demonstrated to show the accuracy and efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.