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61.
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. 相似文献
62.
63.
Bilender P. Allahverdiev 《Mathematical Methods in the Applied Sciences》2019,42(1):229-236
In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators. 相似文献
64.
Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models. 相似文献
65.
Ciprian A. Tudor Nakahiro Yoshida 《Stochastic Processes and their Applications》2019,129(9):3499-3526
We develop the asymptotic expansion theory for vector-valued sequences of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence . Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of and we illustrate our results by several examples. 相似文献
66.
In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result. 相似文献
67.
Recently Dadush et al. (2017) have devised a polynomial submodular function minimization (SFM) algorithm based on their LP algorithm. In the present note we also show a weakly polynomial algorithm for SFM based on the recently developed linear programming feasibility algorithm of Chubanov (2017) to stimulate further research on SFM. 相似文献
68.
Empirical potential structure refinements have been made to recent high-energy x-ray diffraction data, providing molecular models of deeply supercooled water. The average O-O coordination number is found to drop from 5.13 at 293?K to 4.85 at 244?K, within 3.5?Å. Triplet O-O-O bond angle distributions reveal a broad peak centred at 96.4° at 293?K which shifts to 100.0° at 244?K, indicative of the local geometry becoming increasingly tetrahedral with decreasing temperature. However, although the number of non-bonded interstitial molecules between the first and second shells is depleted upon cooling, the number of interstitial molecules forming triplets that are embedded within the hydrogen bonded tetrahedral network at θOOO?=?53°, remains constant. This is consistent with previous observations of an invariant O-O coordination number with temperature (4.24 out to 3.3?Å) and corresponds to non-bonded molecules positioned at close to half the ideal tetrahedral angle. Both -O-O-O- and hydrogen-bonded -O-H-O- ring length distributions show increases in 6 and 7-membered rings upon supercooling. This is concomitant with a shift and increase in intensity of peaks at r4 ~8.7?Å and r5 ~10.8?Å in the oxygen-oxygen pair distribution function, which in the models correspond to correlations between adjacent and next-nearest-neighbour hydrogen-bonded rings. 相似文献
69.
We study the well‐posedness of the fractional differential equations with infinite delay on Lebesgue–Bochner spaces and Besov spaces , where A and B are closed linear operators on a Banach space X satisfying , and . Under suitable assumptions on the kernels a and b, we completely characterize the well‐posedness of in the above vector‐valued function spaces on by using known operator‐valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied. 相似文献
70.
《Stochastic Processes and their Applications》2019,129(6):2086-2129
Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift. 相似文献