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The authors investigate the complete moment convergence for arrays of rowwise independent random elements in Rademacher p Banach spaces. The results obtained in this paper improve the corresponding theorems of Hu et al. (Hu, T.-C., Rosalsky, A., Volodin, A., Zhang, S., 2021. A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type p Banach spaces. II, Stochastic Anal. Appl., 39 (1), 177-193). Some corollaries and examples are also presented. [ABSTRACT FROM AUTHOR]

This paper presents a way to regularize the t-channel singularity (which appears when a massive, stable t-channel mediator of a given process is allowed to be on-shell, making the cross section infinite) in a general case of particles of any spin 0 1 2 1 interacting within a thermal medium. Those interactions result in a finite lifetime of the mediator and allow to introduce an effective momentum- and temperature-dependent width. As a result, the would-be-singular cross section becomes finite. A complete derivation and an analytical result for the width are provided. For an illustration, the method is used to calculate the thermal widths and cross sections within the Vector-Fermion Dark Matter model. [ABSTRACT FROM AUTHOR]

In this paper, we present a more general approach based on a Picard integral scheme for nonlinear partial differential equations with a variable time-fractional derivative of order α (x , t) ∈ (1 , 2) and space-fractional order s ∈ (0 , 1) , where v = u ′ (t) is introduced as the new unknown function and u is recovered using the quadrature. In order to get rid of the constraints of traditional plans considering the half-time situation, integration by parts and the regularity process are introduced on the variable v. The convergence order can reach O (τ 2 + h 2) , different from the common L 1 , 2 − α schemes with convergence rate O (τ 2 , 3 − α (x , t)) under the infinite norm. In each integer time step, the stability, solvability and convergence of this scheme are proved. Several error results and convergence rates are calculated using numerical simulations to evidence the theoretical values of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a underwater wireless sensor network, which is composed of an autonomous underwater vehicle (AUV) and the underwater data collection stations. Constrained by limited resources, at each decision epoch the AUV selects one underwater data collection station to update the data and then uploads it to the surface base station. Different from other underwater communication models, we consider the influence of underwater environment on the AUV and develop an AUV model with random lifetime, meanwhile, we further propose that the information arrives randomly with different importance levels. The system model is formulated into a discounted Markov decision process with infinite horizon. Taking the age of information and the importance of information as the performance metrics, the optimal scheduling strategy of the AUV is developed, and the threshold structure characteristics of the optimal strategy are proved. Finally, the numerical examples are given to illustrate the theoretical results, and the impacts of system parameters on the optimal strategy and the value function are also investigated. [ABSTRACT FROM AUTHOR]

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results to the case with infinite variance GARCH innovations as considered in Zhang, Sin, and Ling (2015, Stochastic Processes and their Applications 125, 482–512). This paper addresses this question. In particular, the limit distributions of the ADF for random walk models with short-memory linear noise driven by infinite variance GARCH innovations are studied. We show that when the tail index α, the limit distributions are completely different from that of CGT and the estimator of the parameters of the lag terms used in the ADF regression is not consistent. This paper provides a broad treatment of unit-root models with linear GARCH noises, which encompasses the commonly entertained unit-root IGARCH model as a special case. [ABSTRACT FROM AUTHOR]

This paper proposes using the uncertainty of information (UoI), measured by Shannon’s entropy, as a metric for information freshness. We consider a system in which a central monitor observes M binary Markov processes through m communication channels (m

The multi-task allocation has become the key to be solved urgently in applying a coal gangue sorting robot system (CGSRS) in raw coal with high throughput. This paper constructs a multi-task allocation framework of CGSRS for time-varying raw coal flow (TVRCF), including task decomposition, task allocation, and collaborative strategy. Establish the TVRCF decomposition model using the tumbling time window method to obtain the gangue model. A multi-task allocation model based on M/M/s queuing model with impatient customers is proposed because arrival time, granularity, and spatial position of the gangue model are uncertain. By introducing trajectory function and designing benefit function, to solve environment states of sorting area. Creating an iterative mechanism for environment states based on the infinite Markov process, using service time and arrival time interval. An adaptive weights rule based on the greedy algorithm (GAW) is proposed to improve the benefit of multi-task allocation. Simulating 18 groups of TVRCF with 9 productivity. Experimental results show that the proposed framework suits the multi-task allocation of CGSRS to TVRCF. The GAW rule always ensures the optimal sorting rate, the near-optimal task completion success rate, and the manipulator utilization rate. In addition, the stability of the GAW rule is best. [ABSTRACT FROM AUTHOR]

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The Szegö kernel has many applications to problems in conformal mapping and satisfies the Kerzman-Stein integral equation. The Szegö kernel for an annulus can be expressed as a bilateral series and has a unique zero. In this paper, we show how to represent the Szegö kernel for an annulus as a basic bilateral series (also known as q -bilateral series). This leads to an infinite product representation through the application of Ramanujan's sum. The infinite product clearly exhibits the unique zero of the Szegö kernel for an annulus. Its connection with the basic gamma function and modified Jacobi theta function is also presented. The results are extended to the Szegö kernel for general annulus and weighted Szegö kernel. Numerical comparisons on computing the Szegö kernel for an annulus based on the Kerzman-Stein integral equation, the bilateral series, and the infinite product are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence of infinite product of strongly quasi-nonexpansive mappings on geodesic spaces with curvature bounded above by one. Our main applications behind this study are to solve convex feasibility by alternating projections, and to solve minimizers of convex functions and common minimizers of several objective functions. To prove our main results, we introduce a new concept of orbital Δ -demiclosed mappings which covers finite products of strongly quasi-nonexpansive, Δ -demiclosed mappings, and hence is applicable to the convergence of infinite products. [ABSTRACT FROM AUTHOR]

In this paper certain continued fractions of the ratios of 2Ψ2-series have been established. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of representation of Horn's hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn's hypergeometric function H 4 ratios are constructed. The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian continued fraction. It is proven that the branched continued fraction, which is an expansion of one of the ratios, uniformly converges to a holomorphic function of two variables on every compact subset of some domain H , H ⊂ C 2 , and that this function is an analytic continuation of this ratio in the domain H. The application to the approximation of functions of two variables associated with Horn's double hypergeometric series H 4 is considered, and the expression of solutions of some systems of partial differential equations is indicated. [ABSTRACT FROM AUTHOR]

This paper studies how the degree of heterogeneity among hedge funds' demand orders for a risky asset affects the possibility of their defaults being clustered. We find that fire-sales caused by margin calls is a necessary, yet not a sufficient condition for defaults to be clustered. We show that when the degree of heterogeneity is sufficiently high, poorly performing HFs are able to obtain a higher than usual market share, which leads to an improvement of their performance. Consequently, their survival time is prolonged, increasing the probability of them remaining in operation until the downturn of the next leverage cycle. This leads to an increase in the probability of poorly and high-performing hedge funds to default in sync at a later time, and thus also in the probability of collective defaults. Our analytical results establish a connection between the nontrivial aggregate statistics and the presence of infinite memory in the process governing the hedge funds' defaults. [ABSTRACT FROM AUTHOR]

Consider the AR(1) model, X t = θ X t − 1 + u t , where { u t ; t ≥ 1 } is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a stochastic Lotka–Volterra competitive model with the Ornstein–Uhlenbeck process and infinite delays. First, we verify the existence and uniqueness of the global solution of the system with any initial value. Then, we investigate the pth moment boundedness, asymptotic pathwise estimation, and asymptotic behavior of the solutions of the stochastic system in turn. In addition, we develop sufficient conditions for the existence of a stationary distribution of positive solutions to the stochastic system by establishing a series of suitable Lyapunov functions. Finally, by solving the corresponding six-dimensional Fokker–Planck equation, we obtain the accurate expression of the local density function of the linear system corresponding to the stochastic system. [ABSTRACT FROM AUTHOR]

In this paper we consider the Sturm-Liouville equation y″ + (ρ² ∅²(x) - q(x)) y = 0 (1) on a finite interval I, say I = [0, 1], under the assumption that I contains a finite number of arbitrary type turning points, which are zeros of ∅ in I. According to the four types of turning points, first we obtain the asymptotic forms of the solutions of (1), and then based on Hadamard's factorization theorem we use this asymptotic estimates to study the infinite product representation of solutions of such equations. Infinite product form of the solution has a basic application in studies of inverse spectral problems. [ABSTRACT FROM AUTHOR]

This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests of Nielsen (2009. "A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic." Econometric Theory25: 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop the asymptotic theory for these FVR tests under this setup. We show that the limiting distributions of the tests are free of serial correlation nuisance parameters, but depend on the tail index of the infinite variance process. Then, we compare the finite sample size and power performance of our FVR unit root tests with the well-known parametric ADF test under the impact of the heavy tailed shocks. Simulations demonstrate that under heavy tailed innovations, the nonparametric FVR tests have desirable size and power properties. [ABSTRACT FROM AUTHOR]

There are two distinct but interrelated questions concerning Aristotle's account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the 'potential' (and not 'actual') infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle's notion of the potential infinite coherent and rigorous with modern tools that can stand as a rival to the widely-accepted view of the infinite as characterized in a mathematical theory of sets. In this paper, I argue that the theoretical roles that Aristotle intends his account of the potential infinite to fulfill lead to a deep and irresoluble tension that can help explain the persistence of debates on both of these questions. I do so by turning to the places where Aristotle attempts to argue for or against the existence of particular infinite processes to show that he slides between different underlying notions of when changes are possible. Making these underlying notions clear can help us better understand the role of Aristotle's account in the history of philosophy, the possible pitfalls for a contemporary theory of the potential infinite, and what each of these debates might learn from each other. [ABSTRACT FROM AUTHOR]

Seepage equation in fissured porous media is a partial differential equation describing the variation of pressure of a given area over time. In traditional seepage equation, the strength of mass source is supposed to be deterministic. However, the mass source in practice is often affected by noise such as transformation of underground environment and geological activities. To depict the noise, some scholars attempted to employ a technique called Winner process. Unfortunately, it is unreasonable to model the noise in seepage equation with Winner process, since change rate of pressure will be infinite. As a alternative tool in uncertainty theory, Liu process is introduced to model the noise, which can refrain from the problem of infinity. Then this paper deduces the uncertain seepage equation in fissured porous media driven by Liu process. Furthermore, the analytic solution and its inverse uncertainty distribution are derived. Finally, a paradox of stochastic seepage equation in fissured porous media is presented. [ABSTRACT FROM AUTHOR]

It is well known that ergodicity and the strong law of large numbers (SLLN) play important roles in stochastic control and stochastic approximations. For a class of regime-switching functional diffusion processes with infinite delay, this paper establishes exponential ergodicity in a Wasserstein distance under certain "averaging conditions." It follows from such an ergodicity property that an SLLN for additive functionals of the regime-switching diffusions is obtained based on the property of uniform mixing. Finally, an example is presented to illustrate the application of ergodicity and the SLLN to a numerical algorithm for stochastic optimization. [ABSTRACT FROM AUTHOR]

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink's inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017). [ABSTRACT FROM AUTHOR]

In modern operating systems and programming languages adapted to multicore computer architectures, parallelism is abstracted by the notion of execution threads. Multi-threaded systems have two major specificities: on the one part, new threads can be created dynamically at runtime, so there is no bound on the number of threads participating in long-running executions. On the other part, threads have access to a memory allocation mechanism that cannot allocate infinite arrays. These specificities make it challenging to adapt some algorithms to multi-threaded systems, in particular those that need to assign one shared register per process. This paper explores the synchronization power of shared objects in multi-threaded systems by extending the famous Herlihy's wait-free hierarchy to take these constraints into consideration. It proposes to subdivide the set of objects with an infinite consensus number into nine new degrees, depending on their ability to synchronize a bounded, finite or infinite number of processes, with or without the need to allocate an infinite array. To show the relevance of the proposed extension, for each new degree it is either proved that it is empty, or an object illustrating it is proposed. [ABSTRACT FROM AUTHOR]

In this paper, we study a variant of the state-dependent sweeping process with velocity constraint. The constraint C(⋅,u) depends upon the unknown state u, which causes one of the main difficulties in the mathematical treatment of quasi-variational inequalities. Our aim is to show how a fixed point approach can lead to an existence theorem for this implicit differential inclusion. By using Schauder's fixed point theorem combined with a recent existence and uniqueness theorem in the case where the moving set C does not depend explicitly on the state u (i.e. C:=C(t)) given in [4], we prove a new existence result of solutions of the quasi-variational sweeping process in the infinite dimensional Hilbert spaces with a velocity constraint. Contrary to the classical state-dependent sweeping process, no conditions on the size of the Lipschitz constant of the moving set, with respect to the state, is required. [ABSTRACT FROM AUTHOR]

In this paper we consider a zero-sum Markov stopping game on a general state space with impulse strategies and infinite time horizon discounted payoff where the state dynamics is a weak Feller-Markov process. One of the key contributions is our analysis of this problem based on "shifted" strategies, thereby proving that the original game can be practically restricted to a sequence of Dynkin's stopping games without affecting the optimalty of the saddle-point equilibria and hence completely solving some open problems in the existing literature. Under two quite general (weak) assumptions, we show the existence of the value of the game and the form of saddle-point (optimal) equilibria in the set of shifted strategies. Moreover, our methodology is different from the previous techniques used in the existing literature and is based on purely probabilistic arguments. In the process, we establish an interesting property of the underlying Feller-Markov process and the impossibility of infinite number of impulses in finite time under saddle-point strategies which is crucial for the verification result of the corresponding Isaacs-Bellman equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider expansions of functions into infinite products of power binomials. We also propose a formula for representing the exponential function by such products and formulas for calculating the number of partitions of natural numbers. [ABSTRACT FROM AUTHOR]

Internet of Things (IoT) consists of physical things or objects that are connected through a network of sensors, software, and electronics. Mainly, IoT devices are of restricted processing and storage capacities. On the other hand, infinite storage and processing capacities are available over the cloud. Thus by merging these two methods, the mutual advantages have been discussed in the past years. Due to heterogeneous resource requirements of IoT application's task, it is not so easy to schedule these over the cloud. Existing heuristic-based scheduling strategies had mainly developed considering either minimization of makespan or minimization of cost. But, for the present scenario, an efficient schedule plan is required to schedule IoT applications over cloud that minimizes the execution time along with execution cost while preserving the task dependencies constraints as well as user-defined constraints like budget and deadline. In this paper, Cost–time computational intelligent heuristics based upon PEFT i.e. CTPEFT has been proposed to give a trade-off schedule plan between computational cost and time beneath the user-specified deadline and budget constraints. To validate the effectiveness of the proposed heuristic, extensive simulation experiments have been conducted while considering different synthetic IoT application tasks. CTPEFT has been compared with our previously proposed algorithm, i.e. BDHEFT as well as with other competing algorithms like BHEFT, and HCPPEFT. Simulation results shows that CTPEFT heuristic can generate better cost-makespan trade-off plan as compared to BDHEFT, BHEFT, and HCPPEFT. [ABSTRACT FROM AUTHOR]

This paper concerns a class of fractional impulsive neutral functional differential equations with an infinite delay driven by the Rosenblatt process. A set of sufficient conditions are established for the existence of new mild solutions using fixed point theory. Finally, an illustrative example is provided to demonstrate the applicability of the theoretical result. [ABSTRACT FROM AUTHOR]

Photothermal spectroscopy is a method of measuring the optical absorption and thermal properties of semiconductor materials using high-sensitivity spectroscopic techniques. Heating occurs due to light, which is absorbed but not dissipated by emission. In this paper, a new model is provided that can be used to understand the process of optical thermal transfer and the interaction between elastic plasma waves and heat. The proposed photothermal model is described by the Moore–Gibson–Thompson heat equation. Using the proposed model, the thermal and photoacoustic effects in an infinite isotropic and homogeneous body with a cylindrical cavity of semiconductor material crossed into a fixed magnetic field and subjected to high-intensity laser heat flux were investigated. The inner surface of the cavity is considered to be traction-free, and the carrier density is photogenerated by a laser pulse heat flux that decays exponentially. The numerical calculations for the components of thermal stresses, displacement, temperature field, and carrier density are obtained using the Laplace transform approach. The propagation of heat, elastic, and plasma waves, as well as the distributions of each investigated field, were examined and explained. The comparison is also used to see how different thermal response features, such as thermal relaxation, laser pulse duration, and lifetime, affect the thermoelastic response. [ABSTRACT FROM AUTHOR]

According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer's claim. [ABSTRACT FROM AUTHOR]

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic behaviour is quite well understood. However, recently new examples of transport processes emerged where the corresponding semigroup is not strongly continuous. Due to this lack of strong continuity, there are currently only few results on the long-term behaviour of these semigroups. In this paper, we discuss the asymptotic behaviour for a certain class of these transport processes. In particular, it is proved that the solution semigroups behave asymptotically periodic with respect to the operator norm as a consequence of a more general result on the long-term behaviour by positive semigroups containing a multiplication operator. Furthermore, we revisit known results on the asymptotic behaviour of transport processes on infinite networks and prove the asymptotic periodicity of their extensions to the space of bounded measures. [ABSTRACT FROM AUTHOR]

Every real estate investment decision making, because of the high capital-intensive character of properties, requires careful analysis of information. Availability of the information, market specificity and unpredictable or sudden changes on it cause that all real estate investments are subject to considerable risk and uncertainty. This specificity causes that, one can never be sure, that the collected set of information is complete though reliable for decision inference. The process of property market information collection, from numerical point of view is infinite since the information can be continuously supplemented or clarified. That is the reason for alternative to commonly (classically) used methods search that are effective in the selection of closest solutions optimal for multidimensional real functions, taking into account the global maximum. The paper attempts to decrease the impact of the factors that cause uncertainty on the quality of real estate investment decisions through the tools based on the simulation of the process of natural selection and biological evolution application proposal. The aim of the study is to analyse the potential of the methodology based on genetic algorithms (GA) as part of the automated valuation models component in the uncertainty conditions and support investment decisions on the real estate market. The developed hybrid model (based on genetic algorithm and Hellwig's method compound) allows to select properties adequate to the adopted assumptions, i.e. individuals best suited to the environment. The tool can be used by real estate investment advisors and potential investors. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate a special difference of harmonic numbers. We obtain some limits and inequalities involving harmonic numbers and in the last part of the paper some open problems for investigation are posed. [ABSTRACT FROM AUTHOR]

We consider two types of continued fraction expansions of the generating functions of Cauchy numbers. One type has been often studied by many authors, but another has not. In this paper, we give several continued fraction expansions of hypergeometric Cauchy numbers, shifted Cauchy numbers and leaping Cauchy numbers. In special cases, continued fraction expansions of the classical Cauchy numbers of both kinds are deduced. [ABSTRACT FROM AUTHOR]

In this paper, we describe a Bayesian nonparametric approach to make inference for a spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all spherically symmetric distributions and we derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of the Dirichlet invariant process to a spherically symmetric distribution. In addition, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches the mixtures of Dirichlet processes. Moreover, we develop our approach to obtain the Bayesian nonparametric posterior distribution for functionals of the distribution's support when the support is symmetric with respect to the parallel lines of axes. This suggests a Bayesian nonparametric bootstrapping scheme. The estimates can be derived based on posterior averaging. Then, our simulation results demonstrate that our suggested bootstrapping technique improves the accuracy of the estimates. [ABSTRACT FROM AUTHOR]

In this paper, we present a smoothing Levenberg-Marquardt algorithm for the solution of the semi-infinite programming (SIP) problem. We first reformulate the KKT system of SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing Levenberg-Marquardt algorithm. The feasibility is ensured via the aggregated constraint, and at each iteration of the presented algorithm only a quadratic programming has to be solved. Global and local superlinear convergence of this algorithm is established under a local error bound condition, which is much weaker than the nonsingularity condition. Preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper, by using the best Sobolev constant method, we obtain some new Lyapunov-type inequalities for a class of even-order partial differential equations; the results of this paper are new which generalize and improve some early results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain new inequalities for the logarithmic mean and the complete elliptic integral of the first kind. In order to prove the inequalities, we use the monotonicity property of sequences defined by these functions. Additionally, we apply our approach to previous studies. As a result, we get refinements of known inequalities. [ABSTRACT FROM AUTHOR]

In this paper we propose a method for solving systems of nonlinear inequalities with predefined accuracy based on nonuniform covering concept formerly adopted for global optimization. The method generates inner and outer approximations of the solution set. We describe the general concept and three ways of numerical implementation of the method. The first one is applicable only in a few cases when a minimum and a maximum of the constraints convolution function can be found analytically. The second implementation uses a global optimization method to find extrema of the constraints convolution function numerically. The third one is based on extrema approximation with Lipschitz under- and overestimations. We obtain theoretical bounds on the complexity and the accuracy of the generated approximations as well as compare proposed approaches theoretically and experimentally. [ABSTRACT FROM AUTHOR]

We present a relation between Tsallis’s entropy and generalized Kerridge inaccuracy which is called generalized Shannon inequality and is well-known generalization in information theory and then give its application in coding theory. The objective of the paper is to establish a result on noiseless coding theorem for the proposed mean code length in terms of generalized information measure of order ξ. [ABSTRACT FROM AUTHOR]

This paper proposes a fault tolerant control scheme based on an unknown input observer for a wind turbine system subject to an actuator fault and disturbance. Firstly, an unknown input observer for state estimation and fault detection using a linear parameter varying model is developed. By solving linear matrix inequalities (LMIs) and linear matrix equalities (LMEs), the gains of the unknown input observer are obtained. The convergence of the unknown input observer is also analysed with Lyapunov theory. Secondly, using fault estimation, an active fault tolerant controller is applied to a wind turbine system. Finally, a simulation of a wind turbine benchmark with an actuator fault is tested for the proposed method. The simulation results indicate that the proposed FTC scheme is efficient. [ABSTRACT FROM AUTHOR]

Linear differential equations usually arise from mathematical modeling of physical experiments and real-world problems. In most applications these equations are linked to initial or boundary conditions. But sometimes the solution under consideration is characterized by its asymptotic behavior, which leads to the question how to infer from the asymptotic growth of a solution to its initial values. In this paper we show that under some mild conditions the initial values of the desired solution can be computed by means of a continuous-time analogue of a modified matrix continued fraction. For numerical applications we develop forward and backward algorithms which behave well in most situations. The topic is closely related to the theory of special functions and its extension to higher-dimensional problems. Our investigations result in a powerful tool for solving some classical mathematical problems. To demonstrate the efficiency of our method we apply it to Poincaré type and Kneser's differential equation. [ABSTRACT FROM AUTHOR]

In many real-world engineering applications, a uniform design needs to be conducted in a constrained experimental domain that includes linear/nonlinear and inequality/equality constraints. In general, these constraints make the constrained experimental domain small and irregular in the decision space. Therefore, it is difficult for current methods to produce a predefined number of samples and make the samples distribute uniformly in the constrained experimental domain. This paper presents a two-phase differential evolution for uniform designs in constrained experimental domains. In the first phase, considering the constraint violation as the fitness function, a clustering DE is proposed to guide the population toward the constrained experimental domain from different directions promptly. As a result, a predefined number of samples can be obtained in the constrained experimental domain. In the second phase, maximizing the minimum Euclidean distance among samples is treated as another fitness function. By optimizing this fitness function, the samples produced in the first phase can be scattered uniformly in the constrained experimental domain. The performance of the proposed method has been tested and compared with another state-of-the-art method. Experimental results suggest that our method is significantly better than the compared method in the uniform designs of a new type of automotive crash box and five benchmark test problems. Moreover, the proposed method could be considered as a general and promising framework for other uniform designs in constrained experimental domains. [ABSTRACT FROM AUTHOR]

In this paper, wemainly study somemonotonicity properties for the generalized (p,q) - elliptic integrals and the generalized Grötzsch function. As applications, we obtain some sharp functional inequalities for the generalized Grötzsch function and thus get improvements and extensions of some previous results. [ABSTRACT FROM AUTHOR]