Class Of Generalized Functions Research Articles

On Some Classes with Norms of Meromorphic Function Spaces Defined by General Spherical Derivatives

The main concerned target of this article is to define and study some concerned classes of meromorphic function spaces using the general spherical derivatives. The general Besov-type classes of meromorphic functions as well as the general normal functions are considered intensively and both are compared deeply with each other. Specifically, multiple results concerning general meromorphic-type classes as well as non-normal classes are obtained by the help of general spherical derivatives. The concerned results are proved by constructing some specific mild conditions on the sequences of points belonging to the concerned meromorphic-type classes. The obtained results generalize and improve the corresponding previous results in some concerned respects. The concerned proofs and methods are simply presented.

Determining the competition outcome in the chemostat: General response functions and delayed growth

Competitive exclusion has been proven to be true mainly for competition in the chemostat with monotone response functions. For the case with nonmonotone response functions, strong restrictions are imposed on the property of response functions in the literature to ensure the competitive exclusion. In this work, by constructing a novel Liapunov functional, we show that only one species can survive when n species are competing for a single essential resource in the chemostat. The conditions are quite generic and our result applies to chemostat competition models with differential removal rates, delayed growth, and a large class of general response functions including the simplified Holling type IV response functions.

Refinements on Some Classes of Complex Function Spaces

Some weighted classes of hyperbolic function spaces are defined and studied in this paper. Finally, by using the chordal metric concept, some investigations for a class of general hyperbolic functions are also given.

Stability results for second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay

In this paper, we consider a second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay and a very general class of memory kernel functions. Under some suitable conditions and by introducing a suitable Lyapunov functional, we state and prove explicit and general stability results of the energy. We give also some applications to illustrate our results. This work generalizes the previous results without time delay term to those with time-varying delay.

Limit theory of combinatorial optimization for random geometric graphs

In the random geometric graph G(n,rn), n vertices are placed randomly in Euclidean d-space and edges are added between any pair of vertices distant at most rn from each other. We establish strong laws of large numbers (LLNs) for a large class of graph parameters, evaluated for G(n,rn) in the thermodynamic limit with nrnd= const., and also in the dense limit with nrnd→∞, rn→0. Examples include domination number, independence number, clique-covering number, eternal domination number and triangle packing number. The general theory is based on certain subadditivity and superadditivity properties, and also yields LLNs for other functionals such as the minimum weight for the traveling salesman, spanning tree, matching, bipartite matching and bipartite traveling salesman problems, for a general class of weight functions with at most polynomial growth of order d−ε, under thermodynamic scaling of the distance parameter.

Portfolio selection with drawdown constraint on consumption: a generalization model

In this study, we generalize the results of Arun (The Merton problem with a drawdown constraint on consumption. Working paper, 2013) on the optimal consumption and investment problem of an infinitely lived agent who does not accept her consumption falling below a fixed proportion of her historically highest level, the so-called drawdown constraint on consumption. We extend the results to a general class of utility functions. We use the martingale method to study the dual problem, which involves the choice of a maximum consumption process. The dual problem can be formulated as a two-dimensional singular control problem, with the free boundary depending on a state variable of the maximum process. We establish the duality theorem and provide semi-closed form solutions regarding the optimal strategies. To highlight our methodology, we present some special cases of utility functions that do not allow for the dimension reduction considered in Arun (2013).

New integral inequalities for strongly nonconvex functions involving Raina function

In this paper, the authors defined a new general class of functions, the so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional integral operator are obtained. Some new results as a special cases are given as well.

On Sampled–Data Leaderless Consensus Tracking of Nonlinear Multi–Agent Time–Delay Systems

Abstract This paper deals with the sampled-data leaderless consensus tracking problem of nonlinear time-delay multi-agent systems (MASs) over strongly directed networks. In particular, a new methodology for the design of sampled-data controllers achieving the leaderless consensus tracking of nonlinear MASs affected by state-delays is proposed. Firstly, the notion of steepest descent consensus feedback (SDCF), induced by a general class of Lyapunov-Krasovskii functionals, is introduced. Then, it is proved that there exists a suitably small maximum inter-sampling time such that the digital implementation of SDCFs (continuous or not) achieves the leaderless consensus tracking in a semi-global practical sense of the related sampled-data closed-loop MAS. The stabilization in the sample-and-hold sense theory is used as a tool for proving the results. The case of time-varying sampling intervals as well as the stability analysis of the inter-sampling system behaviour is included in the theory here developed. An example is studied in order to validate the results.

A Unified Theory for Robust Bayesian Prediction Under a General Class of Regret Loss Functions

A Unified Theory for Robust Bayesian Prediction Under a General Class of Regret Loss Functions

Present Bias

Present bias is the inclination to prefer a smaller present reward to a larger later reward, but reversing this preference when both rewards are equally delayed. Such behavior violates stationarity of temporal choices, and hence exponential discounting. This paper provides a weakening of the stationarity axiom that can accommodate present‐biased choice reversals. We call this new behavioral postulate Weak Present Bias and characterize the general class of utility functions that is consistent with it. We show that present‐biased preferences can be represented as those of a decision maker who makes her choices according to conservative present‐equivalents, in the face of uncertainty about future tastes.

An Inverse Problem for LTV ODE’s

It is well known that any linear combination of products of polynomials and exponentials (a.k.a. Bohl functions) are annihilated by LTI-ODE’s. In this paper, we consider the more general classes of piecewise Bohl functions and of real analytic functions and present the realization of the latter as solutions of linear differential polynomials with real analytic coefficients. In particular, we show that the minimal order depends solely on the multiplicity of the zeros of the given function. We extend the problem further to meromorphic functions without poles on the real line. We briefly comment on piecewise-defined functions and the nonhomogeneous problem.

Poisson distribution series on a general class of analytic functions

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

A General Class of Control Lyapunov Functions and Sampled-Data Stabilization

Several important contributions toward sampled-data and hybrid feedback stabilization have appeared in the literature. This article extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with a nonzero drift term, under the presence of a generalized control Lyapunov function associated with appropriate Lie algebraic hypotheses concerning the dynamics of the system. The main results of this article constitute a generalization of the well-known “Artstein-Sontag” theorem on asymptotic stabilization by means of an almost smooth feedback controller. The analysis is limited to the affine single-input nonlinear systems with nonzero drift term; however, the results can easily be extended to the multi-input case. An illustrative example of the derived results is included.

Extensions of coefficient estimates for new classes of bi-univalent functions defined by Sǎlǎgean integro-differential operator

Abstract In this paper, we introduce and investigate three new general classes of bi-starlike and bi-convex functions of Ma–Minda type defined by the Sǎlǎgean integro-differential operator. Bounds of the first three coefficients | a 2 | {\lvert a_{2}\rvert} , | a 3 | {\lvert a_{3}\rvert} and | a 4 | {\lvert a_{4}\rvert} are given.

The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

Tail bounds on hitting times of randomized search heuristics using variable drift analysis

AbstractDrift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing,etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, for example the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. On all these problems, the probability of deviating by anr-factor in lower-order terms of the expected time decreases exponentially withr. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Finally, user-friendly specializations of the general drift theorem are given.

General bounds for incremental maximization

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value kin {mathbb {N}} that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such an incremental solution, i.e., the worst ratio over all k between the incremental solution after k steps and an optimum solution of cardinality k. We consider a large class of problems that contains many important cardinality constrained maximization problems like maximum matching, knapsack, and packing/covering problems. We provide a general 2.618-competitive incremental algorithm for this class of problems, and we show that no algorithm can have competitive ratio below 2.18 in general. In the second part of the paper, we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step. This algorithm is known to be 1.58-competitive for submodular objective functions, but it has unbounded competitive ratio for the class of incremental problems mentioned above. We define a relaxed submodularity condition for the objective function, capturing problems like maximum (weighted) d-dimensional matching, maximum (weighted) (b-)matching and a variant of the maximum flow problem. We show a general bound for the competitive ratio of the greedy algorithm on the class of problems that satisfy this relaxed submodularity condition. Our bound generalizes the (tight) bound of 1.58 slightly beyond sub-modular functions and yields a tight bound of 2.313 for maximum (weighted) (b-)matching. Our bound is also tight for a more general class of functions as the relevant parameter goes to infinity. Note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems, and our bounds for the greedy algorithm carry over both.

Towards a general class of parametric probability weighting functions

In this study, we present a novel methodology that can be used to generate parametric probability weighting functions, which play an important role in behavioral economics, by making use of the Dombi modifier operator of continuous-valued logic. Namely, we will show that the modifier operator satisfies the requirements for a probability weighting function. Next, we will demonstrate that the application of the modifier operator can be treated as a general approach to create parametric probability weighting functions including the most important ones such as the Prelec and the Ostaszewski, Green and Myerson (Lattimore, Baker and Witte) probability weighting function families. Also, we will show that the asymptotic probability weighting function induced by the inverse of the so-called epsilon function is none other than the Prelec probability weighting function. Furthermore, we will prove that, by using the modifier operator, other probability weighting functions can be generated from the dual generator functions and from transformed generator functions. Finally, we will show how the modifier operator can be used to generate strictly convex (or concave) probability weighting functions and introduce a method for fitting a generated probability weighting function to empirical data.

Adaptive friction compensations for mechanical systems with measurement delay

Application performance of mechanical positioning systems might not coincide with the theory, mainly due to nonlinearities or imperfections of system models. Although it is sometimes possible to ignore these mismatches, systems generally suffer from performance degradation or even instability eventually. Especially, friction force and time delay are two major factors of these undesired effects. Hence, in this paper, Smith predictor-based controllers and an adaptive Coulomb friction observer are designed to enhance position tracking performance of a mechanical system including time delay. In fact, implemented hierarchical control scheme provides two-degree of freedom to control both velocity and position separately. The proposed observer structure is mainly motivated by the Friedland-Park observer but could be considered as an extension of it which characterizes a general class of nonlinear functions for friction estimation. To assure its functionality with delayed measurements, different velocity predictor schemes are designed and their performances are compared. As a guideline for observer design, some conditions for exponential stability and robustness analysis are presented. Simulation results demonstrate that the proposed control system enhances the tracking performance even when the actual friction is a compound of various static and dynamic terms.

Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes

Spatio-temporal data indexed by sampling locations and sampling time points are encountered in many scientific disciplines such as climatology, environmental sciences, and public health. Here, we propose a novel spatio-temporal expanding distance (STED) asymptotic framework for studying the properties of statistical inference for nonstationary spatio-temporal models. In particular, to model spatio-temporal dependence, we develop a new class of locally stationary spatio-temporal covariance functions. The STED asymptotic framework has a fixed spatio-temporal domain for spatio-temporal processes that are globally nonstationary in a rescaled fixed domain and locally stationary in a distance expanding domain. The utility of STED is illustrated by establishing the asymptotic properties of the maximum likelihood estimation for a general class of spatio-temporal covariance functions. A simulation study suggests sound finite-sample properties and the method is applied to a sea-surface temperature dataset.