Boundedness Assumption Research Articles

Lagrange identity method for microstretch thermoelastic materials

Our paper is concerned with some basic theorems for microstretch thermoelastic materials. By using the Lagrange identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.

On the mean curvature of spacelike surfaces in certain three-dimensional Robertson–Walker spacetimes and Calabi–Bernstein’s type problems

Several uniqueness results for the spacelike slices in certain Robertson–Walker spacetimes are proved under boundedness assumptions either on the mean curvature function of the spacelike surface or on the restriction of the time coordinate on the surface when the mean curvature is a constant. In the nonparametric case, a uniqueness result and a nonexistence one are proved for bounded entire solutions of some constant mean curvature spacelike differential equations.

On the integrability of money-demand functions by the Sidrauski and the shopping-time models

This paper investigates which properties money-demand functions must satisfy so that they are consistent with Lucas’s [Lucas Jr., R.E., 2000. Inflation and welfare. Econometrica 68, 247–274] versions of the Sidrauski and the shopping-time models. We conclude that shopping-time-integrable money-demand functions are necessarily also Sidrauski-integrable, but that the converse is not necessarily true, unless a boundedness assumption on the nominal interest rate is made. Both the log–log with an interest-rate elasticity greater than or equal to one and the semi-log money demands may serve as counterexamples. All the models and results are also extended to the case in which there are several assets in the economy performing monetary functions.

An online gradient method with momentum for two-layer feedforward neural networks

An online gradient method with momentum for two-layer feedforward neural networks is considered. The momentum coefficient is chosen in an adaptive manner to accelerate and stabilize the learning procedure of the network weights. Corresponding convergence results are proved, that is, the weak convergence result is proved under the uniformly boundedness assumption of the activation function and its derivatives, moreover, if the number of elements of the stationary point set for the error function is finite, then strong convergence result holds.

Working the Field: Kumasi Central Market as Community, Employer, and Home

AbstractThe huge Central Market in Kumasi, Ghana is a prized workplace for more than 20,000 traders. Being physically present is a primary work method for market traders, and also for an ethnographer. Lending a hand in various trading tasks clarified the decisions and intentions associated with them, their physical demands, and the politics of the market. The market also made intellectual demands; it immediately challenged the assumptions of homogeneity and boundedness still then rarely problematized for residential communities. Different traders had different relationships to it; that difference was what constituted the market and bound them to it. Translocal ethnography is now beginning to explain how members dispersed over geography and social structure can create a more committed and resilient community. Market commodity groups commanded loyalty precisely because they bridged the most significant conflicts of interest, incorporating the retailers, wholesalers and traveling buyers most likely to quarrel over a sale as buyer and meaning its social institutions as much as its territory. This new perspective on difference also makes a place for the ethnographer, as one more woman making her living from the market. Gender, age, ethnicity, education and class significantly affect the symbolic and material public resources available to traders. Is it so very perverse that they also inflect ethnography?

Confidence Intervals for Negative Binomial Random Variables of High Dispersion

We consider the problem of constructing confidence intervals for the mean of a Negative Binomial random variable based upon sampled data. When the sample size is large, it is a common practice to rely upon a Normal distribution approximation to construct these intervals. However, we demonstrate that the sample mean of highly dispersed Negative Binomials exhibits a slow convergence in distribution to the Normal as a function of the sample size. As a result, standard techniques (such as the Normal approximation and bootstrap) will construct confidence intervals for the mean that are typically too narrow and significantly undercover at small sample sizes or high dispersions. To address this problem, we propose techniques based upon Bernstein's inequality or the Gamma and Chi Square distributions as alternatives to the standard methods. We investigate the impact of imposing a heuristic assumption of boundedness on the data as a means of improving the Bernstein method. Furthermore, we propose a ratio statistic relating the Negative Binomial's parameters that can be used to ascertain the applicability of the Chi Square method and to provide guidelines on evaluating the length of all proposed methods. We compare the proposed methods to the standard techniques in a variety of simulation experiments and consider data arising in the serial analysis of gene expression and traffic flow in a communications network.

Optimal global rates of convergence for nonparametric regression with unbounded data

Estimation of regression functions from independent and identically distributed data is considered. The L 2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates a boundedness assumption on the explanatory variable X is made besides smoothness assumptions on the regression function and moment conditions on the response variable Y . In this article we consider the kernel estimate and show that by replacing the boundedness assumption on X by a proper moment condition the same (optimal) rate of convergence can be shown as for bounded data. This answers Question 1 in Stone [1982. Optimal global rates of convergence for nonparametric regression. Ann. Statist., 10, 1040–1053].

Subset selection strategy

AbstractA new technique for representative subset selection is presented. The advocated method selects unambiguously the most important objects among the calibration set and uses this subset for the model development without significant deterioration in the predictive ability. The method is called boundary subset selection and it is an inherent part of the Simple Interval Calculation (SIC) approach. SIC is a method for linear modeling, which is based on the assumption of error boundedness. The primary SIC consequence is an object status classification (OSClas) that reveals the most influential objects and also designates the most stable and reliable ones. The OSClas is used as the main tool for representative subset selection. The presented results are compared with widely used Kennard–Stone algorithm and D‐optimal design procedure employing three real‐world examples. Copyright © 2008 John Wiley & Sons, Ltd.

Robust adaptive nonlinear control for uncertain control-affine systems and its applications

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H ∞ control is designed that achieves: (i) an H ∞ tracking performance when the external disturbances are L 2 signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L 2 signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio–Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes.

Pressure representation and boundary regularity of the Navier–Stokes equations with slip boundary condition

We first represent the pressure in terms of the velocity in R + 3 . Using this representation we prove that a solution to the Navier–Stokes equations is in L ∞ ( R + 3 × ( 0 , ∞ ) ) under the critical assumption that u ∈ L loc r , r ′ , 3 r + 2 r ′ ⩽ 1 with r ⩾ 3 , while for r = 3 the smallness is required. In [H.J. Choe, Boundary regularity of weak solutions of the Navier–Stokes equations, J. Differential Equations 149 (2) (1998) 211–247], a boundary L ∞ estimate for the solution is derived if the pressure on the boundary is bounded. In our work, we remove the boundedness assumption of the pressure. Here, our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate for L ∞ -norm of u.

Exponential Inequalities for Positively Associated Random Variables and Applications

We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005). By one of the inequalities, we obtain the convergence rate for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate derived by Oliveira (2005) for the above case.

On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization

In this paper, we present new convergence properties of the primal-dual method based on four types of augmented Lagrangian functions in the context of constrained global optimization. Convergence to a global optimal solution is first established for a basic primal-dual scheme under standard conditions. We then prove this convergence property for a modified augmented Lagrangian method using a safeguarding strategy without appealing to the boundedness assumption of the multiplier sequence. We further show that, under the same weaker conditions, the convergence to a global optimal solution can still be achieved by either modifying the multiplier updating rule or normalizing the multipliers in augmented Lagrangian methods.

The expectation-maximization algorithm for ill-posed integral equations: a convergence analysis

The expectation-maximization (EM) algorithm is a convenient tool for approximating maximum likelihood estimators in situations when available data are incomplete, as is the case for many inverse problems. Our focus here is on the continuous version of the EM algorithm for a Poisson model, which is known to perform unstably when applied to ill-posed integral equations. We interpret and analyse the EM algorithm as a regularization procedure. We show weak convergence of the iterates to a solution of the equation when exact data are considered. In the case of perturbed data, similar results are established by employing a stopping rule of discrepancy type under boundedness assumptions on the problem data.

Abstract convexity for nonconvex optimization duality¶

In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions. ¶Dedicated to the memory of Prof. Dr Alexander Moiseevich Rubinov.

Global convergence of an SQP method without boundedness assumptions on any of the iterative sequences

Usual global convergence results for sequential quadratic programming (SQP) algorithms with linesearch rely on some a priori assumptions about the generated sequences, such as boundedness of the primal sequence and/or of the dual sequence and/or of the sequence of values of a penalty function used in the linesearch procedure. Different convergence statements use different combinations of assumptions, but they all assume boundedness of at least one of the sequences mentioned above. In the given context boundedness assumptions are particularly undesirable, because even for non-pathological and well-behaved problems the associated penalty functions (whose descent is used to produce primal iterates) may not be bounded below for any value of the penalty parameter. Consequently, boundedness assumptions on the iterates are not easily justifiable. By introducing a very simple and computationally cheap safeguard in the linesearch procedure, we prove boundedness of the primal sequence in the case when the feasible set is nonempty, convex, and bounded. If, in addition, the Slater condition holds, we obtain a complete global convergence result without any a priori assumptions on the iterative sequences. The safeguard consists of not accepting a further increase of constraints violation at iterates which are infeasible beyond a chosen threshold, which can always be ensured by the proposed modified SQP linesearch criterion.

On the existence of expected multi-utility representations

We prove the following facts related to the expected multi-utility representation of an affine preorder: If the prize space is not compact and if the lottery set consists of all probabilities on the prize space, standard independence and continuity axioms do not guarantee the existence of a (continuous) representation. If the prize space is σ-compact and lotteries have compact support, a representation exists. When the preorder in question is bounded, this result extends to the set of lotteries that consists of all probabilities on the prize space. For the case of monetary lotteries, the boundedness assumption in this last result can be dropped, provided that the preference relation at hand is monotone and risk-averse.

ON THE EXPONENTIAL INEQUALITY FOR NEGATIVE DEPENDENT SEQUENCE

We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.

Comments and further improvements on “New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks”

In this paper, we point out that global Lipschitz condition on the activation functions should be revised and the boundedness assumption of the activation functions in the above paper can be removed based on a nonlinear measure approach. Moreover, we present some improved sufficient conditions which are less conservative than those in the above paper in terms of linear matrix inequality (LMI).

Clarke Subgradients of Stratifiable Functions

We establish the following result: If the graph of a lower semicontinuous real-extended-valued function $f:\mathbb{R} ^{n}\rightarrow\mathbb{R}\cup\{+\infty\}$ admits a Whitney stratification (so in particular if $f$ is a semialgebraic function), then the norm of the gradient of $f$ at $x\in\mbox{dom\,}f$ relative to the stratum containing $x$ bounds from below all norms of Clarke subgradients of $f$ at $x$. As a consequence, we obtain a Morse-Sard type of theorem as well as a nonsmooth extension of the Kurdyka-Lojasiewicz inequality for functions definable in an arbitrary o-minimal structure. It is worthwhile pointing out that, even in a smooth setting, this last result generalizes the one given in [K. Kurdyka, Ann. Inst. Fourier (Grenoble), 48 (1998), pp. 769-783] by removing the boundedness assumption on the domain of the function.

Construction of a multivariate calibration by the simple interval calculation method

Simple interval calculation is a method for linear modeling and for constructing interval estimates of predictions in a multivariate calibration. Simple interval calculation gives results in a convenient interval form with regard to all the existing uncertainties: measurement errors of predictors and responses, discrepancies of bilinear modeling, and so on. In addition, the simple interval calculation method opens new opportunities for constructing an informative classification of object significance. The method is based on only the assumption of the error boundedness; it uses linear programming algorithms for data analysis. This approach differs substantially from the conventional regression methods used in chemometrics and, therefore, is poorly understood by analysts. This paper gives an elementary explanation of the simple interval calculation method illustrated by the simplest model and real examples.