Bounded Functions Research Articles

Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function

We investigate the behavior of the unbounded cylinder function F x = ∫ 0 T α 1 t d x t 2 k ⋅ ∫ 0 T α 2 t d x t 2 k ⋅ ⋯ ⋅ ∫ 0 T α n t d x t 2 k , k = 1,2 , … whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C 0 0 , T .

Some growth estimations based on $(p,q)$-$\varphi $ relative Gol'dberg type and $(p,q)$-$\varphi $ relative Gol'dberg weak type of entire functions of several complex variables

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of $(p,q)$-$\varphi $ relative Gol'dberg type and $(p,q)$-$\varphi $ relative Gol'dberg weal type where $p$ , $q$ are positive integers and $\varphi (R):[0,+\infty )\rightarrow (0,+\infty )$ is a non-decreasing unbounded function.

Robust least squares one-class support vector machine

Abstract In comparison with the conventional one-class support vector machine (OCSVM), least squares OCSVM (LS-OCSVM) can describe similarity between a new-coming sample and training set more accurately. However, LS-OCSVM is very sensitive to outliers in training set. The main reason lies that the values of square error function for outliers are relatively large, which makes LS-OCSVM put more emphasis on these outliers. To enhance the robustness of LS-OCSVM against outliers, a novel robust LS-OCSVM based on correntropy loss function is proposed. As a result, the unbounded convex square loss function of LS-OCSVM is substituted by a bounded nonconvex correntropy loss function. Experimental results on synthetic and benchmark data sets show that robust LS-OCSVM possesses better anti-outlier and generalization abilities in comparison with its related approaches.

Best Multiplier Approximation of Unbounded Periodic Functions in L_(p,∅_n ) (B),B=[0,2π] Using Discrete Linear Positive Operators

The purpose of this paper is to find the best multiplier approximation of unbounded functions in –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.

English

We discuss the existence of the current gkT, k ∈ ℕ for positive and closed currents T and unbounded plurisubharmonic functions g. Furthermore, a new type of weighted Lelong number is introduced under the name of weight k Lelong number.

A remark on big Birkhoff sums in d-decaying Gauss like iterated function systems

Recently, Liao and Rams [10] considered certain infinite iterated function systems that are natural generalizations of Gauss map. They studied the increasing rate of Birkhoff sums in such systems with polynomial decay of the derivative and calculated the Hausdorff dimensions of the sets of points whose Birkhoff sums share the same increasing rate for different unbounded potential functions. In this remark, we investigate the critical cases for the growth rate function which are not discussed in [10].

Randomized nonlinear one-class support vector machines with bounded loss function to detect of outliers for large scale IoT data

Exponential growth of large scale data industrial internet of things is evident due to the enormous deployment of IoT data acquisition devices. Detection of unusual patterns from large scale IoT data is important though challenging task. Recently, one-class support vector machines is extensively being used for anomaly detection. It tries to find an optimal hyperplane in high dimensional data that best separates the data from anomalies with maximum margin. However, the hinge loss of traditional one-class support vector machines is unbounded, which results in larger loss caused by outliers affecting its performance for anomaly detection. Furthermore, existing methods are computationally complex for larger data. In this paper, we present novel anomaly detection for large scale data by using randomized nonlinear features in support vector machines with bounded loss function rather than finding optimized support vectors with unbounded loss function. Extensive experimental evaluation on ten benchmark datasets shows the robustness of the proposed approach against outliers such as 0.8239, 0.7921 , 0.7501, 0.6711 , 0.6692, 0.4789 , 0.6462 , 0.6812 , 0.7271 and 0.7873 accuracy for Gas Sensor Array, Human Activity Recognition, Parkinson’s, Hepatitis, Breast Cancer, Blood Transfusion , Heart, ILPD and Wholesale Customers datasets respectively. In addition to this, introduction of randomized nonlinear feature helps to considerably decrease the computational complexity and space complexity from O(N3) to O(Bkn) and O(N2) to O(Bkn). Thus, very attractive for larger datasets.

On Different Relative Growth Factors of Entire Functions

In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.

Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

In this paper, we propose a non parametric M-estimator of the regression function and we investigate its asymptotic properties, when the response variable is subject to both random left truncation and right censoring. In most works, non parametric M-estimation requires the use of an objective function ψ supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform consistency rate is established under α-mixing dependence. A large simulation study with one and bi-dimensional regressor is conducted for fixed and local bandwidths to highlight the good behavior of our estimator.

Enclosure of the numerical range and resolvent estimates of non-selfadjoint operator functions

In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates. The enclosure and upper estimate of the norm of the resolvent are optimal given the estimate of the joint numerical range.

Stability and Synchronization of a Fractional Neutral Higher-Order Neural Network System

Abstract We discuss the stability and synchronization of some neural network systems with more than one feature. They are of higher-order, of fractional order and also involving delays of neutral type. Each one of these features presents substantial difficulties to overcome. We prove stability and synchronization of Mittag-Leffler type. This rate is fairly reasonable in case of fractional order. This leads us to prove a neutral fractional version of the well-known Halanay inequality which is interesting by itself. Another feature of the present work is the treatment of unbounded activation functions. The condition of uniform boundedness of the activation functions was commonly used in the literature.

An optimal control approach to day-to-day congestion pricing for stochastic transportation networks

Congestion pricing has become an effective instrument for traffic demand management on road networks. This paper proposes an optimal control approach for congestion pricing for day-to-day timescale that incorporates demand uncertainty and elasticity. Travelers make the decision to travel or not based on the experienced system travel time in the previous day and traffic managers take tolling decisions in order to minimize the average system travel time over a long time horizon. We formulate the problem as a Markov decision process (MDP) and analyze the problem to see if it satisfies conditions for conducting a satisfactory solution analysis. Such an analysis of MDPs is often dependent on the type of state space as well as on the boundedness of travel time functions. We do not constrain the travel time functions to be bounded and present an analysis centered around weighted sup-norm contractions that also holds for unbounded travel time functions. We find that the formulated MDP satisfies a set of assumptions to ensure Bellman’s optimality condition. Through this result, the existence of the optimal average cost of the MDP is shown. A method based on approximate dynamic programming is proposed to resolve the implementation and computational issues of solving the control problem. Numerical results suggest that the proposed method efficiently solves the problem and produces accurate solutions.

A New Metric Yielding a Richer Class of Unbounded Functions Having Compact Hulls in the Shift Flow

Compact subspaces of function spaces with the shift flow figure prominently into the study of dynamical systems where the evolution variable (usually time) is $$\mathbb {R}, \mathbb {Z}, \mathbb {R}^+$$ or $$\mathbb {Z}^+$$ , i.e. continuous or discrete flows or semi-flows. Many important theories depend on this compactness. Up to this point theorems guaranteeing compactness have been limited to three function spaces. These are the functions continuous on $$\mathbb {R}$$ with the topology of uniform convergence on compact subsets of $$\mathbb {R}$$ , the space $$L^p_{loc}(\mathbb {R})$$ with the $$L^p_{loc}(\mathbb {R})$$ topology and finally the non metrizable space $$L^{\infty }_{loc}(\mathbb {R})$$ with an induced weak $$^*$$ topology. In this publication we introduce a new metric that takes e.g. unbounded rapidly oscillatory functions and shows that their hulls are compact in the shift flow. This extends the results obtained in the 1970’s on Lifting Theorems and Spectral Theory by the author and George Sell, as well as any application involving a compact dynamical system.

Growth, relations and prime spectrum of monomial algebras

We show that monomial algebras defined by r_n relations of each degree can (under mild assumptions) be mapped onto prime monomial algebras with prescribed growth functions tightly bounded by any function growing slower than r_n . Using the same method, we are able to construct finitely generated, prime monomial algebras with GK-dimension 2 admitting arbitrarily long chains of prime ideals, providing an answer to a question of Bergman from 1989. Unlike the previously known examples, our algebras are computable, concretely constructed and concrete upper bounds of the form n^2f(n) can be put on their growth rates, for arbitrarily slow unbounded non-decreasing function f .

Equidistribution on homogeneous spaces and the distribution of approximates in Diophantine approximation

The present paper is concerned with equidistribution results for certain flows on homogeneous spaces and related questions in Diophantine approximation. Firstly, we answer in the affirmative, a question raised by Kleinbock, Shi and Weiss regarding equidistribution of orbits of arbitrary lattices under diagonal flows and with respect to unbounded functions. We then consider the problem of Diophantine approximation with respect to rationals in a fixed number field. We prove a number field analogue of a famous result of W. M.Schmidt which counts the number of approximates to Diophantine inequalities for a certain class of approximating functions. Further we prove "spiraling" results for the distribution of approximates of Diophantine inequalities in number fields. This generalizes the work of Athreya, Ghosh and Tseng as well as Kleinbock, Shi and Weiss.

Robust bounded control for nonlinear uncertain systems with inequality constraints

A novel bounded control for nonlinear uncertain systems with inequality constraints is considered. First, a state transformation is applied to satisfy the inequality constraints of the controlled outputs. Therefore, the controlled outputs are within the desired bounds. Next, a diffeomorphism is introduced for the control inputs. Based on that, the control inputs are transformed to be bounded functions. The maximum and minimum of the control inputs can be artificially set by choosing a proper bounding function. This control scheme is able to guarantee uniform boundedness and uniform ultimate boundedness. The simulation shows that the control cost of the novel bounded control and the error of the controlled system are smaller than LQR control, regardless of the uncertainty.

Relative (p,q)-φ order and relative (p,q)-φ type based on some growth properties of composite p-adic entire functions

Let K be a complete ultrametric algebraically closed field and A (K) be the K-algebra of entire functions on K. For any p adic entire functions f ∈ A (K) and r > 0, we denote by |f| (r) the number sup {|f (x) | : |x| = r} where |·| (r) is a multiplicative norm on A (K) . In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-ϕ order, relative (p, q)-ϕ type and relative (p, q)-ϕ weak type where p, q are any two positive integers and ϕ (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

Permutations with Orders Coprime to a Given Integer

Let $m$ be a positive integer and let $\rho(m,n)$ be the proportion of permutations of the symmetric group $\mathrm{Sym}(n)$ whose order is coprime to $m$. In 2002, Pouyanne proved that $\rho(n,m)n^{1-\frac{\phi(m)}{m}}\sim \kappa_m$ where $\kappa_m$ is a complicated (unbounded) function of $m$. We show that there exists a positive constant $C(m)$ such that, for all $n \geq m$,\[C(m) \left(\frac{n}{m}\right)^{\frac{\phi(m)}{m}-1} \leq \rho(n,m) \leq \left(\frac{n}{m}\right)^{\frac{\phi(m)}{m}-1}\]where $\phi$ is Euler's totient function.

Global Lagrange Stability of Inertial Neutral Type Neural Networks with Mixed Time-Varying Delays

This paper deals with the Lagrange stability of inertial neutral type neural networks with mixed time-varying delays. Two different types of activation functions are considered, including bounded and general unbounded activation functions. Under a proper variable transformation, the original inertial system is converted to a first order differential network. Based on Lyapunov method and applying inequality techniques and analytical method, some sufficient criteria are derived to ensure the global Lagrange exponential stability of the addressed neural networks. Moreover, the global exponential attractive sets are established. These results here generalize and improve the earlier publications on inertial neural networks. Finally, some numerical examples with simulations are given to demonstrate the effectiveness of our theoretical results.

Approximation by Generalized Lupaş Operators Based on q-Integers

The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.