On the univalence of an integral operator

Pescar, Virgil

doi:10.1016/j.aml.2010.01.022

Cited by 15 publications

(8 citation statements)

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“…where h x, z, q 1 × 1 is the transfer function of dynamical block, τ and t are the time variables, x and z denote spatial variables defined on the domain Ω, while q is the time forward shift operator, v x, t denotes the system intermediate variable, c Θin z, t ∈ ℝ and υ x, t ∈ ℝ stand for the input and state output of the system at time t separately, and d x, t ∈ ℝ includes the unmodeled dynamics and the stochastic disturbance. In addition, the integral operator is used for spatial operation and sum operator for temporal operation [22,23]. Here only the single-input single-output system is considered for simplicity.…”

Section: Spatial-temporal Wienermentioning

confidence: 99%

Enhanced Oil Recovery for ASP Flooding Based on Biorthogonal Spatial‐Temporal Wiener Modeling and Iterative Dynamic Programming

Shi

2018

Complexity

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Because of the mechanism complexity, coupling, and time-space characteristic of alkali-surfactant-polymer (ASP) flooding, common methods are very hard to be implemented directly. In this paper, an iterative dynamic programming (IDP) based on a biorthogonal spatial-temporal Wiener modeling method is developed to solve the enhanced oil recovery for ASP flooding. At first, a comprehensive mechanism model for the enhanced oil recovery of ASP flooding is introduced. Then the biorthogonal spatial-temporal Wiener model is presented to build the relation between inputs and states, in which the Wiener model is expanded on a set of spatial basis functions and temporal basis functions. After inferring the necessary condition of solutions, these basis functions are determined by the snapshot method. Furthermore, a theorem is proved to identify parameters in the Wiener model. Combined with the least square estimation (LSE), all unknown parameters are determined. In addition, the ARMA model is applied to build the model between states and outputs, whose parameters are identified by recursive least squares (RLS). Thus, the whole modeling process for ASP flooding is finished. At last, the IDP algorithm is applied to solve the enhanced oil recovery problem for ASP flooding based on the identification model to obtain the optimal injection strategy. Simulations on the ASP flooding with four injection wells and nine production wells show the accuracy and effectiveness of the proposed method.

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Section: Spatial-temporal Wienermentioning

confidence: 99%

Enhanced Oil Recovery for ASP Flooding Based on Biorthogonal Spatial‐Temporal Wiener Modeling and Iterative Dynamic Programming

Shi

2018

Complexity

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“…for γ i , η i > 0 with i = 1, n. This operator was studied by Pescar in [3] and Ularu in [5]. We study the properties of this operator on the classes CVH(β) and S * (α).…”

Section: Remark 1 This Class Is Well Defined For Rementioning

confidence: 99%

An integral operator on the classes S*(α) and CVH(β)

Ularu

Breaz

2013

Annales UMCS, Mathematica

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Abstract. The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class CVH(β) and also we estimate the first two coefficients for functions obtained by this operator applied on the class CVH(β). Preliminary and definitions.We consider the class of analytic functions f (z), in the open unit disk, U = {z ∈ C : |z| < 1}, having the form:This class is denoted by A. By S we denote the class of all functions from A which are univalent in U . We denote by K(α) the class of all convex functions of order α (0 ≤ α < 1) that satisfy the inequality:2000 Mathematics Subject Classification. 30C45.

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“…Also, the integral operators in (1.4), (1.5) and (1.6) were studied by Pescar and Breaz [8]. Many univalent conditions associated with these integral operators in (1.1) to (1.6) were obtained by several authors [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…The integral operators in (1.2) and (1.3) were introduced and investigated by Pescar [7]. Also, the integral operators in (1.4), (1.5) and (1.6) were studied by Pescar and Breaz [8].…”

Section: Introductionmentioning

confidence: 99%