A mass exchange network (MEN), which consists of one or more mass exchangers, is a useful tool to realize pollution prevention in process industries. When a staged column is employed as a mass exchanger to synthesize ...
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A mass exchange network (MEN), which consists of one or more mass exchangers, is a useful tool to realize pollution prevention in process industries. When a staged column is employed as a mass exchanger to synthesize a MEN, the number of trays must be rounded up to the next largest integer after obtaining an optimal design, which increases the capital cost. While designing a chemical process plant, when the capital cost increases, the operating cost should decrease. However, the operating cost was considered to be a fixed value in previous research even if the capital cost increased after rounding up the number of trays. Therefore, the total annual cost (TAC, including capital cost and operating cost) remained higher than the real optimal objective. To solve this problem, an integral function is added to the mathematical model to obtain the optimal MEN structure in this study. The application on two universal MEN synthesis mathematical models based on the Composition-Interval Diagram (CID) and stage-wise superstructure illustrate the practicability of the integral function. These modified models are applied to two examples of coke-oven gas sweetening and dephenolization of wastewater. The optimal results obtained in this study are found to be better in comparison to other works in the literature. This study demonstrates that the integral function can solve a series of MEN synthesis problems involving stage columns. Furthermore, a more accurate design scheme for MENS and a structure with lower TAC can be obtained by this function.
In this study,we consider the global optimization problem in a *** use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the *** on the integral ...
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In this study,we consider the global optimization problem in a *** use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the *** on the integral function,we propose an algorithm for solving the global optimization ***,we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.
This paper studies the exponential stability of continuous-time planar piecewise-linear systems (PPLS). By introducing a novel conception of integral function of PPLS and showing its properties, a sufficient and neces...
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This paper studies the exponential stability of continuous-time planar piecewise-linear systems (PPLS). By introducing a novel conception of integral function of PPLS and showing its properties, a sufficient and necessary condition for the exponential stability is derived. Furthermore, the exponential growth rate of system trajectories can be obtained accurately by computing the convergence radius of integral function. The algorithm for computing the integral function is developed and two examples are given to demonstrate the proposed approach.
An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed f...
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An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm.
This paper studies the exponential stability of linear time-varying (LTV) systems using the recent proposed integral function. By showing the properties of the integral function and applying the Bellman-Gronwall Lemma...
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This paper studies the exponential stability of linear time-varying (LTV) systems using the recent proposed integral function. By showing the properties of the integral function and applying the Bellman-Gronwall Lemma, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, the exponential decay rate of the system trajectories can be obtained by computing the radii of convergence of integral function. The algorithm for computing the integral function is also developed and two classical examples are given to illustrate the proposed approach.
As shown by an example, the integral function f : R-n --> R, defined by f (x) = integral(a)(b) [B(x, t)](+) g(t) dt, may not be a strongly semismooth function, even if g( t) = 1 and B is a quadratic polynomial with...
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As shown by an example, the integral function f : R-n --> R, defined by f (x) = integral(a)(b) [B(x, t)](+) g(t) dt, may not be a strongly semismooth function, even if g( t) = 1 and B is a quadratic polynomial with respect to t and infinitely many times smooth with respect to x. We show that f is a strongly semismooth function if g is continuous and B is affine with respect to t and strongly semismooth with respect to x, i.e., B(x, t) = u(x) t + v(x), where u and v are two strongly semismooth functions in R-n. We also show that f is not a piecewise smooth function if u and v are two linearly independent linear functions, g is continuous and g not equal 0 in [a, b], and n greater than or equal to 2. We apply the first result to the edge convex minimum norm network interpolation problem, which is a two-dimensional interpolation problem.
Ibm :: 1620 :: General Program Library :: 7.0.043 the Numerical Calculation of the Definite integral of a Real function Using Simpsons Rule by published by
Ibm :: 1620 :: General Program Library :: 7.0.043 the Numerical Calculation of the Definite integral of a Real function Using Simpsons Rule by published by
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