Yan et al. [38] introduced an **inverse** DEA **model** for resource planning, given decision-makers' prefer- ences. Jahanshahloo et al. [39] developed the **inverse** **model** of Yan et al. [38] and presented **inverse** DEA **model** to estimate outputs, given changes in inputs. Ja- hanshahloo et al. [40] developed an **inverse** DEA **model** to estimate inputs, given outputs increase and improve- ments in eciency score. Furthermore, they estimated maximum reduction in inputs without changing e- ciency scores. Jahanshahloo et al. [41] ran a sensitivity analysis by **inverse** DEA **model**. They determined upper and lower bounds for inputs and outputs by two multi-objective **linear** programming problems and converted multi-objective **linear** programme to a **linear** program. Jahanshahloo et al. [42] addressed inter- temporal dependency among eciencies of a DMU o

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full nonlinear dynamics without gaining scheduling tech- niques and timescale separations, which leads to a closed- form suboptimal control law. In [5,6], the back-stepping procedure is synthesized for the purposes of stabilization and trajectory tracking, which is generally robustness applied to the system of parameters uncertainty and un- modeled **dynamic** to some extent. The various types of aerial robot UAV based on quadrotor concept are put forward in [5-8], using the superiority of fix-wing plant and rotor-wing helicopter to enhance the VTOL ability and flying range. So, in general, the **dynamic** **inverse** method is more suitable for various types of aerial robots due to its start from original **model**. In [9], the **dynamic** **inverse** control with zero **dynamic** for non-**linear** affine **model** system is proposed. In [10], the hierarchical flight control is synthesis for rotorcraft-based UAV. In present paper, the hierarchical structure of improved **dynamic** **inverse** method for quadrotor trajectory tracking is pro- posed, which can balance the deviation of **model** inaccu- racy to enhance the robustness of control system.

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To overcome the problem, neural networks studied and provided successfully to capture the dynamics of nonlinear and complex systems have been proposed and formulated [8-13]. Neural networks have several advantages of distributed information processing and the inherent potential for parallel computation. The potential for the processing and approximation relates to operating data without the prior knowledge of the process. They can learn adequately accurate models and give good non-**linear** control when **model** equations are not known or only partial state information is available. Neural networks can be employed to be mathematical **model**, estimator and controller. Kittisupakorn et al. [14] demonstrated **dynamic** neural network modeling for hydrochloric acid recovery acid process to predict the concentration profile of a hydrochloric acid recovery process consisting of double fixed-bed ion exchange columns. Rusinowski and Stanek [15] presented a method and example results of calculations of neural modeling of steam boilers. Charoenniyom et al. [16] applied neural network to be a modeling for the methyl methacrylate production process in a batch reactor and Thampasato et al. [17] proposed neural network modeling for a batch crystallizer. For the process control, Nueaklong et al. [18] investigated neural network modeling for hard chrome electroplating process to predict the plating solution temperature in hard chrome electroplating bath and applied the neural network **inverse** **model** as a controller for controlling plating solution temperature to the desired temperature range. Daosud et al. [19] presented the neural network for **inverse** **model** to be a controller for a steel pickling process. Kittisupakorn et al. [20] presented a multi-layer feedforward neural network based **model** predictive control for a steel pickling process. The neural network for forward **model** is applied as mathematical **model** to predict the state variables in the **model** predictive control algorithm. For use the neural network as an estimator, Arpornwichanop and Shomchoam [21] applied neural network as an estimator to estimate the unmeasured state variables for fed-batch bioreactors.

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The preprocessing algorithm for noise reduction is based on a two-stage Wiener filtering concept. The denoised output signal of the first stage enters a second stage where an additional **dynamic** noise reduction is performed. In contrast to the first filtering stage, a gain factorisation unit is incorporated in the second stage to control the intensity of filtering dependent on the signal-to-noise ratio (SNR) of the signal. The components of the two noise reduction cycles are illustrated in Figure 2. First, the input signal is divided into frames. After estimating the **linear** spectrum of each frame, the power spectral density (PSD) is smoothed along the time axis in the PSD Mean block. A voice activity detector (VAD) determines whether a frame contains speech or background noise, and so both the estimated spectrum of the speech frames and the estimated noise spectrum are used to calculate the frequency domain Wiener filter coe ﬃ cients. To get a Mel-warped frequency domain Wiener filter, the **linear** Wiener filter coeﬃcients are smoothed along the frequency axis using a Mel-filterbank. The Mel-warped **Inverse** Discrete Cosine Transform (Mel IDCT) unit calculates the impulse response of the Wiener filter before the input signal is filtered and passes through a second noise reduction cycle. Finally, the constant component of the filtered signal is removed in the “OFF” block.

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(both B62 and B60) and case 28 in Fig. 1 , and case 36 DR 17 in Fig. 2 . In other cases the dynamics of the fall after the peak are fol- lowed by another rise, and antibodies do not settle at a low level within the ﬁrst three months after operation: case 59 in Fig. 1 , case 36 A24 and cases 61 and 69 in Fig. 2 . They either demon- strate a slow **dynamic** around a certain constant level (case 61 in Fig. 2 ) or change dramatically over the ﬁrst three months (case 59 in Fig. 1 and case 69 in Fig. 2 ). There is no obvious relationship be- tween these dynamical patterns, steady state levels and the occur- rence of AMR episodes. In some cases, as shown above, low steady state levels are observed in the no-AMR group and higher levels or dramatic changes are noticeable in the AMR group. There are also cases with the absence of AMR despite high levels of DSA, or presence of AMR despite low DSA levels. Finally, some patients (e.g. case 36 in Fig. 2 ) rejected the kidney, but had multiple DSAs with one type that rose after the initial fall post-transplant (A24) and another type that kept falling to a low steady level (DR17). This visual analysis demonstrates that there is no certain associa- tion between higher levels of post-transplant DSA and the occur- rence of the rejection episodes.

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Abstract: Hysteresis motors are self starting brushless synchronous motors which are being used widely due to their interesting features. Accurate modeling of the motors is crucial to successful investigating the **dynamic** performance of them. The hysteresis loops of the material used in the rotor and their influences on the parameters of the equivalent circuit are necessary to be taken into consideration adequately. It is demonstrated that some of the equivalent circuit parameters vary significantly with input voltage variation and other operating conditions. In this paper, a comprehensive analysis of a hysteresis motor in the start up and steady state regimes are carried out based on a developed d-q **model** of the motor with time-varying parameters being updated during the simulation time. The equivalent circuit of the motor is presented taking into account the major impact of the input voltage. Simulation results performed in Matlab-Simulink environment prove that the existing simple models with constant parameters can not predict the motor performance accurately in particular for variable speed applications. Swings of torque, hunting phenomenon, improvement of power factor by temporarily increasing the stator voltage and start up behavior of the hysteresis machine are some important issues which can accurately be analyzed by the proposed modeling approach.

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The aim of this study was to forecast the production of rice in Pakistan by using best fitted **model** on time-series data for the period 1981-82 to 2015-16 on production of rice in Pakistan. For forecasting purpose, different **linear** and non-**linear** growth models such as **Linear** trend **model**, Quadratic trend **model**, Cubic **model**, Logarithmic and **Inverse** models were used to find the best fitted **model** for production of rice in Pakistan. The best-fitted **model** for future forecast was chosen based upon highest Theil’s U-Statistic, coefficient of determination (R 2 )

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The most commonly used nonlinear granger causality test is based on the study of Back and Brock (1992). Hiemstra and Jones (1994) further modified it by filtering the **linear** dependence from the series and using the residuals term of the vector autoregression **model** to tests the nonlinear causality. Thus, this test does not use the initial stationary variable. The studies of Kyrtsou and Serletis, (2006) states that the financial time series are highly complex. Moreover, in the presence of such dynamics, **linear** filtering of data using VAR methodology before the application of the Hiemstra and Jones test of nonlinear granger causality can lead to serious distortions (Kyrtsou and Serletis (2005)). Thus, Hiemstra and Jones (1994) test may fail to detect the correct causal relationship. The important point that distinguishes this study from the existing literature is methodology adopted to investigate the **dynamic** relationship between variables of interest. The study examines the **dynamic** relationship between stock index and exchange rates using the nonlinear causality test with a special type of nonlinear structure known as bivariate noisy Mackey–Glass **model** of (Kyrtsou and Terraza (2003) and Kyrtsou and Labys (2006). Moreover, in recent years, there is more interest and research on Indian market data due to the country’s rapid growth and potential opportunities for investors. It is estimated that foreign investment in the Indian stock markets may cross $10 billion-mark by the end of September 2009. Parallel to this, many firms that comprises the stock index (S&P CNX Nifty Index of National Stock Exchange) have American Depository Receipts (ADR’s) or General Depository Receipts (GDR’s) which are traded on the NYSE, NASDAQ or on non-American exchanges. Over the years, Indian Rupee is gradually moving towards full convertibility. The two-way fungibility of ADRs/GDRs allowed by RBI has also possibly enhanced the linkages between the stock and foreign exchange markets in India. This background makes the study more interesting and worthy to investigate, whether the **dynamic** linkages between foreign exchange of Indian Rupee/USA Dollar (INR/USD) and stock market index in India exhibits different characteristics vis-à-vis developed market and other emerging markets.

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So at this point, the inverse model to be used will conserve mass and linear vorticity on a single layer for the Southern Ocean, making use of all available hydrographic data to get the [r]

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The format of the paper is as follows. In section 2 we discuss the proposed **model**. Predictive distribu- tions and their Monte Carlo estimates are also dis- cussed. Section 3 presents an illustration. It consists of compositions of vehicles produced by USA, Japan and other countries over the time period 1947-1987. Section 4 contains some concluding remarks.

The common approach for source-term determination is to combine data measured in the environment (e.g., radionu- clide concentrations downwind of the release site) with an atmospheric transport **model** in a top-down approach. Agree- ment between a **model** with calculated source term and measurements can be modeled and optimized using various parameter-estimating methods including the Bayesian ap- proach (Bocquet, 2008), maximum entropy principle (Boc- quet, 2005b), or cost function optimization (Eckhardt et al., 2008). For computational reasons, this problem is typically formulated as a variant of **linear** regression. The vector of measurements is assumed to be explained using a **linear** **model** with a known source-receptor sensitivity (SRS) matrix determined using an atmospheric dispersion **model** (Seibert and Frank, 2004) and an unknown source-term vector. Sim- ple solution via the ordinary least-squares method typically yields a poor solution because the problem is often only par- tially determined and ill-constrained by the available mea- surement data. Many regularization schemes taking into ac- count physically plausible ranges of parameter values such as non-negativity of the emissions, or other a priori infor- mation, for instance on the duration of release, have been proposed providing more realistic solutions. However, es- pecially if the a priori information is incomplete, the reg- ularization terms can also contain tuning parameters which are often selected manually and subjectively. The solution is subsequently highly sensitive to their choice. Therefore, many authors proposed inversion schemes to reduce the de- pendency on these parameters. Davoine and Bocquet (2007) formulated the inversion problem as minimization problem with Tikhonov regularization term. A similar **model** was used by Winiarek et al. (2012), where covariance matrices of both observation errors and source term are assumed to be diagonal with identical elements on each diagonal. The positivity of the source term is enforced using truncation of negative estimates. Three estimation methods were stud- ied to infer **model** parameters: L-curve, Desroziers’ scheme (Desroziers et al., 2005), and brute force using maximum

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fundamental problem to reconstruct images from noisy observations of Radon data. Compared with traditional methods, Colona, Easley and etc. apply shearlets to deal with the **inverse** problem of the Radon transform and receive more eﬀective reconstruction. This paper extends their work to a class of **linear** operators, which contains Radon, Bessel and Riesz fractional integration transforms as special examples. MSC: 42C15; 42C40

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We report on a methodology for identiﬁng the source term based on a non-**linear** least squares regression and **linear** regression coupled with the solution of an advection-diﬀusion equation for an instantaneous point source.This method only depends on the initial guess of the release time and the approximate value of this time can be easily calculated. Furthermore, we ﬁnd that reliably es- timating the parameters requires concentration measurements at a minimum of three downstream locations.

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Abstract: This paper examines the nexus of working capital management and financial performance of selected multinational food and beverages industries in Nigeria for the period between 2006 and 2014 and establishes its linkage with risk-return theory. An explanatory research design is adopted and the secondary data used were gathered from 5 purposively selected quoted food and beverages companies using GLS panel regression analysis. The pooled regression shows that account receivable ratio (ARR) and debt ratio (DER) have negative effect but significant at 1%, working capital (WCA) is also significant at 5% but had positive effect, however, sales growth (SGR) was insignificant. It is also discovered from the Fixed Effect Estimation that working capital management variables such as account receivable ratio (ARR) and debt ratio (DER) have negative effect but significant at 1%, working capital (WCA) is also significant at 5% but has positive effect, while sales growth (SGR) has negative effect but insignificant to the performance of the companies. This signifies reduction in the performances of food and beverages industries which calls for urgent attention since they are posting **inverse** effect. The unison in both estimations shows that those variables are the major factors influencing the performance of food and beverages industries in Nigeria and thus, it is concluded that the management board of these industries should restructure their working capital management policy as it has the tendency of affecting the dividend policy and firms’ liquidity, which invariably affects the maximization of shareholders’ wealth. This can only be done when managers reduce account receivable days; ensure proper debt management technique, improve sales strategies to enhance sales growth as well as maintain optimal working capital level to reflect the risk-return theory of firms.

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Some future study suggestions can be made. The rate dependency of materials should be included. The plastic properties should be defined more carefully and they should correspond better the real nuclear power plant materials. Also, different types of supports and especially more spring-like and softer supports should be studied instead of the very rigid one (when elastic) considered here. The support structure was too complicated to be modelled with only a single spring element, if the nonlinear **dynamic** behaviour and the effects of the surrounding civil structures are to be taken into account. The spring elements are adequate when a longer section of a pipe line is examined and no extensive displacements and plastic hinges are anticipated. Especially the “tube support elements” are worth studying more in the future. In case of pipe or elbow elements, the pipe break load should also be modelled with point loads that have certain predetermined amplitude. A denser mesh would give more detailed local stress results.

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To formulate the above mentioned problem, a set of motion equations and a criterion equation should be solved together. This situation forms a problem in optimal control domain. There are two different methods to solve this problem. The first is the indirect mathematical approach which gives us a unique solution [14] and the second is the direct search approach. This method searches between all solutions of motion equations to reach a solution which fulfills the criterion equation. We choose the latter because of its easier use and faster response. But the direct search without any specific search patterns is not suitable in this special problem. There are many algorithms to conduct the search approach like Genetic algorithm [16] and **dynamic** programming. The former is suitable when we try to find a new optimal trajectory and the latter is more suitable when we try to evaluate the previous trajectories.

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These experimental results demonstrate once again the utility of the SDP estimation approach in highlighting where problems exist in nonlinear modelling and how they may be corrected. They also show how SDP estimation can be used as a tool in Data-Based Mechanistic (DBM) modelling. This is an inductive modelling strategy where less weight is placed on prior assumptions and more weight on the information in the experimental data. Only after carefully analysing the experimental data using appropriate **model** identification and signal processing tools, such as SDP estimation, does the modeller consider, at the mechanistic stage of the procedure, the prior assumptions and hypotheses, in order to see if these are compatible with the identified, data-based **model**. Or, if the data-based **model** is found to be deficient in any ways, as in this case when all the links are moving simultaneously, the modeller must consider whether new data need to be collected in order to examine these deficiencies using a better experimental design. And then, depending on the new SDP estimation results, the parametric form of the nonlinearities can be modified and re-estimated.

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Sun et al. (2012) simulated the thermo-hydraulic behavior of the Canadian SCWR using a simple 1D **model**. The direct Niquist array method was used to decouple the system and pre-compensators were used to convert the system to a diagonally dominant form. However, although the control system design was able to keep the system at stable condition when there were perturbances, the **model** used for the simulation of the reactor was too simple. Then, Sun et al. (2015) included a feed-forward control method in the control system design to reduce the effect of the reactor power on the steam temperature. The results showed that the steam temperature variation due to the disturbances on the reactor power could be significantly suppressed. Later, Sun et al. (2017) found that the response magnitude of the steam temperature to the same amount of feedwater flow rate disturbance at a high power level was smaller than that at a low power level. Then, the original control system design will be not effective when the working conditions changed. A **linear** parameter-varying strategy was proposed to solve such problems. The results showed that the **linear** parameter-varying (LPV) controller not only stabilized the steam temperature under different disturbances but also efficiently suppressed the steam temperature variation at different power levels. Maitri et al. (2017) used the results from CFD simulations of the supercritical water flow in a circular cube by FLUENT to derive the **linear** **dynamic** models around the operating point based on the system identification techniques. Then the **linear** **dynamic** models were validated with the CFD results in the 2D tube flows.

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In approximation theory, the results, which determine structural characteristics of functions from their degree of approximation, are known as **inverse** theorems. There are many-many generalizations of direct and **inverse** results [1, 4, 6, 7, 9, 11]. The excellent textbooks of Timan [10] and of DeVore and Lorentz [3] contain an abundance of information on direct and **inverse** theorems for approximation by algebraic and trigonometric polynomials. In the present paper we study **inverse** approximation estimate for these operators, which were defined as

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path of the boiler. The temperature regime is ensured by increasing or decreasing the amount of water injected into the desuperheater. In the existing power system, a typical automatic control scheme is mainly used, which is called the cascade temperature control system for superheated steam, the control circuit of which includes a PI controller and a correction device [8, 13]. The practice of operating such a system shows that with significant changes in the task, i.e. the desired values of the parameters of the temperature regime, there is a need to reconfigure the values of the coefficients of its control loop. In fact, this is an important objective sign that the functioning of the control system proceeds under conditions of a priori uncertainty. Indeed, the analysis of the operational characteristics of the superheater shows that the control object has a variable value of transport delay, its **dynamic** properties substantially depend on the oxygen content in the exhaust gases, steam consumption, heating surface contamination, as well as on operational factors - load, type and type of fuel burned, conditions of heating surfaces, excess air, etc. [1]. In addition [11], obtaining a mathematical **model** of a superheater is usually associated with the use of experimental methods, in particular, the method of acceleration curves, and, as a result, the mathematical description a priori becomes inaccurate. Thus, the development of a temperature control system for a superheater operating under conditions of a priori uncertainty is expediently carried out using adaptive control methods.

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