Search results for: fractional order bounded variation

Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

Abstract:

The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: Control, limits cycle, robot, stability.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: S. Nagheli, N. Samani, D. A. Barry

Abstract:

In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle.

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: P. Chaipanya, P. Uthansakul, M. Uthansakul

Abstract:

This paper proposes a vertical beamforming concept to a cellular network employing Fractional Frequency Reuse technique including with cell sectorization. Two different beams are utilized in cell-center and cell-edge, separately. The proposed concept is validated through computer simulation in term of SINR and channel capacity. Also, comparison when utilizing horizontal and vertical beam formation is in focus. The obtained results indicate that the proposed concept can improve the performance of the cellular networks comparing with the one using horizontal beamforming.

Keywords: Beamforming, Fractional Frequency Reuse, Inter- Cell Interference, cell sectorization.

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Authors: Shinji Oouchi, Hajime Nomura, Kung-Da Wu, Yong-Run Chen, Jui-Pin Hung

Abstract:

This paper presents the variation of the dynamic characteristics of a spindle with the change of bearing preload. The correlations between the variation of bearing preload and fundamental modal parameters were first examined by conducting vibration tests on physical spindle units. Experimental measurements show that the dynamic compliance and damping ratio associated with the dominating modes were affected to vary with variation of the bearing preload. When the bearing preload was slightly deviated from a standard value, the modal frequency and damping ability also vary to different extent, which further enable the spindle to perform with different compliance. For the spindle used in this study, a standard preload value set on bearings would enable the spindle to behave a higher stiffness as compared with others with a preload variation. This characteristic can be served as a reference to examine the variation of bearing preload of spindle in assemblage or operation.

Keywords: Dynamic compliance, Bearing preload, Modal damping.

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Authors: Elteyeb Eljack, Takashi Ohta

Abstract:

Proper orthogonal decomposition (POD) is used to reconstruct spatio-temporal data of a fully developed turbulent channel flow with density variation at Reynolds number of 150, based on the friction velocity and the channel half-width, and Prandtl number of 0.71. To apply POD to the fully developed turbulent channel flow with density variation, the flow field (velocities, density, and temperature) is scaled by the corresponding root mean square values (rms) so that the flow field becomes dimensionless. A five-vector POD problem is solved numerically. The reconstructed second-order moments of velocity, temperature, and density from POD eigenfunctions compare favorably to the original Direct Numerical Simulation (DNS) data.

Keywords: Pattern Recognition, POD, Coherent Structures, Low dimensional modelling.

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Authors: Jianbo Hu, Hongbao Wang

Abstract:

The widely used Total Variation de-noising algorithm can preserve sharp edge, while removing noise. However, since fixed regularization parameter over entire image, small details and textures are often lost in the process. In this paper, we propose a modified Total Variation algorithm to better preserve smaller-scaled features. This is done by allowing an adaptive regularization parameter to control the amount of de-noising in any region of image, according to relative information of local feature scale. Experimental results demonstrate the efficient of the proposed algorithm. Compared with standard Total Variation, our algorithm can better preserve smaller-scaled features and show better performance.

Keywords: Adaptive, de-noising, feature scale, regularizationparameter, Total Variation.

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Authors: Mert Turanli, Hakan Temeltas

Abstract:

In this paper, we present an adaptive controller for decentralized coordination problem of multiple non-holonomic agents. The performance of the presented Multi-Agent Bounded Gain Forgetting (BGF) Composite Adaptive controller is compared against the tracking error criterion with a Feedback Linearization controller. By using the method, the sensor nodes move and reconfigure themselves in a coordinated way in response to a sensed environment. The multi-agent coordination is achieved through Centroidal Voronoi Tessellations and Coverage Control. Also, a consensus protocol is used for synchronization of the parameter vectors. The two controllers are given with their Lyapunov stability analysis and their stability is verified with simulation results. The simulations are carried out in MATLAB and ROS environments. Better performance is obtained with BGF Adaptive Controller.

Keywords: Adaptive control, Centroidal Voronoi Tessellations, composite adaptation, coordination.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Yanping Liao, Congcong He, Ruigang Zhao

Abstract:

The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Keywords: Constraint parameters, derivative matrix, magnetocardiography, regular term, total variation.

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Authors: Yusuke Uchiyama, Hidetoshi Konno

Abstract:

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.

Keywords: sub-Poisson statistics, hyper gamma distribution, fractional Poisson configuration.

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Authors: Emma K. Sales, Nilda G. Butardo

Abstract:

The project was undertaken to determine the effects of modified tissue culture protocols e.g. age of culture and hormone levels (2,4-D) in generating somaclonal variation. Moreover, the utility of molecular markers (SSR and MSAP) in sorting off types/somaclones were investigated.

Results show that somaclonal variation is in effect due to prolonged subculture and high 2,4-D concentration. The resultant variation was observed to be due to high level of methylation events specifically cytosine methylation either at the internal or external cytosine and was identified by methylation sensitive amplification polymorphism (MSAP).Simple sequence repeats (SSR) on the other hand, was able to associate a marker to a trait of interest.

These therefore, show that molecular markers can be an important tool in sorting out variation/mutants at an early stage.

Keywords: Methylation, MSAP, somaclones, SSR, subculture, 2, 4-D.

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Authors: Leila Fatemi, Morteza Moradi, Azadeh Mansouri

Abstract:

In this paper, the modified optimal sliding mode control with a proposed method to design a sliding surface is presented. Because of the inability of the previous approach of the sliding mode method to design a bounded and suitable input, the new variation is proposed in the sliding manifold to obviate problems in a structural system. Although the sliding mode control is a powerful method to reject disturbances and noises, the chattering problem is not good for actuators. To decrease the chattering phenomena, the optimal control is added to the sliding mode control. Not only the proposed method can decline the intense variations in the inputs of the system but also it can produce the efficient responses respect to the sliding mode control and optimal control that are shown by performing some numerical simulations.

Keywords: Structural Control, optimal control, optimal sliding mode controller, modified sliding surface.

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Authors: Suparat Niwitpong

Abstract:

In this paper we proposed two new confidence intervals for the normal population mean with known coefficient of variation. This situation occurs normally in environment and agriculture experiments where the scientist knows the coefficient of variation of their experiments. We propose two new confidence intervals for this problem based on the recent work of Searls [5] and the new method proposed in this paper for the first time. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. Monte Carlo simulation will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.

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Authors: Aras Adhami Mirhoseini, Mohammad J. Yazdanpanah

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In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

Keywords: Sliding mode control, Strict-feedback form, Unmatched uncertainty, output regulation.

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Authors: M. Fadlallah, G. Ghibaudo, C. G. Theodorou

Abstract:

The dynamic variation in memory devices such as the Static Random Access Memory can give errors in read or write operations. In this paper, the effect of low-frequency and random telegraph noise on the dynamic variation of one SRAM cell is detailed. The effect on circuit noise, speed, and length of time of processing is examined, using the Supply Read Retention Voltage and the Read Static Noise Margin. New test run methods are also developed. The obtained results simulation shows the importance of noise caused by dynamic variation, and the impact of Random Telegraph noise on SRAM variability is examined by evaluating the statistical distributions of Random Telegraph noise amplitude in the pull-up, pull-down. The threshold voltage mismatch between neighboring cell transistors due to intrinsic fluctuations typically contributes to larger reductions in static noise margin. Also the contribution of each of the SRAM transistor to total dynamic variation has been identified.

Keywords: Low-frequency noise, Random Telegraph Noise, Dynamic Variation, SRRV.

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Authors: N. Ghatwary, A. Ahmed, H. Jalab

Abstract:

In this paper, an approach for the liver tumor detection in computed tomography (CT) images is represented. The detection process is based on classifying the features of target liver cell to either tumor or non-tumor. Fractional differential (FD) is applied for enhancement of Liver CT images, with the aim of enhancing texture and edge features. Later on, a fusion method is applied to merge between the various enhanced images and produce a variety of feature improvement, which will increase the accuracy of classification. Each image is divided into NxN non-overlapping blocks, to extract the desired features. Support vector machines (SVM) classifier is trained later on a supplied dataset different from the tested one. Finally, the block cells are identified whether they are classified as tumor or not. Our approach is validated on a group of patients’ CT liver tumor datasets. The experiment results demonstrated the efficiency of detection in the proposed technique.

Keywords: Fractional differential (FD), Computed Tomography (CT), fusion.

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Authors: Madhukar Nagare, Pankaj Dutta

Abstract:

Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n fuzzy observations in a newsvendor inventory setting in presence of fuzzy random variable demand capturing both fuzzy perception and randomness of customer demand. The stress of this paper is in providing solution procedure that attains optimality in two steps with demand information availability in linguistic phrases leading to fuzziness along with stochastic variation. The first step of solution procedure identifies and prefers one best fuzzy opinion out of all expert opinions and the second step determines optimal order quantity from the selected event that maximizes profit. The model and solution procedure is illustrated with a numerical example.

Keywords: Fuzzy expected value, Fuzzy random demand, Hybrid uncertainty, Optimal order quantity, Single-period inventory

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Authors: Makoto Nagatomo, Yasuo Uchida, Makoto Sakamoto, Tuo Zhang, Tatsuma Kurogi, Takao Ito, Tsunehiro Yoshinaga, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani

Abstract:

This paper presents a four-dimensional computational model, k-neighborhood template A-type three-dimensional bounded cellular acceptor (abbreviated as A-3BCA(k)), and discusses the hierarchical properties. An A-3BCA(k) is a four-dimensional automaton which consists of a pair of a converter and a configuration-reader. The former converts the given four-dimensional tape to the three- and two- dimensional configuration and the latter determines the acceptance or nonacceptance of given four-dimensional tape whether or not the derived two-dimensional configuration is accepted. We mainly investigate the difference of the accepting power based on the difference of the configuration-reader. It is shown that the difference of the accepting power of the configuration-reader tends to affect directly that of the A-3BCA(k) for the case when the converter is deterministic. On the other hand, results are not analogous for the nondeterministic case.

Keywords: Cellular acceptor, configuration-reader, converter, finite automaton, four-dimension, on-line tessellation acceptor, parallel/sequential array acceptor, turing machine.

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Authors: Mahdi Yaghobi, Mohammad Haeri

Abstract:

The current methods of predictive controllers are utilized for those processes in which the rate of output variations is not high. For such processes, therefore, stability can be achieved by implementing the constrained predictive controller or applying infinite prediction horizon. When the rate of the output growth is high (e.g. for unstable nonminimum phase process) the stabilization seems to be problematic. In order to avoid this, it is suggested to change the method in the way that: first, the prediction error growth should be decreased at the early stage of the prediction horizon, and second, the rate of the error variation should be penalized. The growth of the error is decreased through adjusting its weighting coefficients in the cost function. Reduction in the error variation is possible by adding the first order derivate of the error into the cost function. By studying different examples it is shown that using these two remedies together, the closed-loop stability of unstable nonminimum phase process can be achieved.

Keywords: GPC, Stability, Varying Weighting Coefficients.

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Authors: Jackson H. W. Chang, Jedol Dayou, Justin Sentian

Abstract:

Long terms variation of solar insolation had been widely studied. However, its parallel observations in short time scale is rather lacking. This paper aims to investigate the short time scale evolution of solar radiation spectrum (UV, PAR, and NIR bands) due to atmospheric aerosols and water vapors. A total of 25 days of global and diffused solar spectrum ranges from air mass 2 to 6 were collected using ground-based spectrometer with shadowband technique. The result shows that variation of solar radiation is the least in UV fraction, followed by PAR and the most in NIR. Broader variations in PAR and NIR are associated with the short time scale fluctuations of aerosol and water vapors. The corresponding daily evolution of UV, PAR, and NIR fractions implies that aerosol and water vapors variation could also be responsible for the deviation pattern in the Langley-plot analysis.

Keywords: Aerosol, short time scale variation, solar radiation, water vapor.

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Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: Li Wu

Abstract:

By using linear regression methodology to analyze the data of daily precipitation from 1961-2012, this paper studied the variation tendency of precipitation in Chenzhou. The outcome showed: (1) The annual precipitation was decreasing for 52 years and the difference of precipitation variation tendency among four seasons was remarkable. The precipitation of spring and autumn showed more remarkable decrease than of summer; but the precipitation of winter significantly increased. (2) The annual precipitation frequency tended to lower, which was consistent with the tendency of yearly variation. The seasonal precipitation frequency was greatly different, namely, precipitation frequency in spring and autumn decreased, co-occurring with the phenomenon of mutation; but the winter precipitation frequency increased notably. (3) The precipitation intensity displayed a tendency of increase, including spring, autumn and winter; among them, winter had the most obvious tendency to increase, and autumn had the most yearly variation. Summer was the only season with a tendency of decreasing in precipitation intensity. (4) Annual extreme precipitation tended to reduce, spring, summer and autumn are all included; whereas, winter extreme precipitation tended to increase at the rate of 0.1d/10a. (5) The daily maximum precipitation intensity increased slightly and it varied greatly.

Keywords: Chenzhou, precipitation variation, precipitation frequency, precipitation intensity.

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Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: XianYu Zhao, JinXu Guo

Abstract:

Recently, low-dose computed tomography (CT) has become highly desirable due to increasing attention to the potential risks of excessive radiation. For low-dose CT imaging, ensuring image quality while reducing radiation dose is a major challenge. To facilitate low-dose CT imaging, we propose an improved statistical iterative reconstruction scheme based on the Penalized Weighted Least Squares (PWLS) standard combined with total variation (TV) minimization and sparse dictionary learning (DL) to improve reconstruction performance. We call this method "PWLS-TV-DL". In order to evaluate the PWLS-TV-DL method, we performed experiments on digital phantoms and physical phantoms, respectively. The experimental results show that our method is in image quality and calculation. The efficiency is superior to other methods, which confirms the potential of its low-dose CT imaging.

Keywords: Low dose computed tomography, penalized weighted least squares, total variation, dictionary learning.

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Authors: R. Henry, J-B. Paulin, St. Fauchille, Ph. Delord, K. Benkirane, A. Brunel

Abstract:

In this paper the CVA computation of interest rate swap is presented based on its rating. Rating and probability default given by Moody’s Investors Service are used to calculate our CVA for a specific swap with different maturities. With this computation the influence of rating variation can be shown on CVA. Application is made to the analysis of Greek CDS variation during the period of Greek crisis between 2008 and 2011. The main point is the determination of correlation between the fluctuation of Greek CDS cumulative value and the variation of swap CVA due to change of rating.

Keywords: CDS, Computation, CVA, Greek Crisis, Interest Rate Swap, Maturity, Rating, Swap.

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Authors: Wei Yi Lim, M. Annamalai Arasu, M. Kumarasamy Raja, Minkyu Je

Abstract:

In this paper, the design of wide-swing constant transconductance (g_m) bias circuit that generates bias voltage for low-noise amplifier (LNA) circuit design by using an off-chip resistor is demonstrated. The overall transconductance (G_m) generated by the constant g_m bias circuit is important to maintain the overall gain and noise figure of the LNA circuit. Therefore, investigation is performed to study the variation in G_m with process, temperature and supply voltage (PVT).  Temperature and supply voltage are swept from -10 °C to 85 °C and 1.425 V to 1.575 V respectively, while the process conditions are also varied to the extreme and the g_m variation is eventually concluded at between -3 % to 7 %. With the slight variation in the g_m value, through simulation, at worst condition of state SS, we are able to attain a conversion gain (S₂₁) variation of -3.10 % and a noise figure (NF) variation of 18.71 %. The whole constant g_m circuit draws approximately 100 µA from a 1.5V supply and is designed based on 0.13 µm CMOS process. 

Keywords: Transconductance, LNA, temperature, process.

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Authors: Tadashi Watanabe

Abstract:

Transient shape variation of a rotating liquid dropletis simulated numerically. The three dimensional Navier-Stokes equations were solved by using the level set method. The shape variation from the sphere to the rotating ellipsoid, and to the two-robed shapeare simulated, and the elongation of the two-robed droplet is discussed. The two-robed shape after the initial transient is found to be stable and the elongation is almost the same for the cases with different initial rotation rate. The relationship between the elongation and the rotation rate is obtained by averaging the transient shape variation. It is shown that the elongation of two-robed shape is in good agreement with the existing experimental data. It is found that the transient numerical simulation is necessary for analyzing the largely elongated two-robed shape of rotating droplet.

Keywords: Droplet, rotation, two-robed shape, transient simulation.

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