Search results for: Modified Shannon entropy

Authors: Devendra Kumar Pandey, Debabrata Chakraborty

Abstract:

The advancement in various concrete ingredients like plasticizers, additives and fibers, etc. has enabled concrete technologists to develop many viable varieties of special concretes in recent decades. Such various varieties of concrete have significant enhancement in green as well as hardened properties of concrete. A prudent selection of appropriate type of concrete can resolve many design and application issues in construction projects. This paper focuses on usage of self-compacting concrete, high early strength concrete, structural lightweight concrete, fiber reinforced concrete, high performance concrete and ultra-high strength concrete in the structures. The modified properties of strength at various ages, flowability, porosity, equilibrium density, flexural strength, elasticity, permeability etc. need to be carefully studied and incorporated into the design of the structures. The paper demonstrates various mixture combinations and the concrete properties that can be leveraged. The selection of such products based on the end use of structures has been proposed in order to efficiently utilize the modified characteristics of these concrete varieties. The study involves mapping the characteristics with benefits and savings for the structure from design perspective. Self-compacting concrete in the structure is characterized by high shuttering loads, better finish, and feasibility of closer reinforcement spacing. The structural design procedures can be modified to specify higher formwork strength, height of vertical members, cover reduction and increased ductility. The transverse reinforcement can be spaced at closer intervals compared to regular structural concrete. It allows structural lightweight concrete structures to be designed for reduced dead load, increased insulation properties. Member dimensions and steel requirement can be reduced proportionate to about 25 to 35 percent reduction in the dead load due to self-weight of concrete. Steel fiber reinforced concrete can be used to design grade slabs without primary reinforcement because of 70 to 100 percent higher tensile strength. The design procedures incorporate reduction in thickness and joint spacing. High performance concrete employs increase in the life of the structures by improvement in paste characteristics and durability by incorporating supplementary cementitious materials. Often, these are also designed for slower heat generation in the initial phase of hydration. The structural designer can incorporate the slow development of strength in the design and specify 56 or 90 days strength requirement. For designing high rise building structures, creep and elasticity properties of such concrete also need to be considered. Lastly, certain structures require a performance under loading conditions much earlier than final maturity of concrete. High early strength concrete has been designed to cater to a variety of usages at various ages as early as 8 to 12 hours. Therefore, an understanding of concrete performance specifications for special concrete is a definite door towards a superior structural design approach.

Keywords: High performance concrete, special concrete, structural design, structural lightweight concrete.

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Authors: K. Anitha Sheela, J. Tarun Kumar

Abstract:

HSDPA is a new feature which is introduced in Release-5 specifications of the 3GPP WCDMA/UTRA standard to realize higher speed data rate together with lower round-trip times. Moreover, the HSDPA concept offers outstanding improvement of packet throughput and also significantly reduces the packet call transfer delay as compared to Release -99 DSCH. Till now the HSDPA system uses turbo coding which is the best coding technique to achieve the Shannon limit. However, the main drawbacks of turbo coding are high decoding complexity and high latency which makes it unsuitable for some applications like satellite communications, since the transmission distance itself introduces latency due to limited speed of light. Hence in this paper it is proposed to use LDPC coding in place of Turbo coding for HSDPA system which decreases the latency and decoding complexity. But LDPC coding increases the Encoding complexity. Though the complexity of transmitter increases at NodeB, the End user is at an advantage in terms of receiver complexity and Bit- error rate. In this paper LDPC Encoder is implemented using “sparse parity check matrix" H to generate a codeword at Encoder and “Belief Propagation algorithm "for LDPC decoding .Simulation results shows that in LDPC coding the BER suddenly drops as the number of iterations increase with a small increase in Eb/No. Which is not possible in Turbo coding. Also same BER was achieved using less number of iterations and hence the latency and receiver complexity has decreased for LDPC coding. HSDPA increases the downlink data rate within a cell to a theoretical maximum of 14Mbps, with 2Mbps on the uplink. The changes that HSDPA enables includes better quality, more reliable and more robust data services. In other words, while realistic data rates are only a few Mbps, the actual quality and number of users achieved will improve significantly.

Keywords: AMC, HSDPA, LDPC, WCDMA, 3GPP.

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Authors: Federico Pérez González, Iñaki Goiricelaia Ordorika, Pedro Iriondo Bengoa

Abstract:

A new method for low complexity image coding is presented, that permits different settings and great scalability in the generation of the final bit stream. This coding presents a continuoustone still image compression system that groups loss and lossless compression making use of finite arithmetic reversible transforms. Both transformation in the space of color and wavelet transformation are reversible. The transformed coefficients are coded by means of a coding system in depending on a subdivision into smaller components (CFDS) similar to the bit importance codification. The subcomponents so obtained are reordered by means of a highly configure alignment system depending on the application that makes possible the re-configure of the elements of the image and obtaining different levels of importance from which the bit stream will be generated. The subcomponents of each level of importance are coded using a variable length entropy coding system (VBLm) that permits the generation of an embedded bit stream. This bit stream supposes itself a bit stream that codes a compressed still image. However, the use of a packing system on the bit stream after the VBLm allows the realization of a final highly scalable bit stream from a basic image level and one or several enhance levels.

Keywords: Image compression, wavelet transform, highlyscalable, reversible transform, embedded, subcomponents.

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Authors: C. Ardil

Abstract:

The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.

Keywords: stealth fighter aircraft selection, fuzzy uncertainty theory (FUT), fuzzy entropic decision (FED), fuzzy linguistic variables, triangular fuzzy numbers, multiple criteria decision making analysis, MCDMA, TOPSIS, WSM, WPM

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Authors: Mohammad Pooyan, Ali Taheri, Morteza Moazami-Goudarzi, Iman Saboori

Abstract:

In this paper we present a novel approach for wavelet compression of electrocardiogram (ECG) signals based on the set partitioning in hierarchical trees (SPIHT) coding algorithm. SPIHT algorithm has achieved prominent success in image compression. Here we use a modified version of SPIHT for one dimensional signals. We applied wavelet transform with SPIHT coding algorithm on different records of MIT-BIH database. The results show the high efficiency of this method in ECG compression.

Keywords: ECG compression, wavelet, SPIHT.

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Authors: L. M. Stefan, A. M. Pana, M. Silion, M. Balan, G. Bandur, L. M. Rusnac

Abstract:

The field of polymeric biomaterials is very important from the socio-economical viewpoint. Synthetic carbohydrate polymers are being increasingly investigated as biodegradable, biocompatible and biorenewable materials. The aim of this study was to synthesize and characterize some derivatives based on D-mannose. D-mannose was chemically modified to obtain 1-O-allyl-2,3:5,6-di- O-isopropylidene-D-mannofuranose and 1-O-(2-,3--epoxy-propyl)- 2,3:5,6-di-O-isopropylidene-D-mannofuranose. The chemical structure of the resulting compounds was characterized by FT-IR and NMR spectroscopy, and by HPLC-MS.

Keywords: D-mannose, biopolymers , spectroscopy, synthesis.

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Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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Authors: S. S. Gautam, S. Samanta

Abstract:

The aim of the paper work is to investigate and predict the static performance of journal bearing in turbulent flow condition considering micropolar lubrication. The Reynolds equation has been modified considering turbulent micropolar lubrication and is solved for steady state operations. The Constantinescu-s turbulence model is adopted using the coefficients. The analysis has been done for a parallel and inertia less flow. Load capacity and friction factor have been evaluated for various operating parameters.

Keywords: hydrodynamic bearing, micropolar lubrication, coupling number, characteristic length, perturbation analysis

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Authors: Federico Pérez González, Iñaki Goirizelaia Ordorika, Pedro Iriondo Bengoa

Abstract:

In this work a new method for low complexity image coding is presented, that permits different settings and great scalability in the generation of the final bit stream. This coding presents a continuous-tone still image compression system that groups loss and lossless compression making use of finite arithmetic reversible transforms. Both transformation in the space of color and wavelet transformation are reversible. The transformed coefficients are coded by means of a coding system in depending on a subdivision into smaller components (CFDS) similar to the bit importance codification. The subcomponents so obtained are reordered by means of a highly configure alignment system depending on the application that makes possible the re-configure of the elements of the image and obtaining different importance levels from which the bit stream will be generated. The subcomponents of each importance level are coded using a variable length entropy coding system (VBLm) that permits the generation of an embedded bit stream. This bit stream supposes itself a bit stream that codes a compressed still image. However, the use of a packing system on the bit stream after the VBLm allows the realization of a final highly scalable bit stream from a basic image level and one or several improvement levels.

Keywords: Image compression, wavelet transform, highly scalable, reversible transform, embedded, subcomponents.

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Authors: Turgay Temel, John Hallam

Abstract:

An improved processing description to be employed in biosonar signal processing in a cochlea model is proposed and examined. It is compared to conventional models using a modified discrimination analysis and both are tested. Their performances are evaluated with echo data captured from natural targets (trees).Results indicate that the phase characteristics of low-pass filters employed in the echo processing have a significant effect on class separability for this data.

Keywords: Cochlea model, discriminant analysis, neurospikecoding, classification.

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Authors: Mohammed Golam Sarwer, Lai Man Po, Kai Guo, Q.M. Jonathan Wu

Abstract:

In H.264/AVC video encoding, rate-distortion optimization for mode selection plays a significant role to achieve outstanding performance in compression efficiency and video quality. However, this mode selection process also makes the encoding process extremely complex, especially in the computation of the ratedistortion cost function, which includes the computations of the sum of squared difference (SSD) between the original and reconstructed image blocks and context-based entropy coding of the block. In this paper, a transform-domain rate-distortion optimization accelerator based on fast SSD (FSSD) and VLC-based rate estimation algorithm is proposed. This algorithm could significantly simplify the hardware architecture for the rate-distortion cost computation with only ignorable performance degradation. An efficient hardware structure for implementing the proposed transform-domain rate-distortion optimization accelerator is also proposed. Simulation results demonstrated that the proposed algorithm reduces about 47% of total encoding time with negligible degradation of coding performance. The proposed method can be easily applied to many mobile video application areas such as a digital camera and a DMB (Digital Multimedia Broadcasting) phone.

Keywords: Context-adaptive variable length coding (CAVLC), H.264/AVC, rate-distortion optimization (RDO), sum of squareddifference (SSD).

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Authors: Georgi Yordanov Georgiev, Michael Daly, Erin Gombos, Amrit Vinod, Gajinder Hoonjan

Abstract:

Measures of complexity and entropy have not converged to a single quantitative description of levels of organization of complex systems. The need for such a measure is increasingly necessary in all disciplines studying complex systems. To address this problem, starting from the most fundamental principle in Physics, here a new measure for quantity of organization and rate of self-organization in complex systems based on the principle of least (stationary) action is applied to a model system - the central processing unit (CPU) of computers. The quantity of organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has a fine, S-shaped structure, revealing some of the mechanisms of self-organization. The principle of least action helps to explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self organization to improve their quality. It can be applied to other complex systems from Physics, Chemistry, Biology, Ecology, Economics, Cities, network theory and others where complex systems are present.

Keywords: Organization, self-organization, complex system, complexification, quantitative measure, principle of least action, principle of stationary action, attractor, progressive development, acceleration, stochastic.

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Authors: G. Korotcenkov, B. K. Cho, L. B. Gulina, V. P. Tolstoy

Abstract:

The effect of SnO2 surface modification by Ag nanoclusters, synthesized by SILD method, on the operating characteristics of thin film gas sensors was studied and models for the promotional role of Ag additives were discussed. It was found that mentioned above approach can be used for improvement both the sensitivity and the rate of response of the SnO2-based gas sensors to CO and H2. At the same time, the presence of the Ag clusters on the surface of SnO2 depressed the sensor response to ozone.

Keywords: Ag nanoparticles, deposition, characterization, gas sensors, optimization.

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Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi

Abstract:

In this paper a modification on Levenberg-Marquardt algorithm for MLP neural network learning is proposed. The proposed algorithm has good convergence. This method reduces the amount of oscillation in learning procedure. An example is given to show usefulness of this method. Finally a simulation verifies the results of proposed method.

Keywords: Levenberg-Marquardt, modification, neural network, variable learning rate.

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Authors: Risanuri Hidayat

Abstract:

BER analysis of Impulse Radio Ultra Wideband (IRUWB) pulse modulations over S-V channel model is proposed in this paper. The UWB pulse is Gaussian monocycle pulse modulated using Pulse Amplitude Modulation (PAM) and Pulse Position Modulation (PPM). The channel model is generated from a modified S-V model. Bit-error rate (BER) is measured over several of bit rates. The result shows that all modulation are appropriate for both LOS and NLOS channel, but PAM gives better performance in bit rates and SNR. Moreover, as standard of speed has been given for UWB, the communication is appropriate with high bit rates in LOS channel.

Keywords: IR-UWB, S-V Channel Model, LOS NLOS, PAM, PPM

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Authors: O. S. Ebrahim, K. O. Shawky, M. A. Badr, P. K. Jain

Abstract:

This paper proposes an intelligent, supervisory, hysteresis liquid-level control with three-state energy saving mode (ESM) for induction motor (IM) in fluid transportation system (FTS) including storage tank. The IM pump drive comprises a modified star/delta switch and hydromantic coupler. Three-state ESM is defined, along with the normal running, and named analog to the computer’s ESMs as follows: Sleeping mode in which the motor runs at no load with delta stator connection, hibernate mode in which the motor runs at no load with a star connection, and motor shutdown is the third energy saver mode. Considering the motor’s thermal capacity used (TCU) and grid-compatible tariff structure, a logic flow-chart is synthesized to select the motor state at no-load for best energetic cost reduction. Fuzzy-logic (FL) based availability assessment is designed and deployed on cloud, in order to provide mobilized service for the star/delta switch and highly reliable contactors. Moreover, an artificial neural network (ANN) state estimator, based on the recurrent architecture, is constructed and learned in order to provide fault-tolerant capability for the supervisory controller. Sequential test of Wald is used for sensor fault detection. Theoretical analysis, preliminary experimental testing and computer simulations are performed to demonstrate the validity and effectiveness of the proposed control system in terms of reliability, power quality and operational cost reduction with a motivation of power factor correction.

Keywords: Artificial Neural Network, ANN, Contactor Health Assessment, Energy Saving Mode, Induction Machine, IM, Supervisory Control, Fluid Transportation, Fuzzy Logic, FL, cloud computing, pumped storage.

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Authors: S.Mousavian, D.Ashouri, M.abdolahi, M.H.Vakili, Y.Rahnama

Abstract:

In this study, the dispersed model is used to predict gas phase concentration, liquid drop concentration. The venturi scrubber efficiency is calculated by gas phase concentration. The modified model has been validated with available experimental data of Johnstone, Field and Tasler for a range of throat gas velocities, liquid to gas ratios and particle diameters and is used to study the effect of some design parameters on collection efficiency.

Keywords: Ammonia, Modelling, Purge gas, Removal efficiency, Venturi scrubber

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Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

A camera in the building site is exposed to different weather conditions. Differences between images of the same scene captured with the same camera arise also due to temperature variations. The influence of temperature changes on camera parameters were modelled and integrated into existing analytical camera model. Modified camera model enables quantitatively assessing the influence of temperature variations.

Keywords: camera calibration, analytical model, intrinsic parameters, extrinsic parameters, temperature variations.

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Authors: Zhuan-de Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

Keywords: Backward MPSD iterative matrix, Jacobi iterative matrix, eigenvalue, p-cyclic matrix.

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Authors: Mohd.F.Shabir, P. Tamilporai, B. Rajendra Prasath

Abstract:

The fundamental aim of extended expansion concept is to achieve higher work done which in turn leads to higher thermal efficiency. This concept is compatible with the application of turbocharger and LHR engine. The Low Heat Rejection engine was developed by coating the piston crown, cylinder head inside with valves and cylinder liner with partially stabilized zirconia coating of 0.5 mm thickness. Extended expansion in diesel engines is termed as Miller cycle in which the expansion ratio is increased by reducing the compression ratio by modifying the inlet cam for late inlet valve closing. The specific fuel consumption reduces to an appreciable level and the thermal efficiency of the extended expansion turbocharged LHR engine is improved. In this work, a thermodynamic model was formulated and developed to simulate the LHR based extended expansion turbocharged direct injection diesel engine. It includes a gas flow model, a heat transfer model, and a two zone combustion model. Gas exchange model is modified by incorporating the Miller cycle, by delaying inlet valve closing timing which had resulted in considerable improvement in thermal efficiency of turbocharged LHR engines. The heat transfer model, calculates the convective and radiative heat transfer between the gas and wall by taking into account of the combustion chamber surface temperature swings. Using the two-zone combustion model, the combustion parameters and the chemical equilibrium compositions were determined. The chemical equilibrium compositions were used to calculate the Nitric oxide formation rate by assuming a modified Zeldovich mechanism. The accuracy of this model is scrutinized against actual test results from the engine. The factors which affect thermal efficiency and exhaust emissions were deduced and their influences were discussed. In the final analysis it is seen that there is an excellent agreement in all of these evaluations.

Keywords: Low Heat Rejection, Miller cycle.

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Authors: C. Villegas-Quezada, J. Climent

Abstract:

Several works regarding facial recognition have dealt with methods which identify isolated characteristics of the face or with templates which encompass several regions of it. In this paper a new technique which approaches the problem holistically dispensing with the need to identify geometrical characteristics or regions of the face is introduced. The characterization of a face is achieved by randomly sampling selected attributes of the pixels of its image. From this information we construct a set of data, which correspond to the values of low frequencies, gradient, entropy and another several characteristics of pixel of the image. Generating a set of “p" variables. The multivariate data set with different polynomials minimizing the data fitness error in the minimax sense (L∞ - Norm) is approximated. With the use of a Genetic Algorithm (GA) it is able to circumvent the problem of dimensionality inherent to higher degree polynomial approximations. The GA yields the degree and values of a set of coefficients of the polynomials approximating of the image of a face. By finding a family of characteristic polynomials from several variables (pixel characteristics) for each face (say Fi ) in the data base through a resampling process the system in use, is trained. A face (say F ) is recognized by finding its characteristic polynomials and using an AdaBoost Classifier from F -s polynomials to each of the Fi -s polynomials. The winner is the polynomial family closer to F -s corresponding to target face in data base.

Keywords: AdaBoost Classifier, Holistic Face Recognition, Minimax Multivariate Approximation, Genetic Algorithm.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

Abstract:

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: M. Mika, , P. Volakova, V. Verner, O. Jankovsky, B. Klapste

Abstract:

We successfully developed a new straw combustion technology that efficiently reduces problems with unmanageable deposits inside straw fueled boilers in Zluticka Heating Plant. The deposits are mainly created by glass-forming melts. We plotted straw compositions in K2O-CaO-SiO2 phase diagram and illustrated they are in the area of low-melting eutectic poi melting of ash and the formation of deposits compositions by injecting additives into biomass fuel ueled points. To prevent the deposits, we modified ash fuel.

Keywords: Biomass, straw, combustion, deposit, heat

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: Mario Mastriani, Alberto E. Giraldez

Abstract:

In this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman-s filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the speckled image into wavelet subbands, we apply the Kalman-s filter to the high subbands, and reconstruct a despeckled image from the modified detail coefficients. Experimental results demonstrate that our method compares favorably to several other despeckling methods on test synthetic aperture radar (SAR) images.

Keywords: Kalman's filter, shrinkage, speckle, wavelets.

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Authors: Eva Vorma, Sandra Muizniece-Brasava, Lija Dukalska, Janis Skalbe

Abstract:

The objective of the research was to evaluate the hardness stability of milk pomade sweets packed in several packaging materials (OPP, Multibarrier 60 HFP, BIALON 65 HFP, BIALON 50 HFP, ECOLEAN) by several packaging technologies – modified atmosphere (MAP) (consisting of 30% CO2+70% N2; 30% N2+70% CO2 and 100% CO2) and control – in air ambiance. Samples were stored at the room temperature +21±1 °C. The studies of the samples were carried out before packaging and after 2, 4, 6, 8, and 10 storage weeks.

Keywords: packaging, shelf life, sherbet with crunchy peanutchips, hardness.

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Authors: López-Gutiérrez R.M., Rodríguez-Orozco E., Cruz-Hernández C., Inzunza-González E., Posadas-Castillo C., García-Guerrero E.E., Cardoza-Avendaño L.

Abstract:

In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure.

Keywords: Hyperchaos synchronization, sixth-order Chua's circuit, observers, simulation, secure communication.

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Authors: Majid Reza Naseh, Mohammad Haeri

Abstract:

This paper introduces an adaptive control scheme to synchronize two identical Chua's systems. Introductory part of the paper is presented in the first part of the paper and then in the second part, a new theorem is proposed based on which an adaptive control scheme is developed to synchronize two identical modified Chua's circuit. Finally, numerical simulations are included to verify the effectiveness of the proposed control method.

Keywords: Chaos synchronization, adaptive control, Chua's circuits.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

We used mathematical model to study the transmission of dengue disease. The model is developed in which the human population is separated into two populations, pregnant and non-pregnant humans. The dynamical analysis method is used for analyzing this modified model. Two equilibrium states are found and the conditions for stability of theses two equilibrium states are established. Numerical results are shown for each equilibrium state. The basic reproduction numbers are found and they are compared by using numerical simulations.

Keywords: Basic reproductive number, dengue disease, equilibrium states, pregnancy.

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