Search results for: fast discrete cosine transform

Authors: János Levendovszky, András Oláh

Abstract:

In this paper, novel statistical sampling based equalization techniques and CNN based detection are proposed to increase the spectral efficiency of multiuser communication systems over fading channels. Multiuser communication combined with selective fading can result in interferences which severely deteriorate the quality of service in wireless data transmission (e.g. CDMA in mobile communication). The paper introduces new equalization methods to combat interferences by minimizing the Bit Error Rate (BER) as a function of the equalizer coefficients. This provides higher performance than the traditional Minimum Mean Square Error equalization. Since the calculation of BER as a function of the equalizer coefficients is of exponential complexity, statistical sampling methods are proposed to approximate the gradient which yields fast equalization and superior performance to the traditional algorithms. Efficient estimation of the gradient is achieved by using stratified sampling and the Li-Silvester bounds. A simple mechanism is derived to identify the dominant samples in real-time, for the sake of efficient estimation. The equalizer weights are adapted recursively by minimizing the estimated BER. The near-optimal performance of the new algorithms is also demonstrated by extensive simulations. The paper has also developed a (Cellular Neural Network) CNN based approach to detection. In this case fast quadratic optimization has been carried out by t, whereas the task of equalizer is to ensure the required template structure (sparseness) for the CNN. The performance of the method has also been analyzed by simulations.

Keywords: Cellular Neural Network, channel equalization, communication over fading channels, multiuser communication, spectral efficiency, statistical sampling.

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Authors: Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao

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In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.

Keywords: Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.

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Authors: Akram A. Mustafa

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In this paper an approaches for increasing the effectiveness of error detection in computer network channels with Pulse-Amplitude Modulation (PAM) has been proposed. Proposed approaches are based on consideration of special feature of errors, which are appearances in line with PAM. The first approach consists of CRC modification specifically for line with PAM. The second approach is base of weighted checksums using. The way for checksum components coding has been developed. It has been shown that proposed checksum modification ensure superior digital data control transformation reliability for channels with PAM in compare to CRC.

Keywords: Pulse-Amplitude Modulation, checksum, transmission, discrete.

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Authors: Amit Kr. Happy

Abstract:

This paper is motivated by the importance of multi-sensor image fusion with specific focus on Infrared (IR) and Visible image (VI) fusion for various applications including military reconnaissance. Image fusion can be defined as the process of combining two or more source images into a single composite image with extended information content that improves visual perception or feature extraction. These images can be from different modalities like Visible camera & IR Thermal Imager. While visible images are captured by reflected radiations in the visible spectrum, the thermal images are formed from thermal radiation (IR) that may be reflected or self-emitted. A digital color camera captures the visible source image and a thermal IR camera acquires the thermal source image. In this paper, some image fusion algorithms based upon Multi-Scale Transform (MST) and region-based selection rule with consistency verification have been proposed and presented. This research includes implementation of the proposed image fusion algorithm in MATLAB along with a comparative analysis to decide the optimum number of levels for MST and the coefficient fusion rule. The results are presented, and several commonly used evaluation metrics are used to assess the suggested method's validity. Experiments show that the proposed approach is capable of producing good fusion results. While deploying our image fusion algorithm approaches, we observe several challenges from the popular image fusion methods. While high computational cost and complex processing steps of image fusion algorithms provide accurate fused results, but they also make it hard to become deployed in system and applications that require real-time operation, high flexibility and low computation ability. So, the methods presented in this paper offer good results with minimum time complexity.

Keywords: Image fusion, IR thermal imager, multi-sensor, Multi-Scale Transform.

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Authors: Z. Saidi, A.O. Boudraa, J.C. Cexus, S. Bourennane

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In this paper, a new time-delay estimation technique based on the cross IB-energy operator [5] is introduced. This quadratic energy detector measures how much a signal is present in another one. The location of the peak of the energy operator, corresponding to the maximum of interaction between the two signals, is the estimate of the delay. The method is a fully data-driven approach. The discrete version of the continuous-time form of the cross IBenergy operator, for its implementation, is presented. The effectiveness of the proposed method is demonstrated on real underwater acoustic signals arriving from targets and the results compared to the cross-correlation method.

Keywords: Teager-Kaiser energy operator, Cross-energyoperator, Time-Delay, Underwater acoustic signals.

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Authors: Dr. H. B. Kekre, Sudeep D. Thepade

Abstract:

Panoramic view generation has always offered novel and distinct challenges in the field of image processing. Panoramic view generation is nothing but construction of bigger view mosaic image from set of partial images of the desired view. The paper presents a solution to one of the problems of image seascape formation where some of the partial images are color and others are grayscale. The simplest solution could be to convert all image parts into grayscale images and fusing them to get grayscale image panorama. But in the multihued world, obtaining the colored seascape will always be preferred. This could be achieved by picking colors from the color parts and squirting them in grayscale parts of the seascape. So firstly the grayscale image parts should be colored with help of color image parts and then these parts should be fused to construct the seascape image. The problem of coloring grayscale images has no exact solution. In the proposed technique of panoramic view generation, the job of transferring color traits from reference color image to grayscale image is done by palette based method. In this technique, the color palette is prepared using pixel windows of some degrees taken from color image parts. Then the grayscale image part is divided into pixel windows with same degrees. For every window of grayscale image part the palette is searched and equivalent color values are found, which could be used to color grayscale window. For palette preparation we have used RGB color space and Kekre-s LUV color space. Kekre-s LUV color space gives better quality of coloring. The searching time through color palette is improved over the exhaustive search using Kekre-s fast search technique. After coloring the grayscale image pieces the next job is fusion of all these pieces to obtain panoramic view. For similarity estimation between partial images correlation coefficient is used.

Keywords: Panoramic View, Similarity Estimate, Color Transfer, Color Palette, Kekre's Fast Search, Kekre's LUV

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Authors: Rohith K Reddy, David Mayerich, Michael Walsh, P Scott Carney, Rohit Bhargava

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Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that provides both chemically and spatially resolved information. The rich chemical content of data may be utilized for computer-aided determinations of structure and pathologic state (cancer diagnosis) in histological tissue sections for prostate cancer. FT-IR spectroscopic imaging of prostate tissue has shown that tissue type (histological) classification can be performed to a high degree of accuracy [1] and cancer diagnosis can be performed with an accuracy of about 80% [2] on a microscopic (≈ 6μm) length scale. In performing these analyses, it has been observed that there is large variability (more than 60%) between spectra from different points on tissue that is expected to consist of the same essential chemical constituents. Spectra at the edges of tissues are characteristically and consistently different from chemically similar tissue in the middle of the same sample. Here, we explain these differences using a rigorous electromagnetic model for light-sample interaction. Spectra from FT-IR spectroscopic imaging of chemically heterogeneous samples are different from bulk spectra of individual chemical constituents of the sample. This is because spectra not only depend on chemistry, but also on the shape of the sample. Using coupled wave analysis, we characterize and quantify the nature of spectral distortions at the edges of tissues. Furthermore, we present a method of performing histological classification of tissue samples. Since the mid-infrared spectrum is typically assumed to be a quantitative measure of chemical composition, classification results can vary widely due to spectral distortions. However, we demonstrate that the selection of localized metrics based on chemical information can make our data robust to the spectral distortions caused by scattering at the tissue boundary.

Keywords: Infrared, Spectroscopy, Imaging, Tissue classification

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Authors: F. Hosseinpour, H. Hajihosseini

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Simulation is a very helpful and valuable work tool in manufacturing. It can be used in industrial field allowing the system`s behavior to be learnt and tested. Simulation provides a low cost, secure and fast analysis tool. It also provides benefits, which can be reached with many different system configurations. Topics to be discussed include: Applications, Modeling, Validating, Software and benefits of simulation. This paper provides a comprehensive literature review on research efforts in simulation.

Keywords: Manufacturing, modeling, simulation, training.

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Authors: Chun-I Fan, Ming-Te Chen

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This manuscript presents a fast blind signature scheme with extremely low computation for users. Only several modular additions and multiplications are required for a user to obtain and verify a signature in the proposed scheme. Comparing with the existing ones in the literature, the scheme greatly reduces the computations for users.

Keywords: Blind signatures, Untraceable electronic cash, Security & privacy, Electronic commerce

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Authors: T. C. Manjunath, B. Bandyopadhyay

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Active vibration control is an important problem in structures. The objective of active vibration control is to reduce the vibrations of a system by automatic modification of the system-s structural response. In this paper, the modeling and design of a fast output sampling feedback controller for a smart flexible beam system embedded with shear sensors and actuators for SISO system using Timoshenko beam theory is proposed. FEM theory, Timoshenko beam theory and the state space techniques are used to model the aluminum cantilever beam. For the SISO case, the beam is divided into 5 finite elements and the control actuator is placed at finite element position 1, whereas the sensor is varied from position 2 to 5, i.e., from the nearby fixed end to the free end. Controllers are designed using FOS method and the performance of the designed FOS controller is evaluated for vibration control for 4 SISO models of the same plant. The effect of placing the sensor at different locations on the beam is observed and the performance of the controller is evaluated for vibration control. Some of the limitations of the Euler-Bernoulli theory such as the neglection of shear and axial displacement are being considered here, thus giving rise to an accurate beam model. Embedded shear sensors and actuators have been considered in this paper instead of the surface mounted sensors and actuators for vibration suppression because of lot of advantages. In controlling the vibration modes, the first three dominant modes of vibration of the system are considered.

Keywords: Smart structure, Timoshenko beam theory, Fast output sampling feedback control, Finite Element Method, State space model, SISO, Vibration control, LMI

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Authors: M. Tarafdar Haque, A. Taheri

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Application of neural networks in execution of programmed pulse width modulation (PPWM) of a voltage source inverter (VSI) is studied in this paper. Using the proposed method it is possible to cancel out the desired harmonics in output of VSI in addition to control the magnitude of fundamental harmonic, contineously. By checking the non-trained values and a performance index, the most appropriate neural network is proposed. It is shown that neural networks may solve the custom difficulties of practical utilization of PPWM such as large size of memory, complex digital circuits and controlling the magnitude of output voltage in a discrete manner.

Keywords: Neural Network, Inverter, PPWM.

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Authors: Karamitsos Ioannis, Orfanidis Konstantinos

Abstract:

In this paper an analysis of blackouts in electric power transmission systems is implemented using a model and studied in simple networks with a regular topology. The proposed model describes load demand and network improvements evolving on a slow timescale as well as the fast dynamics of cascading overloads and outages.

Keywords: Blackout, Generator, Load, Power Load.

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Authors: Smajo Bisanovic, Mensur Hajro, Mersiha Samardzic

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This paper presents quantitative component criticality importance indices applicable for identifying and ranking critical components in the phase of thermal power plants design. Identifying critical components for power plant reliability provides one important input to decision-making and guidance throughout the development project. The study of components criticality importance indices to several characteristic structural schemes of conventional thermal power plant is presented and discussed.

Keywords: Component criticality importance measures, discrete event, reliability, thermal power plant.

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Authors: Olli Luoma, Johannes Tuikkala, Olli Nevalainen

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In this paper, we propose a novel improvement for the generalized Lloyd Algorithm (GLA). Our algorithm makes use of an M-tree index built on the codebook which makes it possible to reduce the number of distance computations when the nearest code words are searched. Our method does not impose the use of any specific distance function, but works with any metric distance, making it more general than many other fast GLA variants. Finally, we present the positive results of our performance experiments.

Keywords: Clustering, GLA, M-Tree, Vector Quantization .

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Authors: M. Chobotová, Ž. Rylková

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Time full of changes which is associated with globalization, tougher competition, changes in the structures of markets and economic downturn, that all force companies to think about their competitive advantages. These changes can bring the company a competitive advantage and that can help improve competitive position in the market. Policy of the European Union is focused on the fast growing innovative companies which quickly respond to market demands and consequently increase its competitiveness. To meet those objectives companies need the right conditions and support of their state.

Keywords: Innovation, performance, measurements metrics, indices.

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Authors: J. Hajri, H. Hrizi, N. Sboui, H. Baudrand

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This paper presents a study of SIW circuits (Substrate Integrated Waveguide) with a rigorous and fast original approach based on Iterative process (WCIP). The theoretical suggested study is validated by the simulation of two different examples of SIW circuits. The obtained results are in good agreement with those of measurement and with software HFSS.

Keywords: Convergence study, HFSS, Modal decomposition, SIW Circuits, WCIP Method.

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.

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Authors: M. Ghazikhani, M. R. Kalateh, Y. K. Toroghi, M. Dehnavi

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In this study, effects of premixed and equivalence ratios on CO and HC emissions of a dual fuel HCCI engine are investigated. Tests were conducted on a single-cylinder engine with compression ratio of 17.5. Premixed gasoline is provided by a carburetor connected to intake manifold and equipped with a screw to adjust premixed air-fuel ratio, and diesel fuel is injected directly into the cylinder through an injector at pressure of 250 bars. A heater placed at inlet manifold is used to control the intake charge temperature. Optimal intake charge temperature results in better HCCI combustion due to formation of a homogeneous mixture, therefore, all tests were carried out over the optimum intake temperature of 110-115 ºC. Timing of diesel fuel injection has a great effect on stratification of in-cylinder charge and plays an important role in HCCI combustion phasing. Experiments indicated 35 BTDC as the optimum injection timing. Varying the coolant temperature in a range of 40 to 70 ºC, better HCCI combustion was achieved at 50 ºC. Therefore, coolant temperature was maintained 50 ºC during all tests. Simultaneous investigation of effective parameters on HCCI combustion was conducted to determine optimum parameters resulting in fast transition to HCCI combustion. One of the advantages of the method studied in this study is feasibility of easy and fast transition of typical diesel engine to a dual fuel HCCI engine. Results show that increasing premixed ratio, while keeping EGR rate constant, increases unburned hydrocarbon (UHC) emissions due to quenching phenomena and trapping of premixed fuel in crevices, but CO emission decreases due to increase in CO to CO2 reactions.

Keywords: Dual fuel HCCI engine, premixed ratio, equivalenceratio, CO and UHC emissions.

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The paper is focused on the operational model for transport the single wagon consignments on railway network by using two different models of train formation. The paper gives an overview of possibilities of improving the quality of transport services. Paper deals with two models used in problematic of train formatting - time continuously and time discrete. By applying these models in practice, the transport company can guarantee a higher quality of service and expect increasing of transport performance. The models are also applicable into others transport networks. The models supplement a theoretical problem of train formation by new ways of looking to affecting the organization of wagon flows.

Keywords: Train formation, wagon flows, marshalling yard, railway technology.

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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

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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: Adebisi. Elizabeth, Banjo

Abstract:

Language and culture are interwoven that they cannot be separated, for the knowledge of a language cannot be complete without having the culture of the language. Indigenous food is a cultural aspect of any language that is expected to be acquired by all the speakers of the language. Indigenous food is known to be vital right from early years, which is also attributed to the healthy living of the ancient people. However it is discovered that the indigenous food is almost being replaced by fast food products such as Indomie noodles, Spaghetti and Macaroni to the extent that majority of the young folks prefer the eating of the fast foods and cannot prepare the indigenous foods which are good for growth and healthy living of people. Therefore, there is need to revitalize and re-educate people on the indigenous food which is an aspect of inter-cultural education of any language to prevent it from being forgotten or neglected.

African foods are many, but this study focused on Nigerian food using some Yoruba dishes as a case study. Examples of Yoruba dishes are pounded yam and melon with vegetable and dried fish soup, beans pudding (moin moin) and pap (eko), water yam pudding with fish and meat (ikokore) and many more. The ingredients needed for the preparation of these indigenous foods contain some basic food nutrients which will be analyzed and their nutritional importance to human bodies will also be discussed.

The process of re- awakening the education of indigenous food to the present and up-coming generation should be via print and electronic media in form of advertisements on posters, billboards, calendars and in rhymes on television programs, radio presentations, video tapes and CD–ROM apart from classroom teaching and learning. Indigenous food is a panacea to healthy living and longevity, a prevention of diseases and a means of accelerated healing of the body through natural foods.

Keywords: Indigenous food, print and electronic media, nutritional values, re-awakening education.

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Authors: Pejman Hosseinioun, Rose Shayeghi, Ghasem Ghorbani Rostam

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Nowadays, obtaining traditional statistics and reports is not adequate for the needs of organizational managers. The managers need to analyze and to transform the raw data into knowledge in the world filled with information. Therefore in this regard various processes have been developed. In the meantime the artificial intelligence-based processes are used and the new topics such as business intelligence and knowledge discovery have emerged. In the current paper it is sought to study the business intelligence and its applications in the organizations.

Keywords: Business intelligence, business intelligence infrastructures, business processes.

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Authors: Vahid Mohammadi Saffarzadeh, Pourya Jafarzadeh, Masoud Mazloom

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This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.

Keywords: PSO, SA, N-queen, CSP

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Authors: S. Safi, A. Zeroual

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In this paper we propose a family of algorithms based on 3rd and 4th order cumulants for blind single-input single-output (SISO) Non-Minimum Phase (NMP) Finite Impulse Response (FIR) channel estimation driven by non-Gaussian signal. The input signal represents the signal used in 10GBASE-T (or IEEE 802.3an-2006) as a Tomlinson-Harashima Precoded (THP) version of random Pulse-Amplitude Modulation with 16 discrete levels (PAM-16). The proposed algorithms are tested using three non-minimum phase channel for different Signal-to-Noise Ratios (SNR) and for different data input length. Numerical simulation results are presented to illustrate the performance of the proposed algorithms.

Keywords: Higher Order Cumulants, Channel identification, Ethernet communication.

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Authors: Malte Brettel, Niklas Friederichsen, Michael Keller, Marius Rosenberg

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The German manufacturing industry has to withstand an increasing global competition on product quality and production costs. As labor costs are high, several industries have suffered severely under the relocation of production facilities towards aspiring countries, which have managed to close the productivity and quality gap substantially. Established manufacturing companies have recognized that customers are not willing to pay large price premiums for incremental quality improvements. As a consequence, many companies from the German manufacturing industry adjust their production focusing on customized products and fast time to market. Leveraging the advantages of novel production strategies such as Agile Manufacturing and Mass Customization, manufacturing companies transform into integrated networks, in which companies unite their core competencies. Hereby, virtualization of the process- and supply-chain ensures smooth inter-company operations providing real-time access to relevant product and production information for all participating entities. Boundaries of companies deteriorate, as autonomous systems exchange data, gained by embedded systems throughout the entire value chain. By including Cyber-Physical-Systems, advanced communication between machines is tantamount to their dialogue with humans. The increasing utilization of information and communication technology allows digital engineering of products and production processes alike. Modular simulation and modeling techniques allow decentralized units to flexibly alter products and thereby enable rapid product innovation. The present article describes the developments of Industry 4.0 within the literature and reviews the associated research streams. Hereby, we analyze eight scientific journals with regards to the following research fields: Individualized production, end-to-end engineering in a virtual process chain and production networks. We employ cluster analysis to assign sub-topics into the respective research field. To assess the practical implications, we conducted face-to-face interviews with managers from the industry as well as from the consulting business using a structured interview guideline. The results reveal reasons for the adaption and refusal of Industry 4.0 practices from a managerial point of view. Our findings contribute to the upcoming research stream of Industry 4.0 and support decision-makers to assess their need for transformation towards Industry 4.0 practices. 

Keywords: Industry 4.0., Mass Customization, Production networks, Virtual Process-Chain.

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Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

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This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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Authors: Saniyam A. Ibragimova, Zhandos M. Basygarayev, Almagul R. Kerimkulova, E. A. Bukenova, Murat K. Gilmanov

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New biostimulator from wheat seeds which by its chemical composition relates to fusicoccin is presented in this article. New biostimulator could be used as powerful hormonal substance that has ability to increase productivity and salt tolerance of agricultural plants. Also on the basis of biostimulator we have developed vegetative method for fast reproduction of perennial plants as desert plant - Tamarix gracilis.

Keywords: Biostimulator, crop productivity, ecology, fussicoccin, salt tolerance.

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Authors: Sunan Payungsak, Atchana Wongchaisuwat, Ladda Meesuk

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Sulfide ion (S2-) is one of the most important ions to be monitored due to its high toxicity, especially for aquatic organisms. In this work, [Ca(2,2'-bipyridine)3]2+-intercalated montmorillonite was prepared and used as a sensor to construct a potentiometric electrode to measure sulfide ion in solution. The formation of [Ca(2,2'- bipyridine)3]2+ in montmorillonite was confirmed by Fourier Transform Infrared spectra. The electrode worked well at pH 4-12 and 4-10 in sulfide solution 10-2 M and 10-3 M, respectively, in terms of Nernstian slope. The sensor gave good precision and low cost.

Keywords: 2, 2'-bipyridine complexes, montmorillonite potentiometry, sulfide ion.

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Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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