Search results for: Possibility Theory
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2075

Search results for: Possibility Theory

1205 Optimal Power Allocation for the Proposed Asymmetric Turbo Code for 3G Systems

Authors: K. Ramasamy, B. Balamuralithara, Mohammad Umar Siddiqi

Abstract:

We proposed a new class of asymmetric turbo encoder for 3G systems that performs well in both “water fall" and “error floor" regions in [7]. In this paper, a modified (optimal) power allocation scheme for the different bits of new class of asymmetric turbo encoder has been investigated to enhance the performance. The simulation results and performance bound for proposed asymmetric turbo code with modified Unequal Power Allocation (UPA) scheme for the frame length, N=400, code rate, r=1/3 with Log-MAP decoder over Additive White Gaussian Noise (AWGN) channel are obtained and compared with the system with typical UPA and without UPA. The performance tests are extended over AWGN channel for different frame size to verify the possibility of implementation of the modified UPA scheme for the proposed asymmetric turbo code. From the performance results, it is observed that the proposed asymmetric turbo code with modified UPA performs better than the system without UPA and with typical UPA and it provides a coding gain of 0.4 to 0.52dB.

Keywords: Asymmetric turbo code, Generator polynomial, Interleaver, UPA, WCDMA, cdma2000.

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1204 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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1203 Study of Mordenite ZSM-5 and NaY Zeolites,Containing Cr, Cs, Zn, Ni, Co, Li, Mn, to Control Hydrocarbon Cold-Start Emission

Authors: V. Golubeva, A. Korableva, O. Anischenko, A. Nemova, N. Yegorushina, L. Kustov, G. Kapustin, U.S.Rohatgi

Abstract:

The implementation of Super-Ultra Low Emission Vehicle standards requires more efficient exhaust gas purification. To increase the efficiency of exhaust gas purification, an the adsorbent capable of holding hydrocarbons up to 250-300 ОС should be developed. The possibility to design such adsorbents by modification of zeolites of mordenite type, ZSM-5 and NaY, using different metals cations has been studied. It has been shown that introducing Cr, Cs, Zn, Ni, Co, Li, Mn in zeolites results in modification of the toluene TPD and toluene sorption capacity. 5%LiZSM-5 zeolite exhibits the most attractive TPD curve, with toluene desorption temperature ranging from 250 to 350ОС. The sorption capacity of 5%Li-ZSM-5 is 0.4 mmol/g. NaY zeolite has the highest sorption capacity, up to 2 mmol/g, and holds toluene up to 350ОС, but at 120ОС toluene desorption starts, which is not desirable, since the adsorbent of cold start hydrocarbons should retain them until 250-300ОС. Therefore 5%LiZSM-5 zeolite was found to be the most promising to control the cold-start hydrocarbon emissions among the samples studied.

Keywords: Hydrocarbon emission control, adsorbents, zeolites, temperature-programmed desorption.

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1202 A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations

Authors: Sachin Bhalekar

Abstract:

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.

Keywords: Caputo derivative, delay, stability, chaos.

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1201 Is It Important to Measure the Volumetric Mass Density of Nanofluids?

Authors: Z. Haddad, C. Abid, O. Rahli, O. Margeat, W. Dachraoui, A. Mataoui

Abstract:

The present study aims to measure the volumetric mass density of NiPd-heptane nanofluids synthesized using a one step method known as thermal decomposition of metal-surfactant complexes. The particle concentration is up to 7.55g/l and the temperature range of the experiment is from 20°C to 50°C. The measured values were compared with the mixture theory and good agreement between the theoretical equation and measurement were obtained. Moreover, the available nanofluids volumetric mass density data in the literature is reviewed.

Keywords: NiPd nanoparticles, nanofluids, volumetric mass density, stability.

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1200 Performance Improvement of MAC Protocols for Broadband Power-Line Access Networks of Developing Countries: A Case of Tanzania

Authors: Abdi T. Abdalla, Justinian Anatory

Abstract:

This paper investigates the possibility of improving throughputs of some Media Access Controls protocols such as ALOHA, slotted ALOHA and Carrier Sense Multiple Access with Collision Avoidance with the aim of increasing the performance of Powerline access networks. In this investigation, the real Powerline network topology in Tanzania located in Dar es Salaam City, Kariakoo area was used as a case study. During this investigation, Wireshark Network Protocol Analyzer was used to analyze data traffic of similar existing network for projection purpose and then the data were simulated using MATLAB. This paper proposed and analyzed three improvement techniques based on collision domain, packet length and combination of the two. From the results, it was found that the throughput of Carrier Sense Multiple Access with Collision Avoidance protocol improved noticeably while ALOHA and slotted ALOHA showed insignificant changes especially when the hybrid techniques were employed.

Keywords: Access Network, ALOHA, Broadband Powerline Communication, Slotted ALOHA, CSMA/CA and MAC Protocols.

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1199 Experimental Investigations on the Influence of Properties of Jatropha Biodiesel on Performance, Combustion, and Emission Characteristics of a DI-CI Engine

Authors: P. V. Rao

Abstract:

The aim of the present research work is to investigate the influence of Jatropha biodiesel properties on various characteristics of a direct injection compression ignition engine. The experiments were performed at different engine operating regimes with the injection timing prescribed by the engine manufacturer for diesel fuel. The engine characteristics with Jatropha biodiesel were compared against those obtained using diesel fuel. From the results, it is observed that the biodiesel performance and emissions are lower than that of diesel fuel. However, the NOx emission of Jatropha biodiesel is more than that of diesel fuel. These high NOx emissions are due to the presence of unsaturated fatty acids and the advanced injection caused by the higher bulk modulus (or density) of Jatropha biodiesel Furthermore, the possibility for reduction of NOx emissions without expensive engine modifications (hardware) was investigated. Keeping this in mind, the Jatropha biodiesel was preheated. The experimental results show that the retarded injection timing is necessary when using Jatropha biodiesel in order to reduce NOx emission without worsening other engine characteristics. Results also indicate improved performance with the application of preheated biodiesel. The only penalty for using preheated biodiesel is the increase of smoke (soot).

Keywords: chemical properties, combustion, exhaust emissions, Jatropha biodiesel

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1198 On Constructing a Cubically Convergent Numerical Method for Multiple Roots

Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

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1197 Collaborative Web Platform for Rich Media Educational Material Creation

Authors: I. Alberdi, H. Iribas, A. Martin, N. Aginako

Abstract:

This paper describes a platform that faces the main research areas for e-learning educational contents. Reusability tackles the possibility to use contents in different courses reducing costs and exploiting available data from repositories. In our approach the production of educational material is based on templates to reuse learning objects. In terms of interoperability the main challenge lays on reaching the audience through different platforms. E-learning solution must track social consumption evolution where nowadays lots of multimedia contents are accessed through the social networks. Our work faces it by implementing a platform for generation of multimedia presentations focused on the new paradigm related to social media. The system produces videos-courses on top of web standard SMIL (Synchronized Multimedia Integration Language) ready to be published and shared. Regarding interfaces it is mandatory to satisfy user needs and ease communication. To overcome it the platform deploys virtual teachers that provide natural interfaces while multimodal features remove barriers to pupils with disabilities.

Keywords: Collaborative, multimedia e-learning, reusability, SMIL, virtual teacher

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1196 On the Relationship between Language Output and Second Language Acquisition

Authors: Haiyan Wang

Abstract:

Many researchers have been discussing the importance of language input in second language acquisition. The author holds that the bigger problem lies in how to activate language learners' language knowledge and raise their language output consciousness and competence. Analyzing the importance of language output based on theory and reality, this paper mainly explores the essence of language output and its revelation for second language acquisition in order to make second language learners really raise their communicative competence.

Keywords: Language output, second language acquisition, communicative competence.

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1195 Age–Related Changes of the Sella Turcica Morphometry in Adults Older Than 20-25 Years

Authors: Yu. I. Pigolkin, M. A. Garcia Corro

Abstract:

Age determination of unknown dead bodies in forensic personal identification is a complicated process which involves the application of numerous methods and techniques. Skeletal remains are less exposed to influences of environmental factors. In order to enhance the accuracy of forensic age estimation additional properties of bones correlating with age are required to be revealed. Material and Methods: Dimensional examination of the sella turcica was carried out on cadavers with the cranium opened by a circular vibrating saw. The sample consisted of a total of 90 Russian subjects, ranging in age from two months and 87 years. Results: The tendency of dimensional variations throughout life was detected. There were no observed gender differences in the morphometry of the sella turcica. The shared use of the sella turcica depth and length values revealed the possibility to categorize an examined sample in a certain age period. Conclusions: Based on the results of existing methods of age determination, the morphometry of the sella turcica can be an additional characteristic, amplifying the received values, and accordingly, increasing the accuracy of forensic biological age diagnosis.

Keywords: Age–related changes in bone structures, forensic personal identification, Sella turcica morphometry, body identification.

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1194 Aligning IS Development with Users- Work Habits

Authors: Abbas Moshref Razavi, Rodina Ahmad

Abstract:

As a primitive assumption, if a new information system is able to remind users their old work habits, it should have a better opportunity to be accepted, adopted and finally, utilized. In this paper some theoretical concepts borrowed from psychodynamic theory e.g. ego defenses are discussed to show how such resemblance can be made without necessarily affecting the performance of the new system. The main assertion is a new system should somehow imitate old work habits, not literally, but through following their paces in terms of the order of habitual tensional states including stimulation, defensive actions and satisfactions.

Keywords: information Systems, users' habits, psychodynamic

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1193 Evolutionary Design of Polynomial Controller

Authors: R. Matousek, S. Lang, P. Minar, P. Pivonka

Abstract:

In the control theory one attempts to find a controller that provides the best possible performance with respect to some given measures of performance. There are many sorts of controllers e.g. a typical PID controller, LQR controller, Fuzzy controller etc. In the paper will be introduced polynomial controller with novel tuning method which is based on the special pole placement encoding scheme and optimization by Genetic Algorithms (GA). The examples will show the performance of the novel designed polynomial controller with comparison to common PID controller.

Keywords: Evolutionary design, Genetic algorithms, PID controller, Pole placement, Polynomial controller

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1192 Debts and Debt-Based Sukuk Related to Risk Shifting Behavior

Authors: Siti Raihana Hamzah

Abstract:

This paper elaborates risk shifting in debt financing system as the ultimate cause of the global financial crisis. In contrast, risk sharing in equity financing like sukuk helps the economic system to be better sustained. Nevertheless, some types of sukuk are haunted by the issue of imitation with bonds. The critics on the imitation issue not only have raised doubt on the ability of sukuk to diminish risk shifting behavior but also the ability of this Islamic financial instrument to ensure better future financial stability. Through that, this paper provides discussion on the possibility of sukuk to induce risk shifting and how equity financing may help sukuk to be free from risk shifting. This paper is important in the sense that sukuk receives a significant demand from investors throughout the world. For this instrument to be supportive in the future economic stability, the issue of imitation needs to be identified and addressed. Furthermore, critics cannot be focused on debts and its ability to gauge the financial flux but also to sukuk due to their structures similarity.

Keywords: Global financial crisis, debt, risk-shifting, risk sharing, equity, sukuk, bonds.

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1191 Surface Activation of Carbon Nanotubes Generating a Chemical Interaction in Epoxy Nanocomposite

Authors: Mohamed Eldessouki, Ebraheem Shady, Yasser Gowayed

Abstract:

Carbon nanotubes (CNTs) are known for having high elastic properties with high surface area that promote them as good candidates for reinforcing polymeric matrices. In composite materials, CNTs lack chemical bonding with the surrounding matrix which decreases the possibility of better stress transfer between the components. In this work, a chemical treatment for activating the surface of the multi-wall carbon nanotubes (MWCNT) was applied and the effect of this functionalization on the elastic properties of the epoxy nanocomposites was studied. Functional amino-groups were added to the surface of the CNTs and it was evaluated to be about 34% of the total weight of the CNTs. Elastic modulus was found to increase by about 40% of the neat epoxy resin at CNTs’ weight fraction of 0.5%. The elastic modulus was found to decrease after reaching a certain concentration of CNTs which was found to be 1% wt. The scanning electron microscopic pictures showed the effect of the CNTs on the crack propagation through the sample by forming stress concentrated spots at the nanocomposite samples.

Keywords: Carbon nanotubes functionalization, crack propagation, elastic modulus, epoxy nanocomposites.

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1190 Reasoning with Dynamic Domains and Computer Security

Authors: Yun Bai

Abstract:

Representing objects in a dynamic domain is essential in commonsense reasoning under some circumstances. Classical logics and their nonmonotonic consequences, however, are usually not able to deal with reasoning with dynamic domains due to the fact that every constant in the logical language denotes some existing object in the static domain. In this paper, we explore a logical formalization which allows us to represent nonexisting objects in commonsense reasoning. A formal system named N-theory is proposed for this purpose and its possible application in computer security is briefly discussed.

Keywords: knowledge representation and reasoning, commonsensereasoning, computer security

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1189 Bifurcation Analysis for a Physiological Control System with Delay

Authors: Kejun Zhuang

Abstract:

In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.

Keywords: Physiological control system, global Hopf bifurcation, periodic solutions.

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1188 Global Existence of Periodic Solutions in a Delayed Tri–neuron Network

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.

Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.

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1187 New Algorithms for Finding Short Reset Sequences in Synchronizing Automata

Authors: Adam Roman

Abstract:

Finding synchronizing sequences for the finite automata is a very important problem in many practical applications (part orienters in industry, reset problem in biocomputing theory, network issues etc). Problem of finding the shortest synchronizing sequence is NP-hard, so polynomial algorithms probably can work only as heuristic ones. In this paper we propose two versions of polynomial algorithms which work better than well-known Eppstein-s Greedy and Cycle algorithms.

Keywords: Synchronizing words, reset sequences, Černý Conjecture

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1186 A Comparison of Fuzzy Clustering Algorithms to Cluster Web Messages

Authors: Sara El Manar El Bouanani, Ismail Kassou

Abstract:

Our objective in this paper is to propose an approach capable of clustering web messages. The clustering is carried out by assigning, with a certain probability, texts written by the same web user to the same cluster based on Stylometric features and using fuzzy clustering algorithms. Focus in the present work is on comparing the most popular algorithms in fuzzy clustering theory namely, Fuzzy C-means, Possibilistic C-means and Fuzzy Possibilistic C-Means.

Keywords: Authorship detection, fuzzy clustering, profiling, stylometric features.

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1185 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

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1184 Enzymatic Activity of Alfalfa in a Phenanthrene-contaminated Environment

Authors: Anna Yu. Muratova, Vera V. Kapitonova, Marina P. Chernyshova, Olga V. Turkovskaya

Abstract:

This research was undertaken to study enzymatic activity in the shoots, roots, and rhizosphere of alfalfa (Medicago sativa L.) grown in quartz sand that was uncontaminated and contaminated with phenanthrene at concentrations of 10 and 100 mg kg-1. The higher concentration of phehanthrene had a distinct phytotoxic effect on alfalfa, inhibiting seed germination energy, plant survival, and biomass accumulation. The plant stress response to the environmental pollution was an increase in peroxidase activity. Peroxidases were the predominant enzymes in the alfalfa shoots and roots. The peroxidase profile in the shoots differed from that in the roots and had different isoenzyme numbers. 2,2'-Azinobis-(3-ethylbenzo-thiazoline-6-sulphonate) (ABTS) peroxidase was predominant in the shoots, and 2,7-diaminofluorene (2,2-DAF) peroxidase was predominant in the roots. Under the influence of phenanthrene, the activity of 2,7-DAF peroxidase increased in the shoots, and the activity of ABTS peroxidase increased in the roots. Alfalfa root peroxidases were the prevalent enzyme systems in the rhizosphere sand. Examination of the activity of alfalfa root peroxidase toward phenanthrene revealed the possibility of involvement of the plant enzyme in rhizosphere degradation of the PAH.

Keywords: Medicago sativa, enzymatic activity, peroxidase, phenanthrene.

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1183 Persistence of Termination for Non-Overlapping Term Rewriting Systems

Authors: Munehiro Iwami

Abstract:

A property is called persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property. In this paper,we show that termination is persistent for non-overlapping term rewriting systems and we give the example as application of this result. Furthermore we obtain that completeness is persistent for non-overlapping term rewriting systems.

Keywords: Theory of computing, Model-based reasoning, termrewriting system, termination

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1182 Hazardous Waste Generated in the Peruvian Textile Industry: Haute Couture, Alpaca Fiber and Tannery

Authors: Huiman C. Alberto

Abstract:

The research cites the various hazardous waste generated in the textile industry. The method used is descriptive and comparative, the process consisted of the search and evaluation of information, both nationally and internationally. The results indicate: (1) Waste is generated from the alpaca fiber industry in the various stages of camelid rearing, they stand out for their dangerousness: excreta, residual fiber and yarn scraps. (2) The main hazardous waste generated by the tannery industry are grease, hides, hair, plastic containers with traces of toxic substances, chips and pieces of leather with chrome. (3) Three companies' Solid Waste Management Plans were analyzed, randomly selected, and none of them detail waste treatment processes and warn of the lack of supervision by the authorities. It is concluded that the hazardous waste generated can affect human and environmental health. There is the possibility of taking advantage of certain hazardous waste such as manure and alpaca fiber, after treatment; while non-hazardous waste from the tannery such as yarn, panel weaving, cloth, scraps, and thread, can be used to produce new products, generating a production chain in favor of the entrepreneur himself.

Keywords: Alpaca fiber, excreta, Haute couture, hazardous waste tannery, hazardous waste treatment, textile waste,

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1181 Protecting the Privacy and Trust of VIP Users on Social Network Sites

Authors: Nidal F. Shilbayeh, Sameh T. Khuffash, Mohammad H. Allymoun, Reem Al-Saidi

Abstract:

There is a real threat on the VIPs personal pages on the Social Network Sites (SNS). The real threats to these pages is violation of privacy and theft of identity through creating fake pages that exploit their names and pictures to attract the victims and spread of lies. In this paper, we propose a new secure architecture that improves the trusting and finds an effective solution to reduce fake pages and possibility of recognizing VIP pages on SNS. The proposed architecture works as a third party that is added to Facebook to provide the trust service to personal pages for VIPs. Through this mechanism, it works to ensure the real identity of the applicant through the electronic authentication of personal information by storing this information within content of their website. As a result, the significance of the proposed architecture is that it secures and provides trust to the VIPs personal pages. Furthermore, it can help to discover fake page, protect the privacy, reduce crimes of personality-theft, and increase the sense of trust and satisfaction by friends and admirers in interacting with SNS.

Keywords: Social Network Sites, Online Social Network, Privacy, Trust, Security and Authentication.

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1180 Transformation of Industrial Policy towards Industry 4.0 and Its Impact on Firms' Competition

Authors: Arūnas Burinskas

Abstract:

Although Europe is on the threshold of a new industrial revolution called Industry 4.0, many believe that this will increase the flexibility of production, the mass adaptation of products to consumers and the speed of their service; it will also improve product quality and dramatically increase productivity. However, as expected, all the benefits of Industry 4.0 face many of the inevitable changes and challenges they pose. One of them is the inevitable transformation of current competition and business models. This article examines the possible results of competitive conversion from the classic Bertrand and Cournot models to qualitatively new competition based on innovation. Ability to deliver a new product quickly and the possibility to produce the individual design (through flexible and quickly configurable factories) by reducing equipment failures and increasing process automation and control is highly important. This study shows that the ongoing transformation of the competition model is changing the game. This, together with the creation of complex value networks, means huge investments that make it particularly difficult for small and medium-sized enterprises. In addition, the ongoing digitalization of data raises new concerns regarding legal obligations, intellectual property, and security.

Keywords: Bertrand and Cournot Competition, competition model, Industry 4.0, industrial organization, monopolistic competition.

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1179 Hydrologic Balance and Surface Water Resources of the Cheliff-Zahrez Basin

Authors: Mehaiguene Madjid, Touhari Fadhila, Meddi Mohamed

Abstract:

The Cheliff basin offers a good hydrological example for the possibility of studying the problem which elucidated in the future, because of the unclearity in several aspects and hydraulic installation. Thus, our study of the Cheliff basin is divided into two principal parts: The spatial evaluation of the precipitation: also, the understanding of the modes of the reconstitution of the resource in water supposes a good knowledge of the structuring of the precipitation fields in the studied space. In the goal of a good knowledge of revitalizes them in water and their management integrated one judged necessary to establish a precipitation card of the Cheliff basin for a good understanding of the evolution of the resource in water in the basin and that goes will serve as basis for all study of hydraulic planning in the Cheliff basin. Then, the establishment of the precipitation card of the Cheliff basin answered a direct need of setting to the disposition of the researchers for the region and a document of reference that will be completed therefore and actualized. The hydrological study, based on the statistical hydrometric data processing will lead us to specify the hydrological terms of the assessment hydrological and to clarify the fundamental aspects of the annual flow, seasonal, extreme and thus of their variability and resources surface water.

Keywords: Hydrological assessment, surface water resources, Cheliff, Algeria.

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1178 Analysis of Complex Quadrature Mirror Filter Banks

Authors: Chimin Tsai

Abstract:

This work consists of three parts. First, the alias-free condition for the conventional two-channel quadrature mirror filter bank is analyzed using complex arithmetic. Second, the approach developed in the first part is applied to the complex quadrature mirror filter bank. Accordingly, the structure is simplified and the theory is easier to follow. Finally, a new class of complex quadrature mirror filter banks is proposed. Interesting properties of this new structure are also discussed.

Keywords: Aliasing cancellation, complex signal processing, polyphase realization, quadrature mirror filter banks.

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1177 Order Penetration Point Location using Fuzzy Quadratic Programming

Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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1176 Multiple Periodic Solutions for a Delayed Predator-prey System on Time Scales

Authors: Xiaoquan Ding, Jianmin Hao, Changwen Liu

Abstract:

This paper is devoted to a delayed periodic predatorprey system with non-monotonic numerical response on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.

Keywords: Predator-prey system, periodic solution, time scale, delay, coincidence degree.

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