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Separation of Copper and Nickel by Solvent Extraction Using LIX 664N 被引量:2
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作者 Rashmi Kumar Dahyalal J. Shah Krishna Kant Tiwari 《Journal of Environmental Protection》 2013年第4期315-318,共4页
Separation of copper and nickel by liquid-liquid extraction from aqueous solutions was studied using LIX 664N in kerosene as solvent. Both metals were taken in their sulfate form and ratio of copper to nickel in feed ... Separation of copper and nickel by liquid-liquid extraction from aqueous solutions was studied using LIX 664N in kerosene as solvent. Both metals were taken in their sulfate form and ratio of copper to nickel in feed solutions was maintained as 10:1. LIX 664N concentration in kerosene was varied from 10% to 40% (v/v) and its effect was studied on percent extraction of copper and nickel for organic to aqueous (O:A) phase ratio of 2:1 at pH 2. Experimental results showed that at pH 2, copper was selectively extracted from its mixture with nickel. Selectivity for copper extraction was as high as 6000 with 40% LIX 664N. Calculations using extraction isotherm indicate almost complete recovery of copper in two stages with O:A ratio of 1:1 and in one stage with O:A ratio of 2:1. After extraction of copper, the pH of raffinate containing nickel was adjusted to a value of 9 by addition of ammonia solution. The effect of LIX 664N concentration on extraction of nickel was studied. Up to 80% nickel could be extracted with 30% LIX 664N at O:A phase ratio of 2:1. Stripping of copper from the organic phase with 180 g/l sulfuric acid at O:A phase ratio of 1:1 gave 98.5% copper recovery in a two-stage operation. 展开更多
关键词 COPPER NICKEL LIX 664N SOLVENT EXTRACTION Distribution COEFFICIENT SELECTIVITY
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Extraction and Enrichment of Copper by Liquid Emulsion Membrane Using LIX 664N 被引量:2
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作者 Rashmi Kumar Dahyalal J. Shah Krishna Kant Tiwari 《Journal of Environmental Protection》 2014年第17期1611-1617,共7页
Process intensification using liquid emulsion membranes (LEMs) for extraction of copper has been studied in this work. In LEM process the extraction and stripping processes are combined in one stage. The solubility of... Process intensification using liquid emulsion membranes (LEMs) for extraction of copper has been studied in this work. In LEM process the extraction and stripping processes are combined in one stage. The solubility of the solute or the chemical affinity between the solute and carrier reagent in the membrane results in the separation of the solute from the feed mixture. In this work the membrane phase comprised of LIX 664N as the extractant dissolved in kerosene and Span 80 as surfactant. The stripping phase was sulfuric acid with 180 g/l concentration and feed phase had copper concentration of 3.5 g/l. Effect of various process parameters such as batch contact time, speed of agitation, W:O ratio and treat ratio has been experimentally investigated to get better insight of the process. The maximum enrichment of copper in the internal phase obtained was 11.6 times with batch contact time of 10 minutes, agitation speed of 300 rpm and treat ratio of 6:1. 展开更多
关键词 EXTRACTION ENRICHMENT LIQUID EMULSION Membranes LIX 664N COPPER
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Fritz John Duality in the Presence of Equality and Inequality Constraints
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作者 Iqbal Husain Santosh K. Shrivastav 《Applied Mathematics》 2012年第9期1023-1028,共6页
A dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situation, is formulated which uses Fritz John optimality conditions instead of the Karu... A dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situation, is formulated which uses Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and does not require a constraint qualification. Various duality results, namely, weak, strong, strict-converse and converse duality theorems are established under suitable generalized convexity. A generalized Fritz John type dual to the problem is also formulated and usual duality results are proved. In essence, the duality results do not require any regularity condition if the formulations of dual problems uses Fritz John optimality conditions. 展开更多
关键词 SECOND-ORDER INVEXITY SECOND-ORDER PSEUDOINVEXITY SECOND-ORDER Quasi-Invexity Nonlinear PROGRAMMING Fritz John Type Dual
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Breast Calcifications and Histopathological Analysis on Tumour Detection by CNN
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作者 D.Banumathy Osamah Ibrahim Khalaf +2 位作者 Carlos Andrés Tavera Romero P.Vishnu Raja Dilip Kumar Sharma 《Computer Systems Science & Engineering》 SCIE EI 2023年第1期595-612,共18页
The most salient argument that needs to be addressed universally is Early Breast Cancer Detection(EBCD),which helps people live longer lives.The Computer-Aided Detection(CADs)/Computer-Aided Diagnosis(CADx)sys-tem is ... The most salient argument that needs to be addressed universally is Early Breast Cancer Detection(EBCD),which helps people live longer lives.The Computer-Aided Detection(CADs)/Computer-Aided Diagnosis(CADx)sys-tem is indeed a software automation tool developed to assist the health profes-sions in Breast Cancer Detection and Diagnosis(BCDD)and minimise mortality by the use of medical histopathological image classification in much less time.This paper purposes of examining the accuracy of the Convolutional Neural Network(CNN),which can be used to perceive breast malignancies for initial breast cancer detection to determine which strategy is efficient for the early iden-tification of breast cell malignancies formation of masses and Breast microcalci-fications on the mammogram.When we have insufficient data for a new domain that is desired to be handled by a pre-trained Convolutional Neural Network of Residual Network(ResNet50)for Breast Cancer Detection and Diagnosis,to obtain the Discriminative Localization,Convolutional Neural Network with Class Activation Map(CAM)has also been used to perform breast microcalcifications detection tofind a specific class in the Histopathological image.The test results indicate that this method performed almost 225.15%better at determining the exact location of disease(Discriminative Localization)through breast microcalci-fications images.ResNet50 seems to have the highest level of accuracy for images of Benign Tumour(BT)/Malignant Tumour(MT)cases at 97.11%.ResNet50’s average accuracy for pre-trained Convolutional Neural Network is 94.17%. 展开更多
关键词 Computer-Aided Detection breast cancer detection convolutional neural network class activation map computer-aided diagnosis
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Motion of a permeable shell in a spherical container filled with non-Newtonian fluid
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作者 V.MISHRA B.R.GUPTA 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2017年第12期1697-1708,共12页
This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center... This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis. 展开更多
关键词 micro-polar fluid permeable sphere Darcy law stream function drag force wall correction factor spherical container
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Despeckling of Ultrasound Images Using Modified Local Statistics Mean Variance Filter
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作者 Ranu Gupta Rahul Pachauri Ashutosh Singh 《Computer Modeling in Engineering & Sciences》 SCIE EI 2018年第1期19-32,共14页
This article presents an improved method of despeckling the ultrasound medical images.In this paper a modified local statistics mean variance filter method has been proposed.In the proposed method,more consideration i... This article presents an improved method of despeckling the ultrasound medical images.In this paper a modified local statistics mean variance filter method has been proposed.In the proposed method,more consideration is given to local statistics since local statistical features are more important rather than global features.Various parameters like mean square error,peak signal to noise ratio,quality index,and structural similarity index measure are calculated to analyze the quality of the despeckled image. 展开更多
关键词 LOCAL STATISTICS SPECKLE ULTRASOUND IMAGE
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Probabilistic Selection of QoS Paths for Improving Survivability in MPLS Networks
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作者 Ravindra Kumar Singh Narendra S. Chaudhari Kanak Saxena 《Communications and Network》 2013年第4期328-336,共9页
Many applications do not fit well with the traditional best effort packet delivery policy of the Internet. These include applications such as Internet telephony and video conferencing which require voice and bulky gra... Many applications do not fit well with the traditional best effort packet delivery policy of the Internet. These include applications such as Internet telephony and video conferencing which require voice and bulky graphical images transfer. Therefore, the policies of assigning traffic to various service classes and providing service as per the service level agreement of the user with the network provider came into existence. Multi-protocol Label Switching is the backbone of fast switching technology that helps the network service providers to implement these policies. It provides Quality of service oriented reserved paths from the source to the destination for the user’s traffic. Selection of these paths is a cumbersome task, especially when the traffic forecast is totally unknown. Furthermore, nodes and link failures in the Internet worsen the situation. This paper addresses the issue of selecting Label Switched Paths (LSPs) for various traffic demands in the network so that the resultant network has the characteristics like high failure resistance, low LSP demand blocking probability, low impact from the node or link failure, load balancing and low over-all resource utilization. By extensive simulations, the proposed cost function has been compared with the various cost functions mentioned in the literature and it was found to score over them in major aspects. 展开更多
关键词 MPLS LABEL SWITCHED PATHS Fault TOLERANCE SURVIVABILITY
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Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints
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作者 Iqbal Husain Vikas K. Jain 《Open Journal of Modelling and Simulation》 2013年第2期7-13,共7页
In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function in the presenc... In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function in the presence of equality and inequality constraints. As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-Weir type dual to this problem is formulated and various duality results are established under generalized invexity assumptions. Finally, a special case is deduced from our result. 展开更多
关键词 NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING Problem Efficient Solution Generalized INVEXITY DUALITY NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING Problems with EQUALITY and Inequality
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Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems
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作者 I. Husain Vikas K. Jain 《American Journal of Operations Research》 2012年第4期536-545,共10页
Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type s... Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature. 展开更多
关键词 NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING SECOND-ORDER INVEXITY SECOND-ORDER Pseudoinvexity SECOND-ORDER Quasi-Invexity SECOND-ORDER DUALITY Nonlinear MULTIOBJECTIVE PROGRAMMING
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Study on Temperature Gradients and Protein Enrichment by <i>Aspergillus oryzae</i>in Solid-State Fermentation on Packed Bed Bioreactor Using Jowar (Sorghum) Straw as Substrate
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作者 Ganesh A. Bathe Vilas S. Patil Ashish S. Chaurasia 《Journal of Sustainable Bioenergy Systems》 2012年第3期33-36,共4页
The packed bed solid state bioreactor designated as PBSSB is constructed in the present study. The experiments are carried out in packed bed bioreactor with jowar straw and inoculated with Aspergillus oryzae. Temperat... The packed bed solid state bioreactor designated as PBSSB is constructed in the present study. The experiments are carried out in packed bed bioreactor with jowar straw and inoculated with Aspergillus oryzae. Temperature gradient has been measured at different axial positions. It is found that the organisms grew rapidly during the period from 20 to 30 h during which heat generation is more. These results are in agreement with other researchers. The fermented jowar straw shows threefold increase in protein content. This can be utilized as high value nutritional feed to animals. 展开更多
关键词 Solid-State Fermentation PACKED-BED Bioreactor Aspergillus ORYZAE Jowar STRAW Temperature Gradient
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Constrained Dynamic Game and Symmetric Duality for Variational Problems
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作者 Iqbal Husain Bilal Ahmad 《Journal of Mathematics and System Science》 2012年第3期171-178,共8页
A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results ... A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results are proved under convexity and generalized convexity assumptions on the appropriate functionals. The dynamic game is also viewed as equivalent to a pair of dual variational problems without the condition of fixed points. It is also indicated that the equivalent formulation of a pair of symmetric dual variational problems as dynamic generalization of those had been already studied in the literature. In essence, the purpose of the research is to establish that the solution of variational problems yields the solution of the dynamic game. 展开更多
关键词 Dynamic games variational problems symmetric duality generalized convexity.
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An Optimized Fuzzy Based Ant Colony Algorithm for 5G-MANET 被引量:1
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作者 R.Nithya K.Amudha +5 位作者 A.Syed Musthafa Dilip Kumar Sharma Edwin Hernan Ramirez-Asis Priya Velayutham V.Subramaniyaswamy Sudhakar Sengan 《Computers, Materials & Continua》 SCIE EI 2022年第1期1069-1087,共19页
The 5G demonstrations in a business has a significant role in today’s fast-moving technology.Manet in 5G,drives a wireless system intended at an enormously high data rate,lower energy,low latency,and cost.For this re... The 5G demonstrations in a business has a significant role in today’s fast-moving technology.Manet in 5G,drives a wireless system intended at an enormously high data rate,lower energy,low latency,and cost.For this reason,routing protocols of MANET have the possibility of being fundamentally flexible,high performance,and energy-efficient.The 5G communication aims to afford higher data rates and significantly low Over-The-Air latency.Motivated through supplementary ACO routing processes,a security-aware,fuzzy improved ant colony routing optimization protocol is proposed in MANETs.The goal is to develop aMANET routing protocol that could provide a stable packet transmission ratio,less overhead connectivity,and low end-to-end latency in shared standard scenarios and attack states.MANET demonstrates effective results with hybrid architecture and proved to be effective than other state-of-the-art routing protocols of MANETs,like AODV,its routing organization implemented through Optimized Fuzzy based ACO Algorithm for 5G.Millimeter-wavelengths are required to perform a significant role in 5G.This research proposed to test the efficiency of MANET consisting of only mmWave User Equipment.MANET reduced packet transmission loss of UEs withmmWave,meaning well-transmitted SNR leads directly to a better packet delivery ratio.To verify results,simulation using the NS-3 simulator mmWave module is used. 展开更多
关键词 5G ATTACKS D2D communications MANET mmWave SECURITY
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Interactive Middleware Services for Heterogeneous Systems 被引量:1
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作者 Vasanthi Raghupathy Osamah Ibrahim Khalaf +2 位作者 Carlos Andrés Tavera Romero Sudhakar Sengan Dilip Kumar Sharma 《Computer Systems Science & Engineering》 SCIE EI 2022年第6期1241-1253,共13页
Computing has become more invisible, widespread and ubiquitoussince the inception of the Internet of Things (IoT) and Web of Things. Multipledevices that surround us meet user’s requirements everywhere. Multiple Midd... Computing has become more invisible, widespread and ubiquitoussince the inception of the Internet of Things (IoT) and Web of Things. Multipledevices that surround us meet user’s requirements everywhere. Multiple Middleware Framework (MF) designs have come into existence because of the rapiddevelopment of interactive services in Heterogeneous Systems. This resulted inthe delivery of interactive services throughout Heterogeneous Environments(HE). Users are given free navigation between devices in a widespread environment and continuously interact with each other from any chosen device. Numerous interactive devices with recent interactive platforms (for example, SmartPhones, Mobile Phones, Personal Computer (PC) and Personal Digital Assistant(PDA)) are available in the market. For easy access to information and servicesirrespective of the device used for working and even at the drastic change ofthe environment, the execution of applications on a broad spectrum of computingdevices is propelled by the availability of the above-mentioned platforms. Different applications that need interoperability to coordinate and correspond with eachother should be facilitated. Using a standard interface and data format, HE mustlink various devices from various platforms together to communicate with eachother. To aid the interactive services performed by a middleware framework thatoperates on Application Programming Interface (API) over HEs, this issue aims toendorse an Adaptable Service Application Programming Interface (ASAPI). 展开更多
关键词 MIDDLEWARE SERVICES ONTOLOGY INTEROPERABILITY
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Fuzzy Based Ant Colony Optimization Scheduling in Cloud Computing 被引量:1
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作者 K.Rajakumari M.Vinoth Kumar +3 位作者 Garima Verma S.Balu Dilip Kumar Sharma Sudhakar Sengan 《Computer Systems Science & Engineering》 SCIE EI 2022年第2期581-592,共12页
Cloud computing is an Information Technology deployment model established on virtualization.Task scheduling states the set of rules for task allocations to an exact virtual machine in the cloud computing environment.H... Cloud computing is an Information Technology deployment model established on virtualization.Task scheduling states the set of rules for task allocations to an exact virtual machine in the cloud computing environment.However,task scheduling challenges such as optimal task scheduling performance solutions,are addressed in cloud computing.First,the cloud computing performance due to task scheduling is improved by proposing a Dynamic Weighted Round-Robin algorithm.This recommended DWRR algorithm improves the task scheduling performance by considering resource competencies,task priorities,and length.Second,a heuristic algorithm called Hybrid Particle Swarm Parallel Ant Colony Optimization is proposed to solve the task execution delay problem in DWRR based task scheduling.In the end,a fuzzy logic system is designed for HPSPACO that expands task scheduling in the cloud environment.A fuzzy method is proposed for the inertia weight update of the PSO and pheromone trails update of the PACO.Thus,the proposed Fuzzy Hybrid Particle Swarm Parallel Ant Colony Optimization on cloud computing achieves improved task scheduling by minimizing the execution and waiting time,system throughput,and maximizing resource utilization. 展开更多
关键词 Cloud Computing SCHEDULING ant colony optimization fuzzy logic
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On Second-Order Duality in Nondifferentiable Continuous Programming 被引量:1
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作者 I. Husain Santosh K. Shrivastav 《American Journal of Operations Research》 2012年第3期289-295,共7页
A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-i... A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature. 展开更多
关键词 Continuous PROGRAMMING SECOND-ORDER INVEXITY SECOND-ORDER PSEUDOINVEXITY SECOND-ORDER Quasi-Invexity SECOND-ORDER DUALITY Nonlinear PROGRAMMING
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On Continuous Programming with Support Functions
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作者 Iqbal Husain Santosh K. Shrivastav Abdul Raoof Shah 《Applied Mathematics》 2013年第10期1441-1449,共9页
A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under s... A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined. 展开更多
关键词 Continuous PROGRAMMING SECOND-ORDER Generalized INVEXITY SECOND-ORDER DUALITY Nonlinear PROGRAMMING Support Functions Natural BOUNDARY VALUES
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Duality for a Control Problem Involving Support Functions
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作者 I. Husain Abdul Raoof Shah Rishi K. Pandey 《Applied Mathematics》 2014年第21期3525-3535,共11页
Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programmin... Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined. 展开更多
关键词 Control Problem SUPPORT FUNCTION Generalize CONVEXITY CONVERSE DUALITY Nonlinear PROGRAMMING
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Cloud Security Service for Identifying Unauthorized User Behaviour
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作者 D.Stalin David Mamoona Anam +4 位作者 Chandraprabha Kaliappan S.Arun Mozhi Selvi Dilip Kumar Sharma Pankaj Dadheech Sudhakar Sengan 《Computers, Materials & Continua》 SCIE EI 2022年第2期2581-2600,共20页
Recently,an innovative trend like cloud computing has progressed quickly in InformationTechnology.For a background of distributed networks,the extensive sprawl of internet resources on the Web and the increasing numbe... Recently,an innovative trend like cloud computing has progressed quickly in InformationTechnology.For a background of distributed networks,the extensive sprawl of internet resources on the Web and the increasing number of service providers helped cloud computing technologies grow into a substantial scaled Information Technology service model.The cloud computing environment extracts the execution details of services and systems from end-users and developers.Additionally,through the system’s virtualization accomplished using resource pooling,cloud computing resources become more accessible.The attempt to design and develop a solution that assures reliable and protected authentication and authorization service in such cloud environments is described in this paper.With the help of multi-agents,we attempt to represent Open-Identity(ID)design to find a solution that would offer trustworthy and secured authentication and authorization services to software services based on the cloud.This research aims to determine how authentication and authorization services were provided in an agreeable and preventive manner.Based on attack-oriented threat model security,the evaluation works.By considering security for both authentication and authorization systems,possible security threats are analyzed by the proposed security systems. 展开更多
关键词 Cloud computing user behaviour access control security model
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Load Balancing in IP/MPLS Networks: A Survey
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作者 Ravindra Kumar Singh Narendra S. Chaudhari Kanak Saxena 《Communications and Network》 2012年第2期151-156,共6页
The present era has witnessed tremendous growth of the Internet and various applications that are supported by it. There is an enormous pressure on Internet Service Providers (ISPs) to make available adequate services... The present era has witnessed tremendous growth of the Internet and various applications that are supported by it. There is an enormous pressure on Internet Service Providers (ISPs) to make available adequate services for the traffics like VoIP and Video on demand. Since the resources like computing power, bandwidth etc. are limited, the traffic needs to be engineered to properly exploit them. Due to these limitations, terms like Traffic Engineering, Quality of Service (QoS) came into existence. Traffic Engineering broadly includes techniques like multipath routing & traffic splitting to balance the load among different paths. In this document, we survey various techniques proposed for load balancing that are available on the Internet. We here try not to be exhaustive but analyze the important techniques in the literature. Present survey would help to give a new direction to the research in this realm. 展开更多
关键词 TRAFFIC Engineering LOAD Balancing MPLS NETWORKS
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On a Control Problem Containing Support Functions
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作者 I. Husain A. Ahmed Abdul Raoof Shah 《American Journal of Operations Research》 2014年第5期319-330,共12页
A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker ty... A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions. 展开更多
关键词 Control PROBLEM Support Function OPTIMALITY Conditions GENERALIZED CONVEXITY Wolfe Type DUALITY Nonlinear PROGRAMMING PROBLEM
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