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Interval-Valued Programming Problem with Infinite Constraints

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Journal of the Operations Research Society of China 2018年第4期6卷 611-626页

作者： promila kumar Bharti Sharma Jyoti Dagar Department of Mathematics Gargi CollegeUniversity of DelhiNew DelhiIndia University of Delhi New DelhiIndia

In this paper,we explore a class of interval-valued programming problem where constraints are interval-valued and *** optimality conditions are *** of generalized(Φ,ρ)−invexity is utilized to establish sufficient op... 详细信息

关键词： LU-optimal solution Interval valued Semi-infinite Generalized invexity Duality

Generalized Invexity of Higher Order and Its Applications in Variational Problems

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Applied Mathematics 2015年第9期6卷 1638-1648页

作者： promila kumar Jyoti Gargi College University of Delhi New Delhi India Department of Mathematics University of Delhi Delhi India

In the present paper the definition of invexity for continuous functions is extended to invexity of order m which is further generalized to ρ-pseudoinvexity type I of order m, ρ-pseudoinvexity type II of order m, as well as ρ-quasi invexity type I of order m and ρ-quasiinvexity type II of order m. The central objective of the paper is to study variational problem where the functionals involved satisfy the above stated generalized ρ-invexity assumptions of order m. Wolfe type and Mond Weir type of duals are formulated. Sufficient optimality conditions and duality results are proved. It is demonstrated with the help of an example that the class of ρ-invex functionals of order m is more general than the class of ρ-invex functionals. Further, it may be noted that the results presented in this paper are more powerful than the existing results as this new class of functions defined here satisfies mth derivative test.

关键词： Optimality Variational Problem Higher Order ρ-Invexity Duality

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

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American Journal of Operations Research 2016年第1期6卷 36-43页

作者： Bharti Sharma promila kumar Department of Mathematics University of Delhi New Delhi India Department of Mathematics Gargi College University of Delhi New Delhi India

In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.

关键词： Semi-Infinite Variational Problem Efficient Solution Necessary Optimality Conditions

A comparative evaluation of dentin caries removal with polymer bur and conventional burs—An <i>in vitro</i>study

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Open Journal of Stomatology 2012年第1期2卷 12-15页

作者： Vijay kumar Shakya Anil Chandra Aseem Prakash Tikku promila Verma Rakesh kumar Yadav Department of Conservative Dentistry and Endodontics Chhatrapati Shahuji Maharaj Medical University Lucknow India

Aim: To evaluate the comparative efficacy of Polymer bur (Smartprep) and Conventional burs (Carbide bur & Diamond Points) in selective Dentin caries removal. Materials and method: 15 freshly extracted carious human premolars and molars were selected for this study. These teeth were split in the center of carious lesion, in order to obtain two corresponding half. Thus 30 samples were prepared in this way. These were randomly divided in to 3 groups of 10 samples each. Group 1: The carious portion of these samples was excavated with the help of polymer bur Smartprep (SS White). Group 3: Prepared with Tungsten carbide round bur (No. 018). Group 3: Prepared with the help of Diamond points (No. 018). The period of time involved in this process is measured. After excavation of all carious lesions, a longitudinal section from mid most part of lesion was obtain with the help of diamond disc at slow speed. After staining with caries detector dye “Seek”, the sections were subjected to histological evaluation under stereomicro-scope. The thickness of remaining caries is measured in more or less than 1 mm. Results: The difference in grading of remaining carious dentin between Polymer bur and Conventional burs were statistically non- significant, but Polymer bur taken more time in comparison to Conventional burs. Conclusion: Smartprep bur is more conservative in selectively dentin caries removal than Conventional burs but same time it is more time consuming than Conventional burs.

关键词： Polymer Bur (Smartprep) Carbide Bur & Diamond Points Dentin Caries PBS Buffer