Candy was prepared with 3 different combinations of honey and carrot by using 750 g honey+1,000 g carrot (T1), 1,000 g honey+1,000 g carrot (T2) and 1,250 g honey+1,000 g carrot (T3). To establish the best product, sensory evaluation was done on 9-point Hedonic scale. T1 was found to be most preferred candy. Further the T1 candy was assessed for overall quality during storage at room temperature (25-30°C) for 6 months. Candy can be preserved safely for 6 months in both glass and LDPE packaging materials.

In this paper, we introduce fuzzy mathematical programming (FMP) for decision-making related to software creation by selecting optimal commercial-off-theshelf (COTS) products in a modular software system. Each module in such software systems have different alternatives with variations in their properties, for example, quality, reliability, execution time, size and cost. Due to these variations, componentbased software developers generally deals with the problem of selecting appropriate COTS products. The development of COTS-based systems largely depends on the success of the selection process. Various crisp optimization models of COTS products selection have been proposed in literature. However, in real COTS products selection problem, it is difficult to estimate precisely the values of various model parameters due to lack of sufficient data and also because of measurement errors. Hence, instead of crisp optimization model, if we use flexible optimization model then we might obtain results which are more preferred by the decision maker. In this study, we use multiple methodologies such as quality model, analytical hierarchy process and FMP to develop fuzzy multiobjective optimization model of the COTS products selection. To determine a preferred compromise solution for the multiobjective optimization problem, an interactive fuzzy approach is used.

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For functions f (z) = z + a 2 z 2 + a 3 z 3 + · · · in various subclasses of normalized analytic functions, we consider the problem of estimating the generalized Zalcman coefficient functional φ(f, n, m; λ) := |λa n a m − a n+m−1 |. For all real parameters λ and β < 1, we provide the sharp upper bound of φ(f, n, m; λ) for functions f satisfying Re f ′ (z) > β and hence settle the open problem of estimating φ(f, n, m; λ) recently proposed by Agrawal and Sahoo [S. Agrawal and S. K. Sahoo, On coefficient functionals associated with the Zalcman conjecture, arXiv preprint, 2016]. For all real values of λ, the estimations of φ(f, n, m; λ) are provided for starlike and convex functions of order α (α < 1) which are sharp for λ ≤ 0 or for certain positive values of λ. Moreover, for certain positive λ, the sharp estimation of φ(f, n, m; λ) is given when f is a typically real function or a univalent function with real coefficients or is in some subclasses of close-to-convex functions.2010 Mathematics Subject Classification. 30C45, 30C50, 30C80.

The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadeh's extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.

Drought is one of the most widespread global environmental problems leading to low water availability for plants, which causes a significant loss in growth, productivity and finally their yields. In the present study, the effect of drought stress on growth characteristics, physiological and biochemical parameters of Tectona grandis and Gmelina arborea at seedling stage under nursery conditions have been discussed. Pot culture experiments were conducted in RBD design to observe the effect of moderate drought (MD) and severe drought (SD) stress on the selected seedling sunder nursery conditions for one year. Moderate and severe drought conditions were artificially created with the help of CPE (Cumulative Pan Evaporation) values and PWP (Permanent Wilting Point). The amount of water equal to the calculated field capacity was provided to each polybag at the interval of calculated CPE. Physiological parameters viz. photosynthetic rate, stomatal conductance and transpiration rate of the seedlings were measured. Total Chlorophyll and Proline content were estimated for biochemical analysis. The outcome of the experiment showed that with the increasing age of the seedling, the effect of drought become more pronounced till the end of the experiment in terms of growth characteristics. Also, the severe drought condition was more lethal to the selected species seedlings. Further, the decreasing biomass, physiological parameters and chlorophyll content were found along with increased proline content with the severity of drought stress confirm the result. However, G. arborea found to be more affected than T. grandis. Hence, it can be concluded that the T. grandis species is better for plantation in an area with the moderate drought and can be maintained in severe drought climatic conditions. The plantations of suitable tree species in drought-prone areas will be helpful in sustainable forest management and resilient the forest ecosystem to climate change.