The investigation of Non-Darcian Benard Marangoni Convection (NDBMC) is carried out in a Superposed Fluid-Porous (SFP) layer, which consists of an incompressible, sparsely packed single component fluid saturated porous layer above which lies a layer of the same fluid, with temperature dependent heat sources in both the layers. The upper surface of the SFP layer is free with Marangoni effects depending on Temperature, where the lower surface of the SFP layer is rigid. The thermal Marangoni numbers are obtained in closed form for two sets of thermal boundaries set (i) Adiabatic-Adiabatic and set (ii) Adiabatic-Isothermal. Influence of temperature dependent heat source in terms of internal Rayleigh numbers, viscosity ratio, Darcy Number, thermal diffusivity ratio on NDBMC, is investigated in detail.
In a composite layer that comprises of a porous layer which is sparsely packed and saturated with two component incompressible fluid and above this porous layer lays a layer of the same fluid, with variable heat sources or sinks in both the layers double diffusive non-Darcian Benard Marangoni (DDNBM) convection is investigated. The upper surface of the composite layer has Marangoni effects which depend on temperature and concentration, whereas the lower surface is rigid. The inverted parabolic, parabolic and linear temperature profile is applied to this composite layer, which is surrounded by adiabatic boundaries. The appropriate thermal Marangoni numbers (TMANs) which are the eigen values (EVs) are calculated for all the three temperature gradients. The impact of different parameters on the EVs with respect to depth ratio is examined, thoroughly. The parameters that effect DDNBM convection are found.
Nonparametric tests for location problems have received much attention in the literature. Many nonparametric tests have been proposed for one, two and several samples location problems. In this paper a class of test statistics is proposed for two sample location problem when the underlying distributions of the samples are symmetric. The class of test statistics proposed is linear combination of U-statistics whose kernel is based on subsamples extrema. The members of the new class are shown to be asymptotically normal. The performance of the proposed class of tests is evaluated using Pitman Asymptotic Relative Efficiency. It is observed that the members of the proposed class of tests are better than the existing tests in the literature.
The special two-sample location problem is an important problem which is useful in comparing the performance of two measuring instruments. The problem of comparing the performances of two packing machines in which one machine may underfill the packets and the other may overfill the packets on an average, fits into special twosample location setup wherein one wishes to test for the point of symmetry versus an appropriate alternative. The only test available in the literature to the best of our knowledge is the class of tests due to Shetty and Umarani [13] which is based on U-statistics. In this paper, two classes of test statistics are proposed which are based on extremes of subsamples. The performances of the proposed classes of tests are Parameshwar V. Pandit and Deepa R. Acharya 48 evaluated in terms of Pitman asymptotic relative efficiency with respect to the test due to Shetty and Umarani [13]. It is observed that the members of proposed classes of tests perform better than the test due to Shetty and Umarani [13], for those distributions considered for evaluation.
Extending the result of Bor(2016) and subsequently Majhi et al, a new result concerning absolute indexed Riesz Summability factors, using quasi power increasing sequence, has been established.
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