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Abstract:

The necessary and sufficient conditions for a point ),(21μμ in the −μμ21plane to be constituted of the first and second moment of a probability distribution have been established in the present paper. The main results are reported in Theorem 1 and Theorem 2.

Keywords:

probability distribution , first moment of a probability distribution ,second moment of a probability distribution ,

Refference:

I. Shohat, J.A. and Tamarkin, J. D. The Problem of Moments, American Mathematical Society,1963.

II. Banerjee, M.B. and Shandil, R.G. A theorem of mean and standard deviation of a statistical variate, Ganita, 46,21-23.

III. Kapur, J.N. On inequality between moments of probability distribution, Ganita, 47,37-41.

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Abstract:

The Soret effect of temperature gradient on separation in generalized magnetohydrodynamic (MHD) Couette flow of a binary mixture of incompressible conducting viscous fluids between two parallel plates has been investigated analytically in the case when one plane is subjected to zero heat flux while the other has prescribed temperature. The expressions for velocity, temperature and the concentration are obtained analytically and the behaviour of concentration is shown graphically. It is observed that the temperature gradient separates the binary mixture components and the lighter component gets collected near the moving wall.

Keywords:

magnetohydrodynamic,Couette flow,viscous fluids,heat flux ,temperature gradient,

Refference:

I. Alchaar S., Vasseur P., Bilgen E.: J. Num. Heat TransferA, 27, 107 (1995).

II. Bian W., Vasseur P., Bilgen E., Meng F.: Int. Jour. Heat Fluid Flow, 17, 36 (1996).

III. Goel A.K., Agrawal S.C.: Ind. Jour. Pure & Appl. Math., 29, 929 (1998).

IV. Chauhan D. S., Vyas P.: Proc. Nat. Acad. Sci. India, 66A, 63 (1996).

V. Sutton G.W., Sherman A.: Engineering Magnetohydrodynamics, McGrawHill Pub. (1st Ed.), London, 351 (1965).

VI. Yen J.T., Chang C. C. : Ziet. Angew. Math. Physik.,15, 400 (1964).

VII. Zimmermann G., Muller U., Davis S.H.: J. Fluid Mech., 238, 657 (1992).

VIII. Shah N.A.: Ph.D. Thesis, Dibrugarh University, India (1996).

IX. B.R.Sharma, R.N.Singh: Bull. Cal. Math. Soc.,5, 96, 367 (2004).

X. Landau L.D., E.M.Lifshitz: Electrodynamics of continuous Media, Pergamon Press. Oxford, New York, English Ed., 104 (1960).

XI. Landau L.D., Lifshitz E.M.: Fluid Mechanics, Second Ed. Pergamon Press, London (1963).

XII. Hurle D.T.J., E.Jakeman: J.Fluid Mech. 4, 47, 667 (1971).

XIII. Srivastava A.C.: Proc. National Acad. Sci. India, A2. 69, 103 (1999).

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Abstract:

The aim of the present is to study compact fuzzy set using the definition of C. L. Chang and obtain its several aspects .

Keywords:

fuzzy set, compact fuzzy set,fuzzy topological spaces,

Refference:

I. Ali D. M., Ph.D. Thesis, Banaras Hindu University, 1990.

II. Chang C. L., Fuzzy Topological Spaces, J. Math. Anal. Appl. , 24(1968), 182 – 190.

III. David H., , Fuzzy Topological Groups, J. Math. Anal. Appl. , 67(1979), 549 – 564.

IV. Gantner T. E. and Steinlage R. C., Compactness in Fuzzy Topological Spaces, J. Math. Anal. Appl. , 62(1978), 547 – 562.

V. Lipschutz S., Theory and problems of general topology, Schaum’s outline series, McGraw-Hill book publication company, Singapore, 1965 .

VI. Mendelson B., Introduction to Topology, Allyn and Bacon Inc, Boston, 1962.

VII. Pu Pao – Ming and Liu Ying – Ming, Fuzzy topology. I. Neighborhood Structure of a fuzzy point and Moore – Smith Convergence ; J. Math. Anal. Appl. 76 (1980) , 571 – 599.

VIII.Murdeshwar M. G., General topology, wiley eastern limited, New Delhi Bangalore Bombay, Calcutta, 1983.

IX. Zadeh L. A., Fuzzy Sets, Information and Control, 8(1965), 338 – 353.

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Abstract:

In the subject matter of mathematical statistics, let the domain of mathematical activity that draws its inspiration from and nurtures the lead provided by the seminal paper of the American Economist and Nobel Prize (1970) winner P.A. Samuelson entitled, “How Deviant can you be?” and published in the Journal of the American Statistical Association in 1968, on the maximum and the minimum deviations, from the mean (denoted presently by m and 'm respectively) in a set of n observations with given mean μ and standard deviation σ, be henceforth defined as the Samuelson Domain. The present communication is in the Samuelson Domain. A circle theorem in the −σmplane is rigorously established and exhibited step by step for the sheer delight of its simplicity and elegance. A crude first approximation yields a result that is inferior to Samuelson’s but a more precise investigation of the consequences of the circle theorem shows that Samuelson’s famous work on the existence of bounds, for a set of n real numbers, in terms of σμ, and n can be improved upon provided n exceeds a critical value.

Keywords:

Samuelson Domain ,mean ,standard deviation ,maximum and the minimum deviations,critical value,

Refference:

I. Samuelson,P.A., How deviant can you be?, J. American Statistical Association, 63,1522-1525,1968.

II. Banerjee, M.B. and Shandil, R.G., A theorem on mean and standard deviation of a statistical variate, Ganita,46, 21-23,1995.

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Abstract:

The effects of induced magnetic field on a free convective heat transfer transient flow of fluid past an infinite vertical plate through a porous medium have been investigated numerically. A mathematical model of the problem is developed from the basis of studying magneto-fluid dynamics(MFD) and the equations are solved by the finite difference method. The numerical values of non-dimensional velocity, induced magnetic field and temperature are computed for the different values of associated parameters in different times. In order to discuss the results, the obtained numerical values of flow variables are plotted in graphs. Finally the important findings of this work are concluded here.

Keywords:

magnetic field ,free convective heat transfer ,magneto-fluid dynamics ,non-dimensional velocity,

Refference:

I.Finston M. “Free convection past a vertical plate” J. Appl. Math. Phy. Vol. 7, pp 527 – 529 (1956).

II.Sparrow E. M. and Gregg J. L. “Similar solutions for free convection from a non-isothermal vertical plate” ASME J. Heat Trans. Vol. 80, pp 379 – 386 (1958).

III.Soundalgekar V. M. and Ganesan P. “Finite difference analysis of transient free convection on an isothermal flat plate” Reg. J. Energy Heat Mass Trans. Vol. 3, pp 219 – 224 (1981).

IV.Camargo R. Luna E. and Treviňo C. “Numerical study of the natural convective cooling of a vertical plate” Heat Mass Trans. Vol. 32, pp 89 – 95 (1996).

V.Yamamoto K. and Iwamura N. “Flow with convective acceleration through a porous medium” J. Engng. Math. Vol. 10, pp 41 – 54 (1976).

VI.Raptis A. Tzivanidis G. and Kafousias N. “Free convection and mass transfer flow through a porous medium bounded by an infinite vertical limiting surface with constant suction” L. Heat Mass Trans. Vol. 8, pp 417 – 424 (1981).

VII.Ahmed N. and Sarma D. “Three dimensional free convection flow and heat transfer through a porous medium” Indian J. Pure Appl. Math.Vol. 26, pp 1345 – 1353 (1997).

VIII.Magyari E. Pop I. and Keller B. “Analytic solutions for unsteady free convection in porous media” J. Eng. Math. Vol. 48, pp 93 – 104 (2004).

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Abstract:

In this paper, a Fuzzy Knowledge – Rule base technique is used to predict the ambient atmospheric temperature. The present study utilizes historical temperature as well as database of various meteorological parameters to develop a prediction process in fuzzy rule domain to estimate temperature. Daily observations of Rain, Atmospheric Pressure, and Relative Humidity are analyzed to predict the Temperature. The topic of Fuzzy Logic as a decision-making technique is introduced. It is recommended that applications of this technique could be effectively applied in the area of operational meteorology. An example of such an application, the forecast of the probability of temperature, is discussed and examples of the method are presented. Other possible meteorological applications are suggested. Additionally, a software package which aids in the development of such applications is briefly described.

Keywords:

Fuzzy Logic ,atmospheric temperature ,Atmospheric Pressure ,Relative Humidity ,probability of temperature,

Refference:

I.Radhika, Y. and M. Shashi, 2009. AtmosphericTemperature Prediction using Support VectorMachines. International Journal of Computer Theoryand Engineering, 1: 55-58.

II. Pal, N.R., S. Pal, J. Das and K. Majumdar, 2003. A Hybrid Neural Network for Atmospheric Temperature Prediction. IEEE Transaction on Geoscience and Remote Sensing, 41: 2783-2791. doi: 10.1109/TGRS.2003.817225.

III. De, S. and A. Debnath, 2009. Artfitial Neural Network Based Prediction of maximum and Minimum Temperature in the summer Monsoon Months over India. Applied Physics Research, 1: 37-44.

IV. Long, J., J. Jian and Y. Cai, 2005. A short – term Climate Prediction model Based on a modular Fuzzy Neural Network. Advances in Atmospheric Sciences, 22: 428-435.

V. Kaonga, C.C., H.W.T. Mapoma, I.B.M. Kosamu and C. Tenthani, 2012. Temperature as an Indicator of Climate Variation at a Local Weather Station. World Applied Sciences Journal, 16(5): 699-706.

VI. Zadeh, L.A., 1965. Fuzzy Sets Information and Control, pp: 338-353.

VII. Kosko, B., 1992. Neural networks and Fuzzy systems. Prentice Hall. Englewood Cliffs, N.J.

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Abstract:

To obtain this present study we studied basic equations. We studied the equation of continuity and derived the Navier-Stockes (N-S) equations of motion for viscous compressible and incompressible fluid flow. Boundary layer and thermal boundary layer equations are also derived. Then we studied similar solution of boundary layer and thermal boundary layer equations. We also performed unsteady solutions of thermal boundary layer equations. We used some non-dimensional variable to non-dimensionalised thermal boundary layer equations. The non-dimensional boundary layer equations are non-linear partial differential equations. To find out the non-similar solutions of unsteady thermal boundary layer equation we used finite difference method. The effect on the velocity and temperature profiles for various parameters entering into the problems are separately discussed and shown graphically.

Keywords:

the Navier-Stockes equations ,viscous compressible and incompressible fluid ,thermal boundary layer,finite difference method,

Refference:

I. Falkner, V. M. and Skan, S. W., 1931. Soam approximate solutions of the boundary equations, Phill. Mag.12, pp. 865-896.

II. Callahan and Marner, 1976. Solving a transisent free convection flow with mass transfer past a semiinfinite plate.

III. G. Revathi, P. Saikrishnan, A. Chamkha, (2013) “Non-similar solution for unsteady water boundary layer flows over a sphere with non-uniform mass transfer”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 Iss: 6, pp.1104 – 1116

IV. T. Javed, M. Sajid, Z. Abbas, N. Ali, (2011) “Non-similar solution for rotating flow over an exponentially stretching surface”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 Iss: 7, pp.903 – 908

V. Prandtl, L., 1935. The mechanics of viscous fluids, Division G., Vol. III, Aerodynamic theory, edited by W.F. Durand, Julius Springer, Berlin.

VI. Raisinghania, M. D., 1982. Fluid Dynamics (with Hydrodynamics).

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Abstract:

The researches in the area of face detection have made significant progress in the past few decades. The main challenge in this stage of face detection is to find a suitable effective method for finding facial features. Sub-areas under feature extraction methods are skin color and texture based segmentation, deformable template matching, snake models, feature searching and constellation analysis. In this paper we represented a review on some important contribution in the field of feature extraction for face detection.

Keywords:

face detection, skin color and texture,snake models, constellation analysis,

Refference:

I.Jeng, S. H., Liao, H. Y. M, Hua, C. C. et al.: Facial Feature Detection Using Geometrical Face Model: An Efficient Approach. Pattern Recognition. Vol. 31, 1998, No. 3, pp. 273–282.

II.Jianguo, W., Tieniu, T.: A New Face Detection Method Based on Shape Information. Pattern Recognition Letters, Vol. 21, 2000, No. 3, pp. 463–471.

III.Shinn-Ying, H., Hui-Ling, H.: Facial Modeling from an Uncalibrated Face Image Using a Coarse-to-Fine Genetic Algorithm. Pattern Recognition, Vol. 34, 2001, No. 9, pp. 1015–1031.

IV. Terrillon J.C., Akamatsu S.: Comparative performance of different chrominance spaces for color segmentation and detection of human faces in complex scenes. Proceedings of Vision Interface 99, May 1999, pp. 180–187.

V. Fan, L., Sung, K. K.: A Combined Feature-Texture Similarity Measure for Face Alignment under Varying Pose. Proceedings of the International Conference on Computer Vision and Pattern Recognition, 2000.

VI. Cascia, M. L., Sclaoff, S.: Fast, Reliable Head Tracking under Varying Illumination. Proceedings of the International Conference on Computer Vision and PatternRecognition, 1999.

VII. Dass, S. C., Jain, A. K.: Markov Face Models. Proceedings of the International Conference on Computer Vision, 2001.

VIII. Bobick, A. F., Davis, J. W.: The Recognition of Human Movement Using Temporal Templates. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, 2001, No. 3, pp. 257–267.

IX. Ying, Z., Schwartz, S.: Discriminant Analysis and Adaptive Wavelet Feature Selection for Statistical Object Detection.ICPR 4,pp. 86-89, 2002.

X. Rowley, H. A., Baluja, S., Kanade, T.: Neural Network-Based Face Detection. IEEE Transactions on Pattern analysis and Machine Intelligence, Vol. 20, 1998, No. 1, pp. 23–30.

XI. Yilmaz, A., Gokmen, M.: Eigenhill vs. Eigenface and Eigenedge. Pattern Recognition, Vol. 34, 2001, No. 1, pp. 181–184.

XII. Lai, J. H., Yuen, P. C., Feng, G. C.: Face Recognition Using Holistic Fourier Invariant Features. Pattern Recognition, Vol. 34, 2001, No. 1, pp. 95–109.

XIII. Park G.T., Bien, Z.: Neural Network-Based Fuzzy Observer with Application to Facial Analysis. Pattern Recognition Letters, Vol. 21, 2000, No. 1, pp. 93–105.

XIV.Georghiades, A. S., Belhumeur, P. N., Kriegman, D. J.: From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23,2001, No. 6, pp. 643–660.

XV. Turk, M., Pentland, A.: Face Recognition Using Eigenfaces. Proceedings of International Conference on Computer Vision and Pattern Recogntion, 1991, pp. 586–591.

XVI. Yongzhong Lu, Jingli Zhou, Shengsheng Yu: A survey of face detection, extraction and recognition, computing and informatics, Vol. 22, 2003.

XVII. Adini, Y., Moses, Y., and Ullman, S.: Face Recognition: The Problems of Compensating for Changes in Illumination Direction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, pp. 721-732.

XVIII. Brunelli R., Poggio T.: Face Recognition through geometrical features. Proceedings European Conf. Computer Vision, pp. 792-800, May 1992.

XIX. Yuille, A.L., Hallinan, P.W., Cohen, D.S.: Feature Extraction from Faces Using Deformable Templates”. International Journal of Computer Vision, Vo1. 8, No. 2, 1992, pp. 99-111.

XX. Beymer, D. J.: Face Recognition under Varying Pose. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1994, pp. 756-761.

XXI. Rao, Rajesh P.N.: Dynamic Appearance-Based Recognition. CVPR 97, IEEE Computer Society, 1997, pp. 540-546.

XXII. Hu, Y., Wang, Z.:A Low-dimensional Illumination Space Representation of Human Faces for Arbitrary Lighting Conditions. ICPR, pp. 1147-1150, Volume 3, 2006.

XXIII. Epstein, R., Hallinan, P.W., Yuille A.L.: 5±2 Eigenimages Suffice: An Empirical Investigation of Low-dimensional Lighting models. Proceedings IEEE Workshop on Physics-Based Vision, 1995, pp. 108-116.

XXIV. Sirovich, L., Kirby, M.: Low-Dimensional Procedure for the Characterization of Human Faces. Journal of the Optical Society of America, Vol. 4, No. 3, March 1987, pp. 519-524.

XXV. Fang J., Qiu Guoping: A Color Histogram-Based Approach to Human Face Recognition. Institute of Electrical Engineers, Michael Faraday House Publications, 2003, pp. 133-136.

XXVI. Cristinacce, D., Cootes, T.F.: A Comparison of Shape Constrained Facial Feature Detectors. Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (FGR), 2004.

XXVII.Sung Kah-Kay, Poggio Tomaso: Example-based Learning for View-Based Human Face Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 1, January 1998.

XVIII. Li, Stan Z., Lu, Juwei: Face Recognition Using the Nearest Feature Line Method. IEEE Transactions on Neural Networks, Vol. 10, No. 2, March 1999, pp. 439-443.

XXIX. Aggarwal, J., Nandhakumar, N.: On the Computation of Motion of Sequences of Images, A Review. Proceedings IEEE, Vol. 69, No. 5, pp. 917-934, 1988.

 

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