Volume-6 , Issue-4 , Aug 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  The Performance of a Ridge Estimator Based on Harmonic Mean

  Satish Bhat, R. Vidya

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.70-76, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.7076

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  Abstract
  Linear dependence between predictors is one of the serious issues in regression analysis. Due to near linear dependence (or multicollinearity) between any two or more predictors, ordinary least squares (OLS) method will yield unstable estimates to the regression coefficients. In the literature, several techniques like Ridge regression, Principal component regression, Partial least squares regression, Liu method of regression etc., have been developed to overcome problem of multicollinearity. Among them Ridge regression is one of the most widely used methods, which will yield more stable estimate’s as compared to OLS estimator. Here we propose a new ridge estimator based on Harmonic mean method. Performance of the ridge estimators is evaluated both theoretically and empirically under a wide range of degree of multicollinearity and error variances. Both methods have indicated that the performance of the suggested estimator is slightly more stable than some existing estimators, which are considered under study with respect to various degrees of multicollinearity, sample size, and error variance.

  Key-Words / Index Term
  Multiple linear regression (MLR), Multicollinearity, Ridge regression, and MSE

  References
  [1] R. Nair, V. Jain, A. Bhagat, R. Agarwal, “An Efficient approach for Sentiment Analysis Using Regression analysis Technique”, International Journal of Computer Sciences and Engineering, Vol. 7, issue 3, pp. 161-165, 2019.
  [2] T. Sur, A. Nath, “An innovative Method to Calculate the Economic Development Index of Important Cities in West Bengal From Satellite Imagery”, International Journal of Computer Sciences and Engineering, Vol. 7, issue 4, pp. 411-417, 2019.
  [3] A. E. Hoerl, “Application of Ridge Analysis to Regression Problems”, Chemical Engineering Progress, Vol. 58, pp. 54–59, 1962.
  [4] A.E. Hoerl, R. W. Kennard, “Ridge Regression: Biased Estimation for Non Orthogonal Problems”, Technometrics, Vol. 12, pp. 69–82, 1970.
  [5] A. E. Hoerl, R.W. Kennard, K. F. Baldwin, “Ridge Regression: Some Simulations”, Communications in Statistics-Theory and Methods, Vol. 4, No., 2, pp.105–123, 1975.
  [6] T. Hastie, R. Tibshirani, “Generalised Additive Models”, Statistical Science, Vol. 1, No., 3, pp. 297–318, 1986.
  [7] A. M. Halawa, M.Y. El Bassiouni, “Tests of Regression Coefficients under Ridge Regression Models”, Journal of Statistical Computation and Simulation, Vol. 65, pp. 341–356, 2000.
  [8] J. F. Lawless, P. Wang, “A Simulation Study of Ridge and Other Regression Estimators”, Communications in Statistics-Theory and Methods, Vol. 5, No., 4, pp. 307–323, 1976.
  [9] M. Nomura, “On the Almost Unbiased Ridge Regression Estimator”, Communications in Statistics – Simulation and Computation, Vol. 17, No., 3, pp. 729–743, 1988.
  [10]G. Khalaf, G. Shukur, “Choosing Ridge Parameter for Regression Problems”, Communications in Statistics-Theory and Methods, Vol. 34, pp. 1177–1182, 2005.
  [11]A.V. Dorugade, D. N. Khashid, “Alternative Method for Choosing Ridge Parameter for Regression”, Applied Mathematical Sciences, Vol .4, No., 9, pp. 447–456, 2010.
  [12]A. V. Dorugade, “New Ridge Parameters for Ridge Regression”, Journal of the Association of Arab Universities for Basic and Applied Sciences. Vol. 15, pp. 94–99, 2014.
  [13]S. Bhat, R. Vidya, “Improvement on Ridge Regression Estimator”, In the Proceedings of the National Conference on Statistical Methods and Data Analysis, Yuvaraja’s College, Mysore, India, ISBN No. 81-7877-093-8, pp. 65–71, 2014.
  [14]S. Bhat, R. Vidya, “A Comparative Study on the Performance of New Ridge Estimators”, Pakistan Journal of Statistics and Operations Research (PJSOR), Vol. 12, No. 2, pp. 317–325, 2016.
  [15]H. D. Vinod, A. Ullah, “Recent Advances in Regression Methods”, Marcel Dekker, New York, 1981.
  [16]K. Liu, “Using Liu Type Estimator to Combat Collinearity”, Communications in Statistics-Theory and Methods. Vol. 32, pp. 1009–1020, 2003.
  [17]S. Bhat, R. Vidya, “A New Ridge Estimator and its Performance”, In the Proceedings of the National Conference on Operations Management, Analytics and Statistical Methods(NOMAS-2017), Mysore, India, ISBN No. 978-9383302-20-8, 2017a.
  [18]S. Bhat, “Contributions to the study of Partial Least Squares Regression(PLSR)”, Ph. D. Thesis, Submitted to University of Mysore, Mysuru, India, chapter 3, pp. 71–105, 2017b.
  [19]G. Khalaf, “A Proposed Ridge Parameter to Improve the Least Square Estimator”, Journal of Modern Applied Statistical Method, Vol. 11, No., 2, pp. 443–449, 2012.
  [20]B. M. Kibria, “Performance of Some Ridge Regression Estimators”, Communications in Statistics-Simulation and Computation, Vol. 32, pp. 419–435, 2003.
  [21]S. Mardikyan, E. Cetin, “Efficient Choice of Biasing Constant for Ridge Regression”, International Journal of Contemporary Mathematical Sciences, Vol. 3, pp. 527–547, 2008.
  [22]D. C. Montgomery, E. A. Peck, G. G. Vining, “Introduction to linear regression Analysis”, 3rd Edition, John Wiley and Sons (Asia), Singapore, 2003.
  [23]G. Muniz, B. M. Kibria, “On Some Ridge Regression Estimators-An Empirical Comparisons”, Communications in Statistics –Simulation and Computation, Vol. 38, No., 3, pp. 621–630, 2009.
  [24]M. Yazid Al-Hassan, “Performance of a New Ridge Regression Estimator”, Journal of the Association of Arab Universities for Basic and Applied Sciences, Vol. 9, 23–26, 2010.
  

  Citation
  Satish Bhat, R. Vidya, "The Performance of a Ridge Estimator Based on Harmonic Mean," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.70-76, 2019

• Open Access   Article

  Modified Ratio-Cum-Product Estimator for Finite Population Mean

  Rajesh Tailor, Priya Mehta

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.77-83, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.7783

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  Abstract
  This paper develops two modified RCP estimators for finite PM. Infact, dual to two RCP estimators have been developed. The BIAS and MSqER of the developed estimators have been obtained upto the first degree of approximation. The developed estimators have been compared with existing estimators and conditions under which the developed estimators are more efficient have been obtained. An empirical study also has been conducted.

  Key-Words / Index Term
  RCP estimator, Finite PM, Bias, MSqER

  References
  [1]. Cochran, W. G. (1940). The estimation of yields of cereal experiments by sampling for ratio of grain to total produce. J. Agril. Sci., 30, 262-275.
  [2]. Parmar, R. (2013). Use of auxiliary information for estimation of some population parameters in sample surveys. Ph.D. thesis, Vikram University, Ujjain (M.P.), India.
  [3]. Robson, D. S. (1957). Application of multivariable polykays to the theory of unbiased ratio type estimation. J. Amer. Statist. Assoc., 50, 1225-1226.
  [4]. Singh, M. P. (1967). Ratio-cum-product method of estimation. Metrika, 12, 1, 34-43.
  [5]. Singh, H. P., Singh, R., Espejo, M. R., Pineda, M. D. and Nadarajah (2005). On the efficiency of a dual to ratio-cum-product estimator in sample surveys. Math. Proc. R. Ir. Acad., 105 A, 2, 51-56.
  [6]. Srivenkataramana, T. (1980). A dual of ratio estimator in sample surveys. Biom. J., 67, 1, 199-204.
  [7]. Upadhyaya, L. N. and Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biom. J., 41, 5, 627-636.
  

  Citation
  Rajesh Tailor, Priya Mehta, "Modified Ratio-Cum-Product Estimator for Finite Population Mean," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.77-83, 2019

• Open Access   Article

  Common Fixed Point Theorems in Complete Hausdörff Uniform Spaces

  Kalishankar Tiwary, Biplab Kumar Bag, Chandan Kamelia

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.84-88, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.8488

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  Some common fixed points of point-valued mappings on a sequentially complete Hausdorff uniform space satisfying contractive type conditions have been obtained.

  Key-Words / Index Term
  Fixed Point, Sequentially complete, Hausdorff Uniform Space

  References
  [1]. Jungck, G. Compatible mappings and common fixed points. Internat. J. Math. & Math. Sci., 9, 1986, 771-779.
  [2]. Kelley, J.L. General Topology. Van Nostrand Reinholt, Princeton, New Jersey, 1955.
  [3]. Sastry, K.P.R., Babu, G.V.R. & Rao, D. Narayana Fixed point theorems in complete metric spaces. Bull. Cal. Math. Soc. 91, 1999, 493-502.
  [4]. Sessa, S. On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. 32, 1982, 149-153.
  [5]. Thron, W.J. Topological structure, Rinehart and Winston, New York, 1966.
  

  Citation
  Kalishankar Tiwary, Biplab Kumar Bag, Chandan Kamelia, "Common Fixed Point Theorems in Complete Hausdörff Uniform Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.84-88, 2019

• Open Access   Article

  A Study of Kahlerian Einstein Manifold with Bochner Curvature Tensor

  P. Bhardwaj, N. Kumar

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.89-92, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.8992

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  The main purpose of the present paper is to study of Kahlerian Einstein manifold with Bochner curvature tensor. Few interesting results for Kahlerian Einstein manifold with Bochner curvature tensor have been obtained. Further we discussed about the theory of Kahlerian Einstein manifold with Bochner curvature tensor with R is non-zero. If a non-affine holomorphically projective transformation satisfying the condition , .then Kahlerian manifold is terns into Kahlerian Einstein manifold. Necessary and sufficient condition that a holomorphically projective transformation is analytic in a Kahlerian Einstein manifold with non–vanishing scalar curvature tensor then its associated vector is analytic. An Kahlerian Einstein manifold, the associated vector of an analytic holomorphically projective transformation is analytic. An Einstein manifold with , any infinitesimal affine transformation is a killing vector. If the associated vector of an analytic holomorphically projective transformation satisfying the condition then a Kahlerian manifold satisfying the condition is not an Einstein manifold.

  Key-Words / Index Term
  Kahlerian manifolds, Einstein manifold, Bochner Curvature Tensor, Kahlerian Einstein manifold, Killing vector, holomorphically projective transformation, Lie derivative, Lie Algebra, contravariant almost analytic vector, Covariant almost analytic vector

  References
  [1] A.K. Singh, ”On Einstein-Kahlerian projective recurrent spaces”, Indian Jour. Pure appl.Math, 10(4),pp.483-492, 1984.
  [2] H.A. Biswa, U.C. De, “On Generalized 3-recurrents space”, Ganit, J. Bangladesh Math. Soc., 14, 85-88, 1994.
  [3] H.H. Khan, S. Uddin, V.A. Khan, “Some results on warped product submanifolds of a Sasakian manifold”, International Journal of Mathematics and Mathematical Sciences, USA, Vol. (2010)1 - 9. doi: 10.1155/2010/743074.
  [4] J. Mikes, “Holomorphicall projective mapping and their generalizations”, journal of mathematical sciences 89, No. 3, 1334-1353, 1998.
  [5] J.Mikes, O. Pokorna, “On holomorphically projective mappings onto Kahlerian spaces”, Rend Circ. Mat. Palermo (2) Suppl. 69, 181-186, 2002.
  [6] K. B. Lal, S.S. Singh, “On Kahlerian space with recurrent Bochner curvature tensor” Acc. Naz. Dei Lance, Rend, 51(3-4), 213-220, 1971.
  [7] K. Yano, ”Totally real Sub manifolds of a Kahlerian manifolds”, J. Differential geometry 11, 351-359, 1976.
  [8] K. Yano, “On complex conformal connection”, Kodai Math Sem. Rep.-26, 137-151, 1975.
  [9] K. Yano, T. Nagano, “Some theorems on projective and conformal transformations”, Indag. Math.14, 451-458, 1957.
  [10] M. Matsumoto, “Kaehlerian space with parallel on vanishing Bochner curvature tensor”, Tensor N.S. 20(1), 25-28, 1969.
  [11] N. Cengiz, O. Tarakc, A.Salirnov, “A note on Kahlerian manifolds”, Turk J. Math 30, 439-445, 2006.
  [12] P. Bhardwaj, N. Kumar, M. Chandra, “An analytical study of generalized ricci 3- recurrent space in Kahlerian manifolds with Bochner curvature tensor”, International Journal of pure and Applied Mathematics, Volume- 118, No.22, 1435-1439, 2018.
  [13] P. Bhardwaj, N. Kumar, M. Chandra, “A study of infinitesimal holomorphically projective transformation in Kahlerian sub-manifold with Bochner curvature tensor”,International Journal of Mathematical Archive-9(7), 1-10, 2018.
  [14] S. Mathai, “Kaehlerian recurrent spaces”, Ganita 20 (2), 121-133, 1969.
  [15] S. Tachibana, “On the Bochner curvature tensor”, Nat. Sci. Report. Ochanomizu University 18(1), 15-19, 1967.
  [16] S. Tachibana, S. Ishihara, “On infinitesimal holomorphically projective transformation in Kahlerian manifolds”, Tohoku Math J., 12, 77-101, 1960.
  [17] S. Tachibana, R.C. Liu, “Notes on Kaehlerian metrics with vanishing Bochner curvature tensor”, Kodai Math. Sem. Rep. 22, pp. 313-321, 1970.
  [18] S. Yamaguchi, T.A. Adati, “On holomorphically sub-projective Kahlerian manifold”, Accademic Dei. Lincei, Serie VIII, LX, Fasc 4 April 1976.
  [19] T. Otsuki, Y. Tashiro, “On curves in Kahlerian spaces”, Math. Jour. Okayama Uni. 4, 4-57, 1954.
  [20] T. Sumitomo, “Projective and conformal transformations in compact Riemannian manifolds”, Tensor, New Series, 9, 113-135, 1959.
  

  Citation
  P. Bhardwaj, N. Kumar, "A Study of Kahlerian Einstein Manifold with Bochner Curvature Tensor," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.89-92, 2019

• Open Access   Article

  Special Type Double Sampling Plans with Minimum Variance

  D. Venkatesan, Amin Shaka Aunali, P. Poojalakshmi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.93-99, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.9399

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  Abstract
  Acceptance sampling plans are usually defined by the Lot size, sample sizes at stage one and stage two along with acceptance numbers at stage one and two. The design of DSP are based on the AOQL, LTPD by without assuming the Outgoing Quality (OQ) and Total Inspection (TI) as random variables. In this paper, OQ and TI are treated random variables and distributional properties are obtained. Based on these properties, a Special Type double sampling plan with minimum variance, treating the outgoing quality and total inspection as random variables under total rectification, is introduced and are illustrated with the practicability of the plan.

  Key-Words / Index Term
  Special Type Double Sampling plans; Outgoing Quality; Total Inspection

  References
  [1] Dodge, H. F. and Romig, H. G., “Sampling Inspection Tables”, 2nd edition, John Wiley and sons, New York, 1959.
  [2] Duncan, A. J., “Quality control and Industrial Statistics”, 5th edition, Richard D. Irown Inc., Homewood, IL, 1986.
  [3] General Electric Company. Defense Systems Department, Tables of the individual and cumulative terms of Poisson distribution. Van Nostrand, 1962.
  [4] Hahn, G. J., “Minimum Size Sampling plans”, Journal of Quality Technology, Vol. 6, pp. 121-127, 1974.
  [5] Hall, J. E., “Minimum Variance and VOQL sampling plans”, Technometrics, Vol. 21, pp. 555-565, 1979.
  [6] Kaviayarasu, V. and Devika V., “Designing of Special Type of Double Sampling Plan for Compliance Testing through Generalized Poison Distribution”, International Journal of Pure and Applied Mathematics, Vol. 117, No. 12, pp. 7-17, 2017.
  [7] Venkatesan, D., “Minimum Variance Double Sampling Attribute Plans”, International Journal of Information and management Sciences, Vol. 16, pp. 63-72, 2005.
  

  Citation
  D. Venkatesan, Amin Shaka Aunali, P. Poojalakshmi, "Special Type Double Sampling Plans with Minimum Variance," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.93-99, 2019

• Open Access   Article

  On Common Fixed Points of Mappings in Hilbert Spaces

  Kalishankar Tiwary, Chandan Kamelia, Biplab Kumar Bag

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.100-103, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.100103

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  Abstract
  In this paper some common fixed points theorems have been proved in Hilbert spaces using the definition of normal structure etc.

  Key-Words / Index Term
  Fixed Point, Normal Structure, Hilbert Space

  References
  [1]. Jungck, G. Commuting mappings and fixed points. Amer. Math. Monthly, 83, 1976, 216-263.
  [2]. Jungck, G. Compatible mappings and common fixed points. Internat. J. Math. & Math. Sci., 9, 1986, 771-779.
  [3]. Kirk, W.A. A fixed point theorem for mapping which do not increase distances. Amer. Math. Monthly, 72, 1965, 1004-1008.
  [4]. Kolmogorov, A.N. & Fomin, S.V. Elements of the theory of functions and functional analysis. Jauka, Moscow, 1989.
  [5]. Pai, D.V. & Veeramani, P. On a fixed point theorem on uniformly convex Banach spaces. Indian J. Pure. Appl. Math., 13, 6, 1982, 647-650.
  [6]. Sastry, K.P.R., Babu, G.V.R. & Rao, D. Narayana Fixed point theorems in complete metric spaces. Bull. Cal. Math. Soc. 91, 1999, 493-502.
  [7]. Sharma, B.K. & Sahu, W.K. A common fixed point theorem under asymptotic regularity at a point. Pure & Appl. Math. Scienence, 34, 1, 1999.
  [8]. Smulian, V. On the principle on inclusion in the space of type (B), Math. Sornik (N.S.), 5, 1939, 327-328.
  [9]. Veerapandi, T. & Kumar, S.A. Common fixed point theorems of a sequence of mappings in Hilbert space. Bull. Cal. Math. Soc. 91, 1999, 299-308.
  

  Citation
  Kalishankar Tiwary, Chandan Kamelia, Biplab Kumar Bag, "On Common Fixed Points of Mappings in Hilbert Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.100-103, 2019

• Open Access   Article

  A New Operation on Sinusoidal Fuzzy Number

  R. Karthika, A. Sahaya Sudha

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.104-107, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.104107

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  Abstract
  Fuzzy numbers exists in many fields such as Management, agriculture, Medicine, Engineering etc. In this paper a new operation on sinusoidal fuzzy number has been defined and introduced. In addition to it, this paper also deals with the study of new basic alpha cut operations on addition, subtraction and multiplication of sinusoidal fuzzy number with the suitable numerical examples.

  Key-Words / Index Term
  Fuzzy arithmetic, Sinusoidal Fuzzy number

  References
  [1] Abhinav Bansal (2011), “Trapezoidal Fuzzy numbers (a, b, c, d): Arithmetic behavior”, International Journal of Physical and Mathematical Sciences, ISSN-2010-1791.
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  [4] Dwyer., (1965), P.S. “Fuzzy sets. Information and Control” l, No.8: 338–353.
  [5] Fuller.R and Majlender.P., (2003), “On weighted possibilistic mean and variance of fuzzy numbers”, Fuzzy Sets and Systems, vol.136, pp.363-374
  [6] Feng.H, Su. P and Zhang.L, (2014),” Design and Analysis of tubular permanent magnet lines wave generator”, The Scientific world journal, Article ID-258109, pages 7
  [7] Heilpern.S., (1997), “Representation and application of fuzzy numbers”, Fuzzy sets and Systems, vol.91, no.2, pp.259-268.
  [8] Klaua.D., (1965),” Über einen Ansatz zur mehrwertigen Mengenlehre. Monatsb. Deutsch”. Akad. Wiss. Berlin 7, 859–876
  [9] Klir.G.J., (2000), Fuzzy Sets: “An Overview of Fundamentals, Applications, and Personal views”. Beijing Normal University Press, pp.44-49.
  [10] Klir., (1997) “Fuzzy arithmetic with requisite constraints”, Fuzzy Sets System, vol. 91, pp. 165–175.
  [11] Kauffmann, A., (1980) Gupta, M., “Introduction to Fuzzy Arithmetic: Theory and Applications”, Van Nostrand Reinhold, New York.
  [12] Malini.S. U, Felbin.C. Kennedy., (2013), “An approach for solving Fuzzy Transportation using Octagonal Fuzzy numbers,” Applied Mathematical Sciences, no.54,2661-2673
  [13] Nasseri.H(2008),” Positive and non-negative”, International Mathematical Forum,3,1777-1780.
  [14] Pandey.R, Pandey N and Paul et al.S.K., (2013),” Voltage mode astable multivibrator using single CDBA”, ISRN Electronics, Article ID-390160, pages 8.
  [15] Rezvani.S., (2011).,” Multiplication Operation on Trapezoidal Fuzzy numbers”, Journal of Physical Sciences, Vol no-15,17-26
  [16] Sun. Q & Song. Q, (2009), “Portable signal generator based on direct digital synthesis”, Instrumental Technique and sensor, vol—4, no-4, pp.67-70
  [17] Sun.Y, Liu.J.Lu. S & Ben.H, (2012), “Design of sinusoidal signal generator based on AD9833 & Potentiometer”, Electrical Measurement and Instrumentation, Vol-7, pp.93-96.
  [18] Yager.R., (1979),” On Solving Fuzzy Mathematical relationships”, Information control,41,29-55.
  [19] Zadeh, L.A., (1965),” Fuzzy Sets”, Information and Control., No.8 pp.338-353.
  [20] Zadeh., (1978),” Fuzzy set as a basis for a theory of possibility”, Fuzzy sets and systems, No.1, pp.3-28.
  [21] Zimmermann, H. J, (1996),” Fuzzy Set Theory and its Applications”, Third Edition, Kluwer Academic Publishers, Boston, Massachusetts.
  [22]. Zhang. G, (2014), “Research of DDS-based high precision multi-channel signal generations systems”, Electronic Measurement Technology, Vol-37, no 4, pp.125-129.
  

  Citation
  R. Karthika, A. Sahaya Sudha, "A New Operation on Sinusoidal Fuzzy Number," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.104-107, 2019

• Open Access   Article

  On Certain Special Vector Fields in a Finsler Space II

  P.K. Dwivedi, S.C. Rastogi, A.K. Dwivedi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.108-112, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.108112

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  Vector fields of different kind have been playing interesting part in the study of both Tensor Analysis and Differential Geometry of Finsler Spaces of two and three- dimensions. In this paper an attempt has been made to define several new special vector fields in a Finsler space of three- dimensions. We have studied their properties and their applications in the study of curvature properties with respect to first curvature tensor in a Finsler space of three- dimensions.

  Key-Words / Index Term
  Vector fields, Finsler space, Three dimensions, Curvature Tensors

  References
  [1] S.C. Rastogi and P. Bajpai, “On certain special vector fields in a Finsler space”, Acta Ciencia Indica, XLIII M no. 2, (2017), 149-152.
  [2] P.K. Dwivedi, S.C. Rastogi and A.K. Dwivedi, “On certain special vector fields in a Finsler space I”, IJAIR, Vol. 8, Issue 3, (2019), 1-6.
  [3] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Otsu, Japan, 1986.
  [4] H.Rund, The differential geometry of Finsler spaces, Springer-Verlag, 1959.
  

  Citation
  P.K. Dwivedi, S.C. Rastogi, A.K. Dwivedi, "On Certain Special Vector Fields in a Finsler Space II," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.108-112, 2019

• Open Access   Article

  Weak X-essential Ideals

  Raplang Nongsiej

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.4 , pp.113-117, Aug-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.113117

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  Abstract
  Weak X-essential ideals are introduced in this paper which are generalizations of essential ideals and X-essential ideals. Some properties of weak X-essential ideals are investigated. In particular, we proved that the property of weak X-essential is preserved under finite intersection, inverse image and factor rings. We also found out conditions on Noetherian rings which ensure that direct sums of weak X-essential ideals are weak essential ideals and vice versa.

  Key-Words / Index Term
  essential submodule, X-essential submodule, weak X-essential ideal

  References
  [1] R.E. Johnson: “Structure Theory of Faithful Rings”, Proc. Amer. Math. Soc. 2(1951), 891-895.
  [2] B. Eckmann and A. Schopf, “Uber Injective Moduln”, Archiv der Math 4(1953), 75-78.
  [3] F. W. Anderson and K.R. Fuller : “Rings and Categories of Modules (Graduate Text in Mathematics 13)”, Springer -Verlag, Berlin Heldelberg-New York, (1974).
  [4] S. Safaeenyan and N. Saboori Shirazi: “Essential Submodules with respect to an Arbitrary Submodule”, Journal of Mathematical Extension, Vol. 7 No. 3, (2013), 15-27.
  [5] M. F. Atiyah and I. G. Macdonald: “Introduction to Commutative Algebras”, Addison Wesley, (1972).
  [6] K. R. Goodearl, R. B. Warfield, Jr: “An Introduction to Non commutative Noetherian Rings Second Edition”, (1989).
  

  Citation
  Raplang Nongsiej, "Weak X-essential Ideals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.113-117, 2019