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Vidhyalakshmi, S.
- Observations on the Non-homogeneous Quintic Equation with Four Unknowns
Authors
1 Department of Mathematics, Shrimati Indira Gandhi College, Trichy–620002, IN
Source
International Journal of Mathematics Research, Vol 5, No 1 (2013), Pagination: 127-133Abstract
We obtain infinitely many non-zero integer quadruples (x, y, z,w) satisfying the quintic equation with four unknowns. xy+6z2 = (k2 + 5)n w5. Various interesting relations between the solutions and special numbers, namely, polygonal numbers, pyramidal numbers, Jacobsthal numbers, Jacobsthal-Lucas number, keynea numbers, Four Dimensional Figurative numbers and Five Dimensional Figurative numbers are exhibited.Keywords
Quintic Equation With Four Unknowns, Integral Solutions, 2- dimentional, 3-dimentional, 4-dimentional and 5-dimensional Figurative numbers.References
- L.E. Dickson,History of Theory of Numbers,Vol.11,Chelsea Publishing company, New York (1952).
- L.J. Mordell, Diophantine equations, Academic Press, London(1969).
- Carmichael ,R.D.,The theory of numbers and Diophantine Analysis,Dover Publications, New York (1959)
- M.A. Gopalan & A.Vijayashankar, An Interesting Diophantine problem x3+y3=2z5 , Narosa Publishing House, Pp 1-6, 2010.
- M.A. Gopalan & A.Vijayashankar, Integral solutions of ternary quintic Diophantine equation x2+(2k+1)y2=z5 , International Journal of Mathematical Sciences 19(1-2), 165-169,(jan-june 2010)
- M.A. Gopalan,G.Sumathi & S.Vidhyalakshmi, Integral solutions of nonhomogeneous ternary quintic equation in terms of pells sequence x3+y3=xy(x+y)=2Z5, accepted for Publication in JAMS(Research India Publication)
- S. Vidhyalakshmi, K.Lakshmi and M.A.Gopalan, Observations on the homogeneous quintic equation with four unknowns x5-y5=2z5+5(x+y)(x2-y2)w2 ,accepted for Publication in International Journal of Multidisciplinary Research Academy(IJMRA)
- M.A. Gopalan & A.Vijayashankar, Integral solutions of non-homogeneous quintic equation with five unknowns xy-zw=R5 , Bessel J.Math.,1(1),23- 30,2011.
- M.A. Gopalan & A.Vijayashankar, solutions of quintic equation with five unknowns x4-y4=2(z2-w2)P3 ,accepted for Publication in International Review of Pure and Applied Mathematics.
- M.A. Gopalan, G. Sumathi & S.Vidhyalakshmi, On the non-homogenous quintic equation with five unknowns x3+y3=z3+w3+6T5, accepted for Publication in International Journal of Multidisciplinary Research Academy (IJMRA).
- Observations on the Non-homogenous Biquadratic Equation with Four Unknowns
Authors
1 Department of Mathematics, Shrimati Indira Gandhi College, Tiruchirappalli–2, IN
Source
International Journal of Mathematics Research, Vol 5, No 1 (2013), Pagination: 135-140Abstract
We obtain infinitey many non-zero integer quadruples (x,y,z,w) satisfying the biquadratic equation with four unknowns 8(x3+y3)=(1+3k2)z3w.. Various interesting relations between the solutions and special numbers, namely, polygonal numbers, pyramidal numbers, Jacobsthal numbers, Jacobsthal- Lucas numbers are obtained.Keywords
Bi-quadratic Equation With Four Unknowns, Integral Solution, Special Numbers.References
- Dickson. I. E. ‘”History of the Theory of Numbers’’, Vol 2. Diophantine Analysis, New York, Dover, 2005.
- Mordell.L J. “ Diophantine Equations’’ Academic Press, New York,1969.
- Carmichael. R.D.” The Theory of numbers and Diophantine Analysis’’ ,New
- York, Dover, 1959.
- Gopalan.M.A., Manju Somanath and Vanitha.N.”Parametric Integral Solution of x2+y3=z4 ’’Acta ciencia Indica,Vol.XXXIIIM,No.4,1261-1265,2007.
- Gopalan.M.A., Pandichelvi.V.”On ternary quartic Diophantine equation x2+ky3=z 4 ’’Pacific-Asian Journal of mathematics,Vol.2, No.1-2,57- 62,2008.
- Gopalan.M.A. Manju somanath and Vanitha.N ,” Integral Solutions of x2+xy+y2 = (k2+3)nz<4’’ Pure and applied mathematika sciences, Vol. LXIX, No.1-2,149-152, 2009.
- Gopalan.M.A,Janaki.G, ”Observation on 2(x2-y2 )+4xy=z 4 ‘’ Acta ciencia indica,Vol.XXXVM,No2,445-448,2009.
- Gopalan.M.A., Sangeetha.G“Integral solutions of ternary quartic equation x2+y2=2xy+z4 ’’Antartica .J.Math.,7(1) 95-101,2010.
- Gopalan.M.A.,A.Vijayasankar,.,”Integral solutions of ternary biquadratic equation x2+3y2=z4 ’’Impact J.Sci.and Tech.Vol.4,No.3,47-51,2010.
- Gopalan,M.A,Vidhyalakshmi.S,Devibala.S,’’Ternary quartic Diophantine equation 24n+3 (x3-y3)=z4 ’’Impact J.Sci.and Tech,Vol4,No 3,57-60,2010.
- Janaki G. Gopalan.M.A.’’Observations on 3(x2-y2 )+9xy=z4 ’’Antartica .J. Math., 7(2),239-245,2010.
- Gopalan, M.A. and Sangeetha.G’,Integral solutions of ternary nonhomogeneous biquadratic equation x4+x2+y2-y=z2+z’’Acta ciencia Indica,VolXXXVIIM,No.4,799-803,2011.
- Gopalan,M.A,Vidhyalakshmi.Sumathi.G,’’On the ternary biquadratic nonhomogenous equation (2k+1)(x2+y2+xy)=z4 '' Indian journal of engineering,Vol.1,No1,37-40,2012.
- Gopalan,M.A,Sumathi.G,Vidhyalakshmi.S,’’Integral solutions of ternary biquadratic non-homogeneous equation (α+1)(x2+y2)+(2k+1)xy=z4 ’’JARCE, Vol. 6, No (2).97-98, 2012.
- Gopalan,M.A,Sumathi.G,Vidhyalakshmi.S,’’Integral solutions of ternary biquadratic non-homogeneous equation (k+1)(x2+y2)-(2k+1)xy=z 4 ’’Archimedes J.Math,Vol.3(1),67-71.2013.
- A Study to Assess Depression among Patients with Non- Communicable Diseases Attending a Tertiary Care Hospital
Authors
1 Sree Balaji Medical College and Hospital, Bharath Institute of Higher Education and Research, Chennai-73, IN
2 Department of Community Medicine, Sree Balaji Medical College and Hospital, Bharath Institute of Higher Education and Research, Chennai-73, IN
Source
Indian Journal of Public Health Research & Development, Vol 10, No 11 (2019), Pagination: 1548-1551Abstract
Background: Misery influences individuals paying little mind to their experience and all ages too. As per the World Health Organization, 300 million individuals have melancholy around the globe. Somewhere in the range of 18 and 25 is most noteworthy among people with the predominance of significant burdensome scenes among grown-ups.
Technique: The unmistakable cross sectional investigation was done on 120 patients with non-transmittable ailment going to a tertiary consideration emergency clinic by arbitrary testing system. . Data would be assembled from patient, relative and guardian about statistic, clinical information utilizing a semi organized proforma. Melancholy will be affirmed by Patient Health Questionnaire (PHQ-2) and seriousness deciphered utilizing Patient Health Questionnaire (PHQ-9).
Results: The predominance of misery among patients with non-transferable malady is observed to be 77%. Wretchedness was for the most part because of weakening of wellbeing and their dread of compounding of disease and passing. There were likewise related elements which further declined the condition like family issues.
Conclusion: The pervasiveness of sadness has been observed to be increasingly regular in patients in extreme type of illness. Subsequently many helped directing and mental trainings should be possible to control or lessen despondency because of horribleness.