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Nagaraja, B.M.,Jung, H.,Yang, D.R.,Jung, K.D. Elsevier Science Publishers 2014 CATALYSIS TODAY - Vol.232 No.-
PtSn/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalysts with different amount of potassium (0.4, 0.7, 0.95, 1.2 and 1.45wt.%) were prepared by an impregnation method, and their catalytic activity in n-butane dehydrogenation was investigated at 823K, an atmospheric pressure and a GHSV of 18,000mL(g<SUB>cat</SUB>h)<SUP>-1</SUP>. The compositions listed in order of n-C<SUB>4</SUB><SUP>=</SUP> yields at 823K were as follows: K<SUB>0.95</SUB>(PtSn)<SUB>1.5</SUB>>(PtSn)<SUB>1.5</SUB>>K<SUB>0.4</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>0.7</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>1.2</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>1.45</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>0.9</SUB>(Pt)<SUB>1.5</SUB>. The K<SUB>0.9</SUB>(Pt)<SUB>1.5</SUB> and K<SUB>0.95</SUB>(Sn)<SUB>1.5</SUB> catalyst severely deactivated in n-butane dehydrogenation. The (PtSn)<SUB>1.5</SUB> (without K) catalyst showed the highest n-butane conversion, while K<SUB>0.95</SUB>(PtSn)<SUB>1.5</SUB> did the highest n-C<SUB>4</SUB><SUP>=</SUP> yield. The small amount of potassium on bimetallic PtSn/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalyst improved n-C<SUB>4</SUB><SUP>=</SUP> selectivity, but slightly decreased n-butane conversion, resulting in the increase of n-C<SUB>4</SUB><SUP>=</SUP> yield. The effect of potassium was caused by blocking the acid sites of Pt catalyst. The TPR and HAADF STEM-EDS study suggested the reduction procedure of the Pt, Sn and K species. However, the higher loaded potassium (1.2 and 1.45wt.%) doped (PtSn)<SUB>1.5</SUB> catalysts were rather highly deactivated because the sizes of Pt particles were increased by weakening the interaction between Pt and Sn. The n-C<SUB>4</SUB><SUP>=</SUP> selectivity of the (PtSn)<SUB>1.5</SUB> catalyst increased with respect to the reaction, while that of the potassium doped catalysts maintained the high n-C<SUB>4</SUB><SUP>=</SUP> selectivity from the beginning of the reaction. Also, different alkali metals (Ca, Na and Li) were tested for the comparison with K. The potassium doped catalyst showed the highest n-C<SUB>4</SUB><SUP>=</SUP> yield among the other alkali metals for n-butane dehydrogenation.
Centroidal mean labeling of graphs-II
R. SAMPATHKUMAR,K. M. Nagaraja,G. Narasimhan,M. H. Ambika 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.2
In this paper the Centroidal mean labeling of graphs such as triangu- lar snake Tn K1, double triangular snake Dn(Tn) K1, TLn K1, the graph obtained by attaching pendent edges to both sides of each vertex of a path Pn; attaching paths of lengths 0; 1; 2; 3; : : : ; n - 1 on both sides of each vertex of Pn; D2(Pn); Middle graph of path Pn; Total graph of path Pn; Splitting graph of path Pn and Duplicating each vertex by an edge in path Pn are discussed.
Schur convexities of ratio of one parameter power exponential mean and its invariant
K. M. Nagaraja,R. Sampathkumar,G. D. Chethankumar,P. Dhanya 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.2
Schur convexities of ratio of one parameter power exponential mean and its invariant
A simple proof strengthening and extension of inequalities
K. M. Nagaraja,V. Lokesha,S. Padmanabhan 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.17 No.1
In this short note, using Weighted Arithmetic and Geometric means We deduce Contra Harmonic mean and Power exponential mean. Also we established some new inequalities involving important means.
α-centroidal mean and its dual
K. M. Nagaraja,P. S. K. Reddy 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.2
n this paper, the -centroidal mean and its dual form in 2 variables are defined. Also, we obtained some interesting results related to monotonicities.
INEQUALITIES FOR THE ARGUMENTS LYING ON LINEAR AND CURVED PATH
( K. M. Nagaraja ),( Serkan Araci ),( V. Lokesha ),( R. Sampathkumar ),( T. Vimala ) 호남수학회 2020 호남수학학술지 Vol.42 No.4
The mathematical proof for establishing some new in- equalities involving arithmetic, geometric, harmonic means for the arguments lying on the paths of triangular wave function (linear) and new parabolic function (curved) over the interval (0; 1) are dis- cussed. The results representing an extension as well as strength-ening of Ky Fan Type inequalities.
SCHUR CONVEXITY AND CONCAVITY OF GNAN MEAN
K. M. Nagaraja,MURALI K,V. Lokesha 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.3
In this paper, the Schur convexity and Schur concavity of the Gnan mean and its dual form in two variables are discussed using strong mathematical induction by grouping of terms.
SCHUR CONVEXITIES OF rth OSCILLATORY MEAN AND ITS DUAL
K. M. Nagaraja,R. SAMPATHKUMAR 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.3
In this paper, we study the dierent kinds of Schur , Schur Geometric and Schur Harmonic Convexity(Concavity) of Oscillatory mean, rth Oscillatory mean and their duals.
NOTE ON DIFFERENT KINDS OF SCHUR CONVEXITIES OF HEINZ TYPE MEAN
K. Sridevi,K. M. Nagaraja,P. S. K. Reddy 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
The Schur convexity of functions relating to special means is a very significant research subject and has attracted the interest of many mathematicians. In this note, a new family of one parameterized Heinz type mean is introduced and we discuss the different kinds of Schur convexity and concavity of Heinz type mean.
Lee, M.H.,Nagaraja, B.M.,Lee, K.Y.,Jung, K.D. Elsevier Science Publishers 2014 CATALYSIS TODAY - Vol.232 No.-
Pt<SUB>0.5</SUB>Sn<SUB>x.x</SUB>/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalysts with different amount of tin (0.5, 0.75, 1.0 and 1.5wt%) were prepared by a co-impregnation method. Propane dehydrogenation was performed at 873K and a GHSV of 53,000mL/(g<SUB>cat</SUB>h). The Pt<SUB>0.5</SUB>/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalyst showed severe deactivation in alkane dehydrogenation reaction. The Sn addition decreased the cracking products of C<SUB>1</SUB>-C<SUB>2</SUB> and the Pt<SUB>0.5</SUB>Sn<SUB>0.75</SUB> catalyst with the highest Pt dispersion showed the highest C<SUB>3</SUB><SUP>?</SUP> yield and C<SUB>3</SUB><SUP>?</SUP> selectivity. n-Butane dehydrogenation was performed at 823K and a GHSV of 18,000mL/(g<SUB>cat</SUB>h). Similarly to propane dehydrogenation, the Sn addition to the Pt<SUB>0.5</SUB>/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalyst decreased the cracking products of C<SUB>1</SUB>-C<SUB>3</SUB>. However, the Pt<SUB>0.5</SUB>Sn<SUB>1.0</SUB> showed the highest n-C<SUB>4</SUB><SUP>?</SUP> yield and the catalyst was steadily deactivated even at 823K differently from propane dehydrogenation at 873K. The small amount of Sn addition improved the C<SUB>3</SUB><SUP>?</SUP> and n-C<SUB>4</SUB><SUP>?</SUP> selectivity by blocking the cracking sites of Pt catalyst. The PtSn alloy formed after the reduction at 500<SUP>o</SUP>C. The PtSn formation can enhance the C<SUB>3</SUB><SUP>?</SUP> and n-C<SUB>4</SUB><SUP>?</SUP> selectivity. The Pt dispersion on the Pt<SUB>0.5</SUB>/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalyst increased with the Sn addition up to 0.75 wt%. The highest Pt metal dispersion was observed on the Pt<SUB>0.5</SUB>Sn<SUB>0.75</SUB> catalyst. The conclusion was given to the Sn effects on the increase of Pt dispersion to enhance the activity as well as on the electronic and geometric effect of PtSn alloy to increase the stability and olefin selectivity.