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NOTE ON SOME CHARACTER FORMULAS
Chaudhary, Mahendra Pal,Chaudhary, Sangeeta,Choi, Junesang The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.4
Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.
NOTE ON SOME CHARACTER FORMULAS
( Mahendra Pal Chaudhary ),( Sangeeta Chaudhary ),( Junesang Choi ) 호남수학회 2016 호남수학학술지 Vol.38 No.4
Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 iden- tities which are chosen among the above-mentioned 14 formulas.
Chaudhary, Ajay K,Chaudhary, Shruti,Ghosh, Kanjaksha,Shanmukaiah, Chandrakala,Nadkarni, Anita H Asian Pacific Journal of Cancer Prevention 2016 Asian Pacific journal of cancer prevention Vol.17 No.3
Background: Matrix metalloproteinase -2 (gelatinase-A, Mr 72,000 type IV collagenase, MMP-2) and -9 (gelatinase-B, Mr 92,000 type IV collagenase, MMP-9) are key molecules that play roles in tumor growth, invasion, tissue remodeling, metastasis and stem-cell regulation by digesting extracellular matrix barriers. MMP-2 and -9 are well known to impact on solid cancer susceptibility, whereas, in hematological malignancies, a paucity of data is available to resolve the function of these regulatory molecules in bone marrow mononuclear cells (BM-MNCs) and stromal cells of myelodysplastic syndrome (MDS) and acute myeloid leukemia (AML). Objectives: The present study aimed to investigate mRNA expression and gelatinase A and B secretion from BM-MNCs in vitro and genotypic associations of MMP-2 (-1306 C/T; rs243865), MMP-9 (-1562 C/T; rs3918242), tissue inhibitor of metalloproteinase -1 (TIMP-1) (372T/C; rs4898, Exon 5) and TIMP-2 (-418G/C; rs8179090) in MDS and AML. Results: The study covered cases of confirmed MDS (n=50), AML (n=32) and healthy controls (n=110). MMP-9 mRNA expression revealed 2 fold increased expression in MDS-RAEB II and 2.5 fold in AML M-4 (60-70% blasts). Secretion of gelatinase-B also revealed the MMP-9 mRNA expression and ELISA data also supported these data. We noted that those patients having more blast crises presented with more secretion of MMP-9 and its mRNA expression. In contrast MMP-9 (-1562 C/T) showed significant polymorphic associations in MDS (p<0.02) and AML (p<0.02). MMP-9 mRNA expression of C/T and T/T genotypes were 1.5 and 2.5 fold increased in MDS and AML respectively. In AML, MMP-2 C/T and T/T genotypes showed 2.0 fold mRNA expression. Only MMP-9 (-1306 C/T) showed significant 4 fold (p<0.001) increased risk with chemical and x-ray exposed MDS, while tobacco and cigarette smokers have 3 fold (p<0.04) risk in AML. Conclusions: In view of our results, MMP-9 revealed synergistic secretion and expression in blast crises of MDS and AML with 'gene' polymorphic effects and is significantly associated with increased risk with tobacco, cigarette and environmental exposure. Release and secretion of these enzymes may influence hematopoietic cell behavior and may be important in the clinical point of view. It may offer valuable tools for diagnosis and prognosis, as well as possible targets for the treatments.
Arbitrary Power Division Ratio Rat-Race Coupler With Negative Group Delay Characteristics
Chaudhary, Girdhari,Jeong, Yongchae THE INSTITUTE OF ELECTRICAL ENGINEERS 2016 IEEE Microwave and Wireless Components Letters Vol. No.
<P>In this letter, we present theoretical and experimental investigations of a rat-race coupler with negative group delay (NGD) characteristics and an arbitrary power division ratio. From the theoretical analysis, the NGD characteristics can be obtained through various transmission paths and have small variations with the power division ratio. The power division ratio is controlled by only the characteristic impedance of the transmission lines. Ideal port isolation and return loss characteristics are obtained at a center frequency for any arbitrary power division ratio. For experimental demonstration, a microstrip line rat-race coupler is implemented with center frequency of 2.14 GHz. The measurement results agree well with simulation results and theoretically predicated values.</P>
Chaudhary, M.P.,Ashine, Ahmed Buseri,Wakene, Feyissa Kaba The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.3
The objective of this research article is to establish two relationships between q-product identities, theta function identities and combinatorial partition identities, using elementary results.
REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES
Chaudhary, Mahendra Pal,Choi, Junesang The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.2
Adiga and Anitha [1] investigated the Ramanujan's continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan's continued fraction (18) to give certain relationships between the Ramanujan's continued fraction and the combinatorial partition identities given by Andrews et al. [3].
CHAUDHARY, M.P.,CHOI, JUNESANG The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.5
Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.
Chaudhary, M.P.,Choi, Junesang The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.5
Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.