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A Note on Continued Fractions and Mock Theta Functions
Srivastava, Pankaj,Gupta, Priya Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.1
Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.
Diagnostic Role of Survivin in Urinary Bladder Cancer
Srivastava, Anupam Kumar,Singh, Pankaj Kumar,Srivastava, Kirti,Singh, Dhramveer,Dalela, Divakar,Rath, Srikanta Kumar,Goel, Madhu Mati,Bhatt, Madan Lal Brahma Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.1
Background: Early diagnosis of carcinoma of bladder remains a challenge. Survivin, a member of the inhibitor of apoptosis (IAP) protein family, is frequently activated in bladder carcinoma. The objective of this study was to investigate urinary survivin as a marker for diagnosis of urinary bladder. Materials and Methods: We examined urinary survivin concentration in 28 healthy individuals, 46 positive controls and 117 cases of histologically proven TCC prior to transurethral resection, using ELISA, and compared values with findings for urinary cytology. Results: Survivin was found to be significantly higher in the cancer group (P<0.05). A cut off value of 17.7 pg/ml was proposed, with an approximate sensitivity of 82.9% and specificity of 81.1% (P<0.0001), whereas urine cytology had a sensitivity of 66.7% and a specificity of 96.0%. Conclusions: Urinary survivin can be used as a non-invasive diagnostic biomarker for TCC bladder, both for primary and recurrent disease.
Srivastava, Pankaj Department of Mathematics 2011 Kyungpook mathematical journal Vol.51 No.4
In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.
A Note on Certain Properties of Mock Theta Functions of Order Eight
Srivastava, Pankaj,Wahidi, Anwar Jahan Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.2
In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.
Gupta Harsh,Ghosh Santanu,Khan Saif A.,Srivastava Himanshu,Srivastava Arvind,Srivastava Pankaj 한국물리학회 2021 Current Applied Physics Vol.24 No.-
-SiNx:H thin films of different stoichiometry grown by PECVD were subjected to irradiation by 100 MeV Au8+ ions with various fluences to understand the effect of stoichiometry on properties of thin films upon irradiation. Ellipsometry and UV–Vis study suggest the variation in the refractive index of thin films with fluence. The evolution of Hydrogen due to irradiation is quantified with the help of ERDA. RBS was probed to study the change in thin films’ composition upon irradiation, which further helps understand the change in thin films’ optical properties. Quenching of photoluminescence in the films with all stoichiometries was also observed due to ion irradiation. X-TEM images show the formation of discontinuous ion tracks of radius 2.5 nm in the film closer to silicon nitride stoichiometry. However, Si rich film does not show the clear formation of tracks. Results are explained in the framework of the Thermal spike mechanism of ion-solid interaction.
Choubey, Pankaj K.,Chung, Kang-Sup,Kim, Min-seuk,Lee, Jae-chun,Srivastava, Rajiv R. Elsevier 2017 Minerals engineering Vol.110 No.-
<P><B>Abstract</B></P> <P>The uncertainty in production and utilization with the availability of lithium rich minerals and brine in a limited land area has grown the attention for the exploitation of those resources not coming under a specific boundary. Approximately 230 billion tons of lithium in ubiquitous sea water and generation of a huge amount of used lithium ion batteries (spent LIBs) in different corner of the end-user countries can play a major role to change the scenario of securing lithium as a raw material for industry. Therefore, it needs to be exploited in such an effective manner that it can assure the mitigation of projected supply risk of this energy-critical element. To explore the commercial viability for their sustainable exploitation, it is imperative to review the methodologies that have been investigated and have clear potential for upscaling.</P> <P>This article deals with the processing of those resources that do not contributes yet to lithium supply in commodity market, and include the lithium recovery from sea water and spent LIBs. A purposive discussion on the electro-dialysis and reverse osmosis for the separation and recovery of lithium from sea water is of vital interest in future. A routinely disposed spent LIBs is a huge reservoir of lithium and need to be recovered as a main product along with the costlier cobalt, while recycling the spent LIBs. The various extraction and recovery processes of lithium are subdivided according to the adopted methodology, selection of lixiviant and obtaining the product in the desired form, whilst the technological and chemical perspective is also discussed. The deliberations on the edges and/or drawbacks, complications and prospects of the different processes are also included. It is believed that this state-of-the-art review can contribute in formulating the strategy for fulfilling the global energy demand by a sustainable recovery of lithium from its non-conventional resources, and can provide future research directions.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Exploitation of Lithium from sea water and spent batteries are critically reviewed. </LI> <LI> Li recovery via adsorption and electrodialysis process from sea water is compared. </LI> <LI> Pretreatment follows dismantling of LIBs to enrich the metals in black mass, LiM<SUB>x</SUB>O<SUB>y.</SUB> </LI> <LI> Acid/alkali leaching followed by solvent extraction to separate the metals. </LI> <LI> Precipitation is applied as a final step to get Li<SUB>2</SUB>CO<SUB>3</SUB> from the both sources. </LI> </UL> </P>
CERTAIN RELATIONS FOR MOCK THETA FUNCTIONS OF ORDER EIGHT
Pathak, Maheshwar,Srivastava, Pankaj Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.4
The aim of the present paper is to establish certain relations for partial mock theta functions and mock theta functions of order eight with other partial mock theta functions and mock theta functions of order two, six, eight and ten respectively.