THE INTEGRAL EXPRESSION INVOLVING THE FAMILY OF LAGUERRE POLYNOMIALS AND BESSEL FUNCTION

Shukla, Ajay Kumar,Salehbhai, Ibrahim Abubaker Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.4

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

Inflammatory Breast Cancer: a Single Centre Analysis

Gogia, Ajay,Raina, Vinod,Deo, Suryanarayan Vishnu,Shukla, Nootan Kumar,Mohanti, Bidhu Kalyan,Sharma, Daya Nand Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.7

Background: Inflammatory breast cancer (IBC) is an aggressive form of locally advanced breast cancer characterized by rapidly progressive breast erythema, pain and tenderness, oedema and paeu d'orange appearance. It accounts for 1-3% of all newly diagnosed cases of breast cancer in the west. Data on IBC from India are lacking. The aim of our study was to assess the clinical-pathological parameters and outcome of IBC at, All India Institute of Medical Sciences, a large tertiary care centre. Materials and Methods: We screened 3,650 breast cancer cases registered from January 2004 to December 2012 and found 41 cases of IBC. Data included demographics as well as clinical, radiological and histopathological characteristics, and were collected from clinical case records using the International Classification of Diseases code (C-50). Patients who presented with IBC as a recurrence, or who had a neglected and advanced breast cancer that simulated an IBC were excluded from this study. Results: The median age was 45 years (range 23-66). The median duration of symptoms was 5 months. The American Joint Committee on Cancer stage (AJCC) distribution was Stage III - 26 and IV - 15 patients. Estrogen receptor (ER), progesterone receptor (PR) positivity and human epidermal growth factor receptor 2 (HER2/neu) positivity were 50%, 46% and 60%, respectively. Triple negativity was found in 15% of the cases. All the non metastatic IBC patients received anthracycline and/ or taxane based chemotherapy followed by modified radical mastectomy, radiotherapy and hormonal therapy as indicated. Pathological complete remission rate was 15%. At a median follow-up of 30 months, the 3 year relapse free survival and overall survival were 30% and 40%respectively. Conclusion: IBC constituted 1.1% of all breast cancer patients at our centre. One third of these had metastatic disease at presentation. Hormone positivity and Her2 neu positivity were found in 50% and 60% of the cases, respectively.

Taxane and Anthracycline Based Neoadjuvant Chemotherapy for Locally Advanced Breast Cancer : Institutional Experience

Gogia, Ajay,Raina, Vinod,Deo, Suryanarayan Vishnu,Shukla, Nootan Kumar,Mohanti, Bidhu Kalyan,Sharma, Daya Nand Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.5

Background: The aim of this study was to assess the response rates (clinical and pathological ) with docetaxel and epirubicin combination chemotherapy and its effect on outcome. Materials and Methods: We retrospectively analysed locally advanced breast cancer (LABC) patients who received NACT from January 2008 to December 2012 in our tertiary care centre. LABC constituted 37% of all breast cancer cases and 120 patients fulfilled the eligibility criteria. The regimens used for NACT were, six cycles of DEC (docetaxel $75mg/m^2$, epirubicin $75mg/m^2$, cyclophosphamide $50mg/m^2$ on Day 1, 3 weekly) and a sequential regimen (4 cycles of FEC, 5-flurouracil $600mg/m^2$, epirubicin $75mg/m^2$, cyclophosphamide $600mg/m^2$ followed by 4 cycles of docetaxel $85mg/m^2$). Results: The median age was 47 years (range 23-72). Ninety six ( 80 %) had T4 disease and 90% had clinically palpable lymph nodes at diagnosis. The median size of primary tumor at presentation was 5.9 cm. Hormone receptor positivity was seen in 55% and HER2/neu positivity, in 25%. Triple negative breast cancers constituted 25 % of the cases. The overall clinical response rate (complete or partial ) was 85% and pathological complete responses were obtained in 15%. Four cases defaulted, 5 patients died of treatment related toxicity and 15% developed febrile neutropenia on DEC. The median duration of follow up was 22 months. The median time to relapse was 20 months and the 3 year relapse free and overall survival rates were 50% and 70% respectively. Conclusions: LABC constituted 37% of all breast cancer cases at our institute. With NACT, pCR was seen in 15% of the cases. Sequential chemotherapy was better tolerated than concurrent anthracyline and taxane chemotherapy with a similar pCR.

Techniques for Formulation of Nanoemulsion Drug Delivery System: A Review

Manish Kumar,Ram Singh Bishnoi,Ajay Kumar Shukla,Chandra Prakash Jain 한국식품영양과학회 2019 Preventive Nutrition and Food Science Vol.24 No.3

Nanoemulsion drug delivery systems are advanced modes for delivering and improving the bioavailability of hydrophobic drugs and the drug which have high first pass metabolism. The nanoemulsion can be prepared by both high energy and low energy methods. High energy method includes high-pressure homogenization, microfluidization, and ultrasonication whereas low energy methods include the phase inversion emulsification method and the self-nanoemulsification method. Low energy methods should be preferred over high energy methods as these methods require less energy, so are more efficient and do not require any sophisticated instruments. However high energy methods are more favorable for food grade emulsion as they require lower quantities of surfactant than low energy methods. Techniques for formulation of nanoemulsion drug delivery system are overlapping in nature, especially in the case of low energy methods. In this review, we have classified different methods for formulation of nanoemulsion systems based on energy requirements, nature of phase inversion, and self-emulsification.

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION

Jana, Ranjan Kumar,Maheshwari, Bhumika,Shukla, Ajay Kumar Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.1

In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

SOME PROPERTIES OF GENERALIZED BESSEL FUNCTION ASSOCIATED WITH GENERALIZED FRACTIONAL CALCULUS OPERATORS

Jana, Ranjan Kumar,Pal, Ankit,Shukla, Ajay Kumar Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.1

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

SOME PROPERTIES OF EXTENDED τ-HYPERGEOMETRIC FUNCTION

Jana, Ranjan Kumar,Maheshwari, Bhumika,Shukla, Ajay Kumar Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4

Recently, Parmar [5] introduced a new extension of the ${\tau}$-Gauss hypergeometric function $_2R^{\tau}_1(z)$. The main object of this paper is to study this extended ${\tau}$-Gauss hypergeometric function and obtain its properties including connection with modified Bessel function of third kind and extended generalized hypergeometric function, several contiguous relations, differential relations, integral transforms and elementary integrals. Various special cases of our results are also discussed.

Salvage Transoral Robotic Surgery for Recurrent or Residual Head and Neck Squamous Cell Carcinoma: A Single Institution Experience

Dabas, Surender,Dewan, Abhinav,Ranjan, Reetesh,Dewan, Ajay Kumar,Shukla, Himanshu,Sinha, Rupal Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.17

Background: The present study was conducted to evaluate the technical feasibility, safety and adequacy of surgical margins with salvage transoral robotic surgery (TORS) for recurrent or residual head and neck squamous cell carcinoma patients. Materials and Methods: Thirty patients who underwent salvage TORS using the 'DaVinci' robot were enrolled in the study and data related to their surgical time, complications and functional outcome were recorded. Results: The feasibility of salvage TORS in our study was observed to be 100%. Positive margins were encountered in only 6.7% of patients. Mean blood loss was 23.3 ml with no patient requiring blood transfusion. Postoperative complications in the form of primary haemorrhage requiring active surgical intervention occurred in 13.3%. Oral feeding could be started as early as the 3rd postoperative day in a few patients, with nasogastric tubes being removed on the 12th postoperative day. Long term gastrostomy tube dependency was seen in 10% cases. Median survival of patients was 19 months. Conclusions: Salvage TORS is a safe, effective and feasible option in the management of treatment failure cases. It offers an alternative surgical approach with unexpected benefits in terms of tracheostomy tube use, Ryle's tube and gastrostomy dependence.

Empirical model for estimating dengue incidence using temperature, rainfall, and relative humidity: a 19-year retrospective analysis in East Delhi

Vishnampettai G. Ramachandran,Priyamvada Roy,Shukla Das,Narendra Singh Mogha,Ajay Kumar Bansal 한국역학회 2016 Epidemiology and Health Vol.38 No.-

OBJECTIVES: Aedes mosquitoes are responsible for transmitting the dengue virus. The mosquito lifecycle is known to be influenced by temperature, rainfall, and relative humidity. This retrospective study was planned to investigate whether climatic factors could be used to predict the occurrence of dengue in East Delhi. METHODS: The number of monthly dengue cases reported over 19 years was obtained from the laboratory records of our institution. Monthly data of rainfall, temperature, and humidity collected from a local weather station were correlated with the number of monthly reported dengue cases. One-way analysis of variance was used to analyse whether the climatic parameters differed significantly among seasons. Four models were developed using negative binomial generalized linear model analysis. Monthly rainfall, temperature, humidity, were used as independent variables, and the number of dengue cases reported monthly was used as the dependent variable. The first model considered data from the same month, while the other three models involved incorporating data with a lag phase of 1, 2, and 3 months, respectively. RESULTS: The greatest number of cases was reported during the post-monsoon period each year. Temperature, rainfall, and humidity varied significantly across the pre-monsoon, monsoon, and post-monsoon periods. The best correlation between these three climatic factors and dengue occurrence was at a time lag of 2 months. CONCLUSIONS: This study found that temperature, rainfall, and relative humidity significantly affected dengue occurrence in East Delhi. This weather-based dengue empirical model can forecast potential outbreaks 2-month in advance, providing an early warning system for intensifying dengue control measures.