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Generalized Incomplete Pochhammer Symbols and Their Applications to Hypergeometric Functions
Sahai, Vivek,Verma, Ashish Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.1
In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.
Sahai, Vivek,Verma, Ashish Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
We obtain q-derivatives of Srivastava's general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava's triple q-hypergeometric series $H_{A,q}$, $H_{B,q}$ and $H_{C,q}$ are also considered.
RECURSION FORMULAS FOR q-HYPERGEOMETRIC AND q-APPELL SERIES
Sahai, Vivek,Verma, Ashish Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1
We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.
Recursion Formulas for Exton's triple Hypergeometric Functions
Sahai, Vivek,Verma, Ashish Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.2
This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and k-variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions.
Sahai, Puja,Baghmar, Saphalta,Nath, Devajit,Arora, Saurabh,Bhasker, Suman,Gogia, Ajay,Sikka, Kapil,Kumar, Rakesh,Chander, Subhash Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.16
Background: The optimal sequence and extent of multimodality therapy remains to be defined for extrapulmonary small cell carcinoma because of its rarity. The purpose of our study was to assess the response to neoadjuvant chemotherapy followed by chemoradiation/radiation in patients with extrapulmonary small cell carcinoma. Materials and Methods: Four consecutively diagnosed patients were included in this study. The primary tumor site was oropharynx in three patients and esophagus in one. The patients with the limited disease were treated with chemotherapy followed by concurrent chemoradiation (n=2) or radiotherapy (n=1). The patient with the extensive disease with the primary site in vallecula was treated with chemotherapy and palliative radiotherapy to the metastatic site. Results: The median follow-up was 22.5 months (range, 8-24 months). Three patients with the limited disease (base of tongue, n=2; esophagus, n=1) were in complete remission. The patient with the extensive disease died of loco-regional tumor progression at 8 months from the time of diagnosis. Conclusions: The combination of chemotherapy and radiotherapy is the preferred therapeutic approach for patients with extrapulmonary small cell carcinoma. Induction chemotherapy followed by concurrent chemoradiation or radiation provides a good loco-regional control in patients with limited disease.
Gupta, Alpa,Sahai, Aarushi,Aggarwal, Vivek,Mehta, Namrata,Abraham, Dax,Jala, Sucheta,Singh, Arundeep The Korean Dental Society of Anesthsiology 2021 Journal of Dental Anesthesia and Pain Medicine Vol.21 No.4
Achieving profound anesthesia in mandibular molars with irreversible pulpitis is a tedious task. This review aimed at evaluating the success of buccal/lingual infiltrations administered with a primary inferior alveolar nerve block (IANB) injection or as a supplemental injection after the failure of the primary injection in symptomatic and asymptomatic patients with irreversible pulpitis in human mandibular molars. The review question was "What will be the success of primary and supplemental infiltration injection in the endodontic treatment of patients with irreversible pulpitis in human mandibular molars?" We searched electronic databases, including Pubmed, Scopus, and Ebsco host and we did a comprehensive manual search. The review protocol was framed according to the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) checklist. We included clinical studies that evaluated and compared the anesthetic outcomes of primary IANB with primary and/or supplementary infiltration injections. Standard evaluation of the included studies was performed and suitable data and inferences were assessed. Twenty-six studies were included, of which 13 were selected for the meta-analysis. In the forest plot representation of the studies evaluating infiltrations, the combined risk ratio (RR) was 1.88 (95% CI: 1.49, 2.37), in favor of the secondary infiltrations with a statistical heterogeneity of 77%. The forest plot analysis for studies comparing primary IANB + infiltration versus primary IANB alone showed a low heterogeneity (0%). The included studies had similar RRs and the combined RR was 1.84 (95% CI: 1.44, 2.34). These findings suggest that supplemental infiltrations given along with a primary IANB provide a better success rate. L'Abbe plots were generated to measure the statistical heterogeneity among the studies. Trial sequential analysis suggested that the number of patients included in the analysis was adequate. Based on the qualitative and quantitative analyses, we concluded that the infiltration technique, either as a primary injection or as a supplementary injection, given after the failure of primary IANB, increases the overall anesthetic efficacy.
On Estimating the Variance of a Normal Distribution With Known Coefficient of Variation
Ray, S.K.,Sahai, A. The Korean Statistical Society 1978 Journal of the Korean Statistical Society Vol.7 No.2
This note deals with the estimations of the variance of a normal distribution $N(\theta,c\theta^2)$ where c, the square of coefficient of variation is assumed to be known. This amounts to the estimation of $\theta^2$. The minimum variance estimator among all unbiased estimators linear in $\bar{x}^2$ and $s^2$ where $\bar{x}$ and $s^2$ are the sample mean and variance, respectively, and the minimum risk estimator in the class of all estimators linear in $\bar{x}^2$ and $s^2$ are obtained. It is shown that the suggested estimators are BAN.
Risk Factors for Pseudarthrosis in Minimally- Invasive Transforaminal Lumbar Interbody Fusion
Michael Faloon,Nikhil Sahai, Conor J. Dunn,Kimona Issa,Daniel Thibaudeau,Kumar Sinha,Ki Soo Hwang 대한척추외과학회 2018 Asian Spine Journal Vol.12 No.5
Study Design: Retrospective cohort study (level of evidence: 4). Purpose: To describe the potential comorbid, operative, and radiographic risk factors for the development of clinically-relevant pseudarthrosis following minimally-invasive transforaminal lumbar interbody fusion (MIS-TLIF). Overview of Literature: MIS-TLIF has shown long-term clinical outcomes with decreased perioperative morbidity and earlier return to work, similar to those of open TLIF. However, unsuccessful fusion still remains a concern. The impacts of various patient, operative, and radiographic risk factors have not been evaluated for their potential association with pseudarthrosis related to MIS-TLIF. Methods: Between 2012 and 2015, 204 consecutive patients underwent one or two-level MIS-TLIF at St. Joseph's University Medical Center, Paterson, NJ, USA; they had a minimum of 1 year of follow-up. The patients were divided into two cohorts: those who developed clinically-relevant pseudarthrosis and those who did not. Clinically-relevant pseudarthrosis was determined by both evidence on computed tomography and presence of continued clinical symptoms at 1-year follow-up. Results: Revision surgery was the only identified non-radiographic factor associated with pseudarthrosis. Disc angle had the highest (R 2=0.8), followed by anterior disc height (R 2=0.79). Although posterior disc height and the ratio of anterior to posterior disc height showed a marked relationship with the outcome, the R 2-values were <0.3, thus indicating a less-strong correlation. The overall pseudarthrosis rate was 8%. No statistically significant differences were identified between the two cohorts with respect to mean age, sex, medical comorbidities, smoking status, or number of levels fused. Conclusions: Clinically-relevant pseudarthrosis is not uncommon following MIS-TLIF. In the current study, undergoing revision surgery, disc angle, and anterior disc height were observed to be associated with clinically-relevant pseudarthrosis. This study demonstrated that the patient population may benefit from an alternate approach.
Mohanti, Bidhu Kalyan,Sahai, Puja,Thakar, Alok,Sikka, Kapil,Bhasker, Suman,Sharma, Atul,Sharma, Seema,Bahadur, Sudhir Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.2
Aims: To describe our institutional experience with high dose rate (HDR) interstitial brachytherapy (IBT) compared with previously reported results on the low dose rate (LDR) practice for head and neck cancer. Materials and Methods: Eighty-four patients with oral cavity (n=70) or oropharyngeal cancer (n=14) were treated with 192Ir HDR-IBT. Seventy-eight patients had stage I or II tumour. The patients treated with IBT alone (n=42) received 39-42 Gy/10-14 fractions (median=40 Gy/10 fractions). With respect to the combination therapy group (n=42), prescription dose comprised of 12-18 Gy/3-6 fractions (median=15 Gy/5 fractions) for IBT and 40-50 Gy/20-25 fractions (median=50 Gy/25 fractions) for external radiotherapy. Brachytherapy was given as 2 fractions per day 6 hours apart with 4 Gy per fraction for monotherapy and 3 Gy per fraction for combination therapy. Results: Four patients were not evaluable in the analysis of outcome. The primary site relapse rates were 23.8% (10/42) and 68.4% (26/38) in patients treated with IBT alone and combination therapy, respectively (p<0.001). Salvage surgery was performed in 19 patients. The 5-year local control rate was estimated at 62% and the disease-free survival (DFS) rate at 52% for all patients. Local control with respect to T1 and T2 tumours was 84% and 42%, respectively. Conclusions: Our present series on HDR-IBT and the previous report on LDR-IBT for head and neck cancer demonstrated similar DFS rates at 5 years (52%). The rate of regional failure in node-negative patients was <20% in both of our series. HDR-IBT offers similar results to LDR-IBT for head and neck cancer.