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The main objective of this paper is to derive contiguous function relations or recurrence relations and obtainan integral representation Appell -series , where .Keywords: Pochhammer -symbol, -gamma function, -beta function, Contiguous functions, Appell -series. Contribution/ OriginalityThis study originates a new formula for Appell's series in the form of a new symbol and contributes for deriving contiguous function relations, obtaining an integral representation of the Appell's series in terms of said symbol .

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Integral inequalities are considered to be important as they have many applications described by a number of researchers. Moreover, the theory of fractional calculus is used in solving differential, integral, and integro-differential equations and also in various other problems involving special functions. In this research article, we present the improved version of generalizations for a Grüss type integral inequality by taking a generalized Riemann-Liouville fractional integral in terms of a new parameter k > 0. We contribute in the on going research by providing mathematical results that can be verified easily.

The current study contributes to the existing literature on the relationship between corporate governance (CG) and social performance (SP) of microfinance institutions (MFIs) by introducing CG index for the first time purely in the perspective of Asian MFIs. Moreover, this research also investigates the existence of endogeneity by checking the reverse causality between CG and SP as many previous studies highlighted the endogenous nature of many governance and performance variables. Using a panel of 173 MFIs in 18 Asian countries for the period of 5 years, a comprehensive CG index (CGI) based on seven internal governance mechanism variables is constructed as an indicator of the overall CG mechanism of MFIs. By employing generalized least squares (GLS) model, our results indicate insignificant impact of CG on many SP variables which are attributed to the endogenous nature of this relationship as the significance of results improved by studying relationship in reverse direction by employing ordered logit model. Our results indicate that SP is an important determinant of CG mechanism of MFIs even after controlling for MFI-related characteristics.

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The process of segmenting medical images serves as a vital technique in partitioning the image into different clusters or homogeneous regions. Lots of techniques and algorithms were developed and applied in various applications. Magnetic Resonance Images (MRI) are used for producing images in the soft tissues of human body. The presence of noise in the MRI images of Brain is a multiplicative factor and the reduction of noise is required to obtain good quality in segmentation. However, the concept of accurate segmentation in MRI images is more important and crucial for the proper diagnosis by computational tools aided to perform clinical studies. More clustering algorithms were developed for the segmentation of images from magnetic resonance. However most of them have their limitations and in order to overcome those limitations, a modified version of k means clustering methodology is proposed. The comparison of existing approaches in segmentation such as C-Means Clustering and K-Means Clustering with the Modified version of K Means Clustering is performed to evaluate the performance. Finally certain outcomes were generated in the clustering algorithm of Fuzzy c- means, k-means and modified version of k means for MRI taken in brain and it was observed that the modified version of clustering technique in Kmeans gives better results for the complete performance by measuring parameters such as the index measure of structural similarity, content of structure, mean squared error and analysis of signal noise ratio.

Background: Oral and Maxillofacial Surgery department is a diverse field in dentistry. Record maintenance has been established as one of the key factors in the success and integrity of health care institutes.Objective: The objective of the study was to evaluate the records of oral and maxillofacial surgery cases reported to oral and maxillofacial surgery department, Abbasi Shaheed Hospital and oral surgery OPD of Karachi Medical and Dental College.Methods: Cross sectional study was conducted in at ASH and KMDC from July 2019 to September 2019. The data from January 2017 to July 2019 was retrospectively noted through electronic surgical record of ASH and records of the Oral Surgery OPD of KMDC. Inclusion criteria was patients records of both genders of 5–70 years age, having complaint of any oral or dental pathology or pathologies, trauma and impactions. Data was calculated manually by calculating frequencies and percentages for the trauma, impaction and pathology cases of patients.Results: In 2017, 239 cases were treated under general anesthesia from which trauma 11. 45% (n=11), followed by 48. 11% (n=115) cases of oral pathologies, total 11.7% (n=28) cases of complicated exodontias. In 2018, among 211, 51.1% (n=108) cases were trauma followed by 39.3% (n=83) cases of oral pathologies, whereas, total 9.4% (n=20) complicated exodontias cases were observed. During 2019 (January to July), 168 cases 36.2% (n=62) cases were diagnosed as trauma, in oral pathology, overall 36.2% (n=62) cases were surgically excised. Total 23.2% (n=39) complicated exodontias. In 2017, 25122 cases were reported in Surgery OPD of Karachi Medical and Dental College. Total 36.2% (n=9097) teeth were extracted from which 1.93% (n=486) cases were surgical impaction. On the other hand, 1.65% (n=416) patients were treated through minor oral surgeries. In 2018, 29008 cases were reported in Surgery OPD. Total 42.7% (n=12377) teeth were extracted from which 0.92% (n=268) cases were surgical impaction. On the other hand, 0.71% (n=208) patients were treated through minor surgeries. In 2019, January till July 13028 cases were reported in Surgery OPD. Total 42.6% (n=5559) teeth were extracted from which 0.66% (n=87) cases were surgical impaction. On the other hand, 0.68% (n=89) patients were treated through minor surgeries.Conclusion: It has been concluded that evaluation of the records of oral and maxillofacial surgery cases reported to oral and maxillofacial surgery department, Abbasi Shaheed Hospital and oral surgery OPD of Karachi Medical and Dental College were high and appropriate measures should be taken in order to manage these problems timely and effectively.