In this paper, certain mixed special polynomial families associated with Appell sequences are introduced and their properties are established. Further, operational rules providing connections between these families and the known special polynomials are established, which are used to derive the identities and results for the members of these new families. Determinantal definitions of the polynomials associated with Appell family is also derived. The approach presented is general.Mathematics Subject Classifications: 33C45, 33C99, 33E20.

In this article, the Laguerre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Certain important properties of these polynomials are established. Further, operational and integral representations for these mixed polynomials are derived.

Background: Invasive hemodynamic monitoring of central venous pressure (CVP) is a useful guide in directing early resuscitative efforts and assists in reducing the morbidity and mortality of the patients with septic shock. Dynamic parameters like ultrasonographic evaluation of the inferior vena cava (IVC) diameters are becoming increasingly popular method to assess the intravascular volume status. Objectives: The objective of this study was to evaluate the relation between CVP and IVC collapsibility in cases of fluid refractory shock. Methods and Materials: This was a prospective observational study. Pediatric patients between 1 and 14 years with fluid refractory shock were evaluated. Their CVP was recorded and IVC diameter was measured by ultrasonography during inspiration and expiration. This was calculated as IVC collapsibility index (IVC-CI). Data analysis was done with descriptive statistics, coefficient of correlation, and analysis of variance, as appropriate using SPSS for Windows software (SPSS Inc. Version 20). Results: A total of 107 patients with shock were included in the study with the mean age of 7.6 years. Septic shock (93%) was the most common cause of shock and the maximum patients (63%) were in cold shock. Most of these patients had acidosis (mean pH 7.22±0.2), high lactate levels (mean 6.3±3.50 mmol/l), and decreased bicarbonate levels (mean 16.98±5.95 mmol/l). When CVP range was ?8 mmHg, the mean IVCCI value was >40% and when the CVP range was ?12 mmHg, the mean IVCCI value was around 20%. Inverse relation between CVP and IVCCI was observed (r=?0.690, p<0.01). Conclusions: There was a strong negative correlation between CVP and IVC collapsibility.

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