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In this paper, we investigate the existence of φ-fixed point for Banach orbital contraction over 𝔄-metric space. Also a fixed point result has been established via asymptotic regularity property over such generalized metric space. Our fixed point theorems have also been applied to the fixed circle problem. Moreover, we give some new solutions to the open problem raised by Özgür and Taş on the geometric properties of φ-fixed points of self-mappings and the existence and uniqueness of φ-fixed circles and φ-fixed discs for various classes of self-mappings.

Background: Parathyroid dysfunction leading to symptomatic hypocalcemia is not uncommon following a total or completion thyroidectomy and is often associated with significant patient morbidity and a prolonged hospital stay. Objectives: To investigate whether postoperative parathyroid hormone level is a parameter to identify hypocalcaemia after total thyroidectomy. Methods: This prospective longitudinal study was carried out with variety of thyroid disorders with indication of total thyroidectomy at BSMMU. Total 103 patient were selected following the inclusion and exclusion criteria. The routine clinical assessment and the preoperative laboratory investigations of the study population were performed before operation. Preoperative and postoperative levels of serum PTH and serum calcium level were measured. Results: Immediate post-operative period 17(16.50%) patients PTH level were low (

Background: Gallstone disease (GD) is one of the most prevalent gastrointestinal disease in worldwide and also in Bangladesh. High triglyceride and low HDL (high density lipoprotein) are associated with cholelithiasis whereas total cholesterol and LDL (low density lipoprotein) have less association. Objectives: To find out the association of cholelithiasis and lipid profile. Material and Methods: This case-control study was conducted on 300 patients in the department of surgery, Rajshahi Medical College Hospital from September, 2018 to August, 2019. Participants were divided into two groups; group A (case group- 150 patients) and group B (control group-150 patients). After overnight fasting 5 ml venous blood was collected and serum lipid profile was measured. Outcomes were expressed in the form of figures and tables. Result: The mean age in case group were 39.79±8.16 years and in control group 38.67±7.99 years respectively with female predominance (72%) and male to female ratio was 1:2.57. out of 150 participants in case group 61% (91) had cholesterol stone. TG level was high both in cholesterol stone 57 (62.62%) and mixed stone 35 (59.32%) in case group. The mean BMI (25.73±2.10) in case group were significantly higher. Post-operative histopathology shown 2 (1.33%) patients associated with malignancy. Conclusion: The increased lipid profile can be good indicator for gall stone diseases and female are more susceptible to form gallstone who have high cholesterol level. Obesity is a risk factor for gallstone so people should maintain an ideal body weight. Gallstones are predisposing factor for malignancy. Sir Salimullah Med Coll J 2021; 29(2): 95-99

Background: Ileal perforation is a very frequent surgical emergency in surgery wards. In tropical country infection is the commonest cause. Repair of perforation, primary repair with loop ileostomy and resection and primary anastomosis are the commonly performed methods. Objectives: To identify the aetiology and assess the outcome of resection and primary anastomosis in multiple ileal Perforation. Study Procedure: This Quasi experimental study was carried out in the Department of Surgery, Rajshahi Medical College Hospital, Rajshahi. 92 patients were included in this study. Thorough clinical, Radiological and biochemical parameters evaluation with postoperative histopathology were performed. All patients treated with resection and primary anastomosis. Different types of Data and variables were recorded through data collection sheet. Mean and frequency of all quantitative and categorical variables were determined. Results: The mean age 42.60±4.44 (age range:18-69) years. Out of 92 patients 74(80.43%) were male and 18(19.56%) were female and ratio was 4.11:1.Presentation were 92(100%) abdominal pain, vomiting 74(80.43%), fever 60(65.21%) and abdominal distension 56(60.86%). Common Cause were typhoid fever 43(46.73%) and nonspecific inflammation 28(30.43%). Patient suffered from wound infection 18(19.44%), dehiscence 7(7.56%), anastomosis leakage 6(6.68%) and 5(5.43%) patient experienced incisional hernia. 74(80.43%) recovered uneventfully, 17(18.47%) recovered with complication and only 1(1.08%) died. Conclusion: Among the infections, typhoid fever is still the prime cause of multiple ileal perforation. Wound infection, wound gap, burst abdomen & primary repair leakage are the common complications. Uneventful outcome is present in majority cases. Delayed presentation, nutritional status and anastomosis from ileocaecal valve are the important deciding factor of worst outcome. Sir Salimullah Med Coll J 2021; 29(2): 153-157

This experimental paper is about the implementation of two types of nanofluid in a three-liter natural convection cavity (H = 20 cm, L = 15 cm and W = 10 cm) and to investigate the effect on the heat transfer. In this experiment, the left wall has constant heat (80 W) and the right wall has a constant temperature that is being cooled by using a fabricated constant temperature water bath. In electronics cooling, this kind of natural convection can be found and the left wall is the location where electronics equipment is mounted and releases constant heat. This surface is getting cooled by the natural convection cavity. ZnO and Al2O3 nanoparticles (both of them create whitish aqueous solution) of low volume fraction (up to 0.05% to maintain the stability in the cavity) are chosen for this purpose so that fluid flow visualization can be observed. Initially, flow visualizations are carried out using smoke and water with color dye. The natural convection loop is observed for both the cases at steady state condition but the water case takes a much longer time. The eye of the vortex is found in both cases. In the case of air, it stays at the center but for water, there is a gradual shift of the vortex eye towards the cold wall over time. However, initially, ZnO nanoparticles are formed from micro-particle by manually grinding but this leads to a very unstable solution (even at 0.01% volume fraction) in distilled water solution even after three hours of ultra-sonication. So, in-house nanoparticle preparation (without using any surfactant in the nanofluid) fails the purpose and thus vendor-supplied nanoparticles will be used for all future investigations.

Background: Urethral stricture diseases are common urological problems in our country. The etiologies include iatrogenic, trauma, infection, congenital and very few are idiopathic. Urethral strictures have the potential for great negative impact on patients. These have several treatment modalities, ranging from simple dilations to complex multistaged urethroplasties. Optical internal urethrotomy and anastomotic urethroplasty are the common procedures among them which are particular topics in this study. Objectives: To evaluate the outcome of two surgical techniques- Optical Internal Urethrotomy (OIU) and Anastomotic Urethroplasty. Methodology: A total of 50 patients with short segment bulbar urethral strictures were consecutively included in the study. Purposive sampling method was applied. The present outcome clinical study was conducted in the department of Urology, National Institute of Kidney Diseases and Urology, Sher-E-Bangla Nagar, Dhaka, Bangladesh over a period of 1 year from February 2016 to January 2017. Student’s t-test and chi-square test were applied for hypothesis testing. ‘P’ value

This paper represents a comprehensive review on the preparation and stability of nanofluid, the convective heat transfer coefficient and different thermo-physical properties such as thermal conductivity, specific heat capacity, viscosity, and so on. Here, for each thermo-physical property, measurement methods, enhancement mechanisms, and criticisms of different studies are also presented. However, based on the available literature, it is concluded that a nanofluid has, in general, better thermo-physical properties even at a very low particle concentration (typically 1% or less) than conventional heat transfer fluids. The only drawback is high viscosity which leads to a higher pressure drop. At a very low particle concentration, this drawback can be minimized. Three tables are provided for three thermo-physical properties namely thermal conductivity, specific heat capacity, and viscosity, which can be used as a ready reference for calculating the nanofluid properties.

Air handling unit (AHU) is one of the most extensively used equipment in large commercial buildings. This device is typically customized and lacks quality system integration which can result in hardwire failures and control errors. Air handling unit Performance Assessment Rules (APAR) is a fault detection tool that uses a set of expert rules derived from mass and energy balances to detect faults in air handling units. APAR is computationally simple enough that it can be embedded in commercial building automation and control systems and relies only upon sensor data and control signals that are commonly available in these systems. Although APAR has advantages over other methods, for example no training data required and easy to implement commercially, most of the time it is unable to provide the root diagnosis of the faults. For instance, a fault on temperature sensor could be bias, drifting bias, inappropriate location, or complete failure. In addition a fault in mixing box can be return and/or outdoor damper leak or stuck. In addition, when multiple rules are satisfied, the list of faults increases. There is no proper way to have the correct diagnosis for rule based fault detection system. To overcome this limitation, we proposed Bayesian Belief Network (BBN) as a diagnostic tool. BBN can be used to simulate diagnostic thinking of FDD experts through a probabilistic way. In this study we developed a new way to detect and diagnose faults in AHU through combining APAR rules and Bayesian Belief network. Bayesian Belief Network is used as a decision support tool for rule based expert system. BBN is highly capable to prioritize faults when multiple rules are satisfied simultaneously. Also it can get information from previous AHU operating conditions and maintenance records to provide proper diagnosis. The proposed model is validated with real time measured data of a campus building. The results show that BBN correctly prioritize faults that are verified by manual investigation.

We state conditions for well-posedness of a fixed point problem for single and multivalued operators, where these operators are deterministic or random. These results are applied to families of different generalized contractions.

In the present paper, we apply random analogue Kannan fixed point theorem [10] to analyze the existence of a solution of a nonlinear stochastic integral equation of the Hammerstein type of the form$$x(t ; \omega)=h(t ; \omega)+\int_S k(t, s ; \omega) f(s, x(s ; \omega)) d \mu(s)$$where $t \in S$, a $\sigma$-finite measure space with certain properties, $\omega \in \Omega$, the supporting set of a probability measure space $(\Omega, \beta, \mu)$ and the integral is a Bochner integral.

Nanofluid is a mixture of a small concentration of nanometer sized solid particle like nanoparticles, nanotubes or nanowires suspended in the liquid and making a colloidal suspension. It is relatively a new field which is less than two decades old. Nanofluid attracts researchers in many ways for their enhanced heat transfer properties. Nanofluid has better heat transfer performance than the base fluid. This paper represents a comprehensive review on the preparation and stability of nanofluid, maintaining stability, evaluating stability etc. and different thermal physical properties like convective heat transfer coefficient for laminar and turbulent region, thermal conductivity, specific heat capacity, viscosity etc. and some transport phenomena like pool boiling heat transfer, flow boiling heat transfer.

This paper deals with an experimental investigation of aerodynamic characteristics of full and partial-length squealer rims in a turbine stage. Full and partial-length squealer rims are investigated separately on the pressure side and on the suction side in the “Axial Flow Turbine Research Facility” (AFTRF) of the Pennsylvania State University. The streamwise length of these “partial squealer tips” and their chordwise position are varied to find an optimal aerodynamic tip configuration. The optimal configuration in this cold turbine study is defined as the one that is minimizing the stage exit total pressure defect in the tip vortex dominated zone. A new “channel arrangement” diverting some of the leakage flow into the trailing edge zone is also studied. Current results indicate that the use of “partial squealer rims” in axial flow turbines can positively affect the local aerodynamic field by weakening the tip leakage vortex. Results also show that the suction side partial squealers are aerodynamically superior to the pressure side squealers and the channel arrangement. The suction side partial squealers are capable of reducing the stage exit total pressure defect associated with the tip leakage flow to a significant degree.

We study the approximate coincidence point of two nonlinear functions introduced by Geraghty in 1973 and Mizoguchi and Takahashi (ℳ𝒯-function) in 1989.

A convenient method is reported for the synthesis of some novel complexes of composition (R 3 SnL 2 ) ClO 4 where L represents pyridine, γ-picoline, 2,2′-bipyridine and 1,10-phenanthroline; and R  n Bu or Ph. All of the new ionic complexes have been characterized by elemental analysis, molar conductance, infrared, multinuclear nuclear magnetic resonance ( 1 H, 13 C and 119 Sn) and 119 Sn Mossbauer spectroscopies. The complexes of composition (R 3 SnL 2 )ClO 4 exist both in solution and in the solid state with trans -trigonal bipyramidal structure where the R-groups occupy the equatorial positions while the ligands are in the axial position.

Several diorganotin dichloride complexes of the type R2SnCl2.L (R=methyl, phenyl and L=phenylazo-, 3-tolylazo-, 4-tolylazo- and 4-chlorophenylazo-2-pyridine) have been synthesized and characterized. Investigation of the complexes by IR, 1H NMR, electronic spectral and 119Sn Mossbauer parameters indicated that their structure involved coordination of the pyridine and azo nitrogen to tin atom. 119Sn Mossbauer data (Q.S.=3.37−3.76 mm/sec.) suggest that the complexes are considered to have the two R-groups occupying trans-position in the distorted octahedral structures. Distortion of C-Sn-C bond angle from the linearity have also been calculated using Parish's relationship and lying among 148–155° (R=methyl) and 148–150° (R=phenyl).

Grain growth of ZnO during the liquid-phase sintering of binary ZnO–Bi2O3 ceramics has been studied for Bi2O3 contents from 3 to 12 wt% and sintering from 900° to 1400°C. The results are considered in combination with previously published studies of ZnO grain growth in the ZnO–Bi2O3 system. For the Bi2O3 contents of the present study, the rate of ZnO grain growth is found to decrease with increasing Bi2O3. Activation analysis, when combined with the results of similar analyses of the previous studies, reveals a change in the rate-controlling mechanism for ZnO grain growth. Following a low-Bi2O3-content region of nearly constant activation energy values of about 150 kJ/mol, further Bi2O3 additions cause an increase of the activation energy to about 270 kJ/mol. consistent with accepted models of liquid-phase sintering, it is concluded that the rate-controlling mechanism of ZnO grain growth during liquid-phase sintering in the presence of Bi2O3 changes from one of a phase-boundary reaction at low Bi2O3 levels to one of diffusion through the liquid phase at about the 5 to 6 wt% Bi2O3 level and above.

The preparation of 1:2 and 1:1 mercury(II) chloride complexes with arylazo ligands is described. These compounds are freely soluble in methanol in they behave as non-electrolytes. Based on molar conductance, 1H n.m.r., electronic spectra and i.r. spectral features down to 200cm−1, complexes of arylazo-2-naphthol(L1H) and arylazopyridines (L3−L6) are considered as neutral, four-coordinated tetrahedral structures while complexes of arylazo-2-carboxylic acid (L2H) appear to be neutral, three-coordinated around mercury(II).

This paper deals with an experimental investigation of aerodynamic characteristics of full and partial-length squealer rims in a turbine stage. Full and partial-length squealer rims are investigated separately on the pressure side and on the suction side in the “Axial Flow Turbine Research Facility” (AFTRF) of the Pennsylvania State University. The streamwise length of these “partial squealer tips” and their chordwise position are varied to find an optimal aerodynamic tip configuration. The optimal configuration in this cold turbine study is defined as the one that is minimizing the stage exit total pressure defect in the tip vortex dominated zone. A new “channel arrangement” diverting some of the leakage flow into the trailing edge zone is also studied. Current results indicate that the use of “partial squealer rims” in axial flow turbines can positively affect the local aerodynamic field by weakening the tip leakage vortex. Results also show that the suction side partial squealers are aerodynamically superior to the pressure side squealers and the channel arrangement. The suction side partial squealers are capable of reducing the stage exit total pressure defect associated with the tip leakage flow to a significant degree.

Aerodynamic losses due to the formation of a leakage vortex near the tip section of rotor blades form a significant part of viscous losses in axial flow turbines. The leakage flow, mainly induced by the pressure differential between the pressure side and suction side of a rotor tip section, usually rolls into a streamwise vortical structure near the suction side part of the blade tip. The current study uses the concept of a tip platform extension that is a very short “winglet” obtained by slightly extending the tip platform in the tangential direction. The use of a pressure side tip extension can significantly affect the local aerodynamic field by weakening the leakage vortex structure. Phase averaged, time accurate total pressure measurements downstream of a single stage turbine facility are provided from a total pressure probe that has a time response of 150 kHz. Complete total pressure maps in all of the 29 rotor exit planes are measured accurately. Various pressure and suction side extension configurations are compared against a baseline case. The current investigation performed in the Axial Flow Turbine Research Facility (AFTRF) of the Pennsylvania State University shows that significant total to total efficiency gain is possible by the use of tip platform extensions.Copyright © 2001 by ASME

The present investigation deals with the numerical visualisation of tip leakage flow from 'partial-length squealer rims' that are constructed separately on the suction side in a single stage turbine rig. After describing the static pressure field on the tip surface with a squealer rim, the vortical flow features around the squealer rim and inside the tip gap are visualised in vertical planes. The leakage flow paths under the control of squealer rims are described in various planes parallel to the blade tip platform on which the squealer rims are attached. Turbine exit total pressure as calculated from the numerical model is presented for the baseline tip and tips with squealer rims. It is clearly shown that a partial squealer rim arrangement can be extremely effective in weakening the tip leakage vortex in a turbine facility provided that the squealer rim height is specified correctly. The study shows that the chordwise length of partial squealer rims near the suction side corner does not significantly affect the desensitisation process. The aerodynamic benefit of using a partial squealer tip arrangement located near the suction side of the tip platform in a turbine stage is demonstrated.

This paper deals with the viscous flow simulations of the complex tip leakage flow in Axial Flow Turbine Research Facility (AFTRF). Special attention is paid to the 3D structure of the tip leakage flow mechanisms in a baseline tip configuration with no desensitisation. Although past experimental studies provide much insight into the physical understanding of the tip region aerodynamics, there are still many areas of the flow-field in which experiments are extremely difficult to perform. Fine details of the entrance flow near the pressure side where the tip leakage jet starts to form, the leakage jet formation between the tip surface and outer casing, the re-circulatory flow zone very near the pressure side corner, the interaction area of the tip vortex with the conventional passage flow, the influence of the relative motion of the outer casing and leakage flow reversal can be visualised with excellent resolution. After the presentation of the measured inlet boundary conditions and a grid independency study, the baseline tip flow simulations are discussed in detail.

In the study of optimization models for the design of water distribution networks, most of the literature has either indicated or explicitly claimed that at the optimal solution each link will consist of at most two pipe segments with adjacent diameters. This paper presents the necessary and sufficient conditions that a given set of pipe diameters is in an optimal solution and as a special case shows that the adjacency property holds if and only if pipe costs are a strictly convex function of a power of pipe diameters.

A computationally efficient two-stage method for the optimal design of branched water distribution networks on flat terrain is proposed. In the initial stage, the Lagrange multiplier method is used to obtain continuous optimal pipe sizes and Lagrange multipliers analytically. It is not necessary here to solve a system of linear equations and only simple arithmetic operations are needed. For any method in which continuous diameters are evaluated, a heuristic procedure is used to round off the continuous diameter into discrete diameters. The present method, however, uses the analytical solution obtained in the first stage to select a restricted candidate list of commercially available pipe sizes for input to an LP model. When the proposed method is applied to branched networks of different sizes and complexities, it is observed to be computationally more efficient than the LP model. Moreover, the optimal solution obtained by the proposed method coincides with the optimal solution obtained by the LP model for all branched networks so far randomly generated.

Coordinative interaction of uranylnitrate with 5-Azoxines containing different substituents in the aniline fragment have been studied. Infrared data suggests that the chelation of azoxines occurred exclusively in the oxinate moiety through the O and N atoms. These complexes have been characterised by spectral, magnetic measurements and elemental analysis.