Four Steps Implicit Method for the Solution of General Second Order Ordinary Differential Equations

Four steps implicit scheme for the solution of second order ordinary differential equation was derived through interpolation and collocation method. Newton polynomial approximation method was used to generate the unknown parameters in the corrector. The method was tested with numerical examples and it was found to be efficient in solving second order ordinary differential equations

Numerical Simulation of Electric Field and Charge Structure within an Isolated Thunderstorm

The study of electrical structure of thunderstorm is a deterministic factor in characterizing the behavior of lightning. It is impossible to measure the value of electric field at every point within the thunderstorm, even when the in situ measurements are made, they are done along the path of balloon-borne instruments or other methods employed in the measurement. The average data obtained from past measurements were employed in determining the electric field generated by the thunderstorm as observed along the horizontal distance using the cylindrical charge model. The data consisted of a screening charge layer firstly located “between” 1.8-2.0 km and later between 10.0-10.2 km respectively above the ground level (agl) to see the effect of positioning on the resultant computation. The lower positive charge center with radius ranging from 0.5 km to 2.0 km was placed at various heights between 2.0 and 6.0 km. This is to determine the effect of cloud base height on the resulting field profile. The main negative charge is accommodated between 4.0 and 7.5 km and the upper positive charge layer existed between 7.5- 10.0 km agl for a cloud base height of 2.0 km and 6.0- 9.5 km agl for a negative charge layer, 7.5- 11.0 km agl for upper positive charge with a cloud base of 4.0 km high. The resulting potential gradient (PG) profiles were obtained for spatial distribution with screening charge layer playing no active role in the thunderstorm electrification. The effects of wind shear due to increasing wind speed with height were also investigated to have a clear picture of the cloud charge dynamics; hence the vertical PG patterns produced by a moving thunderstorm for various cloud cell life-times were modeled. The results showed that a typical tropical thunderstorm can exhibit charge layer more than the normal tripolar structure, and the pocket of lower positive charge can be more than one or larger than the usual size. Wind shear was found to enhance lightning discharges at the surface of charge discontinuities. Keywords: Potential gradient, Wind shear, Cloud charge, Lower positive charge center, Noninductive charging.

Managing risk in the face of adversity: design and outcomes of rapid glaucoma assessment clinics during a pandemic recovery

Background: The provision of timely care to the high volume of glaucoma patients stratified as “low risk” following pandemic-related appointment deferrals continues to prove challenging for glaucoma specialists. It is unknown whether stratification as “low risk” remains valid over time, raising the potential risk of harm during this period if left unmonitored. This study aimed to evaluate whether Rapid Glaucoma Assessment Clinics (RGACs) are an effective method of assessing “low-risk” patients in order to identify those who may need an escalation of care, therefore reducing the risk of the future incidents of preventable vision loss. / Methods: RGACs were developed which comprised a brief advance telephone history by a clinician and then ophthalmic technician-measured visual acuity and intraocular pressure in clinic. We report outcomes from the first month of operation describing attendance patterns, the proportion of patients from this “low risk” cohort requiring escalation and underlying reasons for treatment escalations. / Results: 639 patients were invited to attend RGACs. 75% attended their booked appointment. Pre-attendance telephone consultations were associated with lower non-attendance rates (13.9% vs 29.3%, p < 0.00001). 15% of patients were no longer deemed to remain at “low risk” with further expedited clinical review scheduled. 10.4% of patients required an escalation in treatment following review. / Conclusions: RGACs are an effective approach to deliver high throughput clinical assessments for large numbers of “low-risk” glaucoma patients with deferred appointments. They enable the rapid identification and treatment of patients who would otherwise face significantly delayed review reducing the risk of future preventable vision loss

A systematic review and meta-analysis of school and cognitive function domains of health-related quality of life measures for children and young adults with congenital heart disease

\ua9 2023 The Authors. Birth Defects Research published by Wiley Periodicals LLC.Background: Research on cognitive and school functioning domains of health-related quality of life (HRQOL) for children and adolescents with congenital heart disease (CHD) presents inconsistencies. Objectives: To summarize and synthesize data on school and cognitive function domains of HRQOL for children and young people (CYP) with CHD. Methods: Five electronic databases MEDLINE, Scopus, PsycINFO, EMBASE, ERI, and citations were systematically searched. We included original-research articles reporting the cognitive and school function domains of HRQOL for children and young people with CHD (child and parent reports included). Both fixed and random-effects meta-analyses were performed to estimate pooled mean test scores for cognitive and school function. A total of 34 studies met our inclusion criteria and were synthesized narratively, 17 studies were included in formal meta-analyses. Results: Self-reported cognitive function was lower for children and young people with CHD than healthy controls (SMD −0.28 (−0.42, −0.15)). Parental reports demonstrated similar results to self-reports (SMD −0.54 (−0.91, −0.18)). School function was lower in children and young people with CHD compared with healthy controls in self-reported (SMD −0.30 (−0.48, −0.13)) and parent reported HRQOL (SMD −0.49 (0.64, −0.36)). Self-reported school function domain scores were lower for young (&lt;8 years) (SMD −0.65 (−1.32, 0.03)) and older children (8–18 years) (SMD −0.25 (−0.47, −0.03)) with CHD than their peers. Similarly, parents reported lower school function domain scores for young (&lt;8 years) (SMD −0.68 (−1.29, −0.07)) and older (8–18 years) (SMD −0.46 (−068, −0.25)) children with CHD than typically developing peers. Conclusion: Children born with CHD may experience lower cognitive and school function HRQOL scores than healthy controls (self and proxy-report). This is consistent with a subgroup meta-analysis of young (&lt;8 years) and older (8 years old or more) children with CHD reporting lower school function scores compared to controls

Numerov's Method for the Solution of Second Order Initial Value Problems of Ordinary Differential Equation Using Modified Block Method

Collocation and interpolation method us;ng power series approximate solution to generate a continuous Numerov's is considered in this paper. The existing block method was modified to accommodate the unknown parameter in the corrector. The modified block method generates the independent solution at the grid points. This method was found to be efficient when tested on second order ordinary differential equation. Keywords: Collocation, interpolation, approximate solution, block method, grid poin

FOUR STEPS IMPLICIT METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Four steps implicit scheme for the solution of second order ordinary differential equation was derived&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;through interpolation and collocation method. Newton polynomial approximation method was used to&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;generate the unknown parameters in the corrector. The method was tested with numerical examples&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;and it was found to be efficient in solving second order ordinary differential equations.&nbsp

Planar polymer waveguides with a graded-index profile resulting from intermixing of methacrylates in closed microchannels

Graded-index waveguides are known to exhibit lower losses and considerably larger bandwidths compared to step-index waveguides. The present work reports on a new concept for realizing such waveguides on a planar substrate by capillary filling microchannels (cladding) with monomer solution (core). A graded-index profile is obtained by intermi xing between the core and cladding material at the microchannel interface. To this end, various ratios of methyl methacrylate (MMA) and octafluoropentyl methacrylate (OFPMA) were evaluated as starting monomers and the results showed that the polymers P50:50 (50:50 MMA:OFPMA) and P0:100 (100% OFPMA) were suitable to be applied as waveguide core and cladding material respectively. Light guiding in the resulting P50:50/P0:100 waveguides was demonstrated and the refractive-index profile was quantified and compared with that of conventional step-index waveguides. The results for both cases were clearly different and a gradual refractive index transition between the core and cladding was found for the newly developed waveguides. Although the concept has been demonstrated in a research environment, it also has potential for upscaling by employing drop-on-demand dispensing of polymer waveguide material in pre-patterned microchannels, for example in a roll-to-roll environment

Block Algorithm for General Third Order Ordinary Differential Equation

We present a block algorithm for the general solution o

TWO STEPS BLOCK METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATION

In this paper, an implicit block linear multistep method for the solution of ordinary differential equation&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;was extended to the general form of differential equation. This method is self starting and does not&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;need &nbsp; a &nbsp; predictor &nbsp; to &nbsp; solve &nbsp; for &nbsp; the &nbsp; unknown &nbsp; in &nbsp; the &nbsp; corrector. &nbsp; The &nbsp; method &nbsp; can &nbsp; also &nbsp; be &nbsp; extended &nbsp; to&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;boundary &nbsp; value &nbsp; problems &nbsp;without &nbsp; additional &nbsp; cost. &nbsp; The &nbsp;method was &nbsp; found to &nbsp; be &nbsp;efficient &nbsp; after &nbsp; being&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;tested with numerical problems of second order

Predictors of Post-Operative Hospital Length of Stay Following Complete Repair of Tetralogy of Fallot in a Pediatric Cohort in the North of England

We sought to estimate the median post-operative length of stay (PLOS) and predictors of PLOS following tetralogy of Fallot (ToF) repair at a specialist surgical center in the North of England. The local National Congenital Heart Disease Audit dataset was used to identify patients aged < 2 years who underwent surgical repair for ToF between 1 January 1986 and 13 May 2022. Coefficients representing the median change in PLOS (days) according to predictors were estimated using Quantile regression. There were 224 patients (59.4% male, median age = 9 months, interquartile range (IQR) 5–13 months) with a median PLOS of 9 days (IQR 7–13). In the univariable regression, age (months) and weight (kg) at operation (β =  − 0.17, 95% CI: − 0.33, − 0.01) and (β =  − 0.53, 95% CI: − 0.97, − 0.10), previous (cardiac or thoracic) procedure (β = 5, 95% CI:2.38, 7.62), procedure urgency (elective vs urgent) (β = 2.8, 95% CI:0.39, 5.21), bypass time (mins) (β = 0.03, 95% CI:0.01, 0.05), cross-clamp time (mins) (β = 0.03, 95% CI:0.01, 0.06) and duration of post-operative intubation (days) (β = 0.81, 95% CI:0.67, 0.96), were significantly associated with PLOS. Previous procedure and intubation time remained significant in multivariable analyses. Some patient and operative factors can predict PLOS following complete ToF repair. Information on PLOS is important for health professionals to support parents in preparing for their child's discharge and to make any necessary practical arrangements. Health commissioners can draw on evidence-based guidance for resource planning. The small sample size may have reduced the power to detect small effect sizes, but this regional study serves as a foundation for a larger national study