On Some Optimal Multiple Root-Finding Methods and their Dynamics

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of some of the higher-order methods in the complex plane are also given

Several New Families of Jarratt’s Method for Solving Systems of Nonlinear Equations

In this study, we suggest and analyze a new and wide general class of Jarratt’s method for solving systems of nonlinear equations. These methods have fourth-order convergence and do not require the evaluation of any second or higher-order Fréchet derivatives. In terms of computational cost, all these methods require evaluations of one function and two first-order Fréchet derivatives. The performance of proposed methods is compared with their closest competitors in a series of numerical experiments. It is worth mentioning that all the methods considered here are found to be effective and comparable to the robust methods available in the literature

Exponentially Fitted Variants of the Two-Step Adams-Bashforth Method for the Numerical Integration of Initial Problems

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step Adams- Moulton methods respectively

Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations

[EN] In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial differential equations. In particular, it will be applied for solving three well-known problems, namely, the Burgers equation, Buckmaster equation and FitzHugh–Nagumo equation. Most of the developed methods in the literature for non-linear partial differential equations have not focused on optimizing the time step-size and a very small value must be considered to get accurate approximations. The motivation behind the development of this work is to overcome this trade-off up to much extent using a larger time step-size without compromising accuracy. The optimized hybrid block method considered is proved to be A-stable and convergent. Furthermore, the obtained numerical approximations have been compared with exact and numerical solutions available in the literature and found to be adequate. In particular, without using quasilinearization or filtering techniques, the results for small viscosity coefficient for Burgers equation are found to be accurate. We have found that the combination of the two considered methods is computationally efficient for solving non-linear PDEs.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

A case of idiopathic edema after opioid abuse cessation: can failed aldosterone escape be implicated?

Edema is a recognized complication of ongoing heavy opioid use, regardless of the means of delivery or the specifics of the drug in question. The mechanism responsible remains incompletely understood. Hypotheses currently offered include increased Anti-Diuretic Hormone (ADH) secretion, histamine-mediated permeability changes, independent opioid-receptor mediated fluid retention and an exacerbation of pre-existing vascular compromise. Authors report a case of a 39yr old lady in whom edema emerged 7 months after cessation of opioid abuse. All secondary causes of edema were excluded by an exhaustive battery of investigations. The edema failed to recede with loop diuretics, and resolved only on institution of spironolactone, on which she maintained improvement. This case study reinforces hypotheses of ADH likely mediating opioid associated edema and suggests that aldosterone receptor antagonists are probably a superior class of drugs in opioid-associated edema. It also suggests that the physiological changes caused by opioid use that are responsible for edema are likely stable and persist well beyond the period of actual use. Reformed opioid abusers who never received OST are a huge population whose unique physiological status is likely to yield valuable insights into not just the pathology of opioid-abuse related edema, but the pathology of opioid use as a whole

Perinatal outcome in abnormal placental villus proliferation and mesenchymal dysplasia

Placental mesenchymal dysplasia (PMD) is a rare vascular anomaly which is characterized by mesenchymal stem villous hyperplasia and placentomegaly. Since the modality of treatment changes it is necessary to distinguish PMD from molar pregnancy, placenta mosaicism, chorioangioma, twin pregnancy with co-existent molar pregnancy. On reviewing cases of abnormal placental villus proliferation having features of placental mesenchymal hyperplasia placentomegaly and cystic appearance of placenta in database of our hospital from 2015-2019, we reported 4 cases of abnormal placental villous proliferation. And performed systematic review of existing literature. Provisional   diagnosis of PMD was made as USG and placental morphology showed 30-60% of the placenta with cystic vesicles, placentomegaly with a normal growing fetus. PMD an uncommon vascular anomaly which resembles molar pregnancy but prognosis is different. The fetus was normal in majority of the cases. This clinical entity should be kept in mind to avoid unnecessary termination of pregnancy

Development of a Quality Control Method and Guidelines for Hot Mix Asphalt Using Recycled Concrete Aggregate

Each year, about 122 million tons of aggregates, a major structural component of pavement, are used in asphaltic mixtures in pavement construction. At the same time, aging U.S. infrastructure produces around 200 million tons of demolition waste each year, half of which is concrete debris. Therefore, introducing recycled concrete aggregate (RCA) as hot mix asphalt (HMA) aggregate could not only relieve the disposal pressure but also result in considerable reductions in cost, energy usage, and greenhouse gas emissions in the paving industry. A limited number of studies regarding the use of RCA to substitute virgin aggregate in HMA (RCA-HMA) exist. More importantly, the findings reveal discrepant or even contradictory results, regarding the effects of RCA on almost all the volumetrics and performance indicators of RCA-HMA. Because RCA is different from virgin aggregate, as RCA particles are at least partially covered by a residual cement mortar (RCM) layer, the attached RCM in RCAs from different concrete sources could significantly differ in terms of content, porosity, and distribution on the RCA surface. This study aims to determine the characteristics of RCA and RCM, such as RCM content, specific gravity, and absorption, and to evaluate their effects on the volumetrics and performance indicators of RCA-HMA. This research evaluates the variation in the properties of RCA and RCM obtained from different sources and their effects on RCA-HMA’s performance. The research revealed the properties of RCA from different sources vary significantly. It is insufficient to predict the volumetrics and performance of RCA-HMA using only the information of RCA, such as RCA replacement rate and gradation. Information pertaining to the RCM’s properties, such as the RCM content, specific gravity, and absorption, is critical for the prediction of the RCA-HMA properties, including optimum binder content (OBC), voids in mineral aggregate (VMA), voids filled with asphalt (VFA), resistance to permanent deformation, and moisture damage susceptibility. The results of this investigation can help to ensure reliable performance of RCA-HMA in practice by controlling the properties of RCM in the RCA

Survivin Mutant Protects Differentiated Dopaminergic SK-N-SH Cells Against Oxidative Stress

Oxidative stress is due to an imbalance of antioxidant/pro-oxidant homeostasis and is associated with the progression of several neurological diseases, including Parkinson's and Alzheimer's disease and amyotrophic lateral sclerosis. Furthermore, oxidative stress is responsible for the neuronal loss and dysfunction associated with disease pathogenesis. Survivin is a member of the inhibitors of the apoptosis (IAP) family of proteins, but its neuroprotective effects have not been studied. Here, we demonstrate that SurR9-C84A, a survivin mutant, has neuroprotective effects against H2O2-induced neurotoxicity. Our results show that H2O2 toxicity is associated with an increase in cell death, mitochondrial membrane depolarisation, and the expression of cyclin D1 and caspases 9 and 3. In addition, pre-treatment with SurR9-C84A reduces cell death by decreasing both the level of mitochondrial depolarisation and the expression of cyclin D1 and caspases 9 and 3. We further show that SurR9-C84A increases the antioxidant activity of GSH-peroxidase and catalase, and effectively counteracts oxidant activity following exposure to H2O2. These results suggest for the first time that SurR9-C84A is a promising treatment to protect neuronal cells against H2O2-induced neurotoxicity

Determination of genetic variation for vegetative and floral traits in African marigold (Tagetes erecta)

Twenty-one genotypes of African marigold were (Tagetes erecta L.) evaluated for 11 growth and flowering related traits to study their genetic parameters such as variability, heritability, genetic (GCV), phenotypic (PCV) coefficient of variation and correlation and path coefficient analysis. Analysis of variance for all the traits showed significant differences among genotypes for all the growth and flowering related traits. High range in mean performance has been observed for traits, viz. plant height (64.00-106.67 cm), plant spread (49.33-72.00 cm), flower diameter (3.77- 6.17 cm), days required for flowering (78.67-99.33 days), number of secondary branches (22.13-37.47) and flower duration (26.00-44.83 days). Higher genotypic and phenotypic coefficient of variation was observed for traits such as fresh flower weight per plant, flower fresh weight per 10 flowers, number of flowers per plant, stem girth, flowering duration, etc. The high value (> 90%) of heritability was observed for all traits except plant height, plant spread and stem girth. The genetic advance was found ranged from 1.23 for flower diameter to 288.69 for fresh flower weight per plant. High values of genetic advance as per cent of mean was recorded for number of flowers (59.79%) followed by fresh flower weight per plant (59.32%) and flower fresh weight per 10 flowers (58.09%). Fresh flower weight per plant is significantly and positively correlated both at genotypic and phenotypic level for plant spread, flower fresh weight per flower, number of flowers per plant and flower diameter. Path coefficient analysis at genotypic level revealed that the number of primary branches per plant contributed highest and has significantly positive direct effect on fresh flower weight per plant followed by number of flowers per plant, flower diameter, flower fresh weight per flower, days required for flowering and stem girth. The different genotypes were identified to be performing differently for different quantitative traits. Hence, those genotypes with superior traits could be involved in the hybridization programme for assembling of desirable traits in a single genotype