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 coupled scheme based on uniform algebraic trigonometric tension B-spline and a hybrid block method for Camassa-Holm and Degasperis-Procesi equations.

[EN]In this article, high temporal and spatial resolution schemes are combined to solve the Camassa-Holm and Degasperis-Procesi equations. The differential quadrature method is strengthened by using modified uniform algebraic trigonometric tension B-splines of order four to transform the partial differential equation (PDE) into a system of ordinary differential equations. Later, this system is solved considering an optimized hybrid block method. The good performance of the proposed strategy is shown through some numerical examples. The stability analysis of the presented method is discussed. This strategy produces a saving of CPU-time as it involves a reduced number of grid points

COMPARATIVE STUDY ON ANTIMICROBIAL ACTIVITY OF TULSI (OCIMUM SANCTUM) AND NEEM (AZADIRACHTA INDICA) METHANOL EXTRACT

Objective: This study was focused on to compare the antimicrobial activity of methanolic leaf extracts of tulsi and neem.Methods: We have chosen tulsi (Ocimum sanctum) and neem (Azadirachta indica) to compare their antimicrobial activity toward Gram-positive (Staphylococcus aureus) and Gram-negative (Escherichia coli) bacteria. Phytochemical extracts have been made by the use of methanol as solvent and dried leaf powder by the cold maceration extraction process. Phytochemical analysis for some secondary metabolites has been done using standard protocols. Nutrient agar plates were inoculated with the above-mentioned microorganisms by spreading bacterial inoculum on the surface of the media. Wells (6 mm in diameter) were punched in the agar. The phytochemical extracts of neem and tulsi were allowed to diffuse into the medium, and after incubation of 24 h at 37°C, the zones of inhibition were observed.Results: Statistical analysis showed that tulsi was more effective toward S. aureus while neem was more effective toward E. coli. Minimum inhibitory concentration (MIC) of tulsi for both the microorganisms was 0.4 g/ml, and the MIC of neem for both the microorganisms was 0.2 g/ml. When both the tulsi and neem extract were mixed with each other for every concentration at equal volume, they have shown better effects in comparison to individual neem or tulsi extract and also the MIC got reduced to 0.2 g/ml for both the bacteria.Conclusions: Leaf extracts of both the A. indica and O. sanctum have shown antimicrobial activity against E. coli and S. aureus. A. indica has higher antimicrobial activity against S. aureus, whereas the O. sanctum was found to be more effective against E. coli (indicated by the zone of inhibition). When both the extracts were mixed with each other, they have shown a better effect toward both bacteria

Role of 5-HT in Cerebral Edema after Traumatic Brain Injury

The pathogenesis of edema after traumatic brain injury is complex including the destruction of micro-vessels and alterations in microcirculation around the primary injury and leakage of plasma constituents into the tissue, due to permeability changes of the vessel walls. Many functional molecules like histamine, serotonin, arachidonic acid, prostaglandins and thromboxane have been shown to induce blood–brain barrier (BBB) disruption or cell swelling. It is believed that released 5-HT binds to 5-HT2 receptors stimulating cAMP and prostaglandins in vessels that cause more vesicular transport in endothelial cells leading to serum component’s extravasation. The additional amount of serotonin into the tissue due to injury maintains the state of increased vascular permeability that ultimately causes edema. Serotonin is clearly involved in early cytotoxic edema after TBI. Reduction of serotonin in the nervous tissue reduces swelling and the milder cell changes in the brain or spinal cord of traumatized rats. Inhibition of serotonin synthesis before closed head injury (CHI) in rat models or administration of serotonin antiserum after injury attenuates BBB disruption and brain edema volume swelling, and brain pathology. Maintaining low serotonin levels immediately after injury may show neuroprotection and combat various secondary outcomes that occur after traumatic brain injury

Histone Deacetylase Inhibitors As Potential Therapeutic Agents For Various Disorders

Epigenetic modification acetylation or deacetylation of histone considered as an important element in various disorders. Histone acetyltransferases (HATs) and histone deacetylases (HDACs) are the enzymes which catalyse the acetylation and deacetylation of histone respectively. It helps in regulating the condensation of chromatin and transcription of genes. Lysine acetylation and deacetylation present on the nucleosomal array of histone is the key factor for gene expression and regulation in a normal working living cell. Modification in histone protein will lead to the development of cancer and can cause various neurodegenerative disorders. To safeguard the cells or histone proteins from these diseases histone deacetylase inhibitors are used. In this review, the main focus is upon the role of histone deacetylases inhibitors in various diseases

Cryptography Algorithm

With the arrival and outbreak of high speed internet, www (World Wide Web) and growth of social media, online transaction, application and business, organization across the globe produce too much amount of data every second.  Data Security is the most basic and extreme measures to ensure secure passage of information through internet. As the number of user’s increases rapidly throughout the globe tremendously which directly entice cracker for doing cyber-attack. Moreover data security is becoming necessity as we are heading towards digital globalization. In this paper we will discuss various algorithm used so far starting from classical ciphers to the modern day’s hash function for ensuring safer transmission of information

Cryptography Algorithm

With the arrival and outbreak of high speed internet, www (World Wide Web) and growth of social media, online transaction, application and business, organization across the globe produce too much amount of data every second.  Data Security is the most basic and extreme measures to ensure secure passage of information through internet. As the number of user’s increases rapidly throughout the globe tremendously which directly entice cracker for doing cyber-attack. Moreover data security is becoming necessity as we are heading towards digital globalization. In this paper we will discuss various algorithm used so far starting from classical ciphers to the modern day’s hash function for ensuring safer transmission of information

Healthcare Seeking Behaviour of Hospitalised COVID-19 Patients During Second Wave in Tertiary Care Hospital of Northern India

Background: The Coronavirus Disease (COVID-19) pandemic continues its deadly reign all over the world. Devising effective strategies for detecting and controlling the infection has become ever more critical. Effective prevention and control of the pandemic is entirely dependent on human behavior in terms of practicing preventive and curative measures. During the second wave of COVID-19, people’s perceptions of preventive and curative measures changed. Objective: To study healthcare-seeking behavior of hospitalized COVID-19 patients. Methods: Hospitalized patients due to COVID-19 in the month of March, April and May of 2021 were included in the study. Their attendants/close relatives were contacted telephonically to know about the admitted patients’ healthcare-seeking behavior. Verbal consent was taken from attendants before the commencement of the interview, followed by informing them about the purpose of the interview. Results: Amongst the subjects, there were more males than females (67.5 vs 32.4%), age ranged between 18 to 88 with a mean value of 56.61 ± 14.7 years. Self-medication was significantly associated with study subjects’ mortality (p=0.03). Conclusion: Elderly people were having higher mortality rate than their younger counterparts. People were hesitant to visit primary care physicians after having symptoms of COVID-19