In this study, Volterra-Fredholm integral equation is solved by Hosoya Polynomials. The solutions obtained with these methods were compared on the figure and table. And error analysis was done. Matlab programming language has been used to obtain conclusitions, tables and error analysis within a certain algorithm.

This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross-constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved.

In this paper, using the compatible theory of differential invariants, a class of exact solutions is obtained for nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs) describing rate type materials; these solutions exhibit genuine nonlinearity that leads to the formation of discontinuities such as shocks and rarefaction waves. For certain nonconstant and smooth initial data, the solution to the Riemann problem is presented providing a complete characterisation of the solutions.

This article considers the hydrodynamic problem of an oblique flow of a viscous incompressible fluid around the tip of a dendritic crystal. Approximate analytical solutions of Oseen’s hydrodynamic equations are obtained in 2D and 3D cases using special curvilinear coordinates. It is shown that the projections of the fluid velocity change significantly with a change in the flow slope and Reynolds number. The theory developed in this work has a limiting transition to the previously known solutions for the rectilinear (without tilt) fluid flow around a dendrite.

Sobolev type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate fractional-order time-delay evolution equation of Sobolev type with multi-orders in a Banach space and introduce an analytical representation of a mild solution via a new delayed Mittag-Leffler type function which is generated by linear bounded operators. Furthermore, we derive an exact analytical representation of solutions for multi-dimensional fractional functional dynamical systems with nonpermutable and permutable matrices. We also study stability analysis of the given time-delay system in Ulam-Hyers sense with the help of Laplace transform.

Aim The unique aquatic Pontocaspian (PC) biota of the Black Sea Basin (BSB) is in decline. Lack of detailed knowledge on the status and trends of species, populations and communities hampers a thorough risk assessment and precludes effective conservation. This paper aims to review PC biodiversity trends using endemic molluscs as a model group. We aim to assess changes in PC habitats, community structure and species distribution over the past century and to identify direct anthropogenic threats. Location Black Sea Basin (Bulgaria, Romania, Moldova, Ukraine and Russia). Methods Presence/absence data of target mollusc species was assembled from literature, reports and personal observations. PC biodiversity trends in the NW BSB coastal regions were established by comparing 20th and 21st century occurrences. Direct drivers of habitat and biodiversity change were identified and documented. Results A very strong decline of PC species and communities during the past century is driven by a) damming of rivers, b) habitat modifications negatively affecting salinity gradients, c) pollution and eutrophication, d) invasive alien species and e) climate change. Four out of 10 studied regions, namely, the Danube Delta – Razim Lake system, Dniester Liman, Dnieper-South Bug Estuary and Taganrog Bay-Don Delta contain the entire spectrum of ecological conditions to support PC communities and still host threatened endemic PC mollusc species. Distribution data is incomplete, but the scale of deterioration of PC species and communities is evident from the assembled data, as are major direct threats. Main conclusions PC biodiversity in the BSB is profoundly affected by human activities. Standardised observation and collection data as well as precise definition of PC biota and habitats are necessary for targeted conservation actions. This study will help to set the research and policy agenda required to improve data collection to accommodate effective conservation of the unique PC biota.

Lignin is one of the world’s most abundant organic polymers, and 2-pyrone-4,6-dicarboxylate lactonase (LigI) catalyzes the hydrolysis of 2-pyrone-4,6-dicarboxylate (PDC) in the degradation of lignin. The pH has profound effects on enzyme catalysis and therefore we studied this in the context of LigI. We found that changes of the pH mostly affects surface residues, while the residues at the active site are more subject to changes of the surrounding microenvironment. In accordance with this, a high pH facilitates the deprotonation of the substrate. Detailed free energy calculations by the empirical valence bond (EVB) approach revealed that the overall hydrolysis reaction is more likely when the three active site histidines (His31, His33 and His180) are protonated at the ɛ site, however, protonation at the δ site may be favored during specific steps of reaction. Our studies have uncovered the determinant role of the protonation state of the active site residues His31, His33 and His180 in the hydrolysis of PDC.

We investigate the drying process of monodisperse colloidal film over a wide range of Péclet number (Pe) by using the Brownian dynamics simulation. We analyze the detailed process in three aspects; accumulation front, normal stress, and microstructure. The evolution of particle distribution is quantified by tracking the accumulation front. The accumulated particles contribute to the continuous increase of the normal stress at the interface. At the substrate, the normal stress first stays constant and then increases as the accumulation front touches the substrate. We quantitatively analyze the stress development by a scaled normal stress difference between the two boundaries. At all tested Pe, the stress difference increases to the maximum, followed by a decrease during drying. Interestingly, a mismatch is observed between the stress difference maximum and the initial stress increase at the substrate. The microstructural analysis reveals that this mismatch is related to the microstructural development at the substrate.

Objective Determination of lactate in fetal scalp blood (FBS) during labor has been studied since the 1970s. The internationally accepted cut-off of >4.8mmol/L indicating fetal acidaemia is exclusive for the point-of-care device (POC) LactateProTM, which is no longer in production. The aim of this study was to present a new cut-off for scalp lactate based on neonatal outcomes with the use of StatstripLactate®/StatstripXpress® Lactate system, the only POC lactate meter designed for hospital use. Design Observational Study Setting January 2016 to March 2020 labouring women with an indication for FBS were prospectively included from seven Swedish and one Australian delivery unit. Population Inclusion criteria: singleton pregnancy, vertex presentation, ≥35+0 gestational weeks. Method Based on the optimal correlation between FBS lactate and cord pH/lactate, only cases with ≤25 minutes from FBS to delivery were included in the final calculations. Main outcome measures Metabolic acidosis in cord blood was defined as pH <7.05 plus BDecf >10 mmol/L and/or lactate >10 mmol/L. Results 3334 women were enrolled of which 799 were delivered within 25 minutes. The areas under the ROC curves (AUC) and corresponding optimal lactate cut-off values were as follows; metabolic acidosis AUC 0.87(95% CI:0.77-0.97), cut-off 5.7mmol/L; pH <7.0 AUC 0.83(95% CI:0.68-0.97), cut-off 4.6mmol/L; pH <7.05 plus BD ≥12mmol/L AUC 0.97(95% CI:0.92-1), cut-off 5.8mmol/L; Apgar score <7 at 5 minutes AUC 0.74(95% CI:0.63-0.86), cut-off 5.2mmol/L; and pH <7.10 plus composite neonatal outcome AUC 0.76(95% CI:0.67-0.85), cut-off 4.8mmol/L. Conclusions Suggested intervention threshold for fetal acidemia is scalp lactate of 5.2mmol/L using the StatstripLactate®/StatstripXpress®.

Key points • SARS-CoV-2 is a possible cause of acute severe tracheitis in laryngectomees. • In our series, the clinical picture was characterized by a hemorrhagic tracheitis with a slow resolution pattern. • We observed a histological pattern of erosive inflammation of the respiratory epithelium. • Planned tracheo-bronchoscopy and tracheal toilettes are recommended to prevent critical obstruction of the airway, which can be fatal in patients with associated impairment of lung function caused by SARS-CoV-2 infection. • The present cases highlight the need for close interdisciplinary working and communication in the management of airway complications of COVID-19 infection.

We herein describe an ingenious centrifugal microfluidic system to accomplish a fully automated serial dilution. The liquid flow on the disc was automatically regulated by utilizing ferrowax microvalves systematically integrated into the channels within the specially designed metering structure. By opening the differently positioned microvalves through irradiation of IR laser to allow metering, the same amount of diluent was serially eluted to the dilution chamber from the same diluent chamber. After dilution, the diluted samples were automatically delivered to the respective final product chambers by appropriately opening or closing the microvalves in the connecting channels, followed by rotating the disc. Based on this unique design principle, six consecutive two-fold and ten-fold dilutions were successfully achieved, yielding excellent accuracy in a wide dynamic range up to six orders of magnitude. Very importantly, the overall serial dilution process, including the diluent addition, mixing, and product transfer steps, was completed very rapidly within five minutes, due to the minimized procedures enabled by the automated actuation of the ferrowax microvalves at the rationally designed positions. The centrifugal microfluidic system would serve as a powerful elemental tool to realize the fully automated diagnostic microsystem involving the serial dilution process.

This work is an extension of applying a previously developed fracture mechanics cracking damage model to predict the fatigue lifetime of un-notched round specimens made of a ferrite-pearlite 0.4C-70/30 carbon steel in some cases of variable amplitude loading VAL. The model simulates the collective behavior of growing short fatigue cracks originating from the specimen surface roughness. Material grains of different phases, sizes and strengths are randomly distributed over the minimum circumference. Possible activities of surface cracks are predicted against loading cycles. Relevant published experimental data were utilized for comparison. The present predictions are in agreement with the corresponding experimental results.

In this paper a new interpretation and modification of the SWT function in terms of the total damaging energy density is proposed and discussed. The total damaging energy density is the sum of the damaging part of the strain energy density and complementary energy density corresponding to the first quadrant in damaging σD-εD axes. For cyclic loading with positive mean stress (σm≥0) the proposed function reduces to the original SWT formulation. For cyclic loading with negative mean stress (σm<0) the maximum stress is augmented by 1/3 of absolute value of the mean stress. The proposed approach shows a consistent correlation of the mean stress effects for both positive and negative mean stresses.

Aims: To assess the effect of oral anticoagulant (OAC) administration on incidence of dementia in patients with atrial fibrillation (AF) with Systematic review and meta-analysis in according with the Preferred Reporting Items for Systematic Review and Meta-analysis Protocols. Methods: We systematically searched the electronic databases including Pubmed, Embase, Cochrane library, and ClinicalTrails.gov for relevant articles. The primary outcome was the incidence of dementia. The adjusted risk ratio (RR), odds ratio, or hazard ratio were extracted and pooled by the random-effects models. Subgroup analysis was performed according to the setting observational window. Risk of bias was assessed using the Newcastle-Ottawa Scale, while publication bias was assessed by the Begg’s and Egger’s tests. Results: Nine studies included in this review (2 prospective and 7 retrospective observational studies, including 613,920 patients). The results presented the significant association between OAC therapy and the reduced risk of dementia compared with no treatment (RR [95%CI] =0.72 [0.60, 0.86], I2=97.2%; P =0.000). In the subgroup analysis, the pooled RR became statistically non-significant (including four studies, RR [95%CI] =0.75 [0.51, 1.10], I2=98.8%; P =0.000). There is no significant risk of bias and publication bias. Conclusions: This study indicated the protective effect of OAC therapy for dementia in patients with AF. However, the results are limited because of high heterogeneity, inconsistent direction of effect in subgroup analysis. Further prospective well-designed study is needed with longer follow-up duration in younger patients.

Understanding the neutral (demographic) and adaptive processes leading to the differentiation of species and populations is a critical component of evolutionary and conservation biology. In this context, recently diverged taxa represent a unique opportunity to study the process of genetic differentiation. Northern and southern Idaho ground squirrels (Urocitellus brunneus – NIDGS, and U. endemicus - SIDGS, respectively) are a recently diverged pair of sister species that have undergone dramatic declines in the last 50 years and are currently found in metapopulations across restricted spatial areas with distinct environmental pressures. Here we genotyped single-nucleotide polymorphisms (SNPs) from buccal swabs with restriction site-associated DNA sequencing (RADseq). With these data we evaluated neutral genetic structure at both the inter- and intra-specific level, and identified putatively adaptive SNPs using population structure outlier and genotype-environment association (GEA) analyses. At the interspecific level, we found a clear separation between NIDGS and SIDGS, and evidence for adaptive differentiation relating to differences in hibernation. At the intraspecific level, we identified 3 Evolutionarily Significant Units for NIDGS and 2 for SIDGS plus multiple Management and Adaptive Units. Elevation appears to be the main driver of adaptive differentiation in NIDGS, while neutral variation patterns match and extend that identified in previous studies using microsatellite markers. For SIDGS, neutral substructure generally reflected the effect of natural geographic barriers, while adaptive variation reflected differences in land cover and temperature. These results clearly highlight the roles of neutral and adaptive processes for understanding species and population differentiation, which can have important conservation implications in threatened species.

Background: Sinoatrial node dysfunction and atrial fibrillation (AF) frequently coexist and interact with each other, often to initiate and perpetuate each other. Objective: To determine the effect of AF on the incidence and risk of sick sinus syndrome (SSS). Methods: The association of incident AF with the development of incident SSS was assessed from 2004 to 2013 in 302,229 SSS- and pacemaker-free participants aged ≥60 years in the Korea National Health Insurance Service-Senior cohort. Results: During an observation period of 1,854,800 person-years, incident AF was observed in a total of 12,797 participants (0.69%/year). The incidence of SSS was 0.2 and 3.4 per 1000 person-years in the incident AF and the propensity score matched no-AF groups, respectively. After adjustment, the risk of SSS caused by incident AF was significantly increased, with a hazard ratio (HR) of 13.4 (95% confidence interval [CI]: 8.4–21.4). This finding was consistently observed after censoring for heart failure (HR, 16.0; 95% CI: 9.2–28.0) or heart failure/myocardial infarction (HR, 16.6; 95% CI: 9.3-29.7). Incident AF also was associated with an increased risk of pacemaker implantation related with both SSS (HR, 21.8; 95% CI: 8.7–18.4) and atrioventricular (AV) block (HR, 9.5; 95% CI: 4.9–18.4). These results were consistent regardless of sex and comorbidities. Conclusion: Incident AF was associated with more than ten times increased risk of SSS in an elderly population regardless of comorbidities. Risk of pacemaker implantations related with both sinus node dysfunction and AV block were increased in elderly population with incident AF.

Plexiform schwannoma mainly presented as an asymptomatic nodule located on the head, neck, or upper extremities. The presentation of this tumor on the dorsum of the foot is very rare. Herein, we report a rare case of pretty large plexiform schwannoma on the toe of a male patient.

Forest transition theory posits that socioeconomic development in a country or region may cause its forestland to shift from net loss to net gain. However, forest transition may also occur under various policies, resulting in forest gains in some regions but deforestation in other regions. We used the telecoupling framework to address this crucially important issue that has rarely been examined. Using time series satellite images and statistical yearbook data from 2000 to 2020, this study seeks to understand land use change patterns, the corresponding regional spillover effects, and driving forces behind such patterns in Zhejiang Province, China. The results show that large-scale continuous deforestation has taken place since 2000, causing a total loss of forestland by 186,014 ha. In parallel with this forest loss and a slight decrease in arable land, urban construction land has soared by 169.45%. We found that developed municipalities such as Hangzhou witnessed increases in urban land at the expense of large-scale deforestation in underdeveloped municipalities such as Lishui. We believe that this cross-region land change pattern may arise from the Balance of Arable Land System (BALS) policy that seeks to achieve a goal of no net loss of cropland. Whatever land use policy—such as the BALS policy—must strike a good balance between competitive land uses that have different objectives such as residents’ living, ecology, and production. In addition to enriching the forest transition theory, this study provides a solid basis for future land use decisions in developing regions or countries.