Existence of a renormalized solution of nonlinear parabolic equations with general measure data

In this paper we prove the existence of a renormalized solution for nonlinear parabolic equations of the type:$$\displaystyle{\partial b(x,u)\over\partial t} - {\rm div}\Big(a(x,t,\nabla u)\Big)=\mu\qquad \text{in}\ \Omega\times (0,T),$$ where the right handside is a general measure, $b(x,u)$ is anunbounded function of $u$ and $- {\rm div}(a(x,t,\nabla u))$is a Leray--Lions type operator with growth $|\nabla u|^{p-1}$ in$\nabla u$.

A retrospective analysis of the definitive management of open talus fractures at a major trauma centre, comparing ORIF to FUSION: cohort study and audit of BOAST 4 guidelines

Purpose Open talus fractures are notoriously difficult to manage, and they are commonly associated with a high level of complications including non-union, avascular necrosis and infection. Currently, the management of such injuries is based upon BOAST 4 guidelines although there is no suggested definitive management, and thus, definitive management is based upon surgeon preference. The key principles of open talus fracture management which do not vary between surgeons are early debridement, orthoplastic wound care, anatomic reduction and definitive fixation whenever possible. However, there is much debate over whether the talus should be preserved or removed after open talus fracture/dislocation and proceeded to tibiocalcaneal fusion. Methods A review of electronic hospital records for open talus fractures from 2014 to 2021 returned fourteen patients with fifteen open talus fractures. Seven cases were initially managed with ORIF, and five cases were definitively managed with FUSION, while the others were managed with alternative methods. We collected patient’s age, gender, surgical complications, surgical risk factors and post-treatment functional ability and pain and compliance with BOAST guidelines. The average follow-up of the cohort was 4 years and one month. EQ-5D-5L and FAAM-ADL/Sports score was used as a patient reported outcome measure. Data were analysed using the software PRISM. Results Comparison between FUSION and ORIF groups showed no statistically significant difference in EQ-5D-5L score (P = 0.13), FAAM-ADL (P = 0.20), FAAM-Sport (P = 0.34), infection rate (P = 0.55), surgical times (P = 0.91) and time to weight bearing (P = 0.39), despite a higher proportion of polytrauma and Hawkins III and IV fractures in the FUSION group. Conclusion FUSION is typically used as second line to ORIF or failed ORIF. However, there is a lack of studies that directly compared outcome in open talus fracture patients definitively managed with FUSION or ORIF. Our results demonstrate for the first time that FUSION may not be inferior to ORIF in terms of patient functional outcome, infection rate and quality of life, in the management of patients with open talus fracture patients. Of note, as open talus fractures have increased risks of complications such as osteonecrosis and non-union, FUSION should be considered as a viable option to mitigate these potential complications in these patients.

Examining the Relationship between Energy Consumption and Unfavorable CO2 Emissions on Sustainable Development by Going through Various Violated Factors and Stochastic Disturbance–Based on a Three-Stage SBM-DEA Model

The article applies a three-stage Slacks-Based Measure-Data Envelopment Analysis (SBM-DEA) pattern to examine the relationship between energy consumption and unfavorable CO2 emissions on green sustainable development, for the 11 cities of the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) during 2010–2016, by going through various violated factors and stochastic disturbance. Labor, capital and energy resource are chosen as input variables, while GDP and CO2 emission as output variables. During the three phases consisting of the SBM-DEA model (first stage and third stage) and SFA analysis (second stage), CO2 emission is considered as an unfavorable outcome, while stochastic statistical disturbances and external environmental influences are identified. The results show that the average efficiency of the GBA cities is 0.708, with only Shenzhen, Macao SAR and Hong Kong SAR having an efficiency of 1 during the whole study period. Based on the findings, suggestions are made for the GBA cities’ sustainable development aspects.

Process Corresponding Implications Associated with a Conclusive Model-Fit Current-Voltage Characteristic Curves

NFinFET transistors with various fin widths (110 nm, 115 nm, and 120 nm) are put into measurements, and the data are collected. By using the modified model, the measure data is fitted. Several parameters in the formula of modified model are determined to make both the measured data and the fitting data almost as close as possible. Those parameters are listed and analyzed, including kN (proportional to channel width and gate oxide capacitor, and inversely proportional to the channel length) λ (the inverse of Early Voltage), and sometimes Vth (Threshold Voltage). By kN, the appropriate process control can be high lighted, the corresponding channel concentration can be calculated and thus many implicit physical quantities may be exploited.

A Novel Parametric Model for Nonlinear Hysteretic Behaviors with Strain Stiffening of Magnetorheological Gel Based on Fruit Fly Optimization Algorithm

Magnetorheological (MR) gel is a new branch of MR materials, which can overcome the phenomenon of particle agglomeration existing in MR fluid, thus improving the controllability of materials in engineering applications. In this paper, a novel parametric model for tracking the nonlinear hysteretic behaviors with strain stiffening of MR gel is constructed. The measure data in relative to the five current levels of 0A, 0.2A, 0.5A, 0.8A and 1A under the strain amplitude and frequency of 10% and 0.1Hz respectively are utilized to identify the parameters. The optimal solution for the model parameters is conduced employing the fruit fly optimization algorithm (FOA). The comparison study with two typical model such as Bouc-Wen model and viscoelastic-plastic model is conduced to to evaluate the effectiveness of the developed model. The model parameters are generalized with respect to the loading current, and the reliability of the generalized model is verified. The studies show that the proposed model can perfectly fit the strain stiffening and nonlinearity of sample, which can provide a theoretical basis for the semi-active control of MR gel in practical engineering applications.

Convergence of nonlinear numerical approximations for an elliptic linear problem with irregular data

This work is devoted to the study of the approximation, using two nonlinear numerical methods, of a linear elliptic problem with measure data and heterogeneous anisotropic diffusion matrix. Both methods show convergence properties to a continuous solution of the problem in a weak sense, through the change of variable u = ψ(v), where ψ is a well chosen diffeomorphism between (−1, 1) and R, and v is valued in (−1, 1). We first study a nonlinear finite element approximation on any simplicial grid. We prove the existence of a discrete solution, and, under standard regularity conditions, we prove its convergence to a weak solution of the problem by applying Hölder and Sobolev inequalities. Some numerical results, in 2D and 3D cases where the solution does not belong to H 1(Ω), show that this method can provide accurate results. We then construct a numerical scheme which presents a convergence property to the entropy weak solution of the problem in the case where the right-hand side belongs to L1 . This is achieved owing to a nonlinear control volume finite element (CVFE) method, keeping the same nonlinear reformulation, and adding an upstream weighting evaluation and a nonlinear p−Laplace vanishing stabilisation term.

The impact of environmental regulation on green total factor productivity: An empirical analysis

The transformation of China’s economy from extensive growth to high-quality development is essentially an increase in green total factor productivity (GTFP). China currently has a range of environmental regulation tools, and the question of whether environmental regulation can promote improvement in China’s GTFP requires theoretical and empirical analysis. This article first divides environmental regulation into three types: administrative, market-based and information-based. It then builds an empirical model of the effect of environmental regulation on GTFP. Slacks based measure-data envelope analysis (SBM-DEA) and the Malmquist index are used to measure the GTFP of 30 provinces in China from 2005 to 2018, and a measurement model of the impact of environmental regulation on GTFP is established. The results show that: (1) there are significant differences in GTFP in eastern, central and western China; (2) there is a non-linear relationship between environmental regulations and GTFP.

Evaluation of Relationship Between Laboratory, Electrodiagnostic, and Functional Parameters in Patients With Amyotrophic Lateral Sclerosis; A Cross Sectional Study

Background: Amyotrophic lateral sclerosis (ALS) is an adult-onset motor neuron disease which leads to limb and/or bulbar muscle degeneration with a poor prognosis. Several demographic and biological factors have prognostic importance, but little data exist on the relationship between clinical, electrodiagnostic, and laboratory markers as predictors of disease progression. We aimed to assess the relationships between different aspects of clinical, electrodiagnostic, and laboratory features of ALS patients with their level of functioning. Methods: We included 27 patients with ALS who were diagnosed within two years before enrolment. Clinical assessment and electrodiagnostic studies were done by a neurology resident. The motor unit number index (MUNIX) and compound motor action potential (CMAP) were used as measures of motor unit loss. Serum creatinine, urea, Albumin, and creatine kinase were measured as laboratory markers. We used the Persian version of ALS functional rating scale (ALS-FRS) as the main outcome measure. Data were analyzed using the SPSS software. Pearson's correlation coefficient was calculated to test for correlations. Results: None of the demographic or laboratory parameters correlated with ALS-FRS. Patients with the onset of disease in the limbs had a higher MUNIX score compared to patients with a bulbar onset. Also, increased body mass index was associated with lower CMAP and MUNIX scores (p-value:0.02). Higher serum creatinine levels were significantly associated with higher lower limb MUNIX (p value:0.04). Higher lower limb MUNIX was in turn associated with higher lower limb functional score (ALS-FRS). Conclusion: Decreased serum creatinine may possibly be an indicator of lower limb motor unit loss in patients with ALS. Also, MUNIX scores may be used as surrogates for ALS-FRS in ALS trials. Further research is needed to elucidate the clinical application of these findings.Methods: We included 27 patients with ALS who were diagnosed within two years before enrolment. Clinical assessment and electrodiagnostic studies were done by a neurology resident. The motor unit number index (MUNIX) and compound motor action potential (CMAP) were used as measures of motor unit loss. Serum creatinine, urea, Albumin, and creatine kinase were measured as laboratory markers. We used the Persian version of ALS functional rating scale (ALS-FRS) as the main outcome measure. Data were analyzed using the SPSS software. Pearson's correlation coefficient was calculated to test for correlations. Results: None of the demographic or laboratory parameters correlated with ALS-FRS. Patients with the onset of disease in the limbs had a higher MUNIX score compared to patients with a bulbar onset. Also, increased body mass index was associated with lower CMAP and MUNIX scores (p-value:0.02). Higher serum creatinine levels were significantly associated with higher lower limb MUNIX (p value:0.04). Higher lower limb MUNIX was in turn associated with higher lower limb functional score (ALS-FRS). Conclusion: Decreased serum creatinine may possibly be an indicator of lower limb motor unit loss in patients with ALS. Also, MUNIX scores may be used as surrogates for ALS-FRS in ALS trials. Further research is needed to elucidate the clinical application of these findings.