Negative Shift Research Articles

Influence of Al2O3 atomic-layer deposition temperature on positive-bias instability of metal/Al2O3/β-Ga2O3 capacitors

The influence of Al2O3 atomic-layer deposition (ALD) temperature on the electric characteristics of Al/Al2O3/(2¯01) β-Ga2O3 capacitors was investigated focusing on the positive-bias instability (PBI) of the capacitors. The current in the capacitors increased with ALD temperature, mostly because of the reduced energy barrier height for the electron field emission from the substrate and less negative Al2O3 charge, as revealed by the analysis conducted assuming a space-charge-controlled field emission process. The PBI tests were conducted for cumulative voltage stressing times vastly ranging from 3 × 10−6 to 4 × 105 s. The capacitance–voltage (C–V) characteristics of the capacitors for an ALD temperature of 100 °C displayed negative shifts in the middle of voltage stressing, unlike those for the other ALD temperatures. The bias stability of the capacitors was found to be considerably improved by high-temperature (450 °C) ALD. Additionally, the C–V characteristic shifts caused by the voltage stressing were theoretically reproduced quite accurately, assuming a model proposed in this study. In the simulations, the trap distributions in the Al2O3 films were assumed to be uniform both spatially and energetically. Importantly, the experimental results for various stressing voltages were excellently fitted by the simulations that assumed the same trap distribution. The trap densities in the Al2O3 films thus estimated reduced from 1.2 × 1020 to 2.2 × 1019 cm−3 eV−1 for ALD temperatures of 100–450 °C. This reduction in the trap densities was a major cause of the bias stability enhancement for high-temperature ALD. Moreover, the trap density as a function of ALD temperature qualitatively agreed with the aforementioned Al2O3 charge generated by the current measurements. This agreement provides a strong basis for the validity of the PBI model proposed in this study.

The Construction of Implicit Negative Response and Divergent Stance: Negative Semantic Shift, Discourse Characteristics and Interactive Function of “You benshi(有本事)”

The Construction of Implicit Negative Response and Divergent Stance: Negative Semantic Shift, Discourse Characteristics and Interactive Function of “You benshi(有本事)”

Before and After COVID-19 : A Comparative Analysis of EFL Learning Responses Among First-year College Students

This study explores the impact of the COVID-19 pandemic on the perspectives and experiences of first-year college students in EFL learning. Employing a comprehensive research approach, the study utilizes three primary research tools: surveys, self-evaluations, and academic performance grades. The primary objectives are to understand the shifts in first-year college students’ levels of anxiety and confidence, attitudes, self-perceptions on Englis proficiency, and academic outcomes influenced by the pandemic and to contribute valuable insights to the field of EFL education after the pandemic era.Through a comparative analysis, the study contrasts the responses of 62 first-year college students in 2018, unaffected by the pandemic during their secondary education period, with those of 69 first-year college students in 2023 who experienced the disruptions caused by the pandemic. Contrary to initial assumptions of a negative shift post-COVID-19, the study reveals predominantly positive sentiments in 2023, marked by a significant increase in positivity toward English learning. However, a polarized distribution in self-evaluations emerges, reflecting a significant divergence in students' opinions regarding their English proficiency.The study further explores the academic performance of first-year college students, comparing those before and after the pandemic. An examination of their academic performance grades reveals that the number of first-year college students scoring 80 or higher did not significantly differ between the 2018 and 2023 classes. However, there appears to be a trend towards lower academic scores in 2023 compared to 2018. Concurrently, multiple factors may contribute, one being the observed increase in absenteeism among first-year college students of 2023. This suggests a lasting impact, influencing attendance scores, class attitudes and participation, assignment submissions, and even exam performance. The rise in lower academic scores in 2023, particularly those below 70 (D or below), highlights challenges faced by students in the post-COVID-19 era. This underscores the difficulties encountered by these students during the pandemic period. A clear contrast emerges between first-year college students in 2018 and 2023, as well as among 2023 first-year college students with well-adapted abilities and those facing difficulties.Recognizing and addressing these distinctions is imperative for educators and institutions to provide effective support, acknowledging and nurturing the strengths while aiding students who require additional assistance. This study may contribute to bridging the gap in understanding these differences and challenges among students after the pandemic.

Aptasensors based on silicon nanowire field-effect transistors for electrical detection of thrombin

Arrays of silicon nanowire field-effect transistors (Si NWFETs) were built to detect thrombin (a model biomarker) electrically. The Si NWFETs were created using a conventional top-down CMOS process, allowing them to be co-integrated with CMOS readout circuits in the future. EHTES organosilane was then used to graft aptamer probes onto the HfO2 gate oxide of Si nanowires. We investigated the influence of aptamer grafting and thrombin recognition on the electrical transfer capabilities of Si NWFET aptasensors in details. Our technique was evaluated on a significant number of Si NWFETs, including two distinct chips with 30 aptasensors apiece. According to the findings, aptamer grafting increased the threshold voltage by a positive range of +28.8 mV to +87.7 mV, depending on the aptasensor employed. Thrombin identification, on the other hand, resulted in a negative shift of the threshold voltage between −26.6 and − 23.8 mV. These opposing voltage shifts coincide with the aptamer probes' and thrombin molecules' electric charges, respectively. These findings provide unique demonstration of Si NWFETs manufactured utilizing typical top-down CMOS processing methods, allowing these devices to be used in various biomedical and biosensing applications.

Asymmetric effect of environmental tax on CO2 emissions embodied in domestic final demand in South Africa: A NARDL approach

AbstractMotivated by the pressing need to address environmental concerns, this study explores the relationship between environmental taxes and CO2 emissions embodied in domestic final demand in South Africa. The study uses a non‐linear autoregressive distributed lag (NARDL) model to analyse the asymmetric impact of environmental taxes. Results indicate that environmental taxes have an asymmetric impact on CO2 emissions embodied in domestic final demand in both the short and long runs. Specifically, both positive and negative shifts in environmental taxes are linked with a respective 0.06% decrease and a more pronounced 0.22% decrease in CO2 emissions embodied in domestic final demand. Moreover, positive shocks in the GDP growth rate are associated with an approximately 0.002% uptick in CO2 emissions, while negative shocks lead to a 0.012% decrease. Additionally, both positive and negative shocks in population growth exhibit a significant positive correlation with the response variable. The baseline estimates demonstrate that the joint effect of environmental taxes and the GDP growth rate is correlated with reductions in CO2 emissions embodied in domestic final demand. Similarly, the joint influence of environmental taxes and population growth rate is linked to declines in CO2 emissions. The study highlights the practical policy implications of these findings.

Effect of SiO2Surface Passivation on the Performance of GaN Polarization Superjunction Heterojunction Field Effect Transistors

In this article, the effects of the SiO2surface passivation layer are reported on normally‐on 1.2 kV GaN polarization superjunction (PSJ) heterojunction field effect transistors (HFETs) by comparing the electrical performances of PSJ HFETs with and without SiO2surface passivation. A slight recovery of the 2D electron gas sheet density is observed in the slight negative shift ofVthafter SiO2surface passivation. Passivation also increases the breakdown voltage. This improvement may result from removing positive surface charges in defects along the P‐GaN gate sidewall and top u‐GaN layer after the specifically designed SiO2surface passivation. Furthermore, the SiO2surface passivation can also effectively suppress the surface gate leakage currents in the PSJ HFETs by eliminating the conductive channel created by the positive surface charges in defects.

Interface Trap Effect on the n-Channel GaN Schottky Barrier-Metal-Oxide Semiconductor Field-Effect Transistor for Ultraviolet Optoelectronic Integration.

Ultraviolet (UV) photodetectors are key devices required in the industrial, military, space, environmental, and biological fields. The Schottky barrier (SB)-MOSFET, with its high hole and electron barrier, and given its extremely low dark current, has broad development prospects in the optoelectronics field. We analyze the effects of trap states on the output characteristics of an inversion mode n-channel GaN SB-MOSFET using TCAD simulations. At the oxide/GaN interface below the gate, it was demonstrated that shallow donor-like traps were responsible for degrading the subthreshold swing (SS) and off-state current density (Ioff), while deep donor-like traps below the Fermi energy level were insignificant. In addition, shallow acceptor-like traps shifted the threshold voltage (Vt) positively and deteriorated the SS and on-state current density (Ion), while deep acceptor-like traps acted on a fixed charge. The output characteristics of the GaN SB-MOSFET were related to the resistive GaN path and the tunneling rate due to the traps at the metal (source, drain)/GaN interface. For the UV responses, the main mechanism for the negative Vt shift and the increases in the Ion and spectral responsivity was related to the photo-gating effect caused by light-generated holes trapped in the shallow trap states. These results will provide insights for UV detection technology and for a high-performance monolithic integration of the GaN SB-MOSFET.

Chemo- and bio-stratigraphic constraints on Cretaceous-Paleocene biotic turnover in the southern Tethys low-oxygen margin, Egypt

The late Cretaceous-Danian (K-Pg) organic-rich sequence is a global archive that witnessed abrupt paleo-condition changes during a high sea-level. In Egypt, this sequence is present in the Duwi and Dakhla formations as an E-W belt from the Red Sea to the Western Desert. We analyzed elemental and isotopic distributions in an age-constrained core from the Quseir area to understand paleoclimatic and paleoenvironmental factors influencing its deposition. Calcareous nannofossil and the chemical index of alteration (CIA) confirm a global cooling trend during the late Cretaceous, with two warming episodes indicating early phases of the Deccan volcanism. The Danian stage experienced a warm climate and intense chemical weathering. Mo-U enrichment factors covariation suggest deposition under oxygen-deficient conditions with evident watermass restrictions. High-productivity-indicating taxa were more abundant in Danian strata than in late Cretaceous strata, consistent with organic carbon characteristics. The δ13COrg-δ15N data show temporal heterogeneity due to organic matter type, redox conditions, preservation, stratigraphic condensation, and recycling of isotopically-light CO2. The negative δ13COrg shift around the K-Pg transition is globally correlative. Dynamic pyrite δ34S distribution resulted from variation in riverine influx, degree of pore-water openness, sulfate reduction rate, and diagenetic disproportionation of sulfur intermediates. Generally, radiogenic 187Os/188Os values were observed that were seemingly influenced by continental weathering and subsequent runoff influx of 187Os/188Os under a greenhouse climate. A positive 187Os/188Os shift to 3.68 (187Os/188Osi of 0.74) occurred at the onset of the Dakhla organic-rich spike. However, without a precise correlative stratigraphic framework, a global or regional seawater isotopic shift cannot be confirmed. We suggest that temporal variations in organic matter composition, redox, watermass conditions, and isotope fractionation of the K-Pg sequence in the study area were driven by discrepancies in climate, sea-level, and tectonic uplift. Further integrated approaches are needed to explore the geospheric drivers of this organic-rich sequence in time-equivalent sections.

Wavelets collocation method for singularly perturbed differential–difference equations arising in control system

In this paper, we present a wavelet collocation method for efficiently solving singularly perturbed differential–difference equations (SPDDEs) and one-parameter singularly perturbed differential equations (SPDEs) taking into account the singular perturbations inherent in control systems. These equations represent a class of mathematical models that exhibit a combination of differential and difference equations, making their analysis and solution challenging. The terms that include negative and positive shifts were approximated using Taylor series expansion. The main aim of this technique is to convert the problems by using operational matrices of integration of Haar wavelets into a system of algebraic equations that can be solved using Newton’s method. The adaptability and multi-resolution properties of wavelet functions offer the ability to capture system behavior across various scales, effectively handling singular perturbations present in the equations. Numerical experiments were conducted to showcase the effectiveness and accuracy of the wavelet collocation method, demonstrating its potential as a reliable tool for analyzing and solving SPDDEs in control system.

Tuning the inner- and outer-sphere electron transfer behavior of aqueous {CoW12} polyoxometalate clusters for redox flow batteries exceeding 1.5V

Redox active species as the key component of redox flow batteries (RFBs) directly determine battery performance. Herein, we report a unique redox active specie, {CoW12}, exhibits both outer-sphere electron transfer of the {CoO4} core and inner-sphere electron transfer of the {W12O36} shell in one cluster, which is capable of constructing a symmetric {CoW12}-based RFB with pH-controlled operating voltage output. The DFT calculation discloses the proton-coupled electron transfer process of the {W12O36} shell in thermodynamically and kinetically, explaining the negative shift of the redox potential of {W12O36} shell as the pH increasing from 1 to 4. Interestingly, the redox potential of outer-sphere controlled {CoO4} core is unchanged, which leads to an extension of voltage window from 1.31 to 1.56 V. Consequently, the cycling measurement of the symmetrical battery proves that low capacity decay rate of 0.009 % and high Coulombic efficiency over 99 % can be retained in 400 cycles at pH 4.

Asymmetric link between energy market and crypto market

This paper examines the nonlinear (NL) asymmetric long- and short-run interconnections between energy indices (S&P 500-ENERGY, MSCI-CHINA, and MSCI-WORLD) and the crypto (Bitcoin) market. The daily data have been used from January 1, 2013, to February 24, 2023, archived from the wind database. We use a nonlinear autoregressive distributed lag (NARDL) framework for the research to be empirical. The NARDL test reveals the presence of a nonlinear asymmetric relationship, both in the long-run and short-run, among the MSCI-China, MSCI-World, S&P500-ENERGY indices, and the price of Bitcoin. The S&P 500 energy index and Bitcoin price have an inverse asymmetric connection. The prices of Bitcoin are positively influenced by both positive and negative shifts in the MSCI-CHINA and MSCI-WORLD indices. Overall, this study underscores the growing significance of the cryptocurrency market as a hedge against risks, offering evidence that Bitcoin can be perceived as a safe haven amidst the turbulence of the energy market. This insight holds implications for Bitcoin investors, suggesting its potential as a refuge in times of energy market instability.

Redox conditions across the Upper Cambrian of eastern Laurentia: Implications from geochemical proxies

The lower part of the Martin Point section (∼ 110 m - rhythmites) spans the uppermost Shallow Bay and lowermost Green Point formations (uppermost Franconian–lowermost Trempealeauan) of the Cow Head Group (western Newfoundland, Canada). It records two post-SPICE (Steptoean Positive Carbon Isotope Excursion) events marked by negative δ13Ccarb excursions (NL1 and NL2) that were also documented in South China. The petrographic and chemical screening of the investigated carbonate samples proves the preservation of at least near-primary geochemical signatures. The proxies of weathering (e.g., Mn, Fe, Al, and ∑REE), bioproductivity (e.g., δ13Corg, TOC, P, Ni, Zn, and Cu), and paleoredox (e.g., Cr, Th/U, Ce/Ce*) have been utilized to reconstruct the paleoenvironmental conditions during the post-SPICE events. The TOC, P, Ni, Cu, Cr, ∑REE, Mn, Fe, and U Ca-normalized profiles exhibit a positive pulse at the base of NL2 (upper negative δ13Ccarb excursion), followed by a drop. This might have resulted from shoaling organic-rich anoxic waters into an oxygenated shallow environment during transgression, which led to a negative shift in the δ13Ccarb and a decrease in TOC contents as well as an increase in the δ13Corg. The correlated enrichment in Zn and δ15Norg values and the Ce/Ce* around unity are consistent with the shoaling scenario. A similar scenario seems to be consistent with NL1 (lower negative δ13Ccarb excursion) although the lower resolution of correlated proxy variations makes the interpretations based on a few points and to be therefore taken with caution.

Longitudinal changes in crystalline lens thickness and power in children aged 6-12 years old.

To determine the three-year changes in crystalline lens power (LP) and thickness (LT) in children and their associated factors. Schoolchildren aged 6-12 years living in Shahroud, northeast Iran were examined in 2015 and 2018. The Bennett formula was used to calculate LP. Multiple generalized estimating equations (GEE) analysis was used for data analysis. Among the 8089 examined eyes, the mean LP in Phase 1 and 2, and the three-year change were 21.61 ± 1.47D, 21.00 ± 1.42D, and -0.61 ± 0.52D, respectively. The GEE model showed that negative shifts in LP were less pronounced with increasing age (β = 0.176; p < 0.001), and were also less noticeable in hyperopes compared to emmetropes (β = 0.120; p < 0.001). The changes in LP decreased when outdoor activity increased among urban residents (β = 0.013; p = 0.039), while it increased in rural area (β = -0.020; p = 0.047). Mean three-year change in LT was 0.002 ± 0.13 mm. Female sex and aging by one year increased the LT by 0.022 mm (P < 0.001). However, LT decreased in 6-8-year-olds, while it increased in 10-12-year-old children, both in a linear fashion. The change in LT was less in myopes than in emmetropes (β = -0.018, P-value = 0.010). LP decreases after three years in 6 to 12-year-old children. LT increases slightly after three years in 6 to 12-year-old children. The changes in LP and LT were associated with the refractive errors, place of residence, age and gender and outdoor activity time.

Electrical signals of the plasma membrane and their effect on chlorophyll fluorescence in &lt;i&gt;chara&lt;/i&gt; chloroplasts &lt;i&gt;in vivo&lt;/i&gt;

Action potentials of plant cells are involved in regulation of many cell processes, such as photosynthesis and cytoplasmic streaming. Excitable cells of characean algae submerged in media with elevated K+ content are able to generate hyperpolarizing electrical responses. This active response of plasma membrane arises upon the passage of inward electric current comparable in extent to natural currents circulating in illuminated Chara internodes. It remains currently unknown whether the hyperpolarizing electrical signals in Chara affect the photosynthetic activity. Here we show that the negative shift of cell membrane potential, which causes the K+ influx into the cytoplasm, is accompanied by a delayed decrease in the effective chlorophyll fluorescence yield (F′) and maximal yield (Fm′) under low background light (12.5 µmol m-2 s-1). The transient changes in F′ and Fm′ were evident under illumination only, which indicates their close relation to photosynthetic energy conversion in chloroplasts. The passage of inward current caused an increase in pH at the cell surface (pHo), which reflects a high H+/OH- conductance of the plasmalemma and points to the decrease in cytoplasmic pH due to H+ entry into the cell. The shifts in pHo arising in response to the first hyperpolarizing pulse disappeared upon repeated stimulations, thus indicating the long-term inactivation of plasmalemmal H+/OH- conductance. Despite the suppression of plasmalemmal H+ fluxes, the hyperpolarizing responses and the analyzed chlorophyll fluorescence changes did not disappear. The results indicate the participation of K+ flows between the outer medium, cytoplasm, and stroma in chloroplast functional changes that are reflected by the dynamics of F′ and Fm′.

Interhemispheric connectivity dynamics of brain activity indused by cortical spreading depolarization in rats

Growing experimental and clinical evidence indicates the crucial role of network dysfunction in neurological disorders’ pathogenesis, including migraine, one of the most prevalent chronic brain diseases. Episodic headache attacks, frequently unilateral, accompanied by an aura, are associated with migraine. Migraine aura is a neurological condition characterized by the temporary development of unilateral sensory, motor, and/or speech disturbances. The symptoms are thought to indicate transient cerebral dysfunction in the cerebral cortex resulting from cortical spreading depolarization (SD), a wave of strong cellular depolarization that gradually spreads through the cortex at a rate of 3–5 mm/min. Electrophysiologically, the cortical SD wave is revealed by a high-amplitude slow negative shift in the extracellular potential and temporary suppression of the electrical activity of the cortex (EEG depression). The change in extracellular potential is associated with strong neuroglial depolarization and disruption of local ion homeostasis, which lasts for 1–2 min in healthy neuronal tissue. The SD results in a momentary suppression of the spontaneous electrical activity within the cortex, which is preceded by a brief excitation of the neurons. The neurological symptoms of the aura suggest a unilateral impairment of interhemispheric interactions during the early phase of a migraine attack. Our study investigated the effect of unilateral SD (a probable pathophysiological mechanism of migraine aura) on interhemispheric functional communication in freely behaving rats using local field potentials of the visual and motor cortex. Two methods were used to examine connectivity: mutual information function, computed using the method proposed in [1], and phase synchronization, calculated through the method [2], for four frequency bands: delta (1–4 Hz), theta (4–10 Hz), beta (10–25 Hz), and gamma (25–50 Hz). This was done by performing calculations on non-overlapping twenty-second intervals. Functional connectivity evolution was analyzed using local field potential records collected from homotopic points of the motor and visual cortex of two hemispheres in freely moving rats after inducing a single unilateral cortical SD in the somatosensory cortex. Cortical SD caused a significant wide-band decline (3–4 times) in interhemispheric functional connectivity in both the visual and motor cortex areas. Following the depolarization wave, the functional decoupling of the hemispheres began and progressively intensified, concluding by 5 min after the induction of the cortical SD wave. The network impairment displayed region- and frequency-specific features, with greater prominence observed in the visual cortex than in the motor cortex. The decline in functional connectivity was concurrent with abnormal animal behavior and aberrant activity in the ipsilateral cortex that appeared after the SD wave had ended. The study indicated that unilateral SD leads to a reversible decline in the functional interhemispheric connectivity in the awake animal cortex. Given the crucial role of synchronizing cortical oscillations for processing sensory information and integrating sensorimotor functions, the intracortical functional interactions disruption resulting from a unilateral SD wave, which we discovered in our present study, could contribute to the neuropathological mechanisms of migraine aura and sensory processing dysfunction during a migraine attack.

Voltametric and molecular docking investigations of ferrocenylmethylaniline and its N-acetylated derivative interacting with DNA

N-ferrocenylmethylaniline (FA) and its N-acetylated derivative (NFA) have been synthesized and fully characterized by various physicochemical techniques such as 1H and 13C NMR spectroscopy, their interactions with chicken blood DNA (CB-DNA) were studied by cyclic voltammetry (CV) and molecular docking (MD). The obtained results suggested that both FA and NFA bind strongly via electrostatic interactions to the minor groove of double helix DNA, these electrostatic interactions were evidenced by the findings like a negative formal potential shift in CV and ionic strength effect. The results further show that the obtained binding constants and free binding energies by MD analysis are matched roughly to those obtained from CV. Furthermore, the binding site size was evaluated from voltametric data.

Unsteady drag force on an immersed sphere oscillating near a wall

The unsteady hydrodynamic drag exerted on an oscillating sphere near a planar wall is addressed experimentally, theoretically and numerically. The experiments are performed by using colloidal-probe atomic force microscopy in thermal noise mode. The resonance frequencies and quality factors are extracted from the measurement of the power spectrum density of the probe oscillation for a broad range of gap distances and Womersley numbers. The shift in the resonance frequency of the colloidal probe as the probe goes close to a solid wall infers the wall-induced variations of the effective mass of the probe. Interestingly, a crossover from a positive to a negative shift is observed as the Womersley number increases. In order to rationalize the results, the confined unsteady Stokes equation is solved numerically using a finite-element method, as well as asymptotic calculations. The in-phase and out-of-phase terms of the hydrodynamic drag acting on the sphere are obtained and agree well with the experimental results. All together, the experimental, theoretical and numerical results show that the hydrodynamic force felt by an immersed sphere oscillating near a wall is highly dependent on the Womersley number.

Adaptability enhancement of fractional‐order LLCL‐type grid‐connected inverter to weak grid based on grid voltage weighted feedforward scheme

SummaryGrid‐connected inverter with a novel fractional‐order LLCL filter has the advantage of high grid current tracking accuracy and low total harmonic distortion without passive or active dampers, and the grid voltage full feedforward scheme is an effective method to improve the quality of grid current. However, due to the digital control delay, the suppression of the grid current harmonics is weakened, and the inverter output impedance has an additional negative phase shift, which deteriorates the stability of grid‐connected systems under weak grid. In this paper, a weighted grid voltage fractional‐order feedforward control scheme is proposed based on a quasi‐proportional resonant (QPR) controller, which introduces two weighting factors in the full feedforward path of the grid voltage and compensates the phase lag of the output impedance by designing appropriate weighting factors. Then, an improved scheme combining the QPR controller with a phase compensator is presented. As a result, the suppression ability of grid current harmonics and the adaptability to grid impedance variations are enhanced. Simulation and experimental results verify the effectiveness of the proposed grid voltage fractional‐order weighted feedforward scheme.

Role of technology management for carbon neutrality in Gulf economies: the role of social globalization and financial development.

This study is founded on the United Nations' Sustainable Development Goals (SDGs) for 2030, particularly SDGs 8, 11, 12, and 13, among others. Investigating the impact of nonrenewable energy, social globalization, financial development, and ICT on CO2 emissions in the Gulf nations, data from 1992 to 2019 was employed using advanced panel methodologies. Both linear and nonlinear autoregressive distributed lag techniques, along with a panel causality approach, were utilized for a comprehensive analysis. These extensive investigations offer robust insights into the ecological sustainability dynamics within the Gulf nations. The empirical findings highlight that positive (negative) shifts in social globalization, economic growth, ICT, and nonrenewable energy correlate with an increase (decrease) in CO2 emissions, while positive (negative) shifts in financial development contribute to a decrease (increase) in CO2 emissions. These results emphasize the need for a policy framework aligned with the SDGs, advocating an inclusive policy framework tailored for the Gulf nations, aiming to drive progress towards achieving SDGs 7, 8, 9, 13, and 16.

Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations

A weak Galerkin finite element method is applied to singularly perturbed delay reaction-diffusion problems. A robust uniform convergence has been proved both in the energy and balanced norms using higher-order piecewise discontinuous polynomials on Shishkin meshes. The error analysis for singularly perturbed reaction-diffusion problems with negative or positive shift in the balanced norm has appeared for the first time. The proposed method uses piecewise polynomials of order k ≥ 1 on interior of each element and piecewise constant polynomials on the end points of each element. By the Schur complement technique, the interior degrees of foredoom (DOF) can be eliminated from the discrete system resulting from the numerical scheme, and thus the degrees of freedom of the proposed method comparable with the classical finite element methods, and it is remarkably less than that of the discontinuous Galerkin method. Finally, we give various numerical experiments to verify the theoretical findings.