Correction Term Research Articles

Holography as homotopy

We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L∞ algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L∞ algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L∞ algebra on the boundary. The resulting action is the ‘on-shell action’ conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L∞ algebras.

Renewable Energy Consumption, Climate Change, and Economic Growth: A Case of Selected Countries

This research examines the nexus between renewable energy consumption, climate change, and economic growth across 88 countries, categorized by income levels (high, upper-middle, lower-middle, low, and Arab countries) from 1990-2020. Using the Panel Autoregressive Distributed Lag (PARDL) model, the study captures both short- and long-term relationships among the variables. Key findings reveal that economic growth is linked to rising temperatures, while the impact on precipitation varies across income groups. Non-renewable energy consumption has mixed effects: it mitigates climate change in developed countries but exacerbates pollution in developing nations. Conversely, renewable energy lowers average temperatures in lower-income countries, but in high-income countries, it shows positive correlations with climate change indicators. The significant error correction terms across all panels indicate a quick adjustment toward long-run equilibrium. The study underscores the need for tailored climate and energy strategies, advocating for increased renewable energy infrastructure in developing countries and improved energy efficiency in developed nations. For Arab countries, which face specific climate risks, enhanced regional cooperation on mitigation measures is recommended. This research emphasizes that addressing climate change requires strategies that consider the distinct economic and environmental contexts of different country groups.

Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed-Point Problems

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.

A Fresh Revisit of the Issues and Improvements in Impulse Invariance Filter Design for Infinite Impulse Response Filters

The objective of this paper is to first present some issues with impulse invariance filter (IIF) design during the design of digital infinite impulse response (IIR) filters. Engineers are often confused about some inconsistent observations. For instance, if the impulse response of a digital filter is designed using the impulse invariance procedure, then the analog and digital filters’ frequency and step responses are very different. Two simple remedies are presented in this paper. One is a post-processing approach that scales the frequency and step responses of the digital filter by the sampling interval T. Another one is a pre-processing approach that scales the impulse response of the analog filter by T. However, even after these remedies, there is still a steady state bias in the step response of the digital filter for certain cases where there is discontinuity in the analog impulse response. A recommendation is to include a correction term in the digital filter. After that, the steady state bias in the digital filter is then suppressed. Moreover, the MATLAB R2021a command “impinvar” needs to also include a correction term so that the frequency and step responses can be more accurate in the digital filter. Two comparative studies were carried out to compare the improved IIF filter with three competing digital IIR filter design methods. Although the above issues and improvements have been proposed by researchers in the past, many researchers, engineers, and students are still not aware of them. This paper provides a fresh revisit of these issues and improvements by using figures, equations, and examples. Proper credits are also given to those researchers who first pointed out those issues and improvements. It is hoped that through an open access journal, future rediscovery of issues and improvements in IIF can be prevented.

The analytical approach in testing the Kaniadakis cosmology

Abstract We know that a quantum-corrected cosmological scenario can emerge based on its corrected Friedmann equations corresponding to the corrected entropy of cosmic-horizon using the gravity-thermodynamics conjecture in deriving those equations. In this right, the Kaniadakis entropy associated with the apparent horizon of Friedmann-Robertson-Walker(FRW) Universe leads to a corrected Friedmann equation which contains a correction term as $\Omega_{Ka}=\frac{\alpha\left(H^2+\frac{k}{a^2}\right)^{-1}}{H^{2}}$ where $\alpha\equiv\frac{K^2 \pi^2}{2 G^2}$ ($K$ is the Kaniadakis parameter). Here, we derive the analytical relations between the energy density parameters $\Omega_{m},\Omega_{\Lambda}$ (and the ratio density $\Omega_{Ka}$ of correction term) and the geometrical cosmological parameters $\{q, j\}$. This leads to getting $\Omega_{Ka}=\frac{j-1}{4(q+1)^{2}-(j-1)}$ which enables us to put constrains on $\Omega_{Ka_{0}}$ using the measurable parameters $\{q_{0},j_{0}\}$ and $H_{0}$. It also reveals some interesting aspects of the Kaniadakis cosmology by explaining that the correction term plays different roles both in the presence and in the absence of the cosmological constant $\Lambda$.
This term plays the role of dark energy in the absence of the cosmological constant $\Lambda$, while in the presence of this component, it plays the role of a small correction to dark energy. The value of $\Omega_{Ka}$ then determines the amount of the deviation of Kaniadakis model from the concordance $\Lambda CDM$ model. As a result, the value of $j_{0}$ is found to be close to unit for vanishing cosmological constant $\Lambda=0$ and the maximum value of $\Omega_{Ka0}$; thereby we get $(j_{0}-1)\simeq 0.137$ and $(j_{0}-1)\simeq< 10^{-3}$ for the case of $\Lambda=0$ and $\Lambda\neq0$, respectively

A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate.

Quantum and classical properties of the universe according to unimodular quantum cosmology

Abstract We investigate the dynamical behaviour of wavepacket solutions due to unimodular quantum cosmology. We find early and late time quantum eras of the universe.
An Ehrenfest theorem ensures quasi-classical behaviour for the late time universe if the quantum uncertainties are small. The surprising prediction of late time quantum effects for a flat, homogeneous and isotropic universe with a scalar field with an exponential potential is obtained by the analysis of the uncertainty dynamics using the results of the corresponding classical dynamical system. Furthermore quantum correction terms to the Hubble parameter and the matter density are derived. A positive matter expectation value for the de-Sitter universe raises the question if correction terms due to quantum gravity could contribute to solve the dark matter problem.

Macroeconomic Determinants of the Gap between Domestic and International Gold Prices in Vietnam

This research investigates the factors influencing the disparity between domestic gold prices (SJC gold and 9999 gold) and global gold prices in Vietnam from January 2011 to December 2023. Using the Autoregressive Distributed Lag (ARDL) model, we identify key macroeconomic determinants impacting this price spread, including interest rates, oil prices, and consumer demand. Our findings reveal that higher interest rates are associated with larger price spreads, suggesting that monetary policy plays a significant role in the domestic gold market. Oil prices exhibit a negative relationship with the price spread for 9999 gold, indicating that rising oil prices tend to align domestic gold prices more closely with global trends. Consumer demand notably affects the SJC_Global price spread but not the 9999_Global spread, reflecting the different market dynamics of finished goods versus raw materials. Additionally, the error correction terms in both models indicate a robust mechanism for long-term equilibrium, demonstrating the Vietnamese gold market’s resilience. These insights highlight the need for policymakers to reconsider existing regulations, such as Decree 24, to ensure a stable and efficient gold market. The study concludes that while the Vietnamese gold market exhibits sustainable practices, regulatory revisions are necessary to support both market growth and community development. Future research should consider additional macroeconomic variables and the impact of regulatory changes over time to further understand the dynamics of gold price disparities in Vietnam.

Treatment of 3D diffusion problems with discontinuous coefficients and Dirac curvilinear sources

Three-dimensional diffusion problems with discontinuous coefficients and unidimensional Dirac sources arise in a number of fields. The statement we pursue is a singular-regular expansion where the singularity, capturing the stiff behavior of the potential, is expressed by a convolution formula using the Green kernel of the Laplace operator. The correction term, aimed at restoring the boundary conditions, fulfills a variational Poisson equation set in the Sobolev space H1, which can be approximated using finite element methods. The mathematical justification of the proposed expansion is the main focus, particularly when the variable diffusion coefficients are continuous, or have jumps. A computational study concludes the paper with some numerical examples. The potential is approximated by a combined method: (singularity, by integral formulas, correction, by linear finite elements). The convergence is discussed to highlight the practical benefits brought by different expansions, for continuous and discontinuous coefficients.

Vacancy formation free energy in concentrated alloys: Equilibrium vs. random sampling

Special Quasi-random Structures (SQSs) are often used to model disordered alloys in small simulation cells. Yet, SQS-based sampling yields defect formation energies that do not match the equilibrium values, for instance measured in atomic Monte Carlo simulations, due to the lack of chemical short-range order in random samples. In this paper, our approach to computing chemical potentials in alloys through random sampling techniques is extended to the computation of vacancy formation free energies. By rigorous thermodynamic derivation, we show that vacancy formation free energies computed from randomly sampled local chemical environments must be corrected to ensure its consistency between various available calculations. Indeed, irrespective of the choice of the species being replaced by a vacancy, we should arrive at the same value of the vacancy formation free energy. We propose a simple way to compute this correction term, and compare the outcome with equilibrium Monte Carlo results and with approximations found in the literature.

Causal fermion systems as an effective collapse theory

Abstract It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr"odinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski-Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale~$\ell_{\min}$.

Semi-Classical Limit and Quantum Corrections in Non-Coincidence Power-Law f(Q)-Cosmology

Within the framework of symmetric teleparallel fQ-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in fQ-gravity permits a minisuperspace description, rendering the Wheeler–DeWitt equation a single inhomogeneous partial differential equation. We use the power-law fQ=f0Qμ model, and with the application of linear quantum observables, we calculate the wave function of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.

The GFMxP and the basic extrapolation of the ghost values to solve the Poisson equation for discontinuous functions

In a recent paper, a novel coding of the Ghost Fluid Method for the variable coefficient Poisson equation with discontinuous functions (named GFMxP) was proposed. A lot of numerical tests, with all the required quantities available in a analytic form, were used to demonstrate the ability of the new procedure in modeling a sharp interface and to check the accuracy order of the solutions. In practical applications, however, the real difficulty stands in the estimation of the so-called “ghost values”, that is the values at points where the function is not only unknown, but even not defined. These values allow to compute the corrective terms enabling the use of standard finite difference formulas in presence of a singularity and/or a discontinuity, and can be only determined through some extrapolation procedure, whose truthfulness is essential to achieve a reliable result. The paper deals with such a basic issue, by testing different numerical strategies and demonstrating the strict relationship between the order of the adopted fit-model, the order of the solving scheme for the Poisson equation and the accuracy of the final solution.

Global scale assessment of urban precipitation anomalies

Urbanization has accelerated dramatically across the world over the past decades. Urban influence on surface temperatures is now being considered as a correction term in climatological datasets. Although prior research has investigated urban influences on precipitation for specific cities or selected thunderstorm cases, a comprehensive examination of urban precipitation anomalies on a global scale remains limited. This research is a global analysis of urban precipitation anomalies for over one thousand cities worldwide. We find that more than 60% of the global cities and their downwind regions are receiving more precipitation than the surrounding rural areas. Moreover, the magnitude of these urban wet islands has nearly doubled in the past 20 y. Urban precipitation anomalies exhibit variations across different continents and climates, with cities in Africa, for example, exhibiting the largest urban annual and extreme precipitation anomalies. Cities are more prone to substantial urban precipitation anomalies under warm and humid climates compared to cold and dry climates. Cities with larger populations, pronounced urban heat island effects, and higher aerosol loads also show noticeable precipitation enhancements. This research maps global urban rainfall hotspots, establishing a foundation for the consideration of urban rainfall corrections in climatology datasets. This advancement holds promise for projecting extreme precipitation and fostering the development of more resilient cities in the future.

Impact of External Debt and Energy Consumption on Environmental Quality in Somalia

This study investigates the interconnections between external debt, energy consumption, industrialization, and environmental quality in Somalia over the period 1990 to 2019, utilizing the ARDL bounds testing approach. Notably, a positive correlation is found between energy consumption and CO2 emissions, emphasizing the imperative for sustainable practices. In the long run, external debt is observed to have an insignificant impact on environmental quality, suggesting a strategic opportunity for policymakers to channel external funds towards environmentally sustainable projects. Short-term strategies underscore the positive link between decreased industrialization and improved environmental quality, while a cautious approach to external debt is crucial due to its short-term negative impact. The significance of the error correction term underscores the need for adaptive policies. Overall, the study advocates for comprehensive policies integrating sustainable practices and directing external financing towards eco-friendly projects, alongside a capacity building and technology transfer partnerships for environmentally conscious development in Somalia.

Cash Incentive on Remittance Inflow and its Impact on Economic Growth in Bangladesh

Remittances are crucial for driving economic growth in developing countries like Bangladesh, as they effectively influencenearly all macroeconomic indicators within the financial ecosystem. This study examines the impact of remittance inflow on economic growth in Bangladesh considering the cash incentive policy of the government. The ARDL Bound testing approach is employed for the analysis using a monthly dataset covering the period from January 2015 to April 2023. The evidence from the results provides a substantial and favorable influence of remittances on the economic growth of Bangladesh, both in the short term and the long term. According to the expected error correction term, it is projected that the economy will undergo a correction of its imbalances at an annual rate of 58%. Consequently, a strategic blend of short-term policy adjustments and long-term initiatives has the potential to enhance the influence of remittances in fostering sustainable economic growth and elevating the the quality of life for both expatriates and the nation as a whole.

Fuel Subsidy and Education Sector Financing in Nigeria: A Short-run Adjustment to Equilibrium Approach

This study examined the impact of fuel subsidy on education sector financing in Nigeria from 1990 through 2023. Annual data were obtained from the Nigeria Petroleum Corporation and World Development Indicators, (WDI) on variables such as fuel subsidy, government expenditure on education sector, Oil Revenue, pump price of Premium Motor Spirit and secondary school enrolment in Nigeria. A bound cointegration test and ECM were employed. Granger test for causality was also used to ascertain the direction of causation in the series. The estimated error correction term, ECT (-1) is significant. There is no causal relationship from fuel subsidy to education sector financing. However, education sector financing granger causes fuel subsidy. Premium Motor Spirit and education sector financing were found to granger-cause each other. The study recommends that government should ensure that fuel subsidy is not allowed to deprive education of its fair share of government spending, given that current spending on the sector has been established to have implication for the sectors growth in the future years.

A Unified Hardware Design for Multiplication, Division, and Square Roots Using Binary Logarithms

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, subtraction, and shifts, enabling a unified hardware implementation—a marked departure from conventional methods that handle these operations separately. The proposed design, involving logarithm and antilogarithm calculations, exhibits an algebraically symmetrical pattern that further optimizes the processing flow. Additionally, this study introduces innovative log-domain correction terms specifically designed to minimize computation errors—a critical improvement over existing methods that often struggle with precision. Compared to standard hardware implementations, the proposed design significantly reduces hardware resource utilization and power consumption while maintaining high operational frequency.

Absolute electron impact ionization cross-sections for CF4: Three dimensional recoil-ion imaging combined with the relative flow technique.

Here we present measurements of dissociative and non-dissociative cross-sections for the electron impact of the CF4 molecule. The present experiments are based on a Recoil Ion Momentum Spectrometer (RIMS), a standard gas mixing setup for CF4, and a reference gas. The measurements were carried out at several electron energies up to 1keV, covering the energy range of previous experiments. We apply the relative flow technique (RFT) to convert the relative cross-sections measured by the RIMS into absolute values. Using the combination of RIMS and RFT, ion collection and calibration errors were minimized. The results were compared with theoretical and experimental studies available in the literature. Previous electron impact experiments present relative cross-sections or use correction terms for the absolute cross-sections due to losses of energetic ions. We elucidate the differences between the new measurement method and the existing ones in the literature and explain why the present method can be considered reliable. Furthermore, we show how reducing correction terms affects the results.

Correspondence between grey-body factors and quasinormal modes

Quasinormal modes and grey-body factors are spectral characteristics corresponding to different boundary conditions: the former imply purely outgoing waves to the event horizon and infinity, while the latter allow for an incoming wave from the horizon, thus describing a scattering problem. Nevertheless, we show that there is a link between these two characteristics. We establish an approximate correspondence between the quasinormal modes and grey-body factors, which becomes exact in the high-frequency (eikonal) regime. We show that, in the eikonal regime, the grey-body factors of spherically symmetric black holes can be remarkably simply expressed via the fundamental quasinormal mode, while at smaller ℓ, the correction terms include values of the overtones. This might be interesting in the context of the recently observed connection between grey-body factors and the amplitudes of gravitational waves from black holes. The correspondence might explain why grey-body factors are more stable, i.e. less sensitive, than higher overtones to small deformation of the effective potential.