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In this work we prove that a relationship exists between the elementary paths of the plane lattice Z² and those with growing altitude. Fortunately it is possible to make a more complete combinatorial study of the Z² growing altitude elementary paths and in particular those with barrier. From this combinatorial study we have established an important relationship permitting the calculation of the number of growing altitude elementary paths with barrier and of given length.

Lets a_n be the number of growing altitude elementary paths of length n of the cubic lattice Z³. By numeric simulation shows that the quotient a_n+1/a_n tends rapidly to a constant. Leads to the decision that the sequence (a_n)_n has an asymptotically geometric behaviour. Confirms the intuition and shows that two positive constants α and λ exist, such that α_n = αλⁿ(1 + ε_n) where (ε_n)_n is a sequence tending to 0 as n tends to infinity with the estimation |ε_n| ≤ Cγⁿ where C > 0 and 0 < γ < 1. Explains the rapid convergence of a_n+1/a_n. Determines the constants α and λ and elaborates on a numeric method for their calculus.

Determining the possible configurations number of a native protein involves a combinatorial study of the elementary paths in the cubic lattice Z³ . The main result consists of illustrating a construction of an elementary path called an associated elementary path. This construction allows the calculation of paths of given length.

This study aims to present an empirical investigation on the effect of natural resource rent on income inequality in Algeria over the period 1980–2020.

The analysis is carried out by using the novel developed method dynamic autoregressive distributed lag (ARDL) simulation technique alongside the Kernel-based regularized least squares.

The bounds test revealed a long-run relationship between natural resource rent and income inequality. Our estimation results suggest that natural resource rent, GDP per capita and government expenditures are all associated with lower income inequality in the short and long term. Moreover, the author found that better institutional quality is more likely to reduce income inequality in Algeria. This empirical finding is further validated by the counterfactual shocks from the dynamic ARDL simulation, which reveal a significant decrease in predicted income inequality following a positive change in resource rents and a gradual, significant increase in inequality after a negative change in resource rents.

The present study is the first to use the dynamic ARDL model to investigate the impact of positive and negative changes in natural resource rent on income inequality in Algeria.

The study aims to analyze and compare the influence of country-specific fundamentals and global conditions on sovereign risk of Sri Lanka within the sample period of 2006–2019 while employing Treasury bond rates as proxy for sovereign risk.

The determinant powers of the variables are assessed using the auto regressive distributed lag (ARDL) model to verify both short- and long-run effects on sovereign spreads.

The study finds that Sri Lanka's sovereign spreads are shaped by both country fundamentals and global factors, though local determinants tend to have greater influence when the directions of coefficients are ignored. While the impact of most variables was in line with the researchers' expectations, fiscal deficit was found to have an unconventional negative coefficient which may be explained by investors' optimistic take on Government's involvement in post-war economic development drive during the sample period, enabling Sri Lanka to attract low-cost funding.

The study excludes of impact of the ongoing coronavirus disease-2019 ( COVID-19) health crisis which may unduly distort the data. Further, the research does not capture the impact of change in sentiment owing to market information, debt dynamics and policy changes in Sri Lanka.

The study reveals that a sound monetary policy directed at preserving both the internal and external value of currency as well as a disciplined fiscal policy are imperative to manage Sri Lanka's sovereign risk, particularly in the face of global uncertainties.

The study adds to the literature by investigating the timely importance of a country's internal fundamentals against the global events. Furthermore, the research would complement the scarcity of research regarding that subject focused on the Sri Lankan economy, capturing the rapid variations in the fundamentals that the country has undergone since the end of the civil war while recognizing the growing influence of globalization over the recent years.

This study aims to analyze the effects of natural resource rents on income inequality.

This study uses a panel quantile regression (QR) approach for 42 Sub-Saharan African (SSA) countries over the period 1998–2018.

The results show that natural resource rents have a negative and statistically significant effect on income inequality. Regarding the types of resources, the results show that coal rents increase inequality, while forestry and oil rents reduce income inequality. The results also show that the effects of mining and gas rents vary along the income inequality distribution. Finally, the results reveal a negative and significant effect of natural resource rents on income inequality in all sub-regions except Southern Africa.

The results suggest that the SSA Governments should intensify the implementation of income redistribution policies such as family allowances to poor families with multiple children and public sector job creation. SSA policymakers should also increase access to electricity, and internet, and allocate a portion of oil revenues to create an intergenerational sovereign wealth fund.

First, few studies have analyzed the effects of various types of natural resource rents on income inequality. To this end, this study used the QR method to examine the impact of natural resource rents on inequality, by laying emphasis on various types of natural resources. This study takes into account the likely heterogeneity across countries that may exist when considering a sample such as SSA countries, by examining the effects in the different sub-regions that make up this part of Africa (Central Africa, West Africa, Southern Africa and East Africa).

During the planting process, agricultural products produce large amounts of greenhouse gas (GHG) emissions. This has placed tremendous pressure on sustainable global development. Many countries and regions in the world have adopted intensive subsistence cultivation methods when planting maize; however, limited studies exist on these methods. The main purpose of this research is to show the impact of climate change on maize yields and carbon footprint (CF) in South Korea over 10 years, find the proper operating method and promote the advanced combination of inputs for the sustainable development of maize farmers.

This study used survey data from the South Korea Rural Development Administration of 2010, 2014 and 2019 to estimate the CF of maize planting under intensive subsistence cultivation. Life-cycle assessment was used to determine the CF. Farmers were grouped according to significant differences in yield and GHG emissions. Linear regression was used to measure the dependence of the main contributors on the CF production and carbon efficiency.

In South Korean maize planting, N in chemical fertiliser was the most significant contributor to the CF and organic fertiliser was the most significant input. The use of chemical and organic fertilisers significantly affects the production of the CF and carbon efficiency. Households in the high-yield and low-GHG emission groups are more sustainable because they generate the least GHG when producing and earning through maize cultivation. Globally, maize production in South Korea has a relatively low CF and maize production produces fewer GHG.

This study provides information for policymakers to determine key operational options for reducing GHG emissions using intensive subsistence cultivation of maize production in South Korea and other countries.

The purpose of this paper is to study a novel Mannich adduct of benztriazole-containing diphenylamine (coded as BD) and its anti-oxidation properties as an additive in two typical synthetic ester-based oils.

The anti-oxidation properties in two typical synthetic ester-based oils were evaluated in detail, using rotating pressure vessel oxidation test. The tribological properties of BD in synthetic ester-based oil (A51) were also tested with Optimal SRV-I oscillating friction and wear tester at atmosphere.

The results of tests demonstrated that the novel BD compound is, indeed, a high-performance anti-oxidation additive that was able to remarkably improve the oxidation stability of synthetic ester-based oils, when it was added at only 0.5 per cent concentration and compared with the base oils containing 0.5 per cent of the commercial available antioxidant additives such as 2, 6-di-tert-butyl-4-methylphenol and octyl-butyl diphenylamine. A plausible mechanism of exceptional synergistic anti-oxidation was proposed.

This paper first investigated the anti-oxidation properties and mechanisms of the compound with the structure of BD, which can be very useful and would promote the application of BD antioxidant in the lubricant industry.