The national total expenditure of a country is precipitated on several factors of which revenue generated could be one and very significant. This paper therefore examines the contribution of some selected sources of Nigerian government revenue to total national expenditure. Statistical and econometric techniques used for the data analysis are unit root test, cointegration test, combined estimators’ analysis, the error correction model (ECM) and the feasible generalized linear (FGLS) estimators. Results showed that the variables are non stationary but are stationary at first difference. The long-run relationship of total expenditure on oil revenue, non-oil revenue, federation account and federal retained revenue revealed that the variables are co-integrated and required the use of combined estimators. The effect of non-oil revenue and federal retained revenue is very significant. Investigations on the short-run modeling necessitated the use of FGLS estimators. The effect of ECM and federal retained revenue is very significant. Consequently, other sources of revenue apart from federal retained revenue need to be enhanced and tailored towards improving economic growth and development through national expenditure.

Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). Other aspects are the backdoors discovered in deterministic random generators or recent advances in solving some instances of DLP. The use of alternative algebraic structures like non-commutative or non-associative partial groupoids, magmas, monoids, semigroups, quasigroups or groups, are valid choices for these new kinds of protocols. In this paper, we focus in an asymmetric cipher based on a generalized ElGamal non-arbitrated protocol using a non-commutative general linear group. The developed protocol forces a hard subgroup membership search problem into a non-commutative structure. The protocol involves at first a generalized Diffie-Hellman key interchange and further on the private and public parameters are recursively updated each time a new cipher session is launched. Security is based on a hard variation of the Generalized Symmetric Decomposition Problem (GSDP). Working with GF(2518) a 64-bits security is achieved, and if GF(25116) is chosen, the security rises to 127-bits. An appealing feature is that there is no need for big number libraries as all arithmetic if performed in Z251 and therefore the new protocol is particularly useful for computational platforms with very limited capabilities like smartphones or smartcards.

The paper presents the results of a simulation on a 3D model of undeformed chips and cutting forces during three-pass gear cutting using the power skiving method. At the level of individual blades and teeth in successive angular cutting positions, the main component of the cutting force and the tangential force on the cutter axis are shown. The analysis of the forces acting on a single gear tooth and the continuous cutting forces allowed the development of a methodology for the selection of rational cutting modes – the value of the axial feed, the number of passes with different cutting depths in order to ensure the minimum time consumption and to achieve the required accuracy of the gears in terms of the parameter of the permissible angular deviation of the profile of the cut gear. It is shown that, provided the required machining accuracy is ensured, higher productivity is achieved by increasing the axial feed at a lower depth of cut and increasing the number of passes, rather than by reducing the feed and increasing the depth of cut.