The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, ${\left(LPS\right)}_n$) to its tangent bundle $TM$ associated with a Riemannian connection $D^C$ and a quarter-symmetric metric connection (QSMC) ${\overline{D}}^C$.

In this study, the influence of fuel premixing ratio (PMR) on the performance, combustion, and emission characteristics of dual-fuel operation in the compression ignition (CI) engine have been investigated. For dual fuel operation in CI-engine, two fuels of different reactivity are utilized in the same combustion cycle. In this study, low reactivity fuels (gasoline/butanol) is injected into the intake manifold, and high reactivity fuel (diesel) is directly injected into the cylinder. To operate the conventional CI engine in dual-fuel mode, the intake manifold of the engine was modified and a solenoid based port fuel injector was installed. A separate port fuel injector controller was used for injecting the gasoline or butanol. Suitable instrumentation was used to measure in-cylinder pressure and exhaust gas emissions. Experiments were performed by maintaining the constant fuel energy at different fuel PMR for different engine loads at constant engine speed. The influence of fuel PMR on combustion pressure, heat release rate, and coefficient of variance (COV) of indicated mean effective pressure (IMEP), brake thermal efficiency (BTE), combustion duration, and gaseous emissions were investigated at different engine loads. Premixing of high octane fuel leads to an increase in cyclic combustion variations and unburnt hydrocarbon emissions, which limits the range of fuel premixing. The range of premixing of high octane fuel in dual-fuel CI-engine has not been investigated in the published literature using COV_IMEP and HC. The main objective of the present study is to determine the range of fuel PMR and the best possible fuel PMR for gasoline/butanol-diesel dual fuel CI-engine at 25%, 50% and 100% loads. Additionally, butanol-diesel dual fuel operation is also compared with gasoline-diesel dual fuel operation for 50% engine load. The range of fuel PMR is estimated on the basis of combustion (COV_IMEP) and unburned hydrocarbon (HC) emission characteristics while the best fuel premixing ratio is estimated on the basis of performance and emissions characteristics. The results demonstrate that higher thermal efficiency was achieved for specific combinations of fuel premixing ratio and NO_x emission drastically reduced for both the dual-fuel operations. Particle number emissions are also found lower in dual-fuel operation (using gasoline and butanol) in the determined range of premixing ratio.

The purpose of the present paper is to analyze the concept of the horizontal and complete lifts on the superstructure F(±a^2,±b^2), which is defined as (F^2+a^2)(F^2-a^2)(F^2+b^2)(F^2-b^2) = 0, over the tangent bundles and establish its integrability conditions using the horizontal and complete lifts. Finally, some properties of the third-order tangent bundle are investigated.