W-graph ideals II

In "W-graph ideals" (Robert B. Howlett and Van Minh Nguyen) the concept of a W-graph ideal in a Coxeter group was introduced, and it was shown how a W-graph can be constructed from a given W-graph ideal. In this paper, we describe a class of W-graph ideals from which certain Kazhdan-Lusztig left cells arise. The result justifies the algorithm as illustrated in "W-graph ideals" for the construction of W-graphs for Specht modules for the Hecke algebra of type A.Comment: 16 page

Perron Theorem in the Monotone Iteration Method for Traveling Waves in Delayed Reaction-Diffusion Equations

In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction diffusion systems with time delay. The method is tried out on two classical examples with delay: the predator-prey and Belousov-Zhabotinskii models.Comment: 17 pages. To appear in Journal of Differential Equation

Optimization of the Engineering Properties of Cement Concrete Containing Gravel and Waste Rock Using Dense Packing and Response Surface Methodology

This study introduces a novel methodology for optimizing the distribution of aggregate particles in concrete. Utilizing locally available materials like gravel and waste rock is explored as a sustainable alternative to conventional materials like mountain rock and river sand, which are depleting. Determining the maximum bulk density involves an efficient process of gradually adding different particle sizes of gravel and waste rock to the mixture. The vibrational compaction of the container aids in identifying the optimally combined percentages of these aggregates. Besides, the study also addresses the issue of porosity in concrete. The response surface methodology is employed to optimize the mixture proportions for concrete, considering important factors such as workability, compressive strength, flexural strength, and elastic modulus. This response surface methodology allows for the development of mathematical models that aid in determining the optimal mix ratios. By exploiting the potential of gravel and waste rock, this study aims to procedure cement concrete containing gravels and waste rock (WR) with required compressive strength from 30 MPa to 35 MPa based on reasonable aggregate particle distribution in combination with response surface methodology (RSM) and minimize the disposal of non-biodegradable waste, thereby reducing the environmental pollution. Additionally, utilizing locally available materials helps to effectively use the region's resources for concrete production, promoting sustainability and reducing dependency on scarce resources. The proposed method presents a promising approach to optimizing aggregate distribution in concrete while considering the environmental and resource constraints specific to the Northwest region of Vietnam