In this study, we investigated the selective production of propylene from methanol using monolith-structured ZSM-5 and germanium-modified ZSM-5 nanocatalysts within a fixed-bed reactor system. Optimal reaction conditions were established as 500 °C, 1 bar pressure, and a weight hourly space velocity (WHSV) of 15 h⁻¹, with methanol as the feedstock. To assess the physical and chemical characteristics of the pelletized parent, Ge-modified, and monolith-structured HZSM-5 nanocatalysts, we utilized various analytical techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), Brunauer-Emmett-Teller (BET) surface area analysis, and ammonia temperature-programmed desorption (NH3-TPD). NH3-TPD results indicated a reduction in acidity for the Ge-modified HZSM-5 nanocatalyst, attributed to the partial elimination of strong acid sites. XRD patterns confirmed the presence of the washcoat on the monolith-structured support. Additionally, SEM images of the Ge-modified and monolith-structured HZSM-5 nanocatalysts showed no change in the crystallinity of HZSM-5, while demonstrating a uniform nanocatalyst coating within the channels of the monolith-structured support. The most effective modified nanocatalyst was achieved by incorporating 0.1 wt% germanium into ZSM-5, which resulted in a substantial enhancement of propylene selectivity by 53% and yield by 22.1%. Among the monolith-structured nanocatalysts, variations with single-layer, double-layer, and triple-layer coatings of HZSM-5 were prepared. The single-layer HZSM-5 monolith-coated nanocatalyst exhibited the most significant improvements, with propylene selectivity increasing by 55% and yield by 28.4%. These improvements were attributed to enhanced internal diffusion and reduced mass transfer resistances within the monolith channels, leading to shorter residence times and reduced aromatic formation

In this paper, notions of ∈t-set and Qt-set of a fuzzy set f in a GE-algebra X are introduced and defined fuzzy GEalgebra in terms of ∈t-set. We provided conditions for the ∈t-set and Qt-set of a fuzzy set f to be GE-subalgebras of X. We provided conditions for a fuzzy set in a GE-algebra to be a fuzzy GE-algebra. The concept of fuzzy GE-filter of a GE-algebra is introduced and investigated its properties. We explored the conditions under which the ∈t-set and Qt-set can be GE-filters. Some characterizations of fuzzy GE-filters of GE-algebras are given.

In this paper, the properties of GE-ideals of transitive bordered GE-algebra are studied and characterizations of GE-ideals are given. We have observed that the set of all GEideals of a transitive bordered GE-algebra forms a complete lattice. The notion of bordered GE-morphism is introduced and established fundamental bordered GE-morphism theorem. A congruence relation on a bordered GE-algebra with respect to GE-ideal is introduced and some bordered GE-morphism theorems are derived.

The notions of ξ,-inside GE-derivation and ξ,-outside GE-derivation on a GEalgebra are introduced and its properties are investigated. Conditions for a self-map on GE-algebra to be a ξ,-inside GE-derivation and a ξ,-outside GE-derivation are provided. The ξ,-inside GE-derivation or the ξ,-outside GE-derivation ϱ,are used to form two sets X(ϱ, =ξ, ) and ker(ϱ, ), and GE-subalgebra and GE-, lter are studied for these two sets.

The concept of very true GE-algebra using very true operator is introduced and its properties are studied to expand the scope of research of GE-algebras. The concepts of simple very true GE-algebra and very true GE-filter are introduced. The characterization of simple very true GE-algebra is discussed, and several properties on very true GE-filter are investigated. Using a very true GE-filter, the quotient very true GE-algebra is constructed, and the uniform and topological space are established.

A new sub-structure called (vivid) deductive system is introduced and their properties are examined. Conditions for a subset to be a deductive system are provided. The notion of upper GE-set is also introduced, and an example to show that any upper GE-set may not be a deductive system are supplied. Conditions for an upper GE-set to be a deductive system are provided. An upper GE-set is used to consider conditions for a subset to be a deductive system. The characterization of deductive system is established, and relationship between deductive system and vivid deductive system are created. Conditions for a deductive system to be a vivid deductive system are given, and the extension property for vivid deductive system is constructed.