A synoptic compendium of the legumes of the Mimosoideae clade in northeastern Mexico is presented for the first time, including changes in their botanical nomenclature and retypification of genera. Furthermore, based on new information recently published, the taxonomic limits of several new genera segregated from Acacia (Acaciella, Mariosousa, Senegalia and Vachellia) and Prosopis (Neltuma and Strombocarpa) are clarified and included. Based on field work, collecting botanical samples during the last 30 years, a review of botanical materials and database in national and international, we have completed the diversity of legumes of the Mimosoideae clade of northeastern Mexico. Three tribes (Acacieae, Ingeae and Mimosaeae), 22 genera and 92 species, and 19 infraspecif categories were recorded. Only the genus Painteria is endemic to Mexico. Eighty-eight species are native to Mexico, and four are exotic, Acacia salicina, Neptunia prostrata, Neltuma chilensis and Albizia lebbeck. Twenty-eight species are endemic to Mexico, nine species are endemic of northeastern Mexico, and four species endemic to only one state in Mexico. The 22 registered genera represent 44% and 65% of the generic flora of the Mimosoideae clade for Mexico and the planet respectively while the 92 species registered represent 3% and 18% of the species of the Clade Mimosoideae for the planet and Mexico respectively. According to the new nomenclature of legumes, the number of genera in the Mimosoideae clade in northern Mexico has been increased from 19 to 24.

This research work aims to develop a mathematical modeling for production-inventory systems. Two mathematical models are present: An infinite dimensional, partial differential equation (PDE), production level modeling is present and a finite dimensional system for a coupled dynamic pricing, production rate and inventory level ordinary differential equations (ODE), integrating a proper Lyapunov stability analysis of the dynamical system and simulations.

As part of the Fabaceae project of northeastern Mexico, today we present the compendium of legumes of the subfamilies Caesalpinioideae, Cercidoideae and Detarioideae from this region. As in our previous work on the Mimosoideae Clade, new nomenclatural changes and retypification of genera of the subfamily Caesalpinioideae are included. Also, based on new scientific information published, the taxonomic changes in new genera, recently segregated from the genus Caesalpinia (Conzattia, Coulteria, Denisophytum, Erythrostemon, Guilandina, Hoffmannseggia, and Pomaria) are included. Based on field work, collection of botanical samples over the past 37 years, and reviewing botanical materials in national and international herbaria, the diversity of legumes of the subfamilies Caesalpinioideae, Cercidoideae, and Detarioideae in northeastern Mexico has been recorded. The subfamily Caesalpinioideae includes two tribes, the tribe Caesalpinieae with 12 genera (Caesalpinia, Ceratonia, Coulteria, Delonix, Denisophytum, Erythrostemon, Gleditsia, Guilandina, Hoffmannseggia, Haematoxylum, Parkinsonia, and Pomaria), and 26 species and the tribe Cassieae, which includes three genera (Cassia, Chamaecrita, and Senna) and 28 species. The subfamily Cercidoideae include two genera (Bauhinia and Cercis), and eight species and the subfamily Detarioideae, includes only one genus and one species (Tamarindus indicus). The total flora of these three subfamilies comprize 18 genera and 63 species, it includes 56 native species and seven exotic ones: Bauhinia variegata, Cassia fistula, Ceratonia siliqua, Delonix regia, Erythrostemon gilliesii, Senna alata, and, Tamarindus indicus. The endemism of both subfamilies includes a total of 20 species and 10 infraspecific categories.