Linear-width is a well-regarded width parameter in graph theory. The constructs of linear loose tangle and linear tangle present obstacles to attaining linear-width. In this succinct paper, our primary focus will be the exploration of maximal linear loose tangles.

Loose Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). In this compact paper, we revisit and contemplate the interplay between Loose Tangle and Filter through the lens of a submodular partition function.

An energy model that correlates fan airflow, head, speed, and system power input is essential to detect device faults and optimize control strategies in fan systems. Since the application of variable frequency drives (VFDs) makes the motor efficiency data published by manufacturers inapplicable, the fan efficiency and drive (belt-motor-VFD) efficiency must be identified for each individual system to obtain accurate energy models. The objectives of this paper are to identify an energy model of existing VFD-motor-fan systems using available experimental data and demonstrate its applications in loose belt fault detection and virtual airflow meter development for optimal control. First, an approach is developed to identify the fan head, fan efficiency and drive efficiency curves using available fan head, speed, and system power input as well as temporarily measured airflow rate without measuring shaft power. Then the energy model is identified for an existing VFD-motor-fan system. Finally, the identified model is applied to detect the slipped belt faults and develop the virtual airflow meter. The experiment results reveal that the developed approach can effectively obtain the energy model of VFD-motor-fan systems and the model can be applied to effectively detect slipped belt faults and accurately calculate the fan airflow rate.

Integrating systems acquired from third parties and legacies has become of great necessity in companies. This is mainly due to the need to exchange information between entities, such as banks, suppliers, customers, allies, etc. Therefore, it is essential to guarantee the integrity of the data and keep the integration up to date with the changes that can occur. Furthermore, reducing the transaction risk and avoiding losing information is necessary. Implementing this complex task involving technological and business challenges requires appropriate architecture implementation. This article presents an architecture named Dynamic Canonical Data Model through agnostic messages. The contribution involves treating the low link in integrating software units, also called the integration of loosely coupled software units. In particular, it focuses on internal data and external data integration. The proposal reduces their integration, maintenance time, and cost, maximizing their scalability and promoting reuse. To illustrate their components, a case study undertaken at the Mexican Logistics Company Paquetexpress is presented. The company has evaluated different enterprise application integration systems over 26 years to achieve a standardized integration. The article describes an architecture designed and implemented for this delivery company in a real-world case. The implementation’s source code was registered in the National Registry of Copyrights of Mexico.