The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

We propose a novel method to review K ⊢ φ when K and φ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem

Computing the Clique-width of Cactus Graphs

Similar to the tree-width (twd), the clique-width (cwd) is an invariant of graphs. A well known relationship between tree-width and clique-width is that cwd(G) ≤ 3 · 2twd(G)−1. It is also known that tree-width of Cactus graphs is 2, therefore the clique-width for those graphs is smaller or equal than 6. In this paper, it is shown that the clique-width of Cactus graphs is smaller or equal to 4 and we present a polynomial time algorithm which computes exactly a 4-expression

Low-Exponential Algorithm for Counting the Number of Edge Cover on Simple Graphs

A procedure for counting edge covers of simple graphs is presented. The procedure splits simple graphs into non-intersecting cycle graphs. This is a “low exponential” exact algorithm to count edge covers for simple graphs whose upper bound in the worst case is O(1.465575(m−n) × (m + n)), where m and n are the number of edges and nodes of the input graph, respectively

Estimation of effective diffusion coefficient and its effect on effectiveness factor for hds catalytic process: a multi-scale approach

Effectiveness factors have great relevance in multiphase reactors modeling since they are the conventional way of incorporating the effects of intra-particle resistance reaction rate. This work determines the description level effect of catalytic pellet microstructure on mass and energy effective transport coefficients prediction, isothermal and no isothermal. For such a purpose some results about on evaluation of the effective diffusivity and conductivity with the methodology of volume averaging were applied. The obtained results along with a Langmuir–Hinshelwood/Hougen–Watson kinetic expression were applied to establish the concentration and temperature fields in a catalytic particle. The evaluation of concentration field and effectiveness factors were developed using two different models: pseudohomogeneous mass and energy transport model for a catalytic particle with reaction in all domain, and heterogeneous mass and energy transport model with fluid-catalytic surface interphase reaction for a realistic porous structure model. The results show the differences in concentration and temperature profiles between both models and consequently in effectiveness factors. This could be ascribed to the form of evaluation of effective transport coefficients used in the pseudo-homogeneous model, and presumably to the simple shape of the unit cells used for the solution of the closure problem for the average transport equations with homogeneous reaction

CFD Analysis of BED Textural Characteristics on TBR Behavior: Hydrodynamics and Scaling-up

In recent years, CFD has played an important role in the understanding and design of TBR’s. In this work, through CFD with Eulerian approach, a three-phase heterogeneous reactor model was developed, were the accuracy of Interfacial Momentum Exchange Model (IMEM) for the gas-solid interaction, the effect of a more detailed catalytic bed geometry description, and the pellet shape over TBR hydrodynamics of two fluid phases interacting with the solid phase was studied. Then, a second model was developed, where the validated hy- drodynamic model was coupled with mass transport for an HDS process of light gasoil. Additionally, in order to insight into the scaling up process of a TBRs, the proposed columns behaviors were compared against lit- erature columns using four different ways, and it was found that the best predictions were obtained when the models’ holdup were equaled to those evaluated in literature columns. Since in reliable literature deviations in pressure drop predictions of around 30% can be found, the model results show significant improvement against literature, achieving 5 times better accuracy in predicting pressure drops, and 50% improvement in holdup prediction; the coupled model reproduces the same conversion values compared with literature data, and predicts conversions with 95% accurac

Extremsl Polygonal Arrays for the Merrifield-Simmons Index

For any polygonal array, independently of the number of sides on each polygon the zig-zag polygonal array has the extremal minimum value for the Merrifield-Simmons index. This result generalises a well known fact obtained for hexagonal chains

Exteding Extremal Polygonal Arrays for the Meriifield-Simmons Index

Polygonal array graphs have been widely investigated, and they represent a relevant area of interest in mathematical chemistry because they have been used to study intrinsic properties of molecular graphs. For example, to determine the Merrifield-Simmons index of a polygonal array An that is the number of independent sets of that graph, denoted as i(An)