Algebraic logoi

We introduce normal cores, as well as the more general action cores, in the context of a semi-abelian category, and further generalise those to split extension cores in the context of a homological category. We prove that, if the category is moreover well-powered with (small) joins, then the existence of split extension cores is equivalent to the condition that the change-of-base functors in the fibration of points are geometric. We call a finitely complete category that satisfies this condition an algebraic logos. We give examples of such categories, compare them with algebraically coherent ones, and study equivalent conditions as well as stability under common categorical operations.     

Dynamic control of split flow in packed column supercritical fluid chromatography using dual resistively heated restrictors

Remote control of the vent/detector split flow ratio in packed column supercritical fluid chromatography (pSFC) with flame ionization detector (FID) is demonstrated using a dual heated restrictor method. Restrictors stemming from a Tee at the separation column outlet were, respectively, fixed into an FID and a vent port, and their individual temperatures were controlled using resistively heated wires. Subsequently, both system pressure and split flow could be manipulated. For example, for applied restrictor temperatures examined up to 600°C, corresponding vent/FID split flow ratios between 2 and 7 were observed depending on the port heated. As well, column pressures around 16–23 MPa were also achievable over the same range. Conversely, isobaric altering of the split flow ratio was possible when opposing positive and negative temperature gradients were applied at the two restrictors. Under these conditions, the system pressure varied less than 1% RSD over a 10 min period. As an application, the method was used to establish stable detector operation in the analysis of n‐alkanes under pSFC‐FID conditions that initiated flame instability. Results indicate that this technique could be a relatively simple and inexpensive means of controlling system pressure and detector split flow ratios in pSFC‐FID.     

On distance two graphs of upper bound graphs

For a poset P=(X,≤), the upper bound graph (UB-graph) of P is the graph U=(X,E_U), where uv∈E_U if and only if u≠v and there exists m∈X such that u,v≤m. For a graph G, the distance two graph DS₂(G) is the graph with vertex set V(DS₂(G))=V(G) and u,v∈V(DS₂(G)) are adjacent if and only if d_G(u,v)=2. In this paper, we deal with distance two graphs of upper bound graphs. We obtain a characterization of distance two graphs of split upper bound graphs.     

On the complexity of cutting-plane proofs using split cuts

We prove a monotone interpolation property for split cuts which, together with results from Pudlák (1997) [20], implies that cutting-plane proofs which use split cuts (or, equivalently, mixed-integer rounding cuts or Gomory mixed-integer cuts) have exponential length in the worst case.     

On interval-subgradient and no-good cuts

Interval-gradient cuts are (nonlinear) valid inequalities derived from continuously differentiable nonconvex constraints. In this paper we define interval-subgradient cuts, a generalization to nondifferentiable constraints, and show that no-good cuts with 1-norm are a special case of interval-subgradient cuts. We then briefly discuss what happens if other norms are used.     

Analysis of split weighted least-squares procedures for pseudo-hyperbolic equations

In this paper, we introduce two novel split weighted least-squares finite element procedures for pseudo-hyperbolic equations arising in the modelling of nerve conduction process. By selecting the weighted least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable. Optimal order error estimates are developed and the numerical example is given to show the efficiency of the introduced schemes.     

Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs

Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data uncertainty appears in the problem is made, and it is shown how a valid inequality derived for one scenario can be made valid for other scenarios, potentially reducing solution time. Computational results amply demonstrate the effectiveness of disjunctive cuts in solving several large-scale problem instances from the literature. The results are compared to the computational results of disjunctive cuts based on the subproblem space of the formulation and it is shown that the two methods are equivalently effective on the test instances.     

New structural parameters of fullerenes for principal component analysis

The Kekulé structure count and the permanent of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q, r, q/p and r/p, where p is the number of edges common to two pentagons, q is the number of vertices common to three pentagons and r is the number of pairs of nonadjacent pentagons adjacent to another common pentagon. The cluster analysis of the structural parameters allows classification these parameters. Principal component analysis (PCA) of the structural parameters and the cluster analyses of the fullerenes permit their classification. PCA clearly distinguishes five classes of fullerenes. The cluster analysis of fullerenes is in agreement with PCA classification. Cluster analysis shows greatest similarity for the q–q/p and r–r/p pairs. PCA provides five orthogonal factors F ₁–F ₅. The use of F ₁ gives an error of 28%. The inclusion of F ₂ decreases the error to 2%.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap.