Completeness and Admissibility for General Heuristic Search Algorithms—A Theoretical Study: Basic Concepts and Proofs

We propose a formal generalization for various works dealing with Heuristic Search in State Graphs. This generalization focuses on the properties of the evaluation functions, on the characteristics of the state graphs, on the notion of path length, on the procedures that control the node expansions, on the rules that govern the update operations. Consequently, we present the algorithm family and the sub-family Ã, which include Nilsson's A or A_* and many of their successors such as HPA, B, A ^* , A, C, BF^*, B, IDA^*, D, A^**, SDW. We prove general theorems about the completeness and the sub-admissibility that widely extend the previous results and provide a theoretical support for using diverse kinds of Heuristic Search algorithms in enlarged contexts, specially when the state graphs and the evaluation functions are less constrained than ordinarily.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

The Use of Non-Splitting Injection Techniques for Trace Analysis in Narrow-Bore Capillary Gas Chromatography

The use of hot splitless, cold splitless, and on-column injections for trace analysis in narrow-bore capillary GC is evaluated. Despite the low flow rates for the columns used, the required splitless times for splitless injections can be surprisingly short if liners with a small inside diameter are used. On-column injection can be applied by using an appropriate normal-bore precolumn coupled to the narrow-bore analytical column using a specially designed low dead volume column connector. The effects of the experimental conditions such as sample volume, injection temperature, and initial oven temperature on peak focusing and the discrimination and degradation behavior of the analytes are discussed. The possibilities to obtain sensitive and fast separations are illustrated by various applications.     

Host-guest interaction between cyclen based macrotricyclic ligands and phosphate anions. A potentiometric investigation

The host-guest interaction between orthophosphate, pyrophosphate and triphosphate anions and three cyclen based macrotricyclic ligands possessing ortho- (TOC), meta- (TMC) and para-xylenyl (TPC) linkers was investigated by potentiometric measurements. The ternary species present in solution and their stability constants have been determined. The different behaviours are explained in terms of hydrogen bond formation and coulombic attraction between the organic host and the inorganic guest. The selectivity, illustrated with species distribution diagrams, is discussed. The results unambiguously showed the importance of the distance between the two cyclen cores and emphasized the increasing of the triphosphate species selectivity together with the cavity size of the ligand. A comparison of the present results with those obtained with their mono-bridged homologues is also discussed.     

Cyclen based bis-macrocyclic ligands as phosphates receptors. A potentiometric and NMR study

The host-guest interaction between orthophosphate, pyrophosphate and triphosphate anions and four cyclen based bis-macrocycles ligands possessing ortho-(BOC), meta-(BMC), para-xylenyl (BPC) or 2,6-pyridinyl (BPyC) linker was investigated by potentiometric measurements and NMR spectroscopy. Each ligand gave protonated species in aqueous solution that further formed ternary complexes after binding with anions; these complexes were analyzed as a result of hydrogen bond formation and Coulombic attraction between the organic host and the inorganic guest. The equilibrium constants for all the detected species are reported and the selectivity, illustrated with species distribution diagrams, is discussed. The results unambiguously showed the importance of the distance between the two cyclen cores and underlined, especially for the triphosphate species, the contribution of the nitrogen atom of the pyridinyl spacer as a supplementary anchoring point in acidic medium.     

New intra-intermolecular criss-cross cycloaddition of unsymmetrical allenylazines with alkynes leading to three fused five-membered heterocycles

This report describes a new type of intra-intermolecular criss-cross cycloadditions. Thermal reactions of unsymmetrical allenylazines in the presence of alkynes led to three fused five-membered heterocycles in some cases. In the case of unsymmetrical substituted alkynes, a regioselectivity was observed. The molecular structures of all products are discussed. One X-ray crystal structure is also reported.     

Energetic 2,2‐Dimethyltriazanium Salts: A New Family of Nitrogen‐Rich Hydrazine Derivatives

Amination of 1,1‐dimethylhydrazine with NH₂Cl or hydroxylamine‐O‐sulfonic acid yields 2,2‐dimethyltriazanium (DMTZ) chloride ( 3 ) and sulphate ( 4 ), respectively. The DMTZ cation was paired with the nitrogen‐rich anions 5‐aminotetrazolate ( 5 ), 5‐nitrotetrazolate ( 6 ), 5,5′‐azobistetrazolate ( 7 ), and azide ( 8 ), yielding a new family of energetic salts. The synthesis was carried out by metathesis reactions of salts 3 or 4 and a suitable silver or barium salt. To minimize the risks involved when using heavy metal salts, we used electrodialysis for the synthesis of azide 8 , which avoids the use of highly sensitive species. The DMTZ derivatives were characterized by IR and multinuclear NMR spectroscopy, elemental analysis, and X‐ray diffraction. Thermal stabilities were measured using DSC analysis and their sensitivities towards classical stimuli were determined using standard tests. Lastly, the relationship between hydrogen bonding in the solid state and sensitivity is discussed.