Are Branch and Bound and A* Algorithms Identical?

Heuristic Search and Branch and Bound algorithms have many similarities. In this paper, we address the question of the extent to which they are similar. We firstly show that these algorithms apply the same principles, although generating graphs with different properties: Heuristic Search can explore any kind of graphs, whereas the Branch and Bound algorithm generates particular graphs with a restrictive inheritance property. Nevertheless, we show that the Branch and Bound principles can be used to perform Heuristic Search. We conclude that the two types of algorithms are therefore essentially identical; they only differ at the interpretation level.     

Ètude des reactions de nitration de l'acetamido-3 ethyl-9 carbazole

The nitration of 3-acetamido-, 3-formamido- and 3-carbethoxyamino-9-ethylcarbazoles has been studied. Nitration of 3-acetamido-9-ethylcarbazole substituted the 6 position while 3-formamido- and 3-carbethoxyamino-9-ethylcarbazoles gave 4-nitro derivatives. The nitration of three compounds in the 4- and 6-positions was accomplished. Further substitution of 3-acetamido- and 3-carbethoxyamino- derivatives yielded the 4,6,8-trinitro compounds. Assignment of the structures was based on nmr spectral studies and on unequivocal syntheses.     

The smallest solutions to the diophantine equation

In this paper we discuss a method used to find the smallest nontrivial positive integer solutions to . The method, which is an improvement over a simple brute force approach, can be applied to search the solution to similar equations involving sixth, eighth and tenth powers.

     

Triazino-1,2,4-[4,5-a] indoles. V. Etude du dioxo-1,4 tetrahydro-1,2,3,4 triazino-1,2,4-[4,5-a] indole

1,4-Dioxo - 1,2,3,4- tetrahydro- 1,2,4- triazino[4,5-a] indole (1) was synthesized either by cyclising the N-carbethoxyhydraxizide of indole-2 carboxylic acid (4) or by alkaline rearrangement of 2-(2-indolyl)-5-oxadiazolone (6). The methylation reactions of the dilactam 1 were achieved with dimethyl sulfate or diazo-methane and afforded mixtures of O-methylated and N-methylated derivatives which were isolated and the structure of which were asigned. The tautomerism of dilactam 1 was studied using O-and N-methylated derivatives. The lactim-lactam structure 1a pre-ponderated in solution.     

Relation between silico-aluminous fly ash and its coal of origin

Fly ashes are typical complex solids which incorporate at the same time intrinsic properties derived from the layers （various mineralogical and dimensional spectra） and major transformations generated during prior processing. To use fly ashes in various applications, it is necessary to characterise them completely. The first research to date carried out on silico-aluminous fly ashes in order to characterise them physically, morphologically, chemically and mineralogically, resulted in the recognition that they are relatively simple materials. In the present study, a silico-aluminous fly ash coming from the power station of Albi （France） was selected. Heat treatment at 450 and 1200℃ together with coal simulated the treatment undergone by coal in the power station in order to mimic real coal residue. In conclusion, the diversity of the particles contained in fly ash could only be exolained by the relation existing between the fly ash and its coal of origin.     

Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic

We investigate in this paper the security of HFE and Multi-HFE schemes as well as their minus and embedding variants. Multi-HFE is a generalization of the well-known HFE schemes. The idea is to use a multivariate quadratic system—instead of a univariate polynomial in HFE—over an extension field as a private key. According to the authors, this should make the classical direct algebraic (message-recovery) attack proposed by Faugère and Joux on HFE no longer efficient against Multi-HFE. We consider here the hardness of the key-recovery in Multi-HFE and its variants, but also in HFE (both for odd and even characteristic). We first improve and generalize the basic key recovery proposed by Kipnis and Shamir on HFE. To do so, we express this attack as matrix/vector operations. In one hand, this permits to improve the basic Kipnis-Shamir (KS) attack on HFE. On the other hand, this allows to generalize the attack on Multi-HFE. Due to its structure, we prove that a Multi-HFE scheme has much more equivalent keys than a basic HFE. This induces a structural weakness which can be exploited to adapt the KS attack against classical modifiers of multivariate schemes such as minus and embedding. Along the way, we discovered that the KS attack as initially described cannot be applied against HFE in characteristic 2. We have then strongly revised KS in characteristic 2 to make it work. In all cases, the cost of our attacks is related to the complexity of solving MinRank. Thanks to recent complexity results on this problem, we prove that our attack is polynomial in the degree of the extension field for all possible practical settings used in HFE and Multi-HFE. This makes then Multi-HFE less secure than basic HFE for equally-sized keys. As a proof of concept, we have been able to practically break the most conservative proposed parameters of multi-HFE in few days (256 bits security broken in 9 days).     

Synthesis and Profiling of a Diverse Collection of Azetidine-Based Scaffolds for the Development of CNS-Focused Lead-like Libraries

The synthesis and diversification of a densely functionalized azetidine ring system to gain access to a wide variety of fused, bridged, and spirocyclic ring systems is described. The in vitro physicochemical and pharmacokinetic properties of representative library members are measured in order to evaluate the use of these scaffolds for the generation of lead-like molecules to be used in targeting the central nervous system. The solid-phase synthesis of a 1976-membered library of spirocyclic azetidines is also described.     

Synthesis and characterisation of the ethylene bridged permethylindenyl cerium complex [(EBI*)CeI(THF)

Synthesis, magnetic properties, NMR spectroscopy, and crystallographic details of an ethylene bridged hexamethylindenyl (EBI*) cerium iodide complex [(EBI*)CeI(THF)] are reported.     

Analytical Solution Incorporating History-Dependent Processes for Quick Assessment of Capillary Trapping During CO<Subscript>2</Subscript> Geological Storage

Carbon storage in saline formations is considered as a promising option to ensure the necessary decrease of CO₂ anthropogenic emissions. Its industrial development in those formations is above all conditioned by its safety demonstration. Assessing the evolution of trapped and mobile CO₂ across time is essential in the perspective of reducing leakage risks. In this work, we focus on residual trapping phenomenon occurring during the wetting of the injected CO₂ plume. History dependent effects are of first importance when dealing with capillary trapping. We then apply the classical fractional flow theory (Buckley–Leverett type model) and include trapping and hysteresis models; we derive an analytical solution for the temporal evolution of saturation profile and of CO₂ trapped quantity when injecting water after the gas injection (“artificial imbibition”). The comparison to numerical simulations for different configurations shows satisfactory match and justifies, in the case of industrial CO₂ storage, the assumptions of incompressible flow with no consideration of capillary pressure. The obtained analytical solution allows the quick assessment of both the quantity and the location of mobile gas left during imbibition.