The point decomposition problem over hyperelliptic curves

Computing discrete logarithms is generically a difficult problem. For divisor class groups of curves defined over extension fields, a variant of the Index-Calculus called decomposition attack is used, and it can be faster than generic approaches. In this situation, collecting the relations is done by solving multiple instances of the point m-decomposition problem (PDP\(_m\)). An instance of this problem can be modelled as a zero-dimensional polynomial system. Solving is done with Gröbner bases algorithms, where the number of solutions of the system is a good indicator for the time complexity of the solving process. For systems arising from a PDP\(_m\) context, this number grows exponentially fast with the extension degree. To achieve an efficient harvesting, this number must be reduced as much as possible. Extending the elliptic case, we introduce a notion of summation ideals to describe PDP\(_m\) instances over higher genus curves, and compare to Nagao’s general approach to PDP\(_m\) solving. In even characteristic we obtain reductions of the number of solutions for both approaches, depending on the curve’s equation. In the best cases, for a hyperelliptic curve of genus g, we can divide the number of solutions by \(2^{(n-1)(g+1)}\). For instance, for a type II genus 2 curve defined over \(\mathbb {F}_{2^{93}}\) whose divisor class group has cardinality a near-prime 184 bits integer, the number of solutions is reduced from 4096 to 64. This is enough to build the matrix of relations in around 7 days with 8000 cores using a dedicated implementation.     

Scheduling preparation of doses for a chemotherapy service

A fast realization of drugs is an important part in the quality of service of a hospital. In this paper we propose a scheduling method for the preparation of chemotherapy doses in order to reduce the patient waiting time. Two approaches have been defined: an off-line approach and a real time approach. The off-line approach is using a linear programming model for minimizing the maximum tardiness of jobs in a production day. This method is re-used during the real-time resolution combined with a greedy algorithm. The solution obtained respects constraints on the production center and the hospital organization. Our model is currently used in software which helps the decision maker of the service and allows increasing the patient satisfaction and the productivity of the service.     

New control massic polygon of a B-rational curve resulting from a homographic change of parameter

We deal with the homographic and affine change of parameter of rational curves represented as BR-curves. Forcomputational purposes in CAGD and CAM we determine the new massic polygon through four different methods and we study the particular case of Bézier curves among the applications.     

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.     

Phase equilibria modeling of biodiesel related mixtures using the GCA-EoS model

In this work, a group-contribution equation of state that takes into account association effects (GCA-EoS) is extended to model the phase behavior of fatty esters (biodiesel) in binary mixtures with glycerol, alcohols and water and ternary mixtures with glycerol and methanol. A new associating group (glycerol hydroxyl group: OH^Gly) was defined to take into consideration the association effects in the glycerol molecule. Self-association of methanol, water and glycerol and cross-association between methanol–glycerol, alcohol–ester, water–ester and glycerol–ester groups were considered. New pure-group, binary interaction and association parameters have been determined. The correlations and predictions of the model are found in acceptable agreement with selected experimental data reported in the literature.