Efficient pairing computation on supersingular Abelian varieties

We present a general technique for the efficient computation of pairings on Jacobians of supersingular curves. This formulation, which we call the eta pairing, generalizes results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic 3. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma–Lee method. These ideas are applied to elliptic and hyperelliptic curves in characteristic 2 with very efficient results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.      

Multiple voting location and single voting location on trees

We examine voting location problems in which the goal is to place, based on an election amongst the users, a given number of facilities in a graph. The user preference is modeled by shortest path distances in the graph. A Condorcet solution is a set of facilities to which there does not exist an alternative set preferred by a majority of the users. Recent works generalize the model to additive indifference and replaced user majority by γ-proportion.     

Efficient frontier of utility and CVaR

We study the efficient frontier problem of maximizing the expected utility of terminal wealth and minimizing the conditional VaR of the utility loss. We establish the existence of the optimal solution with the convex duality analysis. We find the optimal value of the constrained problem with the sequential penalty function and the dynamic programming method.      

1,1,2,2-Tetrahydroperoxy-1,2-Diphenylethane: An efficient and high oxygen content oxidant in various oxidative reactions

Several oxidative approaches namely thiocyanation of aromatic compounds, epoxidation of alkenes, amidation of aromatic aldehydes, epoxidation of α, β-unsaturated ketones, oxidation of sulfides to sulfoxides and sulfones, bayer-villeger reaction, bromination and iodation of aniline and phenol derivatives oxidative esterification, oxidation of pyridines and oxidation of secondary, allylic and benzyllic alcohols were carried out using 1,1,2,2-Tetrahydroperoxy-1,2-Diphenylethane as the potential solid oxidant which can be stored for several months without any loss in its activity. All of the procedures were accomplished via mild reaction conditions and the products were afforded in high yields and short reaction times.     

A new proof approach to lower semicontinuity for parametric vector equilibrium problems

In this note, the lower semicontinuity of the set of efficient solutions to generalized systems is established by using a new proof method which is different from the one used in Gong (J Optim Theory Appl 138:197–205, 2008). Our result improve his corresponding one.     

On the density of proper efficient points

In this paper, our aim is to discuss the density of proper efficient points. As an interesting application of the results in this paper, we want to prove a density theorem of Arrow, Barankin, and Blackwell.

     

The solution of inverse radiation problems using an efficient computational technique

In our previous work (Park, Kim, JQSRT 58 (1) (1997) 115), an efficient computational technique for solving the radiative transfer equations for participating media has been devised, which is as accurate as the S₄ method but consumes much less computer time. In the present investigation, we employ this technique to solve an inverse radiation problem of determining the time-varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three-dimensional participating media where radiation and conduction occurs simultaneously. The present technique is found to identify the strength of the heat source efficiently without a priori information about the unknown function to be estimated.     

Constructing efficient solutions structure of multiobjective linear programming

It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure.