On approximately monotone and approximately Hölder functions

Periodica Mathematica Hungarica - A real valued function f defined on a real open interval I is called $$\Phi $$ -monotone if, for all $$x,y\in I$$ with $$x\le y$$ it satisfies $$\begin{aligned}...     

Infeasible interior-point method for symmetric optimization using a positive-asymptotic barrier

We propose a new primal-dual infeasible interior-point method for symmetric optimization by using Euclidean Jordan algebras. Different kinds of interior-point methods can be obtained by using search directions based on kernel functions. Some search directions can be also determined by applying an algebraic equivalent transformation on the centering equation of the central path. Using this method we introduce a new search direction, which can not be derived from a usual kernel function. For this reason, we use the new notion of positive-asymptotic kernel function which induces the class of corresponding barriers. In general, the main iterations of the infeasible interior-point methods are composed of one feasibility and several centering steps. We prove that in our algorithm it is enough to take only one centering step in a main iteration in order to obtain a well-defined algorithm. Moreover, we conclude that the algorithm finds solution in polynomial time and has the same complexity as the currently best known infeasible interior-point methods. Finally, we give some numerical results.     

Satisfactory graph partition,variants, and generalizations

The Satisfactory Partition problem asks for deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [M. Gerber, D. Kobler, Algorithmic approach to the satisfactory graph partitioning problem, European Journal of Operational Research 125 (2000) 283–291] and studied further by other authors. In this paper we first review some applications and related problems. Then, we survey structural, complexity, and approximation results obtained for Satisfactory Partition and for some of its variants and generalizations. A list of open questions concludes this survey.     

Co-Jacobian for Lipschitzian Maps

The notion of co-Jacobian is introduced for locally Lipschitz functions acting between arbitrary normed spaces. The main results of this paper provide a characterization, calculus rules, a mean value theorem, as well as the computation of the co-Jacobian of piecewise smooth functions. Comparisons with known differentiability notions and Mordukhovich’s co-derivatives are derived.     

Bin covering with a general profit function: approximability results

In the recent paper (Benk? et al. 2010) we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a “good and fast” packing or covering. In the present paper we investigate the offline case. For the analysis, a novel view on “offline optimum” is introduced, which appears to be relevant concerning all problems where a final solution is ordering-dependent. We prove that if the item sizes are not allowed to be arbitrarily close to zero, then an optimal offline solution can be found in polynomial time. On the other hand, for unrestricted problem instances, no polynomial-time algorithm can achieve an asymptotic approximation ratio better than 6/7 if $P\ne NP$ .     

Transition between the Lagrange and Hermite–Fejér interpolations. I (Trigonometric case)

We construct a special class of discrete φ-summations to describe the transition between the well known (trigonometric) Lagrange and Hermite–Fejér interpolations. We give general properties, operator norm and convergence order for these cases.     

Measurement of production date (age) of nanogram amount of uranium

JRC-Karlsruhe obtained a swipe sample from a highly enriched uranium seizure, which had taken place in 2011. Due to the very low amount of uranium (nanograms) a new method needed to be developed to determine the U production date (age). The particles on the swipe were collected on a pyrolytic graphite planchet using a vacuum impactor and they were subsequently leached with ccHNO₃. The “bulk” U isotopic composition (²³⁵U: 72.51?±?0.03 wt%) and the production date (December 1992?±?1 year) determined by MC-ICP-MS indicated that the material showed similarity with two other HEU cases seized earlier in Europe.

     

An extension of the Rådström cancellation theorem to cornets

Semigroup Forum - The aim of this paper is to introduce the notion of cornets, which form a particular subclass of ordered semigroups also equipped with a multiplication by natural numbers. The...