In the present research, the aqueous suspensions of nano-sized YSZ particles were prepared using a common and available dispersant (Dolapix CE64) at different pH values and their stability were evaluated through the sedimentation height, viscosity measurement, and microstructural observation. Different amounts of dispersant were tested and the optimum percentage was examined by measuring the vi...

Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem. The robust APTAS receives a single input item to be added to the packing at each step. It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item. At each step, the total size of items which may migrate between bins mu...

A new short proof is given for Brandt and Harrington's theorem about conformal uniformizations of planar nitely connected domains as domains with boundary components of speciied shapes. This method of proof generalizes to periodic domains. Letting the uniformized domains degenerate in a controlled manner, we deduce the existence of packings of speciied shapes and with speciied combinatorics. Th...

Classifications of published research place new results in a historical context and in so doing identify open problems. An example in wide use classifies results in scheduling theory according to a scheme originated by Graham, Lawler, Lenstra and Rinnooy Kan [10]. A similar effort was made by Dyckhoff [6] for cutting and packing problems. Such classification schemes can be combined with compreh...

We consider the bin packing problem with d different item sizes si and item multiplicities ai, where all numbers are given in binary encoding. This problem formulation is also known as the 1-dimensional cutting stock problem. In this work, we provide an algorithm which, for constant d, solves bin packing in polynomial time. This was an open problem for all d ≥ 3. In fact, for constant d our alg...

The linear coupling method was introduced recently by Allen-Zhu and Orecchia [14] for solving convex optimization problems with first order methods, and it provides a conceptually simple way to integrate a gradient descent step and mirror descent step in each iteration. In the setting of standard smooth convex optimization, the method achieves the same convergence rate as that of the accelerate...

BACKGROUND Comparative genomic analysis has revealed that in each genome a large number of open reading frames have no homologues in other species. Such singleton genes have attracted the attention of biochemists and structural biologists as a potential untapped source of new folds. Cthe_2751 is a 15.8 kDa singleton from an anaerobic, hyperthermophile Clostridium thermocellum. To gain insights ...

The paper is dealing with the problem of finding the densest packings of equal circles in the unit square. Recently, a global optimization method based exclusively on interval arithmetic calculations has been designed for this problem. With this method it became possible to solve the previously open problems of packing 28, 29, and 30 circles in the numerical sense: tight guaranteed enclosures w...