In spite of the parity relations between medieval towns and their country surroundings high level development settlement structures tracked during wide-scale research settlements Southern Russ, new excavations in non-fortified keep brining certain discoveries. This is remarkable at Khodosivka-Roslavske found by Northern Expedition 2007. The working over results 2007—2011 allowed testify highly-...

Almost everywhere you can come across hanging chains and cables. Examples are necklaces, power lines, and cables that support a bridge surface. Do these cables all hang in the same mathematical shape? The first thought of many a pupil will be: this is a parabola, isn't it? In the computer learning environment Coach you can easily measure this on digital images. It will turn out that the parabol...

Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tightbinding model. We address the transport properties in all regimes ballistic, diffusive (metallic), localized and crossover between the latter two. Special attention is given to the region close to the conduction band center, but even there the Anderson localization persists, without signs of...

We prove a very natural generalization of the Borsuk-Ulam antipodal Theorem and deduce from it, in a very straightforward way, the celebrated result of Alon [1] on splitting necklaces. Alon’s result says that t(k− 1) is an upper bound on the number of cutpoints of an opened t-coloured necklace so that the segments we get can be used to partition the set of vertices of the necklace into k subset...

Decaying superheavy particles can be produced by Topological Defects or, in case they are quasistable, as relics from the early Universe. The decays of these particles can be the sources of observed Ultra High Energy Cosmic Rays (E ∼ 10 − 10 GeV ). The Topological Defects as the UHE CR sources are critically reviewed and cosmic necklaces and monopole-antiminopole pairs are identified as most pl...

Monodisperse and size-controlled polymer particles were produced without surfactant or washcoat from O/W monomer emulsions and “on the fly” polymerization under UV irradiation in a very simple needle/tubing system. The effect of the viscosity of the continuous phase on the size of final particles was investigated. The capillary number ratio was found to be relevant to predict the size of the dr...

Cognitive deficits experienced by older adults with dementia limit use of wearable devices (necklaces or bracelets) that summon assistance after the older adult falls. To use these wearable devices, older adults must choose to wear them, remember how to use them, and be conscious after falling. Devices such as the Smart Carpet substitute pre-programmed or automatic functions for functions requi...

The current status of origin of Ultra High Energy Cosmic Rays (UHECR) is reviewed, with emphasis given to elementary particle solutions to UHECR problem, namely to Topological Defects and Super-Heavy Dark Matter (SHDM) particles. The relic superheavy particles are very efficiently produced at inflation. Being protected by gauge discrete symmetries, they can be long lived. They are clustering in...

The Kula Ring described by Bronislaw Malinowski is a system of the ceremonial exchange of gifts among a number of tribal societies inhabiting various island groups in the region east of Papua New Guinea. Two ceremonial gifts continually circulate in opposite directions: necklaces clockwise and armshells counterclockwise. After a brief description of the social system of Kula exchange, a game-th...

We present a class of languages that have an interesting property: For each language L in the class, both the classic greedy algorithm and the classic Lyndon word (or necklace) concatenation algorithm provide the lexicographically smallest universal cycle for L. The languages consist of length n strings over {1, 2, . . . , k} that are closed under rotation with their subset of necklaces also be...