The multiple judge,multiple criteria ranking problem: A fuzzy set approach

This paper investigates the problem of selecting, from a set of issues, those which best satisfy a collection of criteria. A group of judges have fuzzy sets defined over the issues, for each criterion, whose values lie in a finite linearly ordered set $\text{L}$. These judges also have fuzzy sets defined over the set of criteria. The paper discusses methods of aggregating all the fuzzy sets into one fuzzy set μ, defined on the issues, so that μA?L gives the final ranking for issue A.     

Electrical and phase behaviour of the system AgI-PbI2

Mixtures of AgI and PbI₂ form a phase stable at temperatures above 125°C with a substantial solid solubility about the composition 67% AgI, this phase exhibits a high electrical conductivity (～0.1S m^-1). A proposal is made for the basic form of the AgI-PbI₂ equilibrium diagram below 200°C, and comparison made to the systems AgI-ZnI₂ and AgI-CdI₂.     

The majority rule game

All knownvon Neumann-Morgenstern solutions to the majority rule game, (n, k), wheren/2, are discussed. The partitioning and discrimination to the limit solutions are expanded. The problem of interpreting experimental outcomes to games is discussed. We introduce the notion of a historical context of a conflict situation to aid in the prediction and explanation of solutions. Experimental results for the (4, 3) and (5, 3) games are used in our discussion.     

On graphs containing a given graph as center

We examine the problem of embedding a graph H as the center of a supergraph G, and we consider what properties one can restrict G to have. Letting A(H) denote the smallest difference ∣V(G)∣ - ∣V(H)∣ over graphs G having center isomorphic to H it is demonstrated that A(H) ≤ 4 for all H, and for 0 ≤ i ≤ 4 we characterize the class of trees T with A(T) = i. for n ≥ 2 and any graph H, we demonstrate a graph G with point and edge connectivity equal to n, with chromatic number X(G) = n + X(H), and whose center is isomorphic to H. Finally, if ∣V(H)∣ ≥ 9 and k ≥ ∣V(H)∣ + 1, then for n sufficiently large (with n even when k is odd) we can construct a k-regular graph on n vertices whose center is isomorphic to H.     

Admissible measures in one dimension

In this note we show that -admissible measures in one dimension (i.e. doubling measures admitting a -Poincaré inequality) are precisely the Muckenhoupt -weights.

     

How can we test the neutrino mass seesaw mechanism experimentally?

The seesaw mechanism for the small neutrino mass has been a popular paradigm, yet it has been believed that there is no way to test it experimentally. We present a conceivable outcome from future experiments that would convince us of the seesaw mechanism. It would involve data from the CERN Large Hadron Collider, International Linear Collider, cosmology, underground, and low-energy flavor experiments to establish the case.     

Microstructural changes in irradiated silica based glasses

High voltage electron microscopy studies have been performed on irradiated pure silica and borosilicate glasses to check their long-term stability when these materials are employed near high energy radioactive sources, such as in fusion reactors and during the storage of nuclear waste. The intense energetic beam of electrons produced by the Harwell 1 MeV microscope, ranging from 10¹⁷ to 10²⁰ e/cm²/s has been focused upon specimens of various composition and impurity content at different temperatures up to about 850°C. Pure silica samples have also been bombarded with 46.5 MeV Ni+6 ions at the Variable Energy Cyclotron. It is found that while no significant changes are detectable in pure irradiated silica, clear evidence is present in complex borosilicate glasses for the growing of large defect clusters (over 1000 Å, resembling gas bubbles) after electron doses of about 8.5 × 10¹⁹ e/cm² and dose rates exceeding 2 × 10¹⁸ e/cm²/sec. Moreover, small regions, about 100 Å wide, scattering electrons more than the matrix are also present. The nature of this fine microstructure has been established as a phase separation into crystalline tridymite. The observations are discussed in terms of their dependence on temperature, sample thickness, dose and dose rates.