I analyze the hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal. Many of these cardinals are defined by modifying the definition of a high-jump cardinal. A high-jump cardinal is defined as the critical point of an elementary embedding j : V → M such that M is closed under sequences of length sup{ j(f)(κ) | f : κ→ κ }. Some of the other cardinals analyzed i...

With less than 0# two generic extensions of L are identified: one in which א1, and the other א2, is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in [6], and answers some questions raised there. Also, main results of [5] are generalizedassumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it ...

For any graph G, let ni be the number of vertices of degree i, and λ(G) = maxi≤j{ ni+···+nj+i−1 j }. This is a general lower bound on the irregularity strength of graph G. All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite ...

There is a well-known global equivalence between Σ2 sets having the Universal Baire property, two-step Σ3 generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of Σ2 sets being (2 )-cc Universally Baire, which is below 0. In a model obtained, there is a Σ2 set which is weakly ω2-Universally Baire but not ω2-Uni...

Tensile strength is one of the important strength parameters of concrete. Indirect methods have been used up till now for its measurement. These methods though widely accepted, do not furnish the true tensile strength of concrete. This paper presents a new approach for the experimental determination of true tensile strength of concrete. Results obtained by this test are quite encouraging and sh...

Continuous stress–strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally...

This study reports the synthesis and evaluation of a novel furanone-containing antibacterial resin composite. Compressive strength (CS) and S. mutans viability were used to evaluate the mechanical strength and antibacterial activity of the composites. With 5% to 30% addition of the furanone derivative, the composite showed no change in CS but a significant antibacterial activity with a 16% 68% ...