Continuous symmetry of C60 fullerene and its derivatives

Conventionally, the Ih symmetry of fullerene C60 is accepted which is supported by numerous calculations. However, this conclusion results from the consideration of the molecule electron system, of its odd electrons in particular, in a close-shell approximation without taking the electron spin into account. Passing to the open-shell approximation has lead to both the energy and the symmetry lowering up to Ci. Seemingly contradicting to a high-symmetry pattern of experimental recording, particularly concerning the molecule electronic spectra, the finding is considered in the current paper from the continuous symmetry viewpoint. Exploiting both continuous symmetry measure and continuous symmetry content, was shown that formal Ci symmetry of the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the fullerene monoderivatives gives a reasonable explanation of a large variety of their optical spectra patterns within the framework of the same C1 formal symmetry exhibiting a strong stability of the C60 skeleton.Comment: 11 pages. 5 figures. 6 table

Modeling the interaction of computer errors by four-valued contaminating logics

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics

Getting the strain under control: Trans-Varestraint tests for hot cracking susceptibility

A new method for conducting Trans-Varestraint tests for assessing hot cracking susceptibility is proposed. Experiments were carried out, to validate the new method, with an industrial scale rig using tungsten inert gas welding. The hot cracking susceptibility of API-5L X65 and EN3B steel was compared. The results indicated that, by using the new method, the strain applied to the welding bead and consequently to the solidification front was controlled in a repeatable and reliable way. The results also indicated that EN3B has a maximum crack length (a parameter in the test) higher than X65 and it is reached at lower augmented strain thus demonstrating it is more susceptible to hot cracking, while also indicating that there is a capability of predicting the initiation position of hot cracks during welding. By using the method proposed, the capability of setting standardized test procedures for Trans-Varestraint tests is improved. It is recommended that future tests for assessing hot cracking susceptibility should employ the proposed method in order for the results to be comparable and to also study the effect of strain rate in hot cracking of materials