String model with mesons and baryons in modified measure theory

We consider string meson and string baryon models in the framework of the modified measure theory, the theory that does not use the determinant of the metric to construct the invariant volume element. As the outcome of this theory, the string tension is not placed ad hoc but is derived. When the charges are presented, the tension undergoes alterations. In the string meson model there are one string and two opposite charges at the endpoints. In the string baryon model, there are two strings, two pairs of opposite charges at the endpoints and one additional charge at the intersection point, the point where these two strings are connected. The application of the modified measure theory is justified because the Neumann boundary conditions are obtained dynamically at every point where the charge is located and Dirichlet boundary conditions arise naturally at the intersection point. In particular, the Neumann boundary conditions that are obtained at the intersection point differ from that considered before by ’t Hooft in arXiv:hep-th/0408148 and are stronger, which appears to solve the nonlocality problem that was encountered in the standard measure approach. The solutions of the equations of motion are presented. Assuming that each endpoint is the dynamical massless particle, the Regge trajectory with the slope parameter that depends on three different tensions is obtained.

H/D isotope effect on the molar volume and thermal expansion of benzene

Time-of-flight neutron powder diffraction data have been collected from C6H6 and C6D6 between 10 and 276 K, revealing no cross-over in their molar volumes and an almost temperature invariant volume-isotope-effect, in contrast with previously published work.

Astheno–Kähler and Balanced Structures on Fibrations

We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, strong Kähler with torsion (SKT), and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then we provide a construction of astheno-Kähler structures on torus bundles over Kähler manifolds leading to new examples. In particular, we find examples of compact complex non-Kähler manifolds which admit a balanced and an astheno-Kähler metric, thus answering to a question in [52] (see also [24]). One of these examples is simply connected. We also show that the Lie groups SU(3) and G2 admit SKT and astheno-Kähler metrics, which are different. Furthermore, we investigate the existence of balanced metrics on compact complex homogeneous spaces with an invariant volume form, showing in particular that if a compact complex homogeneous space M with invariant volume admits a balanced metric, then its first Chern class c1(M) does not vanish. Finally we characterize Wang C-spaces admitting SKT metrics.

Reducing Risk Through Inversion and Self-Strengthening

A number of new techniques for reliability improvement and risk reduction based on the inversion method, such as: ‘inverting design variables,' ‘inverting by maintaining an invariant,' ‘inverting resulting in a reinforcing counter-force,' ‘negating basic required functions' and ‘moving backwards to general and specific contributing factors' have been introduced for the first time. By using detailed calculations, it has been demonstrated how the new technique ‘repeated inversion maintaining an invariant' can be applied to reduce the risk of collision for multiple ships travelling at different times and with variable speeds. It has been demonstrated that for pressure vessels, an inversion of the geometric parameters by maintaining an invariant volume could result not only in an increased safety but also in a significantly reduced weight. The method of self-strengthening (self-reinforcement) has been introduced for the first time as a systematic method for improving reliability and reducing risk. The method of self-strengthening by capturing a proportional compensating factor and the method of self-strengthening by creating a positive feedback loop have been proposed for the first time as reliability improvement tools. Finally, classifications have been proposed of methods and techniques for risk reduction based on the methods of inversion and self-strengthening.

A VOLUME FORM ON THE KHOVANOV INVARIANT

The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This defines a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister moves to give an invariant volume on the Khovanov homology. In this paper, its construction and invariance under these moves is demonstrated. Also, some examples of the invariant are presented for particular choices for the bases of homology groups to obtain a numerical invariant of knots and links. In these examples, the algebraic torsion seen in the Khovanov chain complex when homology is computed over ℤ is recovered.

The Calabi–Yau equation on the Kodaira–Thurston manifold

We prove that the Calabi–Yau equation can be solved on the Kodaira–Thurston manifold for all given T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.