Extending the dynamics underlying the factorization calculation of two-body decays, we propose simple selection rules for nonresonant three-body B decays. We predict, for instance, that in the Dalitz plot of B → D0π+π−, practically no events should be found in the corner region of E(π) ≤ ΛQCD as compared with the corner of E(π−) ≤ ΛQCD. We also predict that there should be very few three-body d...

We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages {x̄n}n≥1 of sequences with terms in a given finite set {a1, ..., ar}. For every such set we completely characterize the numbers Π (”intermediate values”) with the property that the consecutive averages {x̄n} of every sequence {xn}n≥1 with terms in {a1, ..., ar} cannot increase from a value x̄k < Π ...

H. Steinhaus has asked whether inside each acute triangle there is a point from which perpendiculars to the sides divide the triangle into three parts of equal areas. We present two solutions of Steinhaus’ problem. The n-dimensional case of Theorem 1 below was proved in [6], see also [2] and [4, Theorem 2.1, p. 152]. For an earlier mass-partition version of Theorem 1, for bounded convex masses ...

We generalize a theorem of Burde and de Rham characterizing the zeros of the Alexander polynomial. Given a representation of a knot group π, we define an extension π̃ of π, the Crowell group. For any GLNC representation of π, the zeros of the associated twisted Alexander polynomial correspond to representations of π̃ into the group of dilations of C . A classic theorem of G. Burde, and independen...

Excitation spectra of cation and anion radicals of unsaturated hydrocarbons, hexatriene(±), octatetraene(±), cyclopentadiene(+), 1,3-cyclohexadiene(+), and naphthalene(±), were studied by the symmetry adapted cluster-configuration interaction (SAC-CI) method. The calculated results reasonably reproduced the experimental spectra observed by one of the authors (T.S.) and gave reasonable assignmen...

Miniature and energy efficient propulsion systems hold the key to maturing the technology of swimming microrobots. In this paper, two new methods of propulsion inspired by the motility mechanism of prokaryotic and eukaryotic microorganisms are proposed. Hydrodynamic models for each of the two methods are developed and the optimized design paramteres for each of the two propulsion modes are demo...

In the field of case-based and rule-based reasoning in artificial intelligence, the general formal derivation of so-called similarity measures is still an unresolved open question. In this work the theoretical framework of dimensional analysis is used to derive appropriate similarity measures for a case-based and rule-based reasoning technique. For the subclass of case descriptions in engineeri...

stability of the π-π stacking interactions in the ben||substituted-coronene and hfben||substituted-coronene complexes was studied using the computational quantum chemistry methods (where ben and hfben are benzene and hexaflourobenzene, || denotes π-π stacking interaction, substituted-coronene is coronene molecule which substituted with four x groups, and x= nh2, ch3, oh, h, f, cf3, cn and no). ...

The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density p(t) evolved as iterative map, p(t) = M(t)p(t−∆t) under detail balanced transition matrix M(t), and (2) the invariant phase density π(t) = M(t)∞π(t). A virtual measurement protocol is employed, where variational entropy is zero, generating exact expressions for irreversible entropy cha...

HF level of ab initio calculations with basis-set 6-31G including full counterpoise correction hasbeen applied to compute the AspHis potential with the Ser and HisSer potential with the Asp inAspHisSer trimer. The potential energy surface has a minimum of -16.765 kcal/mol in R1=1.912nm and R2=2.719 nm. The optimum computed curves for two interactions were fitted withintermolecular pair potentia...