Rational Generalised Moonshine from abelian orbifoldings of the Moonshine Module

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p=2,3,5,7 and the other of order pk for k=1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational modular functions for the Monster centralisers related to the Baby Monster, Fischer, Harada-Norton and Held sporadic simple groups. We also derive non-trivial constraints on the possible Monster conjugacy classes to which the elements of the orbifolding abelian group may belong.     

Framed Vertex Operator Algebras, Codes and the Moonshine Module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ?, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge ? are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras. Received: 14 July 1997 / Accepted: 8 September 1997     

Orbifolds,Hopf algebras,and the Moonshine

We describe the modular properties and fusion rules of holomorphic orbifold models by Hopf algebraic techniques, using the representation theory of the orbifold quantum group. We apply this theory to the construction of generalized Thompson series, and discuss its connections with Moonshine.     

On the uniqueness of harmonic coordinates

Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose across the material boundary, and on the conditions at infinity and at a suitable point inside the matter. This is illustrated in detail by simple fully solvable examples of static spherically symmetric spacetimes in global harmonic coordinates. Examples of stationary electrovacuum spacetimes described simply in harmonic coordinates are also given. They can represent the exterior fields of material discs.The use of an appropriate background metric considerably simplifies the calculations.Dedicated to Prof. Jirí Horáek on the occasion of his 60th birthday Undoubtedly, Jirí has been using harmonic coordinates — in flat space these are the Cartesian coordinates — in his quantum calculations happily for years. We hope that his sense for harmony in music and life will also appreciate the harmonic gauge in curved spacetimes ....     

On the uniqueness of Planck's constant

It is shown that, for the case of two different particles associated with two different Planck constants, an appropriate generalized center-of-mass transformation allows one to retain the relevant constants of the motion. Therefore, some of the problems arising from the (postulated or experimentally determined) existence of several quantization constants appear to be avoidable.     

On the relationship between Twistors and Clifford algebras

Basis p-forms of a complexified Minkowski spacetime can be used to realize a Clifford algebra isomorphic to the Dirac algebra of matrices. Twistor space is then constructed as a spin space of this abstract algebra through a Witt decomposition of the Minkowski space. We derive explicit formulas relating the basis p-forms to index one twistors. Using an isomorphism between the Clifford algebra and a space of index two twistors, we expand a suitably defined antisymmetric index two twistor basis on p-forms of ranks zero, one, and four. Together with the inverse formulas they provide a complete passage between twistors and p-forms.     

On the relationship between eulerian and lagrangian turbulent diffusivities

In homogeneous turbulence the eulerian and lagrangian diffusivities of a scalar field are equal. A procedure is described for relating them in inhomogeneous turbulence.     

On the relationship between Killing tensors and Killing-Yano tensors

The conditions that a Killing tensor of order 2 be the contracted product of a Killing-Yano tensor of order 2 with itself are found. All Killing-Yano tensors of order 2 admitted in empty space-times are obtained     

On the relationship between the entropy and enthalpy of interfacial segregation

The general relationship between the excess entropy and enthalpy of segregation is elucidated in terms of basic thermodynamical principles applied to the bulk-interface equilibrium. The linearity reported in several studies of different grain boundary or surface orientations in alloys is accounted for in case at some temperature, the excess entropy varies much more strongly than the ideal solution configurational contribution to the segregation entropy. The theoretical analysis done for monolayer segregation (e.g., of non-metal impurity), shows that the linear relationship can be explicitly quantified by means of a quasi-isotropic interfacial segregation level and the corresponding temperature, and without introducing significant error in case of multilayer segregation.     

On the relationship between various types of kinetic equations

Ryazan Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 10, pp. 944–948, October, 1993.     

On the relationship between identification and discrimination of non-native nasal consonants

To examine the relationship between the identification and discrimination of non-native sounds, nasal consonants varying in place of articulation from Malayalam, Marathi, and Oriya were presented in two experiments to seven listener groups varying in their native nasal consonant inventory: Malayalam, Marathi, Punjabi, Tamil, Oriya, Bengali, and American English. The experiments consisted of a categorial AXB discrimination test and a forced-choice identification test with category goodness ratings. The identification test results were used to classify the non-native contrasts as one of five "assimilation types" of the Perceptual Assimilation Model (PAM) that are predicted to vary in their relative discriminability: two-category (TC), uncategorizable-categorizable (UC), both uncategorizable (UU), category-goodness (CG), and single-category (SC). The results showed that the mean percent correct discrimination scores of the assimilation types, but not the range of scores, were accurately predicted. Furthermore, differences in category goodness ratings in the CG and SC assimilations that were predicted to correlate with discrimination showed a weak, but significant correlation (r= 0.3 1, p<0.05). The implications of the results for models of cross-language speech perception were discussed, and an alternative model of cross-language speech perception was outlined, in which the discriminability of non-native contrasts is a function of the similarity of non-native sounds to each other in a multidimensional, phonologized perceptual space.     

On the uniqueness of the Invariant Equilibrium State and surface tension

Symmetric Equilibrium States and their properties under duality transformation are investigated. Necessary and sufficient conditions are derived for equilibrium states to be transformed into equilibrium states by duality. It is shown that ferromagnetic systems satisfying those conditions have correlation functions bounded by those corresponding to the (+) and free boundary conditions. It is then proved than any Invariant Equilibrium State of a ferromagnetic system is transformed into an equilibrium state by duality and is thus unique if the states defined by the (+), and free boundary conditions coincide on the symmetric algebra. The existence of surface tension between two pure phases is established.     

On the uniqueness of the equilibrium state for plane rotators

We study the classical statistical mechanics of the plane rotator, and show that there is a unique translation invariant equilibrium state in zero external field, if there is no spontaneous magnetization. Moreover, this state is then extremal in the equilibrium states. In particular there is a unique phase for the two dimensional rotator, and a unique phase for the three dimensional rotator above the critical temperature. It is also shown that in a sufficiently large external field the Lee-Yang theorem implies uniqueness of the equilibrium state.     

On the unique mapping relationship between initial and final quantum states

In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific section of its initial state. This constitutes a practical limitation, for example, in numerical analyses of quantum systems, which often make necessary the use of some extra assistance from classical methodologies. Here it is shown how the Bohmian formulation of quantum mechanics removes the ambiguity of quantum mechanics, providing a consistent and clear answer to such a question without abandoning the quantum framework. More specifically, this formulation allows to define probability tubes, along which the enclosed probability keeps constant in time all the way through as the system evolves in configuration space. These tubes have the interesting property that once their boundary is defined at a given time, they are uniquely defined at any time. As a consequence, it is possible to determine final restricted (or partial) probabilities directly from localized sets of (Bohmian) initial conditions on the system initial state. Here, these facts are illustrated by means of two simple yet physically insightful numerical examples: tunneling transmission and grating diffraction.     

On the uniqueness of the Dirac theory in curved and flat spacetime

In this work a number of examples are used to illustrate uniqueness of physical prediction of the Dirac theory in a curved and a flat spacetime. Dirac Hamiltonians in arbitrary, including time‐dependent, gravitational fields uniquely determine physical characteristics of quantum‐mechanical systems irrespective of the choice of the tetrad fields. Direct spin‐rotation coupling that occurs with a certain choice of tetrads does not manifest itself in final physical characteristics of the systems and therefore does not represent a physically relevant effect.     

On the relationship between snowfall intensity and attenuation of short millimeter waves

We measure the dependence of radio wave attenuation at 138, 247, and 340 GHz over a near-ground radio path of length 1025 m on the snowfall intensity R. We find that the relationship between the attenuation coefficient Γ at the frequency ν and the intensity R at distinct stages of a snowfall event is close to functional and is mainly nonlinear. This relationship can be fitted well by the function Γ(ν)=γ(ν)R^m(ν) in the observed range of snowfall intensities (R is not greater than 3 mm/h in terms of the water equivalent). The dependence of Γ on R at different frequencies may change drastically as the snowfall evolves from one stage to another. The data obtained at the mentioned frequencies during the entire observation time reveal that the statistical dependence of Γ on R is close to linear. The mean specific attenuation coefficients determined using this data set turned out to be equal to 0.82, 3.3, and 5.6 dB·km⁻¹/(mm·h⁻¹) at ν equal to 138, 247, and 340 GHz, respectively. The correlation coefficients turned out to be 0.89, 0.94, and 0.98, respectively. The obtained results are compared to the data obtained in other measurements, as well as to the theoretical calculations of the attenuation based on the coupled-dipole method. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 12, pp. 1145–1152, December 1999.