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The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…
Recent work has shown that the many-body expansion of the interaction energy can effectively be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and…
We derive four-dimensional relativistic three-body equations for the case of a field theory with a three-point interaction vertex. These equations describe the coupled 2->2, 2->3, and 3->3 processes, and provide the means of calculating the…
In this article an efficient method to calculate the matrix elements of three-nucleon force is presented. The new method is improved version of partial-wave decomposition presented in Few-Body Syst. 22 (1997) 107, which simplifies…
A new continuum-mechanical formulation is proposed which encompasses all material processes within and surrounding an ice sheet. Using this formulation, the balance of mass and free-surface relations for ice sheets are derived and…
There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify…
Using the trajectory conception of state we give a simple demonstration that the quantum state of a many-body system may be expressed as a set of states in three-dimensional space, one associated with each particle. It follows that the…
Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…
We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out for different choices of bases. The conserved…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…
The four-body bound state with two-body interactions is formulated in Three-Dimensional approach, a recently developed momentum space representation which greatly simplifies the numerical calculations of few-body systems without performing…