Portfolio Construction: The Efficient Diversification of Marketing Investments

Efforts in the marketing sciences can be distinguished between the analysis of individual customers and the examination of portfolios of customers, giving scarce theoretical guidance concerning the strategic allocation of promotional investments. Yet, strategic asset allocation is considered in financial economics theory to be the most important set of investment decisions. The problem addressed in this study was the application of strategic asset allocation theory from financial economics to marketing science with the aim of improving the financial results of investment in direct marketing promotions. This research investigated the components of efficient marketing portfolio construction which include multiattribute numerical optimization, stochastic Brownian motion, peer index tracking schemes, and data mining methods to formulate unique investable asset classes. Three outcomes resulted from this study on optimal diversification: (a) reduced saturative promotional activities balancing inefficient advertising cost and enterprise revenue objectives to achieve an investment equilibrium state; (b) the use of utility theory to assist in the lexicographic ordering of goal priorities; and (c) the solution approach to a multiperiod linear goal program with stochastic extensions. A performance test using a large archival set of customer data illustrated the benefits of efficient portfolio construction. The test asset allocation resulted in significantly more reward than that of the benchmark case. The results of this grounded theory study may be of interest to marketing researchers, operations research practitioners, and functional marketing executives. The social change implication is increased efficiency in allocation of large advertising budgets resulting in improved corporate performance

Method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state

In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave functions in the magnetic unit cell. An exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper's equation. The cyclic-tridiagonal matrix associated with the Harper's equation is then tridiagonalized by another unitary transformation. The obtained eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which showing the merit of our method in studying the large-sized system. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor.Comment: 8 pages; 3 figure

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation

We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary alloys.We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to $Ni_{55}Pd_{45}$, Ni_{88}Cr_12} and $Ni_{50}Pt_{50}$ alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure

Analytic Trajectories for Mobility Edges in the Anderson Model

A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent site-energies, and so take definite values rather than distributions of values. The transformed Hamiltonian is ordered, and may be interpreted as an itinerant electron interacting with a spin on each site. In this new basis, the distinction between extended and localized states is clear, and edges of the bands of extended states, the mobility edges, are calculated as a function of disorder. In two dimensions these edges have been found in both analytic and numerical applications of tridiagonalization, but they have not been found in analytic approaches based on perturbation theory, or the single-parameter scaling hypothesis; nor have they been detected in numerical approaches based on scaling or critical distributions of level spacing. In both two and three dimensions the mobility edges in this work are found to separate with increasing disorder for all disorders, in contrast with the results of calculation using numerical scaling for three dimensions. The analytic trajectories are compared with recent results of numerical tridiagonalization on samples of over 10^9 sites. This representation of the Anderson model as an ordered interacting system implies that in addition to transitions at mobility edges, the Anderson model contains weaker transitions characterized by critical disorders where the band of extended states decouples from individual sites; and that singularities in the distribution of site energies, rather than its second moment, determine localization properties of the Anderson model.Comment: 32 pages, 2 figure

Density Matrix Perturbation Theory

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.Comment: 4 pages, 2 figure

Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.Comment: final version, minor correction

Magnetic anisotropy of vicinal (001) fcc Co films: role of crystal splitting and structure relaxation in step-decoration effect

The uniaxial in-plane magnetic anisotropy (UIP-MA) constant is calculated for a single step on the (001) surface of fcc Co($N$) films. The calculations are done for both an undecorated step and the step decorated with one or more, up to 7, Cu wires. Our objective is to explain the mechanisms by which the decoration decreases the UIP-MA constant, which is the effect observed experimentally for ultrathin Co films deposited on vicinal (001) Cu surfaces and can lead to reorientation of magnetization within the film plane. Theoretical calculations performed with a realistic tight-binding model show that the step decoration changes the UIP-MA constant significantly only if the splitting between the on-site energies of various $d$-orbitals is included for atoms located near the step edge. The local relaxation of atomic structure around the step is also shown to have a significant effect on the shift of the UIP-MA constant. The influence of these two relevant factors is analyzed further by examining individual contributions to the UIP-MA constant from atoms around the step. The magnitude of the obtained UIP-MA shift agrees well with experimental data. It is also found that an additional shift due to possible charge transfer between Cu and Co atoms is very small.Comment: 12 pages,9 figures, RevTeX, submitted to Physical Review B version 3: additions to content version 2: minor correction

Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory

For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of the Phys. Soc. of Japa

An augmented space recursion study of the electronic structure of rough epitaxial overlayers

In this communication we propose the use of the Augmented Space Recursion as an ideal methodology for the study of electronic and magnetic structures of rough surfaces, interfaces and overlayers. The method can take into account roughness, short-ranged clustering effects, surface dilatation and interdiffusion. We illustrate our method by an application of Fe overlayer on Ag (100) surface.Comment: 22 pages, Latex, 6 postscript figure

Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting fermions, and apply it to harmonically confined systems of up to N=1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi (local density) approximation, the exact profiles under harmonic confinement show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let