Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension

We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the calculations. We obtain the bound state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D=1 and 3 dimensions. Our results are valid for $q=1$ value when $l\neq 0$ and for any $q$ value when $l=0$ and D=1 or 3. The $s$% -wave ($l=0$) binding energies for a particle of rest mass $m_{0}=1$ are calculated for the three lower-lying states $(n=0,1,2)$ using pure vector and pure scalar potentials.Comment: 25 page

Non-universal size dependence of the free energy of confined systems near criticality

The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric $\phi^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $\Lambda$ causes a non-universal leading size dependence $f_s \sim \Lambda^{d-2} L^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.Comment: RevTex, 4 page

The Market Fraction Hypothesis under different GP algorithms

In a previous work, inspired by observations made in many agent-based financial models, we formulated and presented the Market Fraction Hypothesis, which basically predicts a short duration for any dominant type of agents, but then a uniform distribution over all types in the long run. We then proposed a two-step approach, a rule-inference step and a rule-clustering step, to testing this hypothesis. We employed genetic programming as the rule inference engine, and applied self-organizing maps to cluster the inferred rules. We then ran tests for 10 international markets and provided a general examination of the plausibility of the hypothesis. However, because of the fact that the tests took place under a GP system, it could be argued that these results are dependent on the nature of the GP algorithm. This chapter thus serves as an extension to our previous work. We test the Market Fraction Hypothesis under two new different GP algorithms, in order to prove that the previous results are rigorous and are not sensitive to the choice of GP. We thus test again the hypothesis under the same 10 empirical datasets that were used in our previous experiments. Our work shows that certain parts of the hypothesis are indeed sensitive on the algorithm. Nevertheless, this sensitivity does not apply to all aspects of our tests. This therefore allows us to conclude that our previously derived results are rigorous and can thus be generalized

Non-adiabatic Fast Control of Mixed States based on Lewis-Riesenfeld Invariant

We apply the inversely-engineered control method based on Lewis-Riesenfeld invariants to control mixed states of a two-level quantum system. We show that the inversely-engineered control passages of mixed states - and pure states as special cases - can be made significantly faster than the conventional adiabatic control passages, which renders the method applicable to quantum computation. We devise a new type of inversely-engineered control passages, to be coined the antedated control passages, which further speed up the control significantly. We also demonstrate that by carefully tuning the control parameters, the inversely-engineered control passages can be optimized in terms of speed and energy cost.Comment: 9 pages, 9 figures, version to appear in J. Phys. Soc. Jp

Cogeneration of Dark Matter and Baryons by Non-Standard-Model Sphalerons in Unified Models

Sphalerons of a new gauge interaction can convert a primordial asymmetry in B or L into a dark matter asymmetry. From the equilibrium conditions for the sphalerons of both the electroweak and the new interactions, one can compute the ratios of B, L, and X, where X is the dark matter number, thus determining the mass of the dark matter particle fairly precisely. Such a scenario can arise naturally in the context of unification with larger groups. An illustrative model embeddable in $SU(6) \times SU(2) \subset E_6$ is described as well as an equally simple model based on SU(7).Comment: 13 pages. Revised introduction and references, changed titl

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Computer program for structural analysis of layered orthotropic ring-stiffened shells of revolution (SALORS): Linear stress analysis option

Program handles segmented, laminar, orthotropic shells with discrete rings. Meridional variations are handled in material properties, temperatures, and wall thickness. Allows for linear variations of temperature through each layer of shell wall