On the quantum density of states and partitioning an integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For N bosons in a one-dimensional harmonic oscillator potential, it is well known that the asymptotic (N→∞) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of sth powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d²(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the s=1 case, we use the modified technique to obtain a new formula for distinct restricted partitions.     

Synthesis of electrically conductive polypyrrole-polystyrene composites using supercritical carbon dioxide: II. Effects of the doping conditions

A polymer composite of polypyrrole (PPy) and polystyrene (PS) was synthesized in this study. Pyrrole was firstly impregnated within the PS substrate where supercritical carbon dioxide (SCCO₂) at 40 °C and 10.5 MPa was used as the solvent. The resulting polymer composite was then soaked in a solution of metallic salt to form an electrically conductive product. Thermal analyses were carried out in this study. Glass transition temperatures from the DSC curves and thermal decomposition temperatures from the TGA curves were observed. These temperatures rise gradually from pure PS, undoped blend to doped composite that indicates blending took place in SCCO₂, and polymerization was proceeding when the pyrrole/PS blend was soaking in the doping solution. Furthermore, various effects of the doping conditions on the conductivity of the PPy/PS composite were investigated. Water and acetonitrile were used as the solvents where the former yielded a higher conductivity of the product. Various doping temperatures were studied and a maximum conductivity was observed at 25 °C. The conductivity also depends on the nature of the oxidant. A bell-shaped profile of the conductivity with respect to the concentration of each oxidant was obtained. The maximum conductivity of the composites with iron compounds as oxidants decreases in the following order of anions: chloride > sulfate > perchloride > nitrate in aqueous solutions. Comparison of the scanning electron microscope results of the composite was presented where chloride and nitrate anions were used as the oxidant. It was found that the composite with higher conductivity has higher bulk density and less porous morphology.     

Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization

Numerical Algorithms - We consider a general ill-posed inverse problem in a Hilbert space setting by minimizing a misfit functional coupling with a multi-penalty regularization for stabilization....     

Micronization of tolbutamide using rapid expansion of supercritical solution with solid co-solvent (RESS-SC) process

Micronization of a sulfonylurea antidiabetic agent, tolbutamide, using rapid expansion of supercritical solution with solid co-solvent (RESS-SC) process was investigated in this study. Menthol was selected as the solid co-solvent in the RESS-SC process owing to its high vapor pressure and ease of removal by sublimation. The tolbutamide particles were micronized successfully from its original mean size of 89.4 ??m to the smallest mean size of 2.1 ??m through the RESS-SC process. The use of solid co-solvent in this process enhanced the saturated solubility of tolbutamide in supercritical carbon dioxide and inhibited the particle growth during pressure expansion after the nozzle. In addition, polymorph conversion from form I to form II after the RESS-SC process was confirmed by XRD and DSC analyses. Measurements of the dissolution rate profiles before and after the RESS-SC process were also investigated. It is shown that the micronized tolbutamide by the RESS-SC process had novelty in dissolution behavior compared to that of the original compound. Its dissolution rate was enhanced by 8.8 times after the RESS-SC process.     

Proximal algorithm for minimization problems in l0-regularization for nonlinear inverse problems

Numerical Algorithms - In this paper, we study a proximal method for the minimization problem arising from l0-regularization for nonlinear inverse problems. First of all, we prove the existence of...     

Local Stability and Local Convergence of the Basic Trust-Region Method

It is proved that the iterative sequence constructed by the Basic Trust-Region Algorithm (see Conn et al. in Trust-region methods, MPS-SIAM series on optimization, Philadelphia, 2000), which uses the Cauchy point method, is locally stable and linearly convergent in a neighborhood of a nonsingular local minimizer.     

Synthesis of electrically conductive polypyrrole-polystyrene composites using supercritical carbon dioxide: I. Effects of the blending conditions

The electrical conductivity for a polymer composite consisting of polypyrrole (PPy) and an insulating host polystyrene (PS) is reported in this study. The host polymer was blended with pyrrole monomer using either supercritical carbon dioxide (SCCO₂) or high-pressure liquid carbon dioxide (HPLCO₂) as the carrying solvent. After the blending process, the blended host polymer was soaked in an oxidant solution. This process is compared with that of oxidant impregnation. With the same processing conditions, a polymer composite with much higher conductivity was obtained when the blending process was carried out before doping in an oxidant agent. Scanning electron microscope (SEM) and elemental analysis reveal that polymerization proceeded when the blended host polymer was soaking in the oxidant solution. It is observed that SCCO₂ provides better conditions for blending the host polymer with pyrrole monomer than HPLCO₂ at the same density. The maximum conductivity of the polymer composites also increases with temperature and pressure at the same SCCO₂ density.