Localization of the Grover Walks on Spidernets and Free Meixner Laws

In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, we discovered a family of models based on the endomorphisms of the U(1)-current algebra ${\mathcal{A} ^{(0)}}$ of Longo-Witten. In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on ${\mathcal{A} ^{(0)}}$ and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.     

Rotational spectrum of the Ar–dimethyl sulfide complex

The rotational spectra of three isotopomers of the Ar–dimethyl sulfide (DMS) complex – normal, ³⁴S, and ¹³C species – were measured in the frequency region from 3.7 up to 24.1 GHz by Fourier transform microwave spectroscopy. The normal species yielded 43 a-type and 79 c-type transitions. No Ar tunneling splitting was observed, while many transitions were split by the internal rotation of the two methyl tops of the DMS unit. In cases where the K-type splitting was close to that due to methyl internal-rotation, several forbidden transitions were observed that followed b-type selection rules. All of the observed transition frequencies were analyzed simultaneously using a phenomenological Hamiltonian also used in previously published work describing the Ar–dimethyl ether (DME) and Ne–DME complexes. The rotational and centrifugal distortion constants and the potential barrier height to methyl-top internal rotation, V₃, were determined. The rotational constants were consistent with an Ar–DMS center of mass (cm) distance of 3.796 (3) Å and a S–cm–Ar angle of 104.8 (2)°. The V₃ potential barrier obtained, 736.17 (32) cm⁻¹, was 97.8% of the DMS monomer barrier. By assuming a Lennard–Jones-type potential, the dissociation energy was estimated to be 2.4 kJ mol⁻¹, which was close to the value for Ar–DME, 2.5 kJ mol⁻¹.     

Comparison of the equilibrium geometry of acetylene (C2H2) and disilyne (Si2H2)

The equilibrium geometry of disilyne is not linear, but is twisted. The potential surfaces of acetylene and disilyne have a critical internuclear distance between the central atoms, where the stable geometry changes from linear to twisted forms the R-dependence of the valence-shell electron energy causes the difference in the structure of the molecules.     

Synthesis of novel polyxanthenes from poly(arylene ether)s containing benzoyl groups

Poly(arylene ether)s ( 3 ), ( 4 ) containing pendant benzoyl groups as precursors for novel polyxanthenes ( 7 ), ( 8 ) were prepared by nucleophilic substitution reaction of 2,5-difluoro-4-benzoylbenzophenone ( 1 ) or 2,5-difluoro-4-(4-dodecylbenzoyl)-4′-dodecylbenzophenone ( 2 ) with hydroquinone derivatives in the presence of potassium carbonate in N,N-dimethylacetamide. The polycondensation proceeded smoothly at 165°C and produced poly(arylene ether)s with inherent viscosities up to 0.80 dL/g. The novel polyxanthenes were synthesized via the reduction of poly(arylene ether)s followed by the Friedel-Crafts cyclization of diol polymers. The structure of the polyxanthenes was characterized by ¹H-NMR and IR spectroscopies. Polyxanthene 8 was quite soluble in chloroform and THF. The 10% weight loss temperature of polyxanthene 7 was 510°C in nitrogen and it was 90°C higher than the corresponding poly(arylene ether) 3 . © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2267–2272, 1997     

Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints

This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit transaction fee is larger when the amount of transaction is smaller. Hence the transaction cost is usually a concave function up to certain point. When the amount of transaction increases, the unit price of assets increases due to illiquidity/market impact effects. Hence the transaction cost becomes convex beyond certain bound. Therefore, the net expected return becomes a general d.c. function (difference of two convex functions). We will propose a branch-and-bound algorithm for the resulting d.c. maximization problem subject to a constraint on the level of risk measured in terms of the absolute deviation of the rate of return of a portfolio. Also, we will show that the minimal transaction unit constraints can be incorporated without excessively increasing the amount of computation.     

Crystal structure and mixed-valence state in 1′,1‴-dibutylbiferrocenium triiodide

In 1′, 1‴-dibutylbiferrocenium triiodide crystals A show temperature-independent trapped-valence state, while crystals B show a valence-delocalization of the mixed-valence state. The mixed-valence states of both crystals are discussed in relation to their crystal structures. Address after October 1991: Department of Chemistry, Faculty of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 724, Japan     

Application of 4-(4-nitrophenyl)-1,2,4-triazoline-3,5-dione to analysis of 25-hydroxyvitamin D3 in human plasma by liquid chromatography/electron capture atmospheric pressure chemical ionization-mass spectrometry.

The utility of 4-(4-nitrophenyl)-1,2,4-triazoline-3,5-dione (NPTAD) as a derivatization reagent in the analysis of 25-hydroxyvitamin D3 [25(OH)D3] using liquid chromatography/electron capture atmospheric pressure chemical ionization-mass spectrometry (LC/ECAPCI-MS) was examined. The derivatives of 25(OH)D3 with NPTAD underwent electron capture in the APCI source in the negative-ion mode and provided 30-fold higher sensitivity compared to an intact compound. This derivatization-LC/ECAPCI-MS method was applied to a plasma 25-hydroxyvitamin D3 assay, and gave satisfactory results in sensitivity, specificity, measurable range and throughput of the analysis.     

A cutting plane algorithm for solving bilinear programs

This paper addresses itself to a special class of nonconvex quadratic program referred to as a bilinear program in the literature. We will propose here a cutting plane algorithm to solve this class of problems. The algorithm is along the lines of H. Tui and K. Ritter, but it differs in its exploitation of the special structure of the problem. Though the algorithm is not guaranteed at this stage of the research to converge to a global optimum, the preliminary results of numerical experiments are encouraging.This research was partially supported by the Office of Naval Research under Contract N-00014-67-A-0112-0011; and U.S. Atomic Energy Commission Contract AT(04-3)-326-PA # 18.