Phantom holomorphic projections arising from Sturm’s formula

A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all positive definite integral binary diagonal quadratic forms. In this article, we show that, up to equivalence, there are exactly 18 (positive definite integral) quinary diagonal quadratic forms that are diagonally 2-universal. Furthermore, we provide a “diagonally 2-universal criterion” for diagonal quadratic forms, which is similar to “15-Theorem” proved by Conway and Schneeberger.     

Sequential Discrete p-Facility Models for Competitive Location Planning

Two new models for duopolistic competitive discrete location planning with sequential acting and variable delivered prices are introduced. If locations and prices are assumed to be set once and for all by the players, the resulting bilevel program is nonlinear. Under the assumption that further price adjustments are possible, i.e., that a Nash equilibrium in prices is reached, the model can be simplified to a linear discrete bilevel formulation. It is shown that in either situation players should not share any locations or markets if they strive for profit-maximization.For the situation with price adjustments, a heuristic solution procedure is suggested. In addition, the bilevel models are shown to serve as a basis from which different well-known location models – as, for example, the p-median problem, the preemptive location problem and the maximum covering problem – can be derived as special cases.     

IR and SFM study of PTCDA thin films on different substrates

FT-IR spectroscopy and SFM were used to investigate the growth of thin films of the organic semiconductor 3,4,9,10-perylenetetracarboxylicdianhydride (PTCDA) deposited by vacuum sublimation onto various substrates, i.e. Ag(111) layers on mica, KBr(100), mica, oxidized Si, and TiO₂ nanoparticles on Si. Layer thicknesses of PTCDA varied from 10 to 1500 nm.The anhydride vibrations of PTCDA differ for the used substrates, which can be connected to the orientation of the molecules relative to the substrate surface and the film morphology as detected in the SFM pictures.     

Alternating π‐conjugated block copolymers with precise block length

A Sonogashira polycondensation reaction has been used to synthesize copolymers consisting of alternating oligo(p‐phenyleneethynylene) with a precise block length as an electron‐rich component and 1,4‐bis(2‐phenylene‐2‐cyanovinylene)benzene or 2,6‐bis(2‐pyridinylene‐ethynylene)pyridine as an electron‐poor component. The copolymers differ in the length of the phenyleneethynylene block (trimer or pentamer) and the content of the electron‐poor component. The length of the phenyleneethynylene block has no influence on the maximum wavelength. The electron‐poor cyano‐block component lowers the optical band‐gap energy of the copolymers. The value is equivalent to that of poly(cyano‐phenylenevinylene) (CN‐PPV) (2.3–2.4 eV). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3574–3587, 2005     

Partition Statistics and Quasiharmonic Maass Forms

Andrews recently introduced k-marked Durfee symbols, which area generalization of partitions that are connected to momentsof Dyson's rank statistic. He used these connections to findidentities relating to their generating functions as well asto prove Ramanujan-type congruences for these objects and findrelations between them. In this paper, we show that the hypergeometricgenerating functions for these objects are natural examplesof quasimock theta functions, which are defined as the holomorphicparts of harmonic Maass forms and their derivatives. In particular,these generating functions may be viewed as analogs of Ramanujan'smock theta functions with arbitrarily high weight. We use theautomorphic properties to prove the existence of infinitelymany congruences for the Durfee symbols. Furthermore, we showthat as k varies, the modularity of the k-marked Durfee symbolsis precisely dictated by the case k = 2. Finally, we use thisrelation in order to prove the existence of general congruencesfor rank moments in terms of level one modular forms of boundedweight.     

Kinetics and isotype profile of antibody responses in rhesus macaques induced following vaccination with HPV 6, 11, 16 and 18 L1-virus-like particles formulated with or without Merck aluminum adjuvant

BACKGROUND: Human papillomaviruses (HPV) are the most common sexually transmitted viruses. Infection of the cervical epithelium by HPVs can lead to the development of cervical cancer. Recent advances in vaccine research have shown that immunization with papillomavirus-like particles (VLPs) containing the major structural viral protein, L1 from HPV 16 can provide protection from the establishment of a chronic HPV 16 infection and related cervical intraepithelial neoplasia (CIN) in baseline HPV 16 naive women. METHODS: To better understand the quantitative and qualitative effects of aluminum adjuvant on the immunogenic properties of an HPV 6, 11, 16 and 18L1 VLP vaccine, we used an HPV-specific, antibody isotyping assay and a competitive immunoassay that measures antibodies to neutralizing epitopes to profile sera from rhesus macaques immunized with the HPV L1 VLP vaccine formulated with or without aluminum adjuvant. RESULTS: Immunization with VLPs formulated with the aluminum adjuvant elicited a significantly stronger immune response with higher peak antibody titers both at four weeks post vaccination (12.7 to 41.9-fold higher) as well as in the persistent phase at week 52 (4.3 to 26.7-fold higher) than that of VLPs alone. Furthermore, the aluminum adjuvant formulated HPV VLP vaccine elicited a predominantly T helper type 2 response, with high levels of IgG1 and IgG4 and low levels of IgG2. The vaccine also elicited high levels of serum IgA, which may be important in providing mucosal immunity to impart protection in the anogenital tract. CONCLUSION: These results show that the HPV 6, 11, 16 and 18 L1-VLP vaccine formulated with Merck aluminum adjuvant elicits a robust and durable immune response and holds promise as a vaccine for preventing cervical cancer.     

Conformations and tautomers of 5a,6-anhydrotetracycline

Ab initio and density functional theory (DFT) calculations have been used to investigate the conformations and tautomeric forms of neutral anhydrotetracycline in aqueous solution.     

Synthesis and Characterization of Li‐containing Boron Carbide r‐Li~1B13C2

Transparent and nearly colorless single crystals of r‐LiB₁₃C₂ were obtained by reaction of boron with Li₂CO₃ in a Cu melt at 1250–1300 °C. The structure analysis [R3 m, a = 5.6535(1), c = 12.5320(2) Å, 421 independent reflections, 22 parameters, R₁ = 0.034, wR₂ = 0.093] revealed a crystal structure that can be described as a filling variant of rhombohedral B₁₃C₂. Li⁺ is located in a void above or below the linear CBC unit. The site occupation is close to 50 % resulting in an electron‐precise composition according to Wade's rules if a positive charge is given to the CBC entity: Li⁺(B₁₂)^2–(CBC)⁺. The displacement parameters of the CBC unit indicate disorder in the [001] direction, that relates to the short Li–C distance and the partial occupation of the Li⁺ site. The composition is confirmed by EELS measurements of single crystals. Band gap calculations give a value of 2.94 eV, which is in agreement to the crystals being colorless. The evaluation of the electron density by application of the QTAIM formalism as proposed by Bader modifies the assignment pictured above according to Wade's rules. In agreement to the electronegativities the carbon atoms carry a negative charge (–2.31/–2.42) and the effective charges are: Li^+0.81(B₁₂)^+2.02(CBC)^–2.83.     

Determining the absolute configuration of two marine compounds using vibrational chiroptical spectroscopy

Chiroptical techniques are increasingly employed for assigning the absolute configuration of chiral molecules through comparison of experimental spectra with theoretical predictions. For assignment of natural products, electronic chiroptical spectroscopies such as electronic circular dichroism (ECD) are routinely applied. However, the sensitivity of electronic spectral parameters to experimental conditions and the theoretical methods employed can lead to incorrect assignments. Vibrational chiroptical methods (vibrational circular dichroism, VCD, and Raman optical activity, ROA) provide more reliable assignments, although they, in particular ROA, have been little explored for assignments of natural products. In this study, the ECD, VCD, and ROA chiroptical spectroscopies are evaluated for the assignment of the absolute configuration of a highly flexible natural compound with two stereocenters and an asymmetrically substituted double bond, the marine antibiotic Synoxazolidinone A (SynOxA), recently isolated from the sub-Arctic ascidian Synoicum pulmonaria. Conformationally averaged nuclear magnetic resonance (NMR), ECD, Raman, ROA, infrared (IR) and VCD spectral parameters are computed for the eight possible stereoisomers of SynOxA and compared to experimental results. In contrast to previously reported results, the stereochemical assignment of SynOxA based on ECD spectral bands is found to be unreliable. On the other hand, ROA spectra allow for a reliable determination of the configuration at the double bond and the ring stereocenter. However, ROA is not able to resolve the chlorine-substituted stereogenic center on the guanidinium side chain of SynOxA. Application of the third chiroptical method, VCD, indicates unique spectral features for all eight SynOxA isomers in the theoretical spectra. Although the experimental VCD is weak and restricted by the limited amount of sample, it allows for a tentative assignment of the elusive chlorine-substituted stereocenter. VCD chiroptical analysis of a SynOxA derivative with three stereocenters, SynOxC, results in the same absolute configuration as for SynOxA. Despite the experimental challenges, the results convincingly prove that the assignment of absolute configuration based on vibrational chiroptical methods is more reliable than for ECD.