Improved synthesis of 6,6,7,7-tetramethyl-1-azabicyclop[2.2.2]octan-2-one and its stability toward base-induced methanolysis

The published method for synthesis of the bridgehead lactam 6,6,7,7-tetramethyl-1-azabicyclo [2.2.2]octan-2-one yields polymers almost exclusively. Use of dilution techniques provides a 27% yield of this highly strained molecule. Base-induced methanolysis of this tetramethyl compound occurs exceedingly slowly compared to some other less crowded homologues. A buttressing effect is postulated to account for part of this effect.     

Quantum signal transmission through a single-qubit chain

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.     

Stereoselective C-X and regioselective C-H activation to,and selective C(sp2)-C(sp3) reductive elimination from,platinum compounds with thiophene-derived ligands

Several thiophene-based N^C ligands were synthesized. Strategically, a bromide was incorporated on the 2-position of the thiophene ring. When allowed to react with the platinum tetramethyl dimer, [Pt₂Me₄(µ-SMe₂)₂], platinum(IV) platinacycles were formed by oxidative addition of the C(sp²)-X bond. These platinum(IV) compounds were characterized by NMR and HRMS. The platinum (IV) compounds were subsequently subjected to thermolysis. A series of reactions occurred, including selective C-C reduction elimination and selective C-H oxidative addition, giving mixtures of platinum(II) products with varying degrees of regioselectivity.     

Self-promoted DNA interstrand cross-link formation by an abasic site

The C4'-oxidized abasic site (C4-AP) is produced in DNA as a result of oxidative stress. A recent report suggests that this lesion forms interstrand cross-links. Using duplexes in which C4-AP is produced from a synthetic precursor, we show that the lesion produces interstrand cross-links in which both strands are in tact and cross-links in which the C4-AP containing strand is cleaved. The yields of these products are dependent upon the surrounding nucleotide sequence. When C4-AP is opposed by dA, cross-link formation occurs exclusively with an adjacent dA on the 5'-side. Moreover, formation of the lower molecular weight cross-link is promoted by an opposing adenine. When the opposing dA is replaced by dT, the activity of the adenine can be rescued by adding the free base. This is a rare example in which DNA promotes its own modification, an observation that is all the more important because of the biological significance of the product produced.     

Generic muchnik reducibility and presentations of fields

We prove that the subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group are finite sums of Euler products of cone integrals over Q and we deduce from this that they have rational abscissa of convergence and some meromorphic continuation. We also define Mal’cev completions of a finitely generated virtually nilpotent group and we prove that the subgroup growth and the normal subgroup growth of the latter are invariants of its Q-Mal’cev completion.     

Standard reference materials for foods and dietary supplements

Well-characterized certified reference materials are needed by laboratories in the food testing, dietary supplement, and nutrition communities to facilitate compliance with labeling laws and improve the accuracy of information provided on product labels, so that consumers can make good choices. As a result of the enactment of the Nutrition Labeling and Education Act of 1990 and the Infant Formula Act of 1980, the National Institute of Standards and Technology (NIST) worked to develop a series of food-matrix standard reference materials (SRMs) characterized for nutrient concentrations. These include SRM 1544 Fatty Acids and Cholesterol in a Frozen Diet Composite, SRM 1546 Meat Homogenate, SRM 1548a Typical Diet, SRM 1566b Oyster Tissue, SRM 1846 Infant Formula, SRM 1946 Lake Superior Fish Tissue, SRM 1947 Lake Michigan Fish Tissue, SRM 2383 Baby Food Composite, SRM 2384 Baking Chocolate, SRM 2385 Slurried Spinach, and SRM 2387 Peanut Butter. With the enactment of the Dietary Supplement Health and Education Act of 1994, NIST has been working to develop suites of dietary supplement SRMs characterized for active and marker compounds and for toxic elements and pesticides, where appropriate. An updated SRM 1588b Organics in Cod Liver Oil, a suite of ephedra-containing materials (SRMs 3240–3245), a carrot extract in oil (SRM 3276), and a suite of ginkgo-containing materials (SRMs 3246–3248) are available. Several other materials are currently in preparation. Dietary supplements are sometimes provided in forms that are food-like; for these, values may also be assigned for nutrients, for example SRM 3244 Ephedra-Containing Protein Powder. Both the food-matrix and dietary supplement reference materials are intended primarily for validation of analytical methods. They may also be used as “primary control materials” in assignment of values to in-house (secondary) control materials to confirm accuracy and to establish measurement traceability to NIST.     

The Bordered Operator and the Index,of a Constrained Critical Point

It is shown that the index of a constrained critical point in the isoperimetric calculus of variations is simply related to the number of negative eigenvalues of a certain bordered operator associated with the second variation. A conjugate point theory for this bordered operator is then established.     

Effect of the qubit relaxation on transport properties of microwave photons

In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.     

Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit

A new mathematical analysis is presented of certain aspects of the behavior of opposed flow polydisperse spray diffusion flames within the framework of a model in which large slip is permitted between the droplets and their host surroundings. The sectional approach is used to model the polydisperse spray. Operating conditions are identified under which the inverses of sectional Stokes numbers are small spray-related parameters to be used in a perturbation analysis of the liquid phase governing equations. The steady state equations and their solutions are similar in form to the equivalent equations considered in previous work of the authors in which dynamical equilibrium of the droplets with the carrier phase was assumed. However, here there is much more mathematical complexity involved in the spray equations solution. A hybrid Eulerian–Lagrangian approach is also suggested to get an insight into the phenomenon of reversal in the motion of the droplets that has been reported in independent experimental and computational research. Computed results based on the analytical solutions up to the 1st order of approximation reveal the influence of large droplet slip on the droplets velocity field and on the spray diffusion flame’s thermal field, for which appreciable heterogeneous combustion can occur under the operating conditions considered.