Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.     

Aerodynamic Measurements: Normative Data for Children Ages 6:0 to 10:11 Years

Normative measures of open quotient, speed quotient, maximum flow declination rate (MFDR), and subglottal pressure were determined for 75 children between the ages of 6 years 0 months and 10 years 11 months. The participants produced a sustained /a/ at low, comfort, and high pitches for a minimum of 5 seconds, and five to seven repetitions of /pa/ at low, comfort, and high pitches. No statistically significant differences were found in the mean measures of any aerodynamic variables (open quotient, speed quotient, maximum flow declination rate, subglottal pressure) between the frequency levels (low, comfort, high pitches). Also, no strong evidence (P > .05) exists that age or sex effect differed between the frequency levels (low, comfort, high) for any of the aerodynamic measures. For /a/ response tasks, mean open quotient measures increased slightly from low to comfort frequency and from comfort to high frequency. Mean speed quotient measures showed minimal differences between low and comfort frequency, with decreased mean measures for high frequency. Mean MFDR measures increased from low to comfort frequency and from comfort to high frequency. Mean subglottal pressure measures increased slightly from low to comfort frequency and from comfort to high frequency.     

Vacuum ultraviolet laser pulsed field ionization-photoelectron study of allyl radical CH2CHCH2

The pulsed field ionization-photoelectron (PFI-PE) spectrum of allyl radical CH2CHCH2 (C3H5) in the energy range of 65 200-66 600 cm-1 has been measured using vacuum ultraviolet laser. Based on the simulation of the rotational structures resolved in the vibrational PFI-PE bands of C3H5+(X 1A1;0(0+) and nu7+=1), the ionization energies (IEs) of C3H5(X 2A2;0(0)) to form C3H5+(X 1A1;0(0+) and nu7+=1) are determined to be 65 584.6+/-2.0 cm-1 (8.131 46+/-0.000 25 eV) and 66 020.9+/-2.0 cm-1 (8.185 56+/-0.000 25 eV), respectively, where nu7+(a1) is the symmetric C-C-C bending mode of C3H5+(X 1A1). These values are compared to IE(C3H5) values obtained in previous experimental and high-level ab initio quantum theoretical studies.     

Aqueous dispersions of magnetite nanoparticles complexed with copolyether dispersants: experiments and theory

Magnetite (Fe3O4) nanoparticles have been synthesized and complexed with carboxylate-functional block copolymers, and then aqueous dispersions of the complexes were investigated as functions of their chemical and morphological structures. The block copolymer dispersants had either poly(ethylene oxide), poly(ethylene oxide-co-propylene oxide), or poly(ethylene oxide-b-propylene oxide) outer blocks, and all of them had a polyurethane center block that contained pendent carboxylate groups. The complexes were formed through interactions of the carboxylates with the surfaces of the magnetite nanoparticles. The magnetite cores of the magnetite-copolymer complexes were near 10 nm in diameter, and the particles were superparamagnetic. Complexes with mass ratios of polymer to magnetite varying from 50:50 to 85:15 were studied. One of our objectives is to design complexes that form stable dispersions of discrete particles in water, yet that can be actuated (moved together) upon exposure to a uniform magnetic field. DLVO calculations that accounted for magnetic attractive interparticle forces, as well as van der Waals, steric, and electrostatic forces are presented. Compositions were identified wherein a shallow, attractive interparticle potential minimum appears once the magnetic term is applied. This suggests that it may be possible to tune the structures of superparamagnetic nanoparticle shells to allow discrete dispersions without a field, yet weak flocculation could be induced upon exposure to a field.     

Semantische Begründung der Derivativen Implikationslogik

Ohne Zusammenfassung     

Synthesis of spiro-fused pyrazolidoylisoxazolines

Routes to structurally unique spiro-fused pyrazolidoylisoxazolines are reported. These methods start with monosubstituted hydrazines or hydrazides and utilize the nitrile oxide 1,3-dipolar cycloaddition reaction to generate the targeted spiro-fused bis-heterocycles. Molecular shape space diversity analyses were performed on these pyrazolidoylisoxazolines showing that manipulation of the appended R groups significantly changes the molecular shape.