The non-Fermi-liquid nature of the metallic states of the Hubbard Hamiltonian

It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian ? in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of ? close to S _F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S _F; σ On the basis of some available accurate numerical results for nσ(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of ? for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε _k underlying ? in determining the low-energy spectral and transport properties of the metallic ground states of ?.     

Dynamical coupling outperforms “majority wins” in organizing redundancy to mitigate noise

Nonlinear Dynamics - Inclusion of redundancy has been one of the primary techniques to reduce the probability of error and to achieve reliability in computing systems and many other engineered...     

Effects of final state interactions in B^ + \to D_S^ + \bar K^0 decay

We investigate the effects of final state interactions (FSI) contributions in the nonleptonic two body $B^ + \to D_S^ + \bar K^0$ decay, however the hadronic decay of $B^ + \to D_S^ + \bar K^0$ is analyzed by using “QCD factorization” (QCDF) method and final state interaction (FSI). First, the $B^ + \to D_S^ + \bar K^0$ decay is calculated via QCDF method and only the annihilation graphs exist in that method. Hence, the FSI must be seriously considered to solve the $B^ + \to D_S^ + \bar K^0$ decay and the D ⁰π⁺(D ⁰*ρ⁺), D ⁺π⁰(D ⁺*ρ⁰) and D ⁺η _c (D ⁺*J/ψ) via the exchange of K ^+(*), K ^0(*) and D _s ^+(*) mesones are chosen for the intermediate states. To estimate the intermediate states amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of $B^ + \to D_S^ + \bar K^0$ decay is less than 8 × 10^?4 and the predicted branching ratio is 0.23 × 10^?9 in the absence of FSI effects and it becomes 6.74 × 10^?4 when FSI contributions are taken into account.     

Reconfigurable T‐junction DNA Origami

DNA self‐assembly allows the construction of nanometre‐scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single‐stranded loops embedded in a double‐stranded DNA template and is programmed by a set of double‐stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T‐junctions formed by hybridization of single‐stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T‐junction origami motifs and that assembly can be performed at room temperature.     

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functions f(s1,s2)=∑∞m，n=1 amnexp(s1λm s2μn) of two complex variables s1 and s2,equipping it with the natural locally convex topology and using the growth parameter,the order of f as defined recently by the authors.Under this topology X becomes a Frechet space.Apart from finding the characterization of continuous linear functionals,linear transformation on X,we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.     

Study of the Effects of N Fertilization and Plant Density on the Essential Oil Composition and Yield of Cuminum cyminum L. Seeds by HS–SME

Headspace-solvent microextraction (HS–SME) with sample ultrasound irradiation was successfully used for the study of the influence of nitrogen fertilization and plant density on the essential oil yield and composition of cumin (Cuminum cyminum L.) seeds. The components were collected into a single microdrop of n-heptadecane and directly injected into a GC–MS injection port for analysis. A simplex method was used for fast optimization of the extraction parameters. The experiments were executed as split-plot based on randomized complete block design. Nitrogen fertilization as the main factor (in four levels) and plant density as subsidiary factor (in three levels) were applied. It was shown that the total GC peak areas of the HS–SME extract, is proportional to the essential oil yield of the cumin seeds obtained by a hydrodistillation method. Furthermore, similar trends in the concentrations of cuminaldehyde and most other volatile components were obtained by the two methods.     

Nano‐structured gemini‐based supramolecular solvent for the microextraction of cyhalothrin and fenvalerate

A novel supramolecular solvent‐based microextraction followed by high‐performance liquid chromatography with ultraviolet detection method has been developed for the extraction and determination of two pyrethroid analytes, cyhalothrin and fenvalerate, in water and soil samples. The liquid–liquid‐phase separation of surfactants has been used in analytical extraction. The surfactant‐rich phase is a nano‐structured liquid, recently named as a supramolecular solvent, generated from the amphiphiles. The alkyl carboxylic acid based supramolecular solvents were introduced before. Coacervates made up of gemini surfactant, consisting of two amphiphilic moieties, were first used as solvent. The effective parameters on extraction (i.e., type of organic solvent, the amount of surfactant and volume of tetrahydrofuran, sample solution pH, salt addition, ultrasonic and centrifugation time) were investigated and optimized. Under the optimum conditions, preconcentration factors of 110 and 145 were obtained for the analytes. The linearity was 0.5–200.0 μg/L with the correlation of determination of (R²) ≥ 0.9984. The limit of detection of the method was (S/N = 3) 0.2 μg/L, and precisions in the range of 6.3–10.3% (RSDs, n = 5) were obtained. This method has been successfully applied to analyze real samples, and good recoveries in the range of 101.2–108.8% were obtained.