Two optimal Dai–Liao conjugate gradient methods

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.     

A new approach in modeling of constant temperature boundary condition in thermal lattice‐Boltzmann method

The lattice‐Boltzmann method is being applied to a diversity of fluid flow and heat transfer problems nowadays. Because of its microscale nature, strict attention should be paid when introducing macroscopic inputs to the model. One of the challenging issues dealing with macroscale and microscale treatment is the implementation of boundary conditions. In this regard constant‐temperature boundaries are frequently used in energy transfer problems. Such boundaries are simply modeled in Navier–Stokes based solvers, but they are not so harnessed in lattice‐Boltzmann models. One of the problems is that the calculated tangential heat flux is not zero along such boundaries in most of the previous models. In the present paper, a model has been developed, which has the capability of controlling tangential heat flux along the constant‐temperature boundaries. It aims to set the heat flux nearly zero along the boundary in midplane grid schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

The multi-attribute grey target decision method for attribute value within three-parameter interval grey number

Based on the grey system theory and methods, the grey-target decision-making problem is discussed, in which the attribute values are grey numbers and the maximum probability of the value of grey number is known. Firstly, the optimal effect vector is the positive bull’s-eye and positive bull’s-eye distance of each scheme is defined. Subjectively or objectively weighting method is integrated to determine the index weight and integrated optimization model of index weight is established. Finally, the critical effect vector is the negative bull’s-eye and negative bull’s-eye distance of each scheme is defined, then relative bull’s-eye distance and comprehensive the bull’s-eye distance of grey target decision-making are given. An example is also presented to illustrate the usefulness and effectiveness of the methods obtained in this paper and provides a new idea for grey target decision-making method research.     

Higgs–Dilaton cosmology: Are there extra relativistic species?

Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs–Dilaton cosmological model predicts the existence of a massless particle – the dilaton – associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs–Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation.     

Light‐Driven Coordination‐Induced Spin‐State Switching: Rational Design of Photodissociable Ligands

The bistability of spin states (e.g., spin crossover) in bulk materials is well investigated and understood. We recently extended spin‐state switching to isolated molecules at room temperature (light‐driven coordination‐induced spin‐state switching, or LD‐CISSS). Whereas bistability and hysteresis in conventional spin‐crossover materials are caused by cooperative effects in the crystal lattice, spin switching in LD‐CISSS is achieved by reversibly changing the coordination number of a metal complex by means of a photochromic ligand that binds in one configuration but dissociates in the other form. We present mathematical proof that the maximum efficiency in property switching by such a photodissociable ligand (PDL) is only dependent on the ratio of the association constants of both configurations. Rational design by using DFT calculations was applied to develop a photoswitchable ligand with a high switching efficiency. The starting point was a nickel–porphyrin as the transition‐metal complex and 3‐phenylazopyridine as the photodissociable ligand. Calculations and experiments were performed in two iterative steps to find a substitution pattern at the phenylazopyridine ligand that provided optimum performance. Following this strategy, we synthesized an improved photodissociable ligand that binds to the Ni–porphyrin with an association constant that is 5.36 times higher in its trans form than in the cis form. The switching efficiency between the diamagnetic and paramagnetic state is efficient as well (72 % paramagnetic Ni–porphyrin after irradiation at 365 nm, 32 % paramagnetic species after irradiation at 440 nm). Potential applications arise from the fact that the LD‐CISSS approach for the first time allows reversible switching of the magnetic susceptibility of a homogeneous solution. Photoswitchable contrast agents for magnetic resonance imaging and light‐controlled magnetic levitation are conceivable applications.     

Bombieri's Theorem in Short Intervals

Under the assumption of sixth power large sieve mean-value of Dirichlet L-function,we improve Bombieri's theorem in short intervals by virtue of the large sieve method and Heath-Brown's identity.     

Binding Number,Minimum Degree,and Cycle Structure in Graphs

A well‐known theorem of Woodall states that if a graph G has binding number at least 3/2, then G is hamiltonian. We generalize Woodall's theorem as follows.     

PROTONATION CONSTANTS AND SOLVENT DEPENDENT SPIN-CROSSOVER BEHAVIOUR OF IRON(II)-2-(2′-PYRIDYL)BENZIMIDAZOLE COMPLEXES

Abstract

2-(2′-Pyridyl)benzimidazole (pybzim = LH) coordinates to iron(II) as a bidentate and forms the tris-ligated complex, [Fe(pybzim)₃]²⁺ as isolated in the solid. Titration of [Fe(pybzim)₃]²⁺ with base demonstrates the successive deprotonation of the imino hydrogens of the coordinated ligands. Protonation constants for the free ligand, pybzim (Iog₁₀ K ^H = 11.33) and the complex, [Fe(pybzim)₃]²⁺ (log₁₀ K ^H ₁ = 9.58, log₁₀ K ^H ₂ = 8.13 and log₁₀ K ^H ₃ = 6.97) were measured in 30% (v/v) H₂O/EtOH. Results show that coordination to iron(II) increases the acidity of the imino hydrogen of the ligand. Spin-crossover behaviour of the complex were studied in different solvents ME, AC, AN, NM, NB, DMF, DMSO and ANL. The complex shows strong spin-crossover behaviour which is solvent dependent. Values of the spin-equilibrium constant (K _sc) and the associated thermodynamic parameters (ΔH _sc = 18.1–21.3 kJ mol^?1 and δS _sc = 69.6–84.4JK^?1 mol^?1) were calculated. An increase of the enthalpy is observed with increasing donor number (DN) of the solvent.     

Planar Digraphs of Digirth Five Are 2‐Colorable

Neumann‐Lara (1985) and ?krekovski conjectured that every planar digraph with digirth at least three is 2‐colorable, meaning that the vertices can be 2‐colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2‐colorable. The result also holds in the setting of list colorings.