Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

Photosensitivity,substituent and solvent-induced shifts in UV-visible absorption bands of naphthyl-ester liquid crystals: a comparative theoretical approach

The substituent- and solvent-induced shifts in UV-visible absorption bands of naphthyl-ester nematic liquid crystals, viz., 4-octylphenyl-6-octyloxy-2-naphthoate (NAPHE1) and 6-octyloxy-2-naphthylyl-4-octyloxybenzoate (NAPHE2), have been investigated using the DFT, CNDO/S and INDO/S methods. A correlation has been made between molecular charge distribution and phase stability based on Mulliken, Loewdin, AM1, PM3, MNDO, CNDO/S and INDO/S methods. The observed π→π* and n→π* electronic transitions have been reported. The substituent- and solvent-induced shifts in absorption bands, transition energies and energy gaps have been discussed. The photosensitivity of the molecules has been analysed based on these shifts. It has been observed that the substituent has a dominant role on both absorption maxima and energy band gap, whereas the solvent has a dominant role only on absorption maxima, and no effect has been observed on the energy gap. These shifts may provide beneficial consequences in determining the end use of compounds.     

Tuning the mesogenic properties of 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals: the effect of a phenoxy end-group in two sterically equivalent series

Two sterically equivalent series of phenoxy-terminated 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals were synthesised, and their mesogenic properties were characterised by polarised optical microscopy and differential scanning calorimetry (DSC). The phenoxy end-group causes a significant increase in melting point and inhibits – at least partially – the mesomorphism of these materials relative to the parent isomers; in most cases, the broad enantiotropic SmC phase formed by the parent isomers is suppressed by the addition of the phenoxy end-group. However, detailed analyses by small-angle X-ray scattering and monodomain 2D X-ray scattering suggest that these compounds form a SmA phase with a partially intercalated bilayer structure in which the phenoxy end-groups are nanosegregated. Such an intercalated bilayer structure might enable the tuning of smectogenic properties by appropriate substitution of the phenoxy end-groups.     

On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates     

一种高稳定性光纤F-P标准具的设计

法布里-珀罗(F-P)标准具广泛应用于光纤通信与光纤传感领域。实心标准具受自身材料的限制,无法满足高稳定性的要求。空气隙标准具采用热膨胀系数极低的垫片,提高了器件的温度稳定性能。介绍了低温漂光纤F-P标准具的设计和制作,出射光自由光谱范围为100GHz,损耗为3dB,0~70℃温度漂移小于3GHz。相比于采用传统方法制作的标准具,该光纤F-P标准具稳定性更高,解决了实心标准具折射率和热膨胀变化大的问题。     

Automatic β-expansions of formal Laurent series over finite fields

We consider β-expansions of formal Laurent series over finite fields. If the base β is a Pisot or Salem series, we prove that the β-expansion of a Laurent series α is automatic if and only if α is algebraic.     

A Note on twin primes and the modular ring Z 6

The modular ring ?₆ defines integers via (6r _i + (i ? 3)) where i is the class and r _i the row when tabulated in an array. Since only Classes 2₆ and 4₆ contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.     

Signal modeling using the gradient search

This letter presents a new method for continuous signal modeling. Firstly, the continuous signal can be represented as a function of the trigonometric functional extension (Fourier series). Fourier series of the signal are parameterized by the fundamental frequency and unknown parameters. Then, the gradient-based iterative identification algorithm is derived, for estimating parameters of the signal model with known and unknown frequencies, separately. Finally, the simulation results indicate that the proposed algorithm is effective.     

Filling the Charge–Discharge Voltage Gap in Flexible Hybrid Zinc-Based Batteries by Utilizing a Pseudocapacitive Material

The high charge–discharge voltage gap is one of the main bottlenecks of zinc–air batteries (ZABs) because of the kinetically sluggish oxygen reduction/evolution reactions (ORR/OER) on the oxygen electrode side. Thus, an efficient bifunctional catalyst for ORR and OER is highly desired. Herein, honeycomb-like MnCo₂O_4.5 spheres were used as an efficient bifunctional electrocatalyst. It was demonstrated that both ORR and OER catalytic activity are promoted by Mn^IV-induced oxygen vacancy defects and multiple active sites. Importantly, the multivalent ions present in the material and its defect structure endow stable pseudocapacitance within the inactive region of ORR and OER; as a result, a low charge–discharge voltage gap (0.43 V at 10 mA cm⁻²) was achieved when it was employed in a flexible hybrid Zn-based battery. This mechanism provides unprecedented and valuable insights for the development of next-generation metal–air batteries.     

Isoregic Thienylene‐Phenylene Polymers: The Effects of Structural Variation and Application to Photovoltaic Devices

Isoregic conjugated polymers composed of thiophene and dialkoxybenzene units were designed to harvest incident light in the mid‐visible energy range (band gap of 2.1 eV). Poly(1,4‐bis(2‐thienyl)‐2,5‐diheptoxybenzene) (PBTB(OC₇H₁₅)₂) and poly(1,4‐bis(2‐thienyl)‐2,5‐didodecyloxybenzene) (PBTB(OC₁₂H₂₅)₂) have shown significant photovoltaic performance as an electron donor when used in tandem with the electron acceptor [6, 6]‐phenyl C₆₁‐butyric acid methyl ester (PCBM) in bulk hetero‐junction photovoltaic devices. Photovoltaic devices incorporating PBTB(OC₇H₁₅)₂ and PCBM have shown AM1.5 efficiencies of ～0.6% with a short circuit current density of 2.5 mA/cm², an open circuit voltage of 0.74 V, and a fill factor of 0.32. Incident Photon‐to‐Current Efficiency (IPCE) of the device was found to be ca. 16% at 410 nm. In order to examine the relationship between the molecular structure of the polymers and their electronic energy levels, and to correlate this with photovoltaic performance, optoelectronic and electrochemical results are discussed in relation to the I‐V characteristics of the devices. Additionally, a computer‐aided simulation is used to gain further insight into the effect of polymer structure on the energetic relationships in the bulk heterojunction devices.