von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Improved error performance for generalised spatial modulation with enhanced spectral efficiency

The existing analytical average bit error rate (ABER) expression of conventional generalised spatial modulation (CGSM) does not agree well with the Monte Carlo simulation results in the low signal‐to‐noise ratio (SNR) region. Hence, the first contribution of this paper is to derive a new and easy way to evaluate analytical ABER expression that improves the validation of the simulation results at low SNRs. Secondly, a novel system termed CGSM with enhanced spectral efficiency (CGSM‐ESE) is presented. This system is realised by applying a rotation angle to one of the two active transmit antennas. As a result, the overall spectral efficiency is increased by 1 bit/s/Hz when compared with the equivalent CGSM system. In order to validate the simulation results of CGSM‐ESE, the third contribution is to derive an analytical ABER expression. Finally, to improve the ABER performance of CGSM‐ESE, three link adaptation algorithms are developed. By assuming full knowledge of the channel at the receiver, the proposed algorithms select a subset of channel gain vector (CGV) pairs based on the Euclidean distance between all CGV pairs, CGV splitting, CGV amplitudes, or a combination of these.     

Molecular structure,vibrational spectroscopic and chemical reactivity of nematogenic p-n-alkylbenzoic acids: A comparative computational analysis

Molecular structure and vibrational spectroscopic studies of higher homologous series nematogenic p-n-alkylbenzoic acids (nBAC) that have 6 (6BAC) and 7 (7BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6-31++G (d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the levels. A comparision of chemical reactivity such as HOMO (E_H), LUMO (E_L) energies, energy gap (E_g), ionization energy (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that the decrement has occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding enhancing the stability of liquid crystal materials by maintaining the conductivity.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

化学法改性煤沥青脱除苯并芘的研究

在管式反应器中采用苯甲酸、聚乙二醇、固体古马隆树脂（S）、液体古马隆树脂（L）为添加剂来降低煤沥青中有害物质苯并芘的含量，以期使得煤沥青可绿色化应用。采用紫外-可见分光光度计分析煤沥青中苯并芘含量。考察了反应温度、反应时间、添加剂添加量、催化剂等工艺条件对添加剂脱除煤沥青中苯并芘的影响。结果表明，不同工艺条件能降低煤沥青中苯并芘的含量。在优化条件下，不同添加剂对苯并芘脱除率由高到低依次为：液体古马隆树脂、聚乙二醇、苯甲酸和固体古马隆树脂。分析其反应机理，这与催化剂的酸性相关，发生亲电取代反应。结果表明，液体古马隆树脂（L）在催化剂存在下对煤沥青中苯并芘脱除率可达73.0%，显示了良好的应用前景。     

A precise sensor fault detection technique using statistical techniques for wireless body area networks

One of the major challenges in wireless body area networks (WBANs) is sensor fault detection. This paper reports a method for the precise identification of faulty sensors, which should help users identify true medical conditions and reduce the rate of false alarms, thereby improving the quality of services offered by WBANs. The proposed sensor fault detection (SFD) algorithm is based on Pearson correlation coefficients and simple statistical methods. The proposed method identifies strongly correlated parameters using Pearson correlation coefficients, and the proposed SFD algorithm detects faulty sensors. We validated the proposed SFD algorithm using two datasets from the Multiparameter Intelligent Monitoring in Intensive Care database and compared the results to those of existing methods. The time complexity of the proposed algorithm was also compared to that of existing methods. The proposed algorithm achieved high detection rates and low false alarm rates with accuracies of 97.23% and 93.99% for Dataset 1 and Dataset 2, respectively.