On the combinatorial lower bound for the extension complexity of the Spanning Tree polytope

This paper concerns the extension complexity of the Minimum Spanning Tree problem on a complete graph with  $n$ nodes. The best known lower bound is the trivial bound, $\Omega \left(n^2\right)$, the best known upper bound is the extended formulation size $O\left(n^3\right)$ (Wong 1980, Martin 1991). We give a nondeterministic communication protocol with cost ${log}_2(n^{2}logn)+O\left(1\right)$ for the support of the spanning tree slack matrix.     

Broadly tunable subterahertz emission from internal branches of the current-voltage characteristics of superconducting Bi2Sr2CaCu2O(8+δ) single crystals

Continuous, coherent subterahertz radiation arises when a dc voltage is applied across a stack of the many intrinsic Josephson junctions in a Bi2Sr2CaCu2O(8+δ) single crystal. The active junctions produce an equal number of I-V characteristic branches. Each branch radiates at a slightly tunable frequency obeying the Josephson relation. The overall output is broadly tunable and nearly independent of heating effects and internal cavity frequencies. Amplification by a surrounding external cavity to allow for the development of a useful high-power source is proposed.     

Electron Transfer Dissociation Mass Spectrometry of Hemoglobin on Clinical Samples

A mass spectrometry-based assay combining the specificity of selected reaction monitoring and the protein ion activation capabilities of electron transfer dissociation was developed and employed for the rapid identification of hemoglobin variants from whole blood without previous proteolytic cleavage. The analysis was performed in a robust ion trap mass spectrometer operating at nominal mass accuracy and resolution. Subtle differences in globin sequences, resulting with mass shifts of about one Da, can be unambiguously identified. These results suggest that mass spectrometry analysis of entire proteins using electron transfer dissociation can be employed on clinical samples in a workflow compatible with diagnostic applications.     

The Size of Exponential Sums on Intervals of the Real Line

We prove that there is a constant c>0 depending only on M≥1 and μ≥0 such that

Application of a nanostructured sensor based on graphene‐ and ethyl 2‐(4‐ferrocenyl[1,2,3]triazol‐1‐yl)acetate‐modified carbon paste electrode for determination of methyldopa in the presence of phenylephrine and guaifenesin

We introduce a new method to determine methyldopa without the interference of phenylephrine and guaifenesin. For this purpose, a carbon paste electrode was modified with graphene and ethyl 2‐(4‐ferrocenyl[1,2,3]triazol‐1‐yl)acetate. According to electrochemical studies, oxidation current of methyldopa on the surface of the modified electrode increased and shifted towards negative potentials. This modified electrode demonstrated two linear ranges of 0.4–30.0 μM and 30.0–500.0 μM with a detection limit of 0.08 μM. No change was observed in the sensitivity of the modified electrode towards methyldopa in the presence of phenylephrine and guaifenesin, which enables the simultaneous or independent measurement of the three moieties. The efficiency of the proposed modified electrode was evaluated through the determination of these substances in real samples.     

Zinc Chloride Anhydrous as New and Effective Catalyst for Conversion of Ketones and Aldehydes to Corresponding Gem‐dihydroperoxides

Zinc chloride anhydrous has been used as an efficient and new catalyst for conversion of ketones and aldehydes to corresponding gem‐dihydroperoxides by aqueous hydrogen peroxide (30%) in room temperature with excellent yields and notable reaction times.     

Canonical Forms for Symmetric and Regular Structures

Matrices associated with symmetric and regular structures can be arranged into certain block patterns known as Canonical forms. Using such forms, the decomposition of structural matrices into block diagonal forms, is considerably simplified. In this paper the main canonical forms are reviewed; and symmetric/regular structural configurations that can be explained with such forms are investigated. The invariant subspaces are formulated and the closed form solutions for the block-diagonalized stiffness matrices are provided in each case. Utility and robustness of the canonical forms in the analysis of structures exhibiting decomposable matrix patterns are demonstrated by numerous examples. Furthermore, a numerical method is proposed to extend the computational advantages of the matrix canonical forms to other nonconforming regular structures.     

Polystyrene-Supported,Al(OTf)3-Catalyzed Chemoselective Synthesis of Acylals from Aldehydes

Cross-linked polystyrene-supported aluminium triflate [Ps-Al(OTf)₃] has been shown to be a mild, efficient, and chemoselective heterogeneous Lewis acid catalyst for acetylation of aldehydes with acetic anhydride. The catalyst can be recovered simply and reused efficiently at least five times without any noticeable loss of catalytic activity.