Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Strong edge-coloring for planar graphs with large girth

A strong edge-coloring of a graph $G=(V,E)$ is a partition of its edge set $E$ into induced matchings. Let $G$ be a connected planar graph with girth $k\ge 26$ and maximum degree $\Delta$. We show that either $G$ is isomorphic to a subgraph of a very special $\Delta$-regular graph with girth $k$, or $G$ has a strong edge-coloring using at most $2\Delta +\lceil \frac{12(\Delta -2)}{k}\rceil$ colors.     

HFIP-Functionalized Co3O4 Micro-Nano-Octahedra/rGO as a Double-Layer Sensing Material for Chemical Warfare Agents

Semiconductor metal oxides (SMO)-based gas-sensing materials suffer from insufficient detection of a specific target gas. Reliable selectivity, high sensitivity, and rapid response–recovery times under various working conditions are the main requirements for optimal gas sensors. Chemical warfare agents (CWA) such as sarin are fatal inhibitors of acetylcholinesterase in the nerve system. So, sensing materials with high sensitivity and selectivity toward CWA are urgently needed. Herein, micro-nano octahedral Co₃O₄ functionalized with hexafluoroisopropanol (HFIP) were deposited on a layer of reduced graphene oxide (rGO) as a double-layer sensing materials. The Co₃O₄ micro-nano octahedra were synthesized by direct growth from electrospun fiber templates calcined in ambient air. The double-layer rGO/Co₃O₄-HFIP sensing materials presented high selectivity toward DMMP (sarin agent simulant, dimethyl methyl phosphonate) versus rGO/Co₃O₄ and Co₃O₄ sensors after the exposure to various gases owing to hydrogen bonding between the DMMP molecules and Co₃O₄-HFIP. The rGO/Co₃O₄-HFIP sensors showed high stability with a response signal around 11.8 toward 0.5 ppm DMMP at 125 °C, and more than 75 % of the initial response was maintained under a saturated humid environment (85 % relative humidity). These results prove that these double-layer inorganic–organic composite sensing materials are excellent candidates to serve as optimal gas-sensing materials.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

Heterogeneous copper‐catalyzed oxidative coupling of oxime acetates with sodium sulfinates: An efficient and practical synthesis of β‐keto sulfones

An efficient and practical route to β‐keto sulfones has been developed through heterogeneous oxidative coupling of oxime acetates with sodium sulfinates by using an MCM‐41‐supported Schiff base‐pyridine bidentate copper (II) complex [MCM‐41‐Sb,Py‐Cu (OAc)₂] as the catalyst and oxime acetates as an internal oxidant, followed by hydrolysis. The reaction generates a variety of β‐keto sulfones in good to excellent yields. This new heterogeneous copper (II) catalyst can be easily prepared via a simple procedure from readily available and inexpensive reagents and exhibits the same catalytic activity as Cu (OAc)₂. MCM‐41‐Sb,Py‐Cu (OAc)₂ is also easy to recover and is recyclable up to eight times with almost consistent activity.     

Tricin isolated from Allium atroviolaceum potentiated the effect of docetaxel on PC3 cell proliferation: role of miR-21

For more effectiveness and overcoming the drug resistance Chemotherapy agents, the combination treatment is raised. Flavonoids with different anti-cancer effects are an appropriate choice as lead compounds. Over expressed MiR-21 in prostate cancer is associated with metastasis and drug resistance to chemotherapy with Docetaxel. In this study, the anticancer effect of 4′, 5, 7-Trihydroxy-3′, 5′-dimethoxyflavone (Tricin) was investigated with Docetaxel on PC3 cell line. Tricin was initially isolated from the Allium atroviolaceum by column chromatography and recrystallization method. The chemical structure of isolate was elucidated by spectroscopic techniques. IC₅₀ of Tricin and Docetaxel were assessed 117.5 ± 4.4 μM and 0.1 ± 0.02 nM by MTT assay, respectively. Analysis of results indicates the synergistic effect of combination therapy on decreased proliferation. MiR-21 in treated cells with Tricin significantly decreased compared to control cells. So, Tricin can be effective in the reduction of metastasis and drug resistance of Docetaxel.     

On a problem of Neumann

A conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of even order which admits an orthogonal polarity contains many Fano subplanes. The number of planes of order less than $n$ previously known to contain a Fano subplane was $O(logn)$, whereas the number of planes of order less than $n$ that our theorem applies to is not bounded above by any polynomial in $n$.     

The graphs that have antivoltages using groups of small order

Given a group $\Gamma$ of order at most six, we characterize the graphs that have $\Gamma$-antivoltages and also determine the list of minor-minimal graphs that have no $\Gamma$-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.