Rings consisting entirely of certain elements

We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; Z₃ ⊕ Z₃; Z₃ ⊕ B where B is a Boolean ring; local ring with nil Jacobson radical; M₂(Z₂) or M₂(Z₃); or the ring of a Morita context with zero pairings where the underlying rings are Z₂ or Z₃.     

Synthesis, characterization, and crystal structure of two zinc(II) halide complexes with the symmetrical bidentate Schiff-base ligand (3,4-MeO-ba)2en

Abstract  

In this study two zinc(II) halide complexes with the Schiff-base ligand (3,4-MeO-ba)₂en [N,N′-bis(3,4-dimethoxybenzylidene)ethane-1,2-diamine] have been synthesized and characterized by elemental analyses (CHN), single-crystal X-ray diffraction, Fourier-transform infrared (FT-IR), and ¹H nuclear magnetic resonance (NMR) spectroscopy. The metal-to-ligand ratio was found to be 1:1 within the formula ZnX₂((3,4-MeO-ba)₂en) (X = Br, I). Crystal structure analysis reveals that the coordination geometry around the zinc(II) ions in the two isotypic complexes is distorted tetrahedral. The Schiff-base ligand (3,4-MeO-ba)₂en acts as a chelating ligand and coordinates via two N atoms to the metal center and adopts an (E,E) conformation. The coordination spheres of the metal atoms are completed by the two halide atoms, which are also involved in weak non-classical hydrogen-bonding interactions of the type C–H···X–Zn.     

"Mass defect" tags for biomolecular mass spectrometry

We present a new class of "mass defect" tags with utility in biomolecular mass spectrometry. These tags, incorporating element(s) with atomic numbers between 17 (Cl) and 77 (Ir), have a substantially different nuclear binding energy (mass defect) from the elements common to biomolecules. This mass defect yields a readily resolvable mass difference between tagged and untagged species in high-resolution mass spectrometers. We present the use of a subset of these tags in a new protein sequencing application. This sequencing technique has advantages over existing mass spectral protein identification methodologies: intact proteins are quickly sequenced and unambiguously identified using only an inexpensive, robust mass spectrometer. We discuss the potential broader utility of these tags for the sequencing of other biomolecules, differential display applications and combinatorial methods.     

Synthesis,Characterization and X‐ray Crystal Structures of [Cu(ncaen)2]ClO4 and [Cu(nca2en)(PPh3)2]BPh4 Complexes

A novel ligand, N,N′‐Bis‐[3‐(2‐nitrophenyl)‐allylidene]‐ethane‐1,2‐diamine (nca₂en), and their corresponding copper(I) complexes, [Cu(ncaen)₂]ClO₄ ( 1 ), and [Cu(nca₂en)(PPh₃)₂]BPh₄ ( 2 ), have been synthesized and characterized by CHN analyses, ¹H and ¹³C‐NMR, IR, and UV‐Vis spectroscopy. The crystal and molecular structures of [Cu(ncaen)₂]ClO₄ ( 1 ), and [Cu(nca₂en)(PPh₃)₂]BPh₄ ( 2 ), were determined by X‐ray crystallography from single‐crystal data. The coordination polyhedron about the copper(I) atom in the two complexes is best described as a distorted tetrahedron. A quasireversible redox behavior is observed for complex 1 and 2 (E_1/2 = 0.55 and 0.95 V, respectively).     

On finite groups with a certain number of centralizers

LetG be a finite group and #Cent(G) denote the number of centralizers of its elements.G is calledn-centralizer if #Cent(G)=n, and primitiven-centralizer if #Cent(G)=#Cent(G/Z(G))=n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and ifG is a finite group such thatG/Z(G)?A₅, then #Cent(G)=22 or 32. Moroever, we prove that A₅ is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of A₅ in terms of the number of centralizers     

Counting the centralizers of some finite groups

For a finite groupG, #Cent(G) denotes the number of centralizers of its elements. A groupG is called n-centralizer if #Cent(G) =n, and primitiven-centralizer if # Cent(G)\text = # Cent\text(\fracGZ(G))\text = n\# Cent(G){\text{ = \# }}Cent{\text{(}}\frac{G}{{Z(G)}}){\text{ = }}n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with exactly six distinct centralizers. We prove that ifG is a 6-centralizer group then % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGhbaabaGaamOwaiaacIcacaWGhbGaaiykaaaacaqGGaGaeyyrIaKa% aeiiaGqaciaa-readaWgaaWcbaGaa8hoaaqabaGccaGGSaGaaeiiai% aa-feadaWgaaWcbaGaa8hnaaqabaGccaGGSaGaaeiiaiaabQfadaWg% aaWcbaGaaeOmaaqabaGccaqGGaGaey41aqRaaeiiaiaabQfadaWgaa% WcbaGaaeOmaaqabaGccaqGGaGaey41aqRaaeiiaiaabQfadaWgaaWc% baGaaeOmaaqabaGccaqGGaGaae4BaiaabkhacaqGGaGaaeOwamaaBa% aaleaacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaa% leaacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaale% aacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaaleaa% caqGYaaabeaaaaa!62C4!\[\frac{G}{{Z(G)}}{\text{ }} \cong {\text{ }}D_8 ,{\text{ }}A_4 ,{\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ or Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} \] .     

Metal organic framework–derived core-shell CuO@NiO nanosphares as hole transport material in perovskite solar cell

Journal of Solid State Electrochemistry - Cu-Ni bimetallic organic frameworks were synthesized by a facile and stepwise solvothermal method, utilizing metal organic framework as precursor....