Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Theoretical analysis of frontier orbitals,electronic transitions,and global reactivity descriptors of M(CO)4L2 type metal carbonyl complexes: a DFT/TDDFT study

Structural Chemistry - Metal carbonyl complexes, which have been known as effective catalysts since early days, find use in many fields both directly and indirectly. Although the use of metal...     

The measurement of the magnetic susceptibility of some elements (Fe,Co, Ni,Ge, Sn,Te) in the liquid state

A magnetic balance was used for measuring the susceptibility of metals and alloys, in an atmosphere of purified argon, up to 1800°c.

Comparison of the susceptibilities of liquid Fe, Co and Ni gives information on the liquid state. The changes in the susceptibilities of Ge, Sn and Te on melting are typical of semi-metallic elements and semiconductors, but their behaviour differs according to the degree of symmetry in the solid state.     

Hypercoordination in Organotin Chemistry – A Novel O,C,O-Coordinating Ligand

Recent results are reported on the application of the novel O,C,O-coordinating pincer ligand {2,6-[P(O)(OEt)₂]₂-4-tert-Bu-C₆H₂} (A) for the synthesis of hypercoordinate organotin(IV) compounds ASnR₃ (R = Ph, Cl), heteroleptic stannylenes ASnR (R = Cl, CH₂SiMe3) and intramolecularly coordinated 1,2,5-oxaphosphastannolanes.     

Metal ion complexation in acetonitrile by cone,di-ionised calix[4]arene-1,2-crown ethers with two pendant dansyl fluorophores

Four cone calix[4]arene-1,2-crown ethers each with two ionisable side arms containing dansyl groups are synthesised. The crown ether ring on the lower rim is varied from crown-4 to crown-5 with hydrogen or tert-butyl groups on the para position of the upper rim. Di(tetramethylammonium) salts of the di-ionised ligands are utilised for spectrofluorimetric titration experiments in MeCN. The influence of alkali metal, alkaline earth metal and selected transition and heavy metal (Co²⁺, Fe²⁺, Hg²⁺, Mn²⁺, Pb²⁺, Zn²⁺ and Fe³⁺) cations on the spectroscopic properties of the two dansyl groups linked to the lower rim of the conformationally locked, di-ionised calix[4]arene-1,2-crown ether frameworks is investigated by emission spectrophotometry. All of the metal cations induce red shifts in the emission spectra of the di-ionised ligands. The metal cations produce enhancement or quenching of the fluorescence emissions. Changes in the fluorescence emission as a function of the metal cation identity, the lower rim crown ether ring size and the absence or presence of upper rim tert-butyl groups are investigated.     

Sonochemical synthesis and electrochemical characterization of α-nickel hydroxide: precursor effects

Sonochemical degradation of urea was employed to synthesize alpha-nickel hydroxide from different nickel salts. Utilization of ultrasound yielded products with properties significantly different than the products obtained by thermal degradation of urea. The effect of intercalating chloride, nitrate, acetate, and sulfate anions on morphology and electrochemical performance was studied. The sulfate-intercalated sample had the smallest interlayer spacing when obtained by the sonochemical method, contradicting all the previous thermal synthesis results. The specific capacitance trend also differed from the literature values, and the value for the sulfate-intercalated sample was larger than that of acetate- and nitrate-intercalated samples. Ultrasonic synthesis increased the specific capacitance of the sulfate-intercalated sample significantly. This sample was also the most reversible and had the highest charge efficiency.     

Preparation of a 99mTc-labeled graft polymer and its in vitro and in vivo evaluation

Journal of Radioanalytical and Nuclear Chemistry - The aim of this study is the synthesis of a novel 99mTc-labeld graft polymer and the biological evaluation of its in vitro and in vivo properties....     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

Novel anhydrous proton conducting copolymers of 1‐vinyl‐1,2,4‐triazole and diisopropyl‐p‐vinylbenzyl phosphonate

Phosphonic acid functional polymers are currently of interest because of their high proton conductivity in humidified and anhydrous systems. In addition, heterocyclic compounds are used in anhydrous proton conducting polymer membranes. In that study, a new copolymer based on 1‐vinyl‐1,2,4‐triazole (VTri) and diisopropyl‐p‐vinylbenzyl phosphonate (VBP) was synthesized, and their thermal, chemical, and proton conducting properties were investigated. The copolymers were synthesized by free radical copolymerization of the corresponding monomers at several monomer feed ratios to obtain P(VTri‐co‐VBP) copolymers. The copolymer samples were then hydrolyzed to produce poly(vinyl triazole‐co‐vinyl phosphonic acid) copolymers. The composition of the copolymers was determined by elemental analysis. The copolymerization and hydrolysis reactions were verified by Fourier transform infrared spectroscopy and ion exchange capacity measurements. Thermogravimetry analysis indicates that the copolymers are thermally stable up to 300°C. In order to increase the proton conductivity, the copolymers were doped with H₃PO₄ at several stoichometric ratios. The proton conductivity increases with triazole and phosphoric acid content. In the absence of humidity, the copolymer electrolyte, P(VTri‐co‐VBPA)1:0.5 X = 2, showed a proton conductivity of 0.005 S/cm at 150°C. Copyright © 2013 John Wiley & Sons, Ltd.     

Zwitterionic amino acids as precursors for nonmetal cation pentaborate salts

Nonmetal cation (NMC) pentaborate structures were synthesized using the amino acid molecules as cations precursors. Chemical composition analysis, infrared spectroscopy, mass analysis, boron nuclear magnetic resonance, and thermal gravimetric analysis (TGA/DTA) methods were used for structural characterization. The hydrogen storage efficiency of molecules was also determined experimentally. The recorded infrared spectra support the structural similarities of the molecules. Stretchings of pentaborate rings and characteristic peaks of amino acids were detected in infrared spectra. When the thermal analysis curves were recorded, it was found that the structures showed similar decomposition steps. Due to the result of thermal decay, glassy boron oxide (B₂O₃) formation was observed as the final decomposition products of all molecules. Peaks associated with boric acid, triborate, and pentaborate were observed in the ¹¹B spectra of these salts. Powder X-ray diffraction spectroscopy supports the presence of BO₃ and BO₄⁻ groups regarding the presence of pentaborate rings. It also indicates the high crystallinity of the structures. The molecular cavities detected by brunauer–emmett–teller analysis were found to be 3.586, 1.922, 1.673, and 1.923 g/cm³. Low-molecular cavities can be attributed to the high hydrogen-bonding capacity of the structures. The hydrogen capture efficiency of the pentaborate salts was found to be in the range of 0.039-0.