Duality for Koszul homology over Gorenstein rings

We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen–Macaulay the Koszul homology algebra satisfies Poincaré duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen–Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.     

Observational Constraints with Recent Data on the DGP Modified Gravity

We study one of the simplest covariant modified-gravity models based on the Dvali-Gabadadze-Porrati (DGP) brane cosmology, a self-accelerating universe. In this model gravitational leakage into extra dimensions is responsible of late-time acceleration. We mainly focus on the effects of the model parameters on the geometry and the age of universe. Also we investigate the evolution of matter density perturbations in the modified gravity model, and obtain an analytical expression for the growth index, f. We show that increasing leads to less growth of the density contrast δ, and also decreases the growth index. We give a fitting formula for the growth index at the present time and indicate that dominant term in this expression verifies the well-known approximation relation f≃Ω _m ^γ . As the observational test, the new Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and the Cluster Baryon Gas Mass Fraction (gas) are used to constrain the parameters of the DGP model. We also combine previous results with large scale structure formation (LSS) from the 2dFGRS survey. Finally to check the consistency of the DGP model, we compare the age of old cosmological objects with age of universe in this model.     

Catalyst free synthesis of fused pyrido[2,3-d]pyrimidines and pyrazolo[3,4-b]pyridines in water

A one-pot,three-component condensation reaction of an aldehyde,benzoyl acetonitrile(3-oxo-3-phenylpropane nitrile) and 6- amino-1,3-dimethylpyrimidine-2,4(1H,3H)-dione or 3-methyl-1-phenyl-1H-pyrazol-5-amine in water to give fused pyrido[2,3- d]pyrimidines and pyrazolo[3,4-b]pyridines in high yields without any catalyst,is described.     

An Easy One-Pot Procedure for the Synthesis of <Emphasis Type="Italic">N</Emphasis>-Sulfonyl Phosphorous Ylides and Sulfonyl Iminophosphoranes

Summary. Reaction of triphenylphosphine and an electron deficient acetylenic ester in the presence of strong N–H acid such as alkyl and aryl sulfamides or acetamide produces phosphorous ylides at room temperature in CH₂Cl₂. The aryl sulfamide phosphoranes undergo a smooth transformation reaction in boiling toluene and produce iminophosphoranes.     

A low-cost optimization framework to solve muscle redundancy problem

Prediction of muscle activations based on optimization procedures mostly leads to a prohibitive computational effort. To overcome this problem, an optimization framework by reformulation of the so-called method of extended inverse dynamics (EID) was developed. A planar, seven-segment model with sixteen muscle groups was used to represent human neuromusculoskeletal dynamics. The muscle activations were estimated based on two methods: EID, which treats the system dynamics (compatibility between muscular and skeletal torques), as an equality constraint, and the proposed method, which employs unconstrained system dynamics of EID (USDEID). The proposed method is based on the idea that the EID equality constraint, which is difficult to satisfy, can be eliminated by reformulation of the governing equations and optimization variables, which not only relaxes the optimization problem and leads to less optimization parameters, but also guarantees the full compatibility of the system dynamics. The comparison of simulation results of optimal muscle activations against experimental data showed a reasonable agreement for both methods during half of a gait cycle. Optimization results showed that USDEID is not only more accurate than EID in terms of the compatibility between the skeletal and muscular system dynamics, but also approximately eight times faster for ten random initial values. USDEID may be used to predict muscle activations, when the computational cost becomes prohibitive.     

Synthesis of 5-[(2-hydroxynaphthalen-1-yl)diazenyl]isophthalic acid and its application to electrocatalytic oxidation and determination of adrenaline,paracetamol, and tryptophan

In this study,Au nanoparticles/poly 5-[(2-hydroxynaphthalen-l-yl)diazenyl]isophthalic acid film modified glassy carbon electrode(AuNPs/poly(NDI)/GCE) has shown excellent electrocatalytic activity toward the oxidation of adrenaline(ADR),paracetamol(PAC),and tryptophan(Trp).The bare glassy carbon electrode(GCE) fails to separate the oxidation peak potentials of these molecules,while the poly(NDI) film modified electrode can resolve them.Electrochemical impedance spectroscopy(EIS)indicates that the charge transfer resistance of the bare electrode decreases as 5-[(2-hydroxynaphthalen-l-yl)diazenyl]isophthalic acid is electropolymerized on the bare electrode.Furthermore,EIS exhibits enhancement of electron transfer kinetics between analytes and the electrode after electrodeposition of Au nanoparticles.Differential pulse voltammetry results show that the electrocatalytic current increases linearly in the ranges of 0.01-680.0 μmol L~1 for ADR,0.05-498.0 μmol L~1 for PAC,and 3.0-632.0 μmol L~1 for Trp;with detection limits(S/N = 3) of 0.009 μmol L~1,0.005 μmol L~1,and 0.09 μmol L~1 for ADR,PAC,and Trp,respectively.The proposed method has been successfully applied for simultaneous determination of ADR,PAC,and Trp in biological samples.     

Base‐Catalyzed Formation of Isoxazoles from Dialkyl Acetylenedicarboxylates and 2‐Nitroacetophenones

The reaction of dialkyl acetylenedicarboxylates with 1‐aryl‐2‐nitroethanones in the presence of pyridine leads to dialkyl 5‐aryloyl‐isoxazole‐3,4‐dicarboxylates through a novel mechanism, which involves a [2+2] cycloaddition/ring opening/cyclization sequence.     

On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

Let (R,𝔪) be a local ring and I an ideal. The aim of the present paper is twofold. At first we continue the investigation to compare fgrade(I,R) with depth R∕I and further we derive some results on the vanishing of Lyubeznik numbers.     

Structural, theoretical and multinuclear NMR study of mercury(II) complexes with a new ambidentate phosphorus ylide

The reaction of the new ambidentate ylide, Ph₃PCHCOCH₂COOC₂H₅ (EAPPY), with HgX₂ (X = Cl, Br and I) in equimolar ratios using methanol as the solvent leads to binuclear complexes of the type [EAPPY·HgX₂]₂ (X = Cl (1), Br (2) and I (3)). Single crystal X-ray analysis reveals the presence of a centrosymmetric dimeric structure containing the ylide and HgX₂ (X = Br or I)_. The IR and NMR data of the product [(EAPPY)·HgCl₂]₂ (1), formed by the reaction of mercury(II) chloride with the same ylide, are similar to those of 2 and 3. Analytical data indicate a 1:1 stoichiometry between the ylide and Hg(II) halide in each of the three products. Theoretical studies indicate that the nature of the R group in ylides of the type Ph₃PCHCOR has a weak effect on the Hg-C(ylide) bond length in binuclear Hg₂L₂I₄ complexes.