A counterexample to a conjecture on flat bilinear forms

We provide a counterexample to a conjecture on the dimension of the nullity of a flat symmetric bilinear form.

     

Simultaneous determination of vanadium and lead in unsegmented flow systems of variable flow rate

Summary A completely continuous flow system and one with injection of the sample based on variable flow rates were used to develop a simultaneous determination for vanadium(V) and lead(II). Each metal ion is complexed with 4-(2-pyridyl-azo) resorcinol at a different pH which was established in the flow system by changing the flow rate. The features of the proposed determinative methods are discussed and compared with those of others reported in the literature.     

Vibrations of double-span uniform beams subject to an axial force

This study deals with the determination of natural frequencies of transverse vibrations of simply supported, clamped, and clamped-simply supported beams with an intermediate support subject to an axial force.Results are presented in graphical fashion as a function of the governing geometric and mechanical parameter.     

Addition and spin exchange rate constants by longitudinal field μSR: The Mu+NO reaction

The addition reaction Mu+NO+M→MuNO+M and the spin exchange reaction Mu(↑) +MO(↓)→Mu(↓)+NO(↑) have been measured by longitudinal field μSR at room temperature in the presence of up to 58 atm of N₂ as inert collider. The pressure dependence of the longitudinal relaxation rate due to the addition reaction (λ_c) demostrates that the system is still in the low pressure regime in this pressure range. The corresponding termolecular rate constant has been determined ask _0,Mu =(1.10±0.25)×10⁻³² cm⁶ molecules⁻² s⁻¹, almost 4 times smaller than the corresponding H atom reactionk _0,H=3.90×10⁻³² cm⁶ molecules⁻² s⁻¹ [I.M. Campbell et al., J. Chem. Soc. Faraday Trans. 1.71 (1975) 2097]. The average value of the spin exchange rate constants in the 2.5–58 atm pressure range,k _SE=(3.16±0.06)×10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, is in good agreement with previous values obtained by transverse field μSR [D.G. Fleming et al., J. Chem. Phys. 73 (1980) 2751].     

Confrontation of nuclear collective models

In the present decade two nuclear collective models have received considerable attention. One of them, which we shall call the Frankfurt model as most of the work on it was done there, extends the Bohr-Mottelson vibrational Hamiltonian H_o to higher than second-order terms in the quadrupole coordinates α_m, m = 2, 1, 0, ?1, ?2, thus being able to describe, besides the vibrational, also rotational and transitional nuclear states. The other uses d and s bosons formed from nucleon pairs for the same objective and it is known as the interacting boson approximation (IBA) model.In the present paper we employ the complete set of eigenstates of H_o(which depend on β, γ and the Euler angles ?_i) to show that both the Frankfurt and IBA Hamiltonians are functions, albeit different ones, of β², β³ cos3γ and H_o only, acting in the Hubert space of these eigenstates. Thus the same computational methods can be used in both models allowing a systematic comparison of their predictions.     

About the stability of high dimensional systems of functional differential equations

Summary In this work, using comparison techniques we obtain sufficient conditions for the stability of the trivial solution of a composite system of neutral type. Moreover, we establish necessary and sufficient conditions for the stability of the null solution of a system of retarded type in hierarchical form. Practical applications are also considered.     

The application of equilibrium dialysis to the determination of drug-cyclodextrin stability constants

The equilibrium dialysis method was applied to the determination of drug-cyclodextrin stability constants using diflunisal and 2-hydroxypropyl--cyclodextrin (HPBCD) as a model system. Analysis of data showed the existence of a linear Scatchard plot, which is indicative of the formation of a 1:1 dlflunisal:LIPBCD complex. The stoichiometry of the complex was verified using the appropriate mass action law equation. The complexation constant (K_c) was 3801 ± 541 M^–1. The K_c obtained using the equilibrium dialysis method was comparable to that obtained using a potentiometric method (5564 ± 56 M^–1).     

Photostimulated reactions of vinyl phosphate esters with triorganostannides. evidence for an SRN1 vinylic mechanism

Ketones are converted into vinyl diethyl phosphate esters (VinDEP), which under photostimulation reacted with sodium trimethylstannide (1) or sodium triphenylstannide (2) in liquid ammonia affording vinylstannanes via a vinylic S(RN)1 mechanism. Thus, (1-phenylvinyl)DEP (3), (3,4-dihydro-1-naphthyl)DEP (7), (3,4-dihydro-2-naphthyl)DEP (9), (E)-(1,2-diphenylvinyl)DEP (12), (E/Z)-(1-methyl-2-phenylvinyl)DEP (14) and (E)-(1-phenyl-2-methylvinyl)DEP (16) react with 1 and 2, under photostimulation, leading to the corresponding substitution products in good to excellent yields (45-89%). On the other hand, there is no reaction between (1-cyclohexenyl)DEP (5) or (1-benzylvinyl)DEP (18) with either 1 or 2, under similar conditions. These reactions appear to be strongly dependent on structural features of the vinyl phosphate since only conjugated vinyl phosphates afforded substitution products. These substitution reactions are completely regioselective and stereoconvergent. It seems to be the first example of a vinylic S(RN)1 process involving organotin anions as nucleophiles.     

Surfactant effects of chlorpromazine and imipramine on lipid bilayers containing sphingomyelin and cholesterol

The surface-active drugs chlorpromazine (CPZ) and imipramine (IP) have been tested on large unilamellar vesicles composed of phosphatidylcholine (PC), sphingomyelin (SM), and cholesterol (Ch) in different proportions. The well-characterized nonionic detergent Triton X-100 (TX) has also been used in parallel experiments. Leakage of vesicular aqueous contents and bilayer solubilization have been measured for each surfactant molecule and vesicle composition. All three surface-active molecules behave in a qualitatively similar way, irrespective of bilayer composition: they induce leakage at concentrations well below their critical micellar concentrations (cmc) and solubilization near the cmc. In these events, the potency of the three surfactants under study increases with decreasing cmc, in the order IP相似文献