New results on elements 111 and 112

Experiments on the synthesis and identification of the nuclei ²⁷²111 and ²⁷⁷112 were performed in order to confirm previous results. Three additional decay chains were measured in the reaction ⁶⁴Ni + ²⁰⁹Bi →²⁷³111^*. The study revealed considerably improved data on the decay chain originating from ²⁷²111. One additional chain was measured in the reaction ⁷⁰Zn + ²⁰⁸Pb →²⁷⁸112^*. The decay properties of the chain starting at ²⁷⁷112 are in excellent agreement with the second chain of the first experiment down to ²⁶⁵Sg, where the new chain ends by a previously unknown spontaneous-fission branch. A re-analysis of all the data on elements 110, 111, and 112 measured at GSI since 1994 (a total of 34 decay chains was investigated) revealed that for 2 chains (the second chain of ²⁶⁹110 measured in 1994 and the first chain of ²⁷⁷112 measured in 1996) the results of the new analysis differed from the previous one. In all other cases the earlier data are exactly reproduced. Received: 21 December 2001 / Accepted: 15 January 2002     

Letter to the Editor

The letter below has been received in August 2000 and we feel that it should be made available to all readers of this journal.     

On semi-fredholm properties of a boundary value problem inR + n

The paper considers a boundary value problem with the help of the smallest closed extensionL ^∼ :H _k →H _{k 0}×B _{h 1}×...×B _{h N} of a linear operatorL :C ₍₀₎ ^∞ (R ₊ ⁿ ) →L(R ₊ ⁿ )×L(R ⁿ⁻¹)×...×L(R ⁿ⁻¹). Here the spacesH _k (the spaces ℬ _h ) are appropriate subspaces ofD′(R ₊ ⁿ ) (ofD′(R ⁿ⁻¹), resp.),L(R ₊ ⁿ ) andC ₍₀₎ ^∞ (R ₊ ⁿ )) denotes the linear space of smooth functionsR ⁿ →C, which are restrictions onR ₊ ⁿ of a function from the Schwartz classL (fromC ₀ ^∞ , resp.),L(R ⁿ⁻¹) is the Schwartz class of functionsR ⁿ⁻¹ →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ^∼) and for the uniqueness of solutionsL ^∼ U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established.     

Electrogenerated chemiluminescence of fluorescein in aqueous alkaline solutions

Fluorescein is shown to emit light when electrolyzed either anodically or cathodically using potential pulses, in aqueous alkaline solutions at a platinum electrode.     

Relative rates of nucleophilic reactions of benzyl carbocation formed in photolysis of benzyl chloride and benzyl acetate in aqueous solution

Benzyl chloride and benzyl acetate were photolyzed in 30% methanol–water mixtures (V/V) at 0°C. The photolysis produces benzyl carbocations that react with nucleophiles. The reaction products were analyzed by gas chromatography or liquid chromatography. From the amounts of products the relative values of rate constants of reactions of benzyl carbocation with nucleophiles N and water k(N)/k(H₂O) were calculated. Benzyl carbocation reacts with I^?, Br^?, Cl^?, and Ac^? ions with approximately diffusion-controlled rate. A value of 2.4 × 10⁷ dm³ mol^?1 s^?1 for the rate constant k(H₂O) and a lifetime of 0.7 ns were estimated for benzyl carbocation in the aqueous solution.     

On\overline {GL(4,\mathbb{R})}-covariant extensions of the Dirac equation

Infinite component generalizations of both massless and massive Dirac equations are constructed which are covariant with respect to the double covering of the general linear group in four dimensions. These generalized Dirac equations can be made covariant with respect to the full diffeomorphism group of the spacetime manifold by replacing ordinary derivatives by covariant derivatives in the usual way.     

Decay studies of K isomers in 254No

A detailed $ \gamma$ spectroscopic decay study of two K isomers in ²⁵⁴No was performed. In addition to the previously reported $ \gamma$ lines two new transitions of E = 778 , 856keV could be attributed to the decay pattern of ^254m1No ( T _1/2 = 275±7 ms). The population of an excited band built up on this isomer ( $\ensuremath K^{\pi} =8^{-}$ by the decay of ^254m2No ( T _1/2 = 198±13 μs) could be proven by measuring delayed $ \gamma$ - $ \gamma$ coincidences between transitions stemming from the decay of both isomeric states. The energies of the band members could be established up to $\ensuremath I^{\pi} = 15^{-}$ . A spontaneous fission branch of (2.0±1.2)×10^-4 was measured for ^254m1No , an upper limit of $ \le$ 1.2×10^-4 was estimated for ^254m2No . These values demonstrate the high stability of multi-quasiparticle configurations against spontaneous fission. Evidence for an $ \alpha$ decay branch of ^254m1No in the order of 1×10^-4 was found.     

An Ehrenfeucht‐Fraïssé game for

In this paper we develop an Ehrenfeucht‐Fraïssé game for . Unlike the standard Ehrenfeucht‐Fraïssé games which are modeled solely after the behavior of quantifiers, this new game also takes into account the behavior of connectives in logic. We prove the adequacy theorem for this game. We also apply the new game to prove complexity results about infinite binary strings.     

Tautomeric populations of the charged species of 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) studied with computer simulations and cluster expansions

Correct net charge and protonation pattern in the polyamine backbone is one of the major factors that define the interactions of this class of compounds. 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) is a isosteric charge deficient analogue of naturally occurring spermine (Spm) with different biological features. The tautomeric populations of each SpmTrien charge state were estimated with computer simulations, molecular dynamics (MD) and quantum mechanical calculations, and cluster expansions separately. In the computer simulations, tautomeric populations of each charge state were obtained by constrained least‐squares fitting the theoretically calculated (GIAO B3LYP/6‐311 + G**) ¹⁵ N NMR chemical shieldings of SpmTrien tautomers to the experimentally measured chemical shifts. Theoretical chemical shieldings were calculated for water complexes of SpmTrien obtained from MD simulations in explicit water. Both methods gave highly similar realistic results. SpmTrien has many major populations of tautomers at biologically relevant charge states of three (+3) and four (+4) thus enabling a large variety of structures for specific ionic interactions. Copyright © 2013 John Wiley & Sons, Ltd.