Tetrahedral clustering in molten lithium under pressure

A series of electronic and structural transitions are predicted in molten lithium from first principles. A new phase with tetrahedral local order characteristic of sp3 bonded materials and poor electrical conductivity is found at pressures above 150 GPa and temperatures as high as 1000 K. Despite the lack of covalent bonding, weakly bound tetrahedral clusters with finite lifetimes are predicted to exist. The stabilization of this phase in lithium involves a unique mechanism of strong electron localization in interstitial regions and interactions among core electrons. The calculations provide evidence for anomalous melting above 20 GPa, with a melting temperature decreasing below 300 K, and point towards the existence of novel low-symmetry crystalline phases.     

Analytic norms in Orlicz spaces

It is shown that an Orlicz sequence space admits an equivalent analytic renorming if and only if it is either isomorphic to or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent -Fréchet norm, but no equivalent analytic norm.

     

On some generalizations of denting points

In this paper a local version is given of a well-known theorem for uniform rotund renorming of superreflexive Banach spaces.     

Reaction of Some Alkenols with Tetrachloromethane

 The reaction of some alkenols with tetrachloromethane in the presence of a radical initiator was investigated. Regarding the effects of structural features of the starting alkenol (number and position of methyl substituents at the double bond and at the carbinol carbon atom, constitutional relationship between the double bond and the hydroxyl group) there are two possible competing reactions: addition and cyclization. In the case of the simplest alkenols (without substituents and with a more remote double bond) addition occurs; mono- and disubstituted secondary and tertiary Δ⁴- and Δ⁵-alkenols cyclize in high yields to give the corresponding cyclic ethers.     

Uniformly smooth renorming of Banach spaces with modulus of convexity of power type 2

An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying δX(ε)?cε², is found. The estimate is asymptotically sharp and is expressed in terms of linear fractional function q(c).     

Smoothness in weakly compactly generated Banach spaces

If $\text{X}{}^1$ is a weakly compactly generated (WCG) Banach space, then X admits an equivalent C¹-smooth norm. If a WCG Banach space X admits a C^k-smooth function with bounded support, then X admits C^k-smooth partitions of unity.     

A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space

LetV be a Banach space whose dualV ^* is Va?ák, that is, weakly countably determined. Then an equivalent locally uniformly rotund norm onV is constructed. According to a recent example of Mercourakis, this is a real extension of an earlier result of Godefroy Troyanski, Whitfield and Zizler, whereV ^* has been a subspace of a weakly compactly generated Banach space.