Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Functional outcomes after stabilization with Dynesys in patients with spinal degenerative diseases

Objective: To know the impact of the Dynesys system on the functional outcomes in patients with spinal degenerative diseases. Summary of background data: Dynesys system has been proposed as an alternative to vertebral fusion for several spinal degenerative diseases. The fact that it has been used in people with different diagnosis criteria using different tools to measure clinical outcomes makes very difficult unifying the results available nowadays. Methods: The data base of Medlars Online International Literature (MEDLINE) via PubMed©, EMBASE©, and the Cochrane Library Plus were reviewed in search of all the studies published until November 2012 in which an operation with Dynesys in patients with spinal degenerative diseases and an evaluation of the results by an analysis of functional outcomes had taken place. No limits were used to article type, date of publication or language. Results: A total of 134 articles were found, 26 of which fulfilled the inclusion criteria after being assessed by two reviewers. All of them were case series, except for a multicenter randomized clinical trial (RCT) and a prospective case-control study. The selected articles made a total of 1507 cases. The most frequent diagnosis were lumbar spinal canal stenosis (LSCS), degenerative disc disease (DDD), degenerative spondylolisthesis (DS) and lumbar degenerative scoliosis (LDS). In cases of lumbar spinal canal stenosis Dynesys was associated to surgical decompression. Several tools to measure the functional disability and general health status were found. Oswestry Disability Index (ODI), the ODI Korean version (K-Odi), Prolo, Sf-36, Sf-12, Roland-Morris disability questionnaire (RMDQ), and the pain Visual Analogue Scale (VAS) were the most used. They showed positive results in all cases series reviewed. In most studies the ODI decreased about 25% (e.g. from a score of 85% to 60%). Better results when dynamic fusion was combined with nerve root decompression were found. Functional outcomes and leg pain scores with Dynesys were statistically non-inferior to posterolateral spinal fusion using autogenous bone. When Dynesys and decompression was compared with posterior interbody lumbar fixation (PLIF) and decompression, differences in ODI and VAS were not statistically significant. Conclusions: In patients with spinal degenerative diseases due to degenerative disc disorders, spinal canal stenosis and degenerative spondylolisthesis, surgery with Dynesys and decompression improves functional outcomes, decreases disability, and reduces back and leg pain. More studies are needed to conclude that dynamic stabilization is better than posterolateral and posterior interbody lumbar fusion. Studies comparing Dynesys with decompression against decompression alone should be done in order to isolate the effect of the dynamic stabilization.

Textural Characterization of Micro- and Mesoporous Carbons Using Combined Gas Adsorption and n-Nonane Preadsorption

Porous carbon and carbide materials with different structures were characterized using adsorption of nitrogen at 77.4 K before and after preadsorption of n-nonane. The selective blocking of the microporosity with n-nonane shows that ordered mesoporous silicon carbide material (OM-SiC) is almost exclusively mesoporous whereas the ordered mesoporous carbon CMK-3 contains a significant amount of micropores (25%). The insertion of micropores into OM-SiC using selective extraction of silicon by hot chlorine gas leads to the formation of ordered mesoporous carbide-derived carbon (OM-CDC) with a hierarchical pore structure and significantly higher micropore volume as compared to CMK-3, whereas a CDC material from a nonporous precursor is exclusively microporous. Volumes of narrow micropores, calculated by adsorption of carbon dioxide at 273 K, are in linear correlation with the volumes blocked by n-nonane. Argon adsorption measurements at 87.3 K allow for precise and reliable calculation of the pore size distribution of the materials using density functional theory (DFT) methods.