On PP-convex Musielak-Orlicz spaces

summary:In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is $P$-convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16]

Ketone Body Metabolism in the Ischemic Heart

Ketone bodies have been identified as an important, alternative fuel source in heart failure. In addition, the use of ketone bodies as a fuel source has been suggested to be a potential ergogenic aid for endurance exercise performance. These findings have certainly renewed interest in the use of ketogenic diets and exogenous supplementation in an effort to improve overall health and disease. However, given the prevalence of ischemic heart disease and myocardial infarctions, these strategies may not be ideal for individuals with coronary artery disease. Although research studies have clearly defined changes in fatty acid and glucose metabolism during ischemia and reperfusion, the role of ketone body metabolism in the ischemic and reperfused myocardium is less clear. This review will provide an overview of ketone body metabolism, including the induction of ketosis via physiological or nutritional strategies. In addition, the contribution of ketone body metabolism in healthy and diseased states, with a particular emphasis on ischemia-reperfusion (I-R) injury will be discussed

P-convexity of Musielak Orlicz function spaces of Bochner type

Sin resume

Isomorphic and isometric structure of the optimal domains for Hardy-type operators

We investigate structure of the optimal domains for the Hardy-type operators including, for example, the classical Ces\`aro, Copson and Volterra operators as well as for some of their generalizations. We prove that, in some sense, the abstract Ces\`aro and Copson function spaces are closely related to the space $L^1$, namely, they contain "in the middle" a complemented copy of $L^1[0,1]$, asymptotically isometric copy of $\ell^1$ and also can be renormed to contain an isometric copy of $L^1[0,1]$. Moreover, the generalized Tandori function spaces are quite similar to $L^\infty$ because they contain an isometric copy of $\ell^\infty$ and can be renormed to contain an isometric copy of $L^\infty[0,1]$. Several applications to the metric fixed point theory will be given. Next, we prove that the Ces\`aro construction $X \mapsto CX$ does not commutate with the truncation operation of the measure space support. We also study whether a given property transfers between a Banach function space $X$ and the space $TX$, where $T$ is the Ces\`aro or the Copson operator. In particular, we find a large class of properties which do not lift from $TX$ into $X$ and prove that the abstract Ces\`aro and Copson function spaces are never reflexive, are not isomorphic to a dual space and do not have the Radon--Nikodym property in general.Comment: 34 pages; we changed the title and added some corrections compared to the first versio

Assessment of Cardiac Function and Energetics in Isolated Mouse Hearts Using 31P NMR Spectroscopy

Bioengineered mouse models have become powerful research tools in determining causal relationships between molecular alterations and models of cardiovascular disease. Although molecular biology is necessary in identifying key changes in the signaling pathway, it is not a surrogate for functional significance. While physiology can provide answers to the question of function, combining physiology with biochemical assessment of metabolites in the intact, beating heart allows for a complete picture of cardiac function and energetics. For years, our laboratory has utilized isolated heart perfusions combined with nuclear magnetic resonance (NMR) spectroscopy to accomplish this task. Left ventricular function is assessed by Langendorff-mode isolated heart perfusions while cardiac energetics is measured by performing 31P magnetic resonance spectroscopy of the perfused hearts. With these techniques, indices of cardiac function in combination with levels of phosphocreatine and ATP can be measured simultaneously in beating hearts. Furthermore, these parameters can be monitored while physiologic or pathologic stressors are instituted. For example, ischemia/reperfusion or high workload challenge protocols can be adopted. The use of aortic banding or other models of cardiac pathology are apt as well. Regardless of the variants within the protocol, the functional and energetic significance of molecular modifications of transgenic mouse models can be adequately described, leading to new insights into the associated enzymatic and metabolic pathways. Therefore, 31P NMR spectroscopy in the isolated perfused heart is a valuable research technique in animal models of cardiovascular disease