Matrix Inequalities for Convex Functions

AbstractMany converses of Jensen's inequality for convex functions can be found in the literature. Here we give matrix versions, with matrix weights, of these inequalities. Some applications to the Hadamard product of matrices are also given

Symmetric duality with invexity in variational problems

AbstractWeak and strong duality results are established under invexity hypotheses for symmetric dual variational problems without positivity constraints. Self-dual problems and static symmetric dual programs are included as special cases

Linear programming with matrix variables

AbstractLinear programming is formulated with the vector variable replaced by a matrix variable, with the inner product defined using trace of a matrix. The theorems of Motzkin, Farkas (both homogeneous and inhomogeneous forms), and linear programming duality thus extend to matrix variables. Duality theorems for linear programming over complex spaces, and over quaternion spaces, follow as special cases

Boundedness properties of fermionic operators

The fermionic second quantization operator $d\Gamma(B)$ is shown to be bounded by a power $N^{s/2}$ of the number operator $N$ given that the operator $B$ belongs to the $r$-th von Neumann-Schatten class, $s=2(r-1)/r$. Conversely, number operator estimates for $d\Gamma(B)$ imply von Neumann-Schatten conditions on $B$. Quadratic creation and annihilation operators are treated as well.Comment: 15 page

The arithmetic-geometric-harmonic-mean and related matrix inequalities

AbstractRecently, Sagae and Tanabe defined a geometric mean of positive definite matrices and proved the harmonic-geometric-arithmetic-mean inequality. Here, we give a reversal of these results

The Hall instability of thin weakly-ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.Comment: 13 pages, 7 figure

Right Ventricular Septal Pacing: Has it come of age?

Prolonged pacing from the right ventricular (RV) apex has been shown to be associated with progressive left ventricular dysfunction as demonstrated by heart failure, atrial fibrillation and an increased morbidity and mortality [1-6]. This has led to an interest in alternate RV pacing sites and in particular the mid RV septum and the RV outflow tract (RVOT) septum [7-11]. These sites are theoretically associated with a more physiological ventricular activation. Despite the perceived advantages of septal pacing, results to date are not confirmatory [12-18]. These studies were generally acute or extended to 6-months and the leads secured to the RVOT and thus were not necessarily septal. On review of the early work of Durrer et al in 1970 [19] the septal regions of the RVOT and mid RV are the first zones of the ventricle to depolarize, suggesting that pacing from these areas on the right side of the septum would achieve as normal a contraction pattern as possible. In contrast, the free wall of the RV is the last zone to be depolarized. When attempting to prove the physiologic and hemodynamic benefits of septal pacing, it seems illogical to choose the RVOT with a mix of both septal and free wall pacing. The potential benefits of septal pacing would possibly be negated by free wall pacing and thus it is not surprising that there has been no consistent benefit over RV apical pacing demonstrated

Identifying persuasive public health messages to change community knowledge and attitudes about bulimia nervosa

Addressing stigma through social marketing campaigns has the potential to enhance currently low rates of treatment seeking and improve the well-being of individuals with the eating disorder bulimia nervosa. This study aimed to evaluate the persuasiveness of health messages designed to reduce stigma and improve mental health literacy about this disorder. A community sample of 1,936 adults (48.2% male, 51.8% female) from Victoria, Australia, provided (a) self-report information on knowledge and stigma about bulimia nervosa and (b) ratings of the persuasiveness of 9 brief health messages on dimensions of convincingness and likelihood of changing attitudes. Messages were rated moderately to very convincing and a little to moderately likely to change attitudes toward bulimia nervosa. The most persuasive messages were those that emphasized that bulimia nervosa is a serious mental illness and is not attributable to personal failings. Higher ratings of convincingness were associated with being female, with having more knowledge about bulimia nervosa, and with lower levels of stigma about bulimia nervosa. Higher ratings for likelihood of changing attitudes were associated with being female and with ratings of the convincingness of the corresponding message. This study provides direction for persuasive content to be included in social marketing campaigns to reduce stigma toward bulimia nervosa.10 page(s