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We discuss representations of product systems (of $W^*$-correspondences) over the semigroup $\mathbb{Z}^n_+$ and show that, under certain pureness and Szego positivity conditions, a completely contractive representation can be dilated to an isometric representation. For $n=1,2$ this is known to hold in general (without assuming the conditions) but, for $n\geq 3$, it does not hold in general (as is known for the special case of isometric dilations of a tuple of commuting contractions). Restricting to the case of tuples of commuting contractions, our result reduces to a result of Barik, Das, Haria and Sarkar. Our dilation is explicitly constructed and we present some applications., Comment: 34 pages. Comments are welcome

We have studied the effect of Fe substitution on magnetic and magnetocaloric properties in La0.7Sr0.3Mn1-xFexO3 (x = 0.05, 0.07, 0.10, 0.15, and 0.20) over a wide temperature range (T = 10-400 K). It is shown that substitution by Fe gradually decreases the ferromagnetic Curie temperature (Tc) and saturation magnetization up to x = 0.15 but a dramatic change occurs for x = 0.2. The x = 0.2 sample can be considered as a phase separated compound in which both short-range ordered ferromagnetic and antiferromagnetic phases coexist. The magnetic entropy change (DSm) was estimated from isothermal magnetization curves and it decreases with increase of Fe content from 4.4 J/KgK at 343 K (x = 0.05) to 1.3 J/KgK at 105 K (x = 0.2), under H = 5 T. The La0.7Sr0.3Mn0.93Fe0.07O3 sample shows negligible hysteresis loss, operating temperature over 60 K range around room temperature with refrigerant capacity of 225 J/Kg, and magnetic entropy of 4 J/kgK which will be an interesting compound for application in room temperature refrigeration., Comment: 26 pages, 12 figures, 3 tables. submitted to Journal of Mag. Mag. Mater

Full-rate (FR) and full-diversity (FD) are attractive features in MIMO systems. We refer to systems which achieve both FR and FD simultaneously as FRFD systems. Non-orthogonal STBCs can achieve FRFD without feedback, but their ML decoding complexities are high. V-BLAST without precoding achieves FR but not FD. FRFD can be achieved in V-BLAST through precoding given full channel state information at the transmitter (CSIT). However, with limited feedback precoding, V-BLAST achieves FD, but with some rate loss. Our contribution in this paper is two-fold: $i)$ we propose a limited feedback (LFB) precoding scheme which achieves FRFD in $2\times 2$, $3\times 3$ and $4\times 4$ V-BLAST systems (we refer to this scheme as FRFD-VBLAST-LFB scheme), and $ii)$ comparing the performances of the FRFD-VBLAST-LFB scheme and non-orthogonal STBCs without feedback (e.g., Golden code, perfect codes) under ML decoding, we show that in $2\times 2$ MIMO system with 4-QAM/16-QAM, FRFD-VBLAST-LFB scheme outperforms the Golden code by about 0.6 dB; in $3\times 3$ and $4\times 4$ MIMO systems, the performance of FRFD-VBLAST-LFB scheme is comparable to the performance of perfect codes. The FRFD-VBLAST-LFB scheme is attractive because 1) ML decoding becomes less complex compared to that of non-orthogonal STBCs, 2) the number of feedback bits required to achieve the above performance is small, 3) in slow-fading, it is adequate to send feedback bits only occasionally, and 4) in most practical wireless systems feedback channel is often available (e.g., for adaptive modulation, rate/power control).