A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities

We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture.Comment: 20 page

Ge quantum dot arrays grown by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface: nucleation, morphology and CMOS compatibility

Issues of morphology, nucleation and growth of Ge cluster arrays deposited by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface are considered. Difference in nucleation of quantum dots during Ge deposition at low (<600 deg C) and high (>600 deg. C) temperatures is studied by high resolution scanning tunneling microscopy. The atomic models of growth of both species of Ge huts---pyramids and wedges---are proposed. The growth cycle of Ge QD arrays at low temperatures is explored. A problem of lowering of the array formation temperature is discussed with the focus on CMOS compatibility of the entire process; a special attention is paid upon approaches to reduction of treatment temperature during the Si(001) surface pre-growth cleaning, which is at once a key and the highest-temperature phase of the Ge/Si(001) quantum dot dense array formation process. The temperature of the Si clean surface preparation, the final high-temperature step of which is, as a rule, carried out directly in the MBE chamber just before the structure deposition, determines the compatibility of formation process of Ge-QD-array based devices with the CMOS manufacturing cycle. Silicon surface hydrogenation at the final stage of its wet chemical etching during the preliminary cleaning is proposed as a possible way of efficient reduction of the Si wafer pre-growth annealing temperature.Comment: 30 pages, 11 figure

Achieving full diversity in multi-antenna two-way relay networks via symbol-based physical-layer network coding

This paper considers physical-layer network coding (PNC) with M-ary phase-shift keying (MPSK) modulation in two-way relay channel (TWRC). A low complexity detection technique, termed symbol-based PNC (SPNC), is proposed for the relay. In particular, attributing to the outer product operation imposed on the superposed MPSK signals at the relay, SPNC obtains the network-coded symbol (NCS) straightforwardly without having to detect individual symbols separately. Unlike the optimal multi-user detector (MUD) which searches over the combinations of all users’ modulation constellations, SPNC searches over only one modulation constellation, thus simplifies the NCS detection. Despite the reduced complexity, SPNC achieves full diversity in multi-antenna relay as the optimal MUD does. Specifically, antenna selection based SPNC (AS-SPNC) scheme and signal combining based SPNC (SC-SPNC) scheme are proposed. Our analysis of these two schemes not only confirms their full diversity performance, but also implies when SPNC is applied in multi-antenna relay, TWRC can be viewed as an effective single-input multiple-output (SIMO) system, in which AS-PNC and SC-PNC are equivalent to the general AS scheme and the maximal-ratio combining (MRC) scheme. Moreover, an asymptotic analysis of symbol error rate (SER) is provided for SC-PNC considering the case that the number of relay antennas is sufficiently large

Polyoxometalate multi-electron-transfer catalytic systems for water splitting

The viable production of solar fuels requires a visible-light-absorbing unit, a H2O (or CO2) reduction catalyst (WRC), and a water oxidation catalyst (WOC) that work in tandem to split water or reduce CO2 with H2O rapidly, selectively, and for long periods of time. Most catalysts and photosensitizers developed to date for these triadic systems are oxidatively, thermally, and/or hydrolytically unstable. Polyoxometalates (POMs) constitute a huge class of complexes with extensively tunable properties that are oxidatively, thermally, and (over wide and adjustable pH ranges) hydrolytically stable. POMs are some of the fastest and most stable WOCs to date under optimal conditions. This Microreview updates the very active POM WOC field; it reports the application of POMs as WRCs and initial self-assembling metal oxide semiconductor–photosensitizer–POM catalyst triad photoanodes. The complexities of investigating these POM systems, including but not limited to the study of POM-hydrated metal-ion–metal-oxide speciation processes, are outlined. The achievements and challenges in POM WOC, WRC, and triad research are outlined

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques