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

Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating Ouzo drop

Evaporating liquid droplets are omnipresent in nature and technology, such as in inkjet printing, coating, deposition of materials, medical diagnostics, agriculture, food industry, cosmetics, or spills of liquids. While the evaporation of pure liquids, liquids with dispersed particles, or even liquid mixtures has intensively been studied over the last two decades, the evaporation of ternary mixtures of liquids with different volatilities and mutual solubilities has not yet been explored. Here we show that the evaporation of such ternary mixtures can trigger a phase transition and the nucleation of microdroplets of one of the components of the mixture. As model system we pick a sessile Ouzo droplet (as known from daily life - a transparent mixture of water, ethanol, and anise oil) and reveal and theoretically explain its four life phases: In phase I, the spherical cap-shaped droplet remains transparent, while the more volatile ethanol is evaporating, preferentially at the rim of the drop due to the singularity there. This leads to a local ethanol concentration reduction and correspondingly to oil droplet nucleation there. This is the beginning of phase II, in which oil microdroplets quickly nucleate in the whole drop, leading to its milky color which typifies the so-called 'Ouzo-effect'. Once all ethanol has evaporated, the drop, which now has a characteristic non-spherical-cap shape, has become clear again, with a water drop sitting on an oil-ring (phase III), finalizing the phase inversion. Finally, in phase IV, also all water has evaporated, leaving behind a tiny spherical cap-shaped oil drop.Comment: 40 pages, 12 figure