There exists no self-dual [24,12,10] code over $${{\mathbb F}_5}$$

Self-dual codes over exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over , using the classification of 24-dimensional odd unimodular lattices due to Borcherds.      

Integer Decomposition Property of Free Sums of Convex Polytopes

Let \({\mathcal{P} \subset \mathbb{R}^{d}}\) and \({\mathcal{Q} \subset \mathbb{R}^{e}}\) be integral convex polytopes of dimension d and e which contain the origin of \({\mathbb{R}^{d}}\) and \({\mathbb{R}^{e}}\), respectively. We say that an integral convex polytope \({\mathcal{P}\subset \mathbb{R}^{d}}\) possesses the integer decomposition property if, for each \({n\geq1}\) and for each \({\gamma \in n\mathcal{P}\cap\mathbb{Z}^{d}}\), there exist \({\gamma^{(1)}, . . . , \gamma^{(n)}}\) belonging to \({\mathcal{P}\cap\mathbb{Z}^{d}}\) such that \({\gamma = \gamma^{(1)} +. . .+\gamma^{(n)}}\). In the present paper, under some assumptions, the necessary and sufficient condition for the free sum of \({\mathcal{P}}\) and \({\mathcal{Q}}\) to possess the integer decomposition property will be presented.     

Non-level semi-standard graded Cohen–Macaulay domain with h-vector (h0,h1,h2)

Let $\mathbb{k}$ be an algebraically closed field of characteristic 0, and $A={?}_{i\in \mathbb{N}}{A}_i$ a Cohen–Macaulay graded domain with $A_0=\mathbb{k}$. If A is semi-standard graded (i.e., A is finitely generated as a $\mathbb{k}[A_1]$-module), it has the h-vector$(h_0,h_1,\dots ,h_s)$, which encodes the Hilbert function of A. From now on, assume that $s=2$. It is known that if A is standard graded (i.e., $A=\mathbb{k}[A_1]$), then A is level. We will show that, in the semi-standard case, if A is not level, then $h_1+1$ divides $h_2$. Conversely, for any positive integers h and n, there is a non-level A with the h-vector $(1,h,(h+1)n)$. Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings).     

Influence of wall heat loss on the emission characteristics of premixed ammonia-air swirling flames interacting with the combustor wall

The influence of wall heat loss on the emission characteristics of ammonia-air swirling flames has been investigated employing Planar Laser-Induced Fluorescence imaging of OH radicals and Fourier Transform Infrared spectrometry of the exhaust gases in combustors with insulated and uninsulated walls over a range of equivalence ratios, ?, and pressures up to 0.5 MPa. Strong influence of wall heat loss on the flames led to quenching of the flame front near the combustor wall at 0.1 MPa, resulting in large unburned NH₃ emissions, and inhibited the stabilization of flames in the outer recirculating zone (ORZ). A decrease in heat loss effects with an increase in pressure promoted extension of the fuel-rich stabilization limit owing to increased recirculation of H₂ from NH₃ decomposition in the ORZ. The influence of wall heat loss resulted in emission trends that contradict already reported trends in literature. NO emissions were found to be substantially low while unburned NH₃ and N₂O emissions were high at fuel-lean conditions during single-stage combustion, with values such as 55 ppmv of NO, 580 ppmv of N₂O and 4457 ppmv of NH₃ at ? = 0.8. In addition, the response of the flame to wall heat loss as pressure increased was more important than the effects of pressure on fuel-NO emission, thereby leading to an increase in NO emission with pressure. It was found that a reduction in wall heat loss or a sufficiently long fluid residence time in the primary combustion zone is necessary for efficient control of NH₃ and N₂O emissions in two-stage rich-lean ammonia combustors, the latter being more effective for N₂O in addition to NO control. This study demonstrates that the influence of wall heat loss should not be ignored in emissions measurements in NH₃-air combustion, and also advances the understanding of previous studies on ammonia micro gas turbines.     

Effects of OH concentration and temperature on NO emission characteristics of turbulent non-premixed CH4/NH3/air flames in a two-stage gas turbine like combustor at high pressure

This study examined the effects of OH concentration and temperature on the NO emission characteristics of turbulent, non-premixed methane (CH₄)/ammonia (NH₃)/air swirl flames in two-stage combustors at high pressure. Emission data were obtained using large-eddy simulations with a finite-rate chemistry method from model flames based on the energy fraction of NH₃ (E_NH3) in CH₄/NH₃ mixtures. Although NO emissions at the combustor exit were found to be significantly higher than those generated by CH₄/air and NH₃/air flames under both lean and stoichiometric primary zone conditions, these emissions could be lowered to approximately 300 ppm by employing far-rich equivalence ratios (?) of 1.3 to 1.4 in the primary zone. This effect was possibly due to the lower OH concentrations under far-rich conditions. An analysis of local flame characteristics using a newly developed mixture fraction equation for CH₄/NH₃/air flames indicated that the local temperature and NO and OH concentration distributions with local ? were qualitatively similar to those in NH₃/air flames. That is, the maximum local NO and OH concentrations appeared at local ? of 0.9, although the maximum temperature was observed at local ? of 1.0. Both the temperature and OH concentration were found to gradually decrease with the partial replacement of CH₄ with NH₃. Consequently, NO emissions from CH₄/NH₃ flames were maximized at E_NH3 in the range of 20% to 30%, after which the emissions decreased. Above 2100 K, the NO emissions from CH₄/NH₃ flames increased exponentially with temperature, which was not observed in NH₃/air flames because of the lower flame temperatures in the latter. But, the maximum NO concentration in CH₄/NH₃ flames was occurred at a temperature slightly below the maximum temperature, just as in NH₃/air flames. The apparent exponential increase in NO emissions from CH₄/NH₃ flames is attributed to a similar trend in the OH concentration at high temperatures.     

Preparation of Cu2ZnSnS4 thin films by hybrid sputtering

In order to fabricate Cu₂ZnSnS₄ thin films, hybrid sputtering system with two sputter sources and two effusion cells is used. The Cu₂ZnSnS₄ films are fabricated by the sequential deposition of metal elements and annealing in S flux, varying the substrate temperature. The Cu₂ZnSnS₄ films with stoichiometric composition are obtained at the substrate temperature up to 400 °C, whereas the film composition becomes quite Zn-pool at the substrate temperature above 450 °C. The Cu₂ZnSnS₄ film shows p-type conductivity, and the optical absorption coefficient and the band gap of the Cu₂ZnSnS₄ film prepared in this experiment are suitable for fabricating a thin film solar cell.     

High-speed wavelength-division multiplexing quantum key distribution system

A high-speed quantum key distribution system was developed with the wavelength-division multiplexing (WDM) technique and dedicated key distillation hardware engines. Two interferometers for encoding and decoding are shared over eight wavelengths to reduce the system's size, cost, and control complexity. The key distillation engines can process a huge amount of data from the WDM channels by using a 1 Mbit block in real time. We demonstrated a three-channel WDM system that simultaneously uses avalanche photodiodes and superconducting single-photon detectors. We achieved 12 h continuous key generation with a secure key rate of 208 kilobits per second through a 45 km field fiber with 14.5 dB loss.     

Magnetization reversal in a preferred oriented (111) L1(0) FePt grown on a soft magnetic metallic glass for tilted magnetic recording

L1(0) FePt is an important material for the fabrication of high density perpendicular recording media, but the ultrahigh coercivity of L1(0) FePt restricts its use. Tilting of the magnetic easy axis and the introduction of a soft magnetic underlayer can solve this problem. However, high temperature processing and the requirement of epitaxial growth conditions for obtaining an L1(0) FePt phase are the main hurdles to be overcome. Here, we introduce a bilayered magnetic structure ((111) L1(0) FePt/glassy Fe(71)Nb(4)Hf(3)Y(2)B(20)/SiO(2)/Si) in which the magnetic easy axis of L1(0) FePt is tilted by ~36° from the film plane and epitaxial growth conditions are not required. The soft magnetic underlayer not only promotes the growth of L1(0) FePt with the preferred orientation but also provides an easy cost-effective micro/nanopatterning of recording bits. A detailed magnetic characterization of the bilayered structure in which the thickness of (111) L1(0) FePt with the soft magnetic Fe(71)Nb(4)Hf(3)Y(2)B(20) glassy underlayer varied from 5 to 60 nm is carried out in an effort to understand the magnetization switching mechanism. The magnetization switching behavior is almost the same for bilayered structures in which FePt layer thickness is >10 nm (greater than the domain wall thickness of FePt). For FePt film ~10 nm thick, magnetization reversal takes place in a very narrow field range. Magnetization reversal first takes place in the soft magnetic underlayer. On further increase in the reverse magnetic field, the domain wall in the soft magnetic layer compresses at the interface of the hard and soft layers. Once the domain wall energy becomes sufficiently large to overcome the nucleation energy of the domain wall in L1(0) FePt, the magnetization of the whole bilayer is reversed. This process takes place quickly because the domain walls in the hard layer do not need to move, and the formation of a narrower domain wall may not be favorable energetically. Our results showed that the present bilayered structure is very promising for the fabrication of tilted bit-patterned magnetic recording media.     

Laser Stark spectroscopy of the ν4 band of CH3C15N: Fermi resonance with 3ν83

Laser Stark spectra for the ν₄ band of CH₃C¹⁵N have been measured by using CO₂ and N₂O lasers. Almost 650 resonances have been assigned to about 140 ro-vibrational transitions with J′ ≤ 34 and K ≤ 11. An anomaly of the rotational structure around K = 7 has been proved to be due to a Fermi interaction by analyzing each K subband separately. Observed data have been fitted to a model which includes ν₄-3ν₈³ Fermi coupling by the method of least squares. The standard deviation of observed from calculated frequencies is 4.6 MHz. Molecular constants derived are also listed.