Quantum-state tomography for spin-l systems

We show that the density matrix of a spin-l system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of 4l+1 different spin directions. It is thus possible to represent the complete quantum statistics of any N-level system within the spherically symmetric three dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five non-orthogonal spin directions is presented and the generalization to spin-l systems is discussed.Comment: 10 pages, including 2 tables, minor modifications in section II, final version for publication in Phys. Rev.

Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Let $k$ be a number field. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ for Kummer varieties over $k$. For example, for any Kummer variety $X$ over $k$, we show that if the Brauer-Manin obstruction is the only obstruction to the Hasse principle for rational points on $X$ over all finite extensions of $k$, then the ($2$-primary) Brauer-Manin obstruction is the only obstruction to the Hasse principle for zero-cycles of any given odd degree on $X$ over $k$. We also obtain similar results for products of Kummer varieties, K3 surfaces and rationally connected varieties

A microwave systems approach to measuring root zone soil moisture

Computer microwave satellite simulation models were developed and the program was used to test the ability of a coarse resolution passive microwave sensor to measure soil moisture over large areas, and to evaluate the effect of heterogeneous ground covers with the resolution cell on the accuracy of the soil moisture estimate. The use of realistic scenes containing only 10% to 15% bare soil and significant vegetation made it possible to observe a 60% K decrease in brightness temperature from a 5% soil moisture to a 35% soil moisture at a 21 cm microwave wavelength, providing a 1.5 K to 2 K per percent soil moisture sensitivity to soil moisture. It was shown that resolution does not affect the basic ability to measure soil moisture with a microwave radiometer system. Experimental microwave and ground field data were acquired for developing and testing a root zone soil moisture prediction algorithm. The experimental measurements demonstrated that the depth of penetration at a 21 cm microwave wavelength is not greater than 5 cm

Nitrification-denitrification in WSP: a mechanism for permanent nitrogen removal in maturation ponds

A pilot-scale primary maturation pond was spiked with 15N-labelled ammonia (15NH4Cl) and 15N labelled nitrite (Na15NO2), in order to improve current understanding of the dynamics of inorganic nitrogen transformations and removal in WSP systems. Stable isotope analysis of δ15N showed that nitrification could be considered as an intermediate step in WSP, which is masked by simultaneous denitrification, under conditions of low algal activity. Molecular microbiology analysis showed that denitrification can be considered a feasible mechanism for permanent nitrogen removal in WSP, which may be supported either by ammonia-oxidising bacteria (AOB) or by methanotrophs, in addition to nitrite-oxidising bacteria (NOB). However, the relative supremacy of the denitrification process over other nitrogen removal mechanisms (e.g., biological uptake) depends upon phytoplanktonic activity

Fatigue testing a plurality of test specimens and method

Described is a fatigue testing apparatus for simultaneously subjecting a plurality of material test specimens to cyclical tension loading to determine the fatigue strength of the material. The fatigue testing apparatus includes a pulling head having cylinders defined therein which carry reciprocating pistons. The reciprocation of the pistons is determined by cyclical supplies of pressurized fluid to the cylinders. Piston rods extend from the pistons through the pulling head and are attachable to one end of the test specimens, the other end of the test specimens being attachable to a fixed base, causing test specimens attached between the piston rods and the base to be subjected to cyclical tension loading. Because all the cylinders share a common pressurized fluid supply, the breaking of a test specimen does not substantially affect the pressure of the fluid supplied to the other cylinders nor the tension applied to the other test specimens

Helicobacter pylori and cancer among adults in Uganda

Data from Africa on infection with Helicobacter pylori (H. pylori) are sparse. Therefore, as part of an epidemiological study of cancer in Uganda, we investigated the prevalence and determinants of antibodies against H. pylori among 854 people with different cancer types and benign tumours. Patients were recruited from hospitals in Kampala, Uganda, interviewed about various demographic and lifestyle factors and tested for antibodies against H. pylori. In all patients combined, excluding those with stomach cancer (which has been associated with H. pylori infection), the prevalence of antibodies was 87% (723/833) overall, but declined with increasing age (p = 0.02) and was lower among people who were HIV seropositive compared to seronegative (p <0.001). Otherwise, there were few consistent epidemiological associations. Among those with stomach cancer, 18/21 (86%) had anti-H. pylori antibodies (odds ratio 0.8, 95% confidence intervals 0.2–2.9, p = 0.7; estimated using all other patients as controls, with adjustment for age, sex and HIV serostatus). No other cancer site or type was significantly associated with anti-H. pylori antibodies. The prevalence of H. pylori reported here is broadly in accord with results from other developing countries, although the determinants of infection and its' role in the aetiology of gastric cancer in Uganda remain unclear

Orbiting passive microwave sensor simulation applied to soil moisture estimation

A sensor/scene simulation program was developed and used to determine the effects of scene heterogeneity, resolution, frequency, look angle, and surface and temperature relations on the performance of a spaceborne passive microwave system designed to estimate soil water information. The ground scene is based on classified LANDSAT images which provide realistic ground classes, as well as geometries. It was determined that the average sensitivity of antenna temperature to soil moisture improves as the antenna footprint size increased. Also, the precision (or variability) of the sensitivity changes as a function of resolution

Critical strength of attractive central potentials

We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears, which converges to the exact critical value.Comment: 18 page

Influence of branch points in the complex plane on the transmission through double quantum dots

We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S-matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.Comment: 30 pages, 14 figure

Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Starting from a system of $N$ radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N \times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N (N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.Comment: 19 pages, 15 figure