Commutative semigroups whose endomorphisms are power functions

Semigroup Forum - For any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ defined by $$f(x) = x^m$$ is an endomorphism of S. We partly solve the...     

Bismuth Film Voltammetric Sensor on Pyrolyzed Photoresist/Alumina Support for Determination of Heavy Metals

Voltammetric sensors based on bismuth film electrodes are an attractive alternative to other sensors for application in electroanalysis of heavy metals. Bismuth film electrodes can be formed by a similar method on the same substrates as mercury. These systems were used most frequently for simultaneous determination of heavy metals such as Pb, Cd and Zn by anodic stripping voltammetry. Our voltammetric sensor was fabricated on an alumina substrate. A photoresist film prepared by pyrolysis of positive photoresist S‐1813 SP15 on the alumina substrate was used as an electrode support for bismuth film deposition. The influence of the Nafion membrane on the measurement sensitivity of the sensor and mechanical stability of the bismuth film were investigated. The sensor was successfully applied for determination of Pb, Cd and Zn in an aqueous solution in the concentration range of 0.2 to 10 µg L^?1 by square wave anodic stripping voltammetry on an in‐situ formed bismuth film electrode with Nafion‐coating. Parameters of the sensor such as sensitivity, linearity, detection limit, repeatability and life‐time were evaluated. In the best case, the detection limits were estimated as 0.07, 0.11 and 0.63 µg L^?1 for Pb, Cd and Zn, respectively. Finally, the applicability of the sensor was tested in analysis of Pb, Cd and Zn in real samples of tap and river water using the method of standard additions.     

Development of a new highly efficient 17 X‐STR multiplex for forensic purposes

Currently, two of the most widely used X‐chromosome STR (X‐STR) multiplexes are composed by ten (GHEP‐ISFG decaplex) and 12 markers (Investigator Argus X‐12 Kit). The number of markers included is a drawback for complex relative testing cases, likewise the large size of some amplicons difficult their application to degraded samples. Here, we present a new multiplex of 17 X‐STRs with the aim of increasing both the resolution power and forensic applicability. This newly proposed set includes the X‐STRs of the GHEP‐ISFG decaplex, four X‐STRs from the Investigator Argus X‐12 Kit, three of them also included in the decaplex, and six additional more. In order to ensure the allele designation, an allelic ladder was developed. The validation of the present multiplex was carried out according to the revised guidelines by the SWGDAM (Scientific Working Group on DNA Analysis Methods). A total of 488 unrelated individuals from four different continents were analyzed. The forensic efficiency evaluation showed high values of combined power of discrimination in males (≥0.999999996) and females (≥0.999999999999995) as well as combined paternity exclusion probabilities in trios (≥0.99999998) and duos (≥0.999996). The results presented herein have demonstrated that the new 17 X‐STR set constitutes a high‐resolution alternative to the current X‐STR multiplexes.     

A mathematical model for the dynamics and synchronization of cows

We formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise linear dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow “oscillators” together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop biological predictions. In particular, our model illustrates that it is possible for cows to synchronize less when the coupling is increased.     

Gaussian entanglement of symmetric two-mode Gaussian states

A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.     

Bands of Localized Electromagnetic Waves in 3D Random Media

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.     

Ulrich bundles on ruled surfaces

In this short note, we study the existence problem for Ulrich bundles on polarized ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient α of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles.