A representation theorem for weak automorphisms of a universal algebra

Given a group G and a descending chainG ₀,G ₁,...,G _n, of normal subgroups ofG, we prove that there exists a universal algebra , such that the chain ...W_n( )...W₁( }) W₀( )W( ) is isomorphic to the chain ...G _n ...G ₁G ₀G, where W( ) is the group of weak automorphisms of , and W_n( ) is the group of weak automorphisms of that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G₀, and G₁=G₂=...=G_n=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments.     

Forward–Backward–Half Forward Dynamical Systems for Monotone Inclusion Problems with Application to v-GNE

Journal of Optimization Theory and Applications - In this paper, the first-order forward–backward–half forward dynamical systems associated with the inclusion problem consisting of...     

Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

Structural and compositional analysis of InBixAsySb(1−x−y) films grown on GaAs(0 0 1) substrates by liquid phase epitaxy

The growth of epitaxial InBi_xAs_ySb_(1−x−y) layers on highly lattice mis-matched semi-insulating GaAs substrates has been successfully achieved via the traditional liquid phase epitaxy. Orientation and single crystalline nature of the film have been confirmed by X-ray diffraction. Scanning electron micrograph shows abrupt interface at micrometer resolution. Surface composition of Bi(x) and As(y) in the InBi_xAs_ySb_(1−x−y) film was measured using energy dispersive X-ray analysis and found to be 2.5 and 10.5 at.%, respectively, and was further confirmed with X-ray photoelectron spectroscopy. Variation of the composition with depth of the film was studied by removing the layers with low current (20 μA) Ar⁺ etching. It was observed that with successive Ar⁺ etching, In/Sb ratio remained the same, while the As/Sb and Bi/Sb ratios changed slightly with etching time. However after about 5 min etching the As/Sb and Bi/Sb ratios reached constant values. The room temperature band gap of InBi_0.025As_0.105Sb_0.870 was found to be in the range of 0.113–0.120 eV. The measured values of mobility and carrier density at room temperature are 3.1×10⁴ cm² V⁻¹ s⁻¹ and 8.07×10¹⁶ cm⁻³, respectively.     

Observation of bulk like magnetic ordering below the blocking temperature in nanosized zinc ferrite

We investigated the magnetic behavior of nanosized zinc ferrite with the help of vibrating sample magnetometry and in-field Mössbauer spectroscopy. The nanoparticles of zinc ferrite with crystallite size ranging from 10 to 62 nm were synthesized by a nitrate method. The structure and phase were determined with the help of X-ray diffraction. Attributes of cation inversion were found with the calculated values of lattice parameter. The saturation magnetization decreases with the increase in crystallite size at room temperature, while these values are almost the same at 10 K for all the samples except the one with crystallite size of 10 nm. The thermal magnetization measurement shows a decrease in blocking temperature with increase in particle size for these samples. The synthesized samples exhibit the presence of antiferromagnetic ordering below the blocking temperature as investigated by in-field Mössbauer spectroscopy.     

Study of size dependent features of swift heavy ion irradiation in nanosized zinc ferrite

In the present work zinc ferrite nanoparticles of different crystallite size were irradiated with 200 MeV Ag¹⁵⁺ ion beam. The structural and magnetic characterization performed for these samples indicate the presence of size dependent irradiation induced changes in the nanoparticles. The superparamgnetic nanoparticles do not alter their behavior after irradiation; however paramagnetic samples exhibit weak ferrimagnetism in the irradiated specimen. Results obtained from these measurements are in agreement with results obtained from the electron paramagnetic resonance spectroscopy.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Z-dependence of the intensity of |Δn|=2 pionic X-rays

The intensity per stopped π^?of|Δn|=2 pionic X-rays are observed to have larger variations with atomic number Z than do the |Δn|=1. The 6–4 intensity has a well-defined maximum at Z=34 with a FWHM of ΔZ ～10.     

Genetic stability assessment of plants regenerated from cryopreserved embryogenic tissues of Dioscorea bulbifera l. Using RAPD,biochemical and morphological analysis

Embryogenic tissues of Dioscorea bulbifera were cryopreserved using the encapsulation-dehydration technique. Genetic stability of plants regenerated from cryopreserved embryogenic tissues was assessed using molecular, biochemical and morphological analysis. The random amplified polymorphic DNA (RAPD) analysis of 60 cryopreserved-derived and 20 in vitro grown (control) plantlets showed that 10 primers produced 62 clear reproducible DNA fragment profiles. The amplification products were monomorphic for all the plantlets except one. A total of 4960 DNA fragments were obtained from this study showing no variation in RAPD profiles. The diosgenin content of cryopreserved-derived plants, analyzed using HPLC, was similar to that of control plants. Morphology and the ability to form microtuber were also found to be unaltered in cryopreserved embryo-derived plantlets. Thus, the D. bulbifera plants regenerated from cryopreserved embryogenic tissues were genetically stable at the molecular, biochemical and morphological levels.