Endomorphisms of the Separated Product of Lattices

To describe the evolution of separated entities remaining separated, we proposeto study endomorphisms (join-preserving maps, sending atoms to atoms) of theseparated product of cao lattices (complete, atomistic orthocomplementedlattices). Morphisms have been used successfully to describe the evolution ofentities, and the separated product is a model for the property lattice of separatedsystems; its set of atoms is the Cartesian product of each atom space. Let L bethe separated product of two cao lattices having the covering property and f anendomorphism of L. We prove that the center F(L) of L is the power set of₁ × ₂ where _i is the atom space ofF(L _i ) (Theorem 1), f preserves irreduciblecomponents (Theorem 2), and if L is irreducible there exist two endomorphismsf ¹ and f ² and a permutation such that the restriction of f to atoms is given byf(p ₁, p ₂) = (f ¹(p ₍₁₎), f ²(p ₍₂₎))(Theorem 3). For generalizations of these resultsto separated products of families of cao lattices, we develop new general argumentsinvolving a topology we define on the set of atoms of a cao lattice.     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

Magnetic-Electric Metamirror and Polarizing Beam Splitter Composed of Anisotropic Nanoparticles

The emergence of new materials and fabrication techniques provides progress in the development of advanced photonic and communication devices. Transition metal dichalcogenides (e.g., molybdenum disulfide, MoS₂) are novel materials possessing unique physical and chemical properties promising for optical applications. In this paper, a metasurface composed of particles made of bulk MoS₂ is proposed and numerically studied considering its operation in the near-infrared range. In the bulk configuration, MoS₂ has a layered structure being a uniaxial anisotropic crystal demonstrating an optical birefringence property. It is supposed that the large-scale and uniform MoS₂ layers are synthesized in a vertical-standing morphology, and then they are patterned into a regular 2D array of disks to form a metasurface. The natural anisotropy of MoS₂ is utilized to realize the splitting of electric and magnetic dipole modes of the disks while optimizing their geometric parameters to bring the desired modes into overlap. At the corresponding resonant frequencies, the metasurface behaves as either an electric or a magnetic mirror, depending on the polarization of incident light. Based on the extraordinary reflection characteristics of the proposed metasurface, it can be considered an alternative to traditional mirrors and optical splitters when designing compact and highly efficient metadevices, which provide polarization and phase manipulation of electromagnetic waves on a subwavelength scale.     

Tuning the morphology and magnetic properties of single-domain SrFe8Al4O19 particles prepared by a citrate auto-combustion method

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Generation of Phosphide Anions from Phosphorus Red and Phosphine in Strongly Basic Systems to Form Organylphosphines and -Oxides

Abstract

Generation of phosphide anions from phosphorus red or phosphine under the action of strong bases followed by their reactions with organyl halides, electrophilic alkenes and alkynes proves to be the most straightforward and well-controlled route to mono-, di- or triorganylphosphines or phosphine oxides of diverse structure.     

Statistics of the Popularity of Chemical Compounds in Relation to the Non-Target Analysis

The idea of popularity/abundance of chemical compounds is widely used in non-target chemical analysis involving environmental studies. To have a clear quantitative basis for this idea, frequency distributions of chemical compounds over indicators of their popularity/abundance are obtained and discussed. Popularity indicators are the number of information sources, the number of chemical vendors, counts of data records, and other variables assessed from two large databases, namely ChemSpider and PubChem. Distributions are approximated by power functions, special cases of Zipf distributions, which are characteristic of the results of human/social activity. Relatively small group of the most popular compounds has been denoted, conventionally accounting for a few percent (several million) of compounds. These compounds are most often explored in scientific research and are practically used. Accordingly, popular compounds have been taken into account as first analyte candidates for identification in non-target analysis.