Discrete Division Research Articles

A Simplified Radiation Characteristic Analysis Method for Defocus-Fed Parabolic Antennas in a W-Band Communication System

With increasing interest in the W-band, there is growing focus on parabolic reflector antennas that are known for efficiently inducing high-gain radiation characteristics. There is particular focus on parabolic antennas with diverse defocus-fed applications, including monopulse tracking, multi-beam formation using multiple feeds, and aperture-shared antennas for multi-band operation. Thus, a new simplified method is presented in this paper to analyze the radiation characteristics of defocus-fed parabolic antennas. The presented method is based on the discrete division of a parabolic reflector surface and considers only simplified wave propagation theory and the effect of the scalar function pattern from the feeder. Additionally, array theory is exclusively applied for the analysis of radiation characteristics. Therefore, the presented method uses a very simplified formula to calculate the radiation characteristics of a defocused parabolic reflector antenna. The performance of the presented method was evaluated by comparing the results with commercial EM tools. The results of the analysis confirm the applicability of the presented method for the analysis of defocus-fed parabolic antennas.

Discretization Method to Improve the Efficiency of Complex Airspace Operation

With the increase in airspace flow, the complexity of the airspace operation environment has also increased. Against this backdrop, improving the operational efficiency of airspace is crucial to ensure its efficient operation. The discrete division of controlled airspace represents a novel methodology for achieving this end. This approach involves visualizing the use of the airspace, quantifying and evaluating the operational efficiencies of airspace environments, and assessing specific metrics during an allocated time period. In this study, a discrete unit model was constructed to hierarchically subdivide complex airspace into static obstacles and aircraft-occupied space units, which facilitated the optimization of decision-making operations for multiple aircraft in airspace using the discrete method. Furthermore, busy airspace units could be effectively avoided. Finally, by using the extended analytic hierarchy process, we evaluated the threshold value of airspace operational efficiency improvement when operation efficiency metrics were enhanced via discrete approaches. The results indicated that the threshold value was 0.02168, classified as “good”, which represented an improvement in comparison with the original value of airspace operational efficiency (0.03173). These findings demonstrated that the application of the discrete division methodology significantly improved the overall operational efficiency of the airspace.

Multi-Time Interval Dynamic Optimization Model of New Energy Output Based on Multi-Energy Storage Coordination

In response to the problem of mismatch between new energy output and multi-energy load requirement in multi-energy power systems, this article proposes a dynamic optimization model for new energy output in multiple time intervals based on multi-energy storage coordination. First, considering the energy conversion characteristics of multi-energy storage, the dynamic optimization method of new energy output based on the discrete division of subinterval of scheduling time is studied. Then, considering the cost of adjusting various resources comprehensively, the optimization objective of new energy output is studied, and a model-solving method based on a directed graph topology distributed algorithm is proposed. Finally, simulation verification was conducted, and the simulation results showed that the method proposed in this paper can effectively suppress the new energy fluctuation and reduce peak-shaving costs.

Electrostatic nature of covalent bond

Based on the toroidal structure of the electron shells of some atoms, discovered by scanning probe microscopy, a classical model for the formation of a covalent bond of homonuclear molecules, such as H2, O2 and similar, is proposed. When there is no spherical symmetry in the charge distribution on the electron shell in an atom, then outside it, in some spatial directions, an electric field is formed, leading to the appearance of Coulomb repulsive forces. Previously developed by Gillespie, the electron pair repulsion model relatively accurately described the interactions of atoms only in compounds of non-transitional elements, since the repulsive forces should increase with decreasing distance between atoms to a degree greater than the second, characteristic of the Coulomb forces. The structure of an atom of a homogeneous molecule is considered in the form of a planetary model, in which the electron shell is presented in the form of a uniformly charged ring, and the nucleus - in the form of a point charge in the center of the ring. Calculation of Coulomb fields between two homogeneous atoms is made. The results of calculating the differences between the fields of the nucleus and the electron shell, obtained by discrete division of the ring charge into 16 elements, are presented. The point charge in the simulation was set positive, and the ring charge was negative. At distances commensurate with the radius of the ring (from 2 to 4 radii), the intensity of the difference field along the axis increases by a factor of 2.3, and in the plane of the ring - by a factor of 1.7. When two "point-ring" systems are oriented in space at 90 degrees to each other, they must be attracted under the influence of not only gravitational, but also Coulomb forces. However, when such systems approach each other, the interaction of the two systems becomes more complex, and the attractive forces are balanced by the repulsive forces of like charges, forming a potential well and creating a stable spatial structure. The distances between point charges (nuclei) in such a system slightly exceed the radii of rings (electron shells), which corresponds to experimental data on the distances between atoms in two-atomic gas molecules.

Unitary Matrix Method for PAPR Reduction of IDFT-VFDM Signals

To enable the frequency reuse between the new radio (NR) and the long-term evolution (LTE) systems, inverse discrete Fourier transform-based Vandermonde-subspace frequency division multiplexing (IDFT-VFDM) has been proposed to exploit the guard intervals of the conventional orthogonal frequency division multiplexing (OFDM) system. One important issue of the IDFT-VFDM system is the high peak-to-average power ratio (PAPR), which distorts the transmitted signal and causes severe performance degradation. Compared to OFDM, the method to reduce the PAPR in IDFT-VFDM requires unique design to guarantee zero interference to the legacy LTE system. To deal with this problem, a unitary matrix based method is proposed to design the precoder at the NR users to reduce the PAPR, which can also guarantee the minimum residual interference to the LTE system. Simulation results are demonstrated to verify the effectiveness of the proposed scheme.

Bit‐level implementation for polynomial cancellation coded DFT‐s‐OFDM transmitters

Polynomial cancellation coded discrete Fourier transform-spread orthogonal frequency division multiplexing (PCC-DFT-s-OFDM) is famous for the flexibility of DFT-s-OFDM on the trade-off between peak-to-average power ratio performance and spectral efficiency. Deploying it on numerous user equipments (UEs) as enhanced uplink signalling becomes a practical issue. In this Letter, a bit-level implementation of PCC mapping is proposed, so that the compatibility of implementation of corresponding circuits on UE transmitters would make the deployment more easily. By taking Long Term Evolution and New Radio standards as examples, the equivalency of bit/symbol-level implementations is validated in terms of bit error rate performance.

Prediction of radiative heat transfer using multi-flux method in space application

Interaction between fluid flow and thermal radiation has received considerable attention due to its numerous applications in engineering field including space applications. To analyse the radiation heat transfer in a radiating fluid, the simultaneous solution of the radiation transfer equation (RTE) and the fluid dynamics equations is required. This means that the numerical procedure used for the RTE must be computationally efficient to permit its inclusion in the other submodels, and must be compatible with the other transport equations. In this context the finite volume method (FVM) and the discrete ordinates method (DOM) are usually being incorporated to simulate radiation problems with curvilinear coordinates. In this paper these two representative methods are examined and compared, especially in terms of the directional dependence of radiation intensity due to the discrete division of a solid angle. The FVM shows more reasonable results than the DOM does, as it has less constraint on the angular discretisation.

Rate-Adaptive DFT-Spread DMT and CDMA-DMT for 1-mm SI-POF Short-Range Links

In this letter, rate-adaptive bit-loading techniques are explored for maximizing the transmission rate of spreading multicarrier modulation schemes over step index plastic optical fiber (SI-POF) short range transmission links. Both the discrete Fourier transform (DFT)-spread discrete multitone (DMT) and code division multiple access-DMT are experimentally evaluated and compared against conventional rate adaptive DMT, over a 50-m intensity modulation direct-detection (IM/DD) link of 1-mm PMMA SI-POF. It is shown that both schemes achieve better performance than DMT, whereas DFT-spread DMT behaves best among them, over the same experimental setup.

Analysis and Simulation of Division- and Label-Structured Population Models

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate.

Spatial Filtering of MEG Signals for User-Specified Spherical Regions

We introduce a spatial filtering method in the spherical harmonics domain for constraining magnetoencephalographic (MEG) multichannel measurements to any user-specified spherical region of interest (ROI) inside the head. The method relies on a linear transformation of the signal space separation inner coefficients that represent the MEG signal generated by sources located inside the head. The spatial filtering is achieved effectively by constructing a spherical harmonics basis vector that is dependent on the center of the targeted ROI and it does not require any discrete division of the headspace into grids like the traditional MEG spatial filtering approaches. The validation and the performance of the method are demonstrated through both simulated and actual bilateral auditory-evoked data experiments.

Toledo Cathedral's Collection of Manuscript Plainsong Choirbooks: A Preliminary Report and Checklist

The Spanish primatial cathedral of Toledo possesses one of the largest surviving collections of indigenously produced plainsong sources deriving from any major ecclesiastical institution in Western Christendom. The collection comprises about 170 volumes for the Mass, Office, and processions, including atlas-size choirbooks produced for use in liturgical functions held in the cathedral's own coro (liturgical choir), and smaller volumes for its various chapels. Bound between leather-covered wooden boards, most of these parchment volumes were copied, illuminated, corrected, and bound in Toledo by the cathedral's regularly contracted lay craftsmen. Around thirty books of non-Toledan provenance have been added to the collection, forming a musical repository comprising in excess of 22,000 folios, the great majority of which, despite serious damage to some volumes, are entirely legible. Despite its extraordinary importance, the Toledo collection of choirbooks has eluded serious scholarly attention for almost exactly a century. In 1905, P. Luciano Serrano, OSB, mentioned having examined los cantorales de la Catedral, and reported that the collection se compone de unos cien volumenes en folio. (1) In fact, the cathedral's indigenously produced collection now consists of around 130 of these large-format heavily bound manuscripts and around forty books of chant in medium and smaller formats. (2) We began cataloging the collection in late 2002, at the request of the then canon-archivist, Don Ramon Gonzalvez Ruiz, and we continued the task on site until mid-2003, with the enthusiastic encouragement of the dean, Don Santiago Calvo. (3) A full catalog of the collection, commissioned by the dean, is now in preparation. We present here a preliminary report, to which a short form of the catalog--a provisional checklist with brief physical description of each book--is attached as an appendix. It must be emphasized, however, that, for reasons of space, the amount of information we present in the provisional checklist is extremely limited. Today, the fondo de cantorales forms a discrete division of the cathedral's Archivo Capitular. (4) It preserves almost all the plainchant choirbooks copied for use in the choir between the second quarter of the sixteenth century and the end of the nineteenth century. In addition, the Archivo Capitular houses separately a small but significant number of earlier chant volumes previously cataloged and integral to the Toledan liturgy, dating from as early as the last quarter of the eleventh century, and through to the last quarter of the fifteenth century. The collection of cantorales is of enormous musical and liturgical interest, by definition the most important (if, alas, incomplete) surviving record of the chant dialect known as canto toledano, and important too for the study of all aspects of manuscript book production in Spain. (5) The artistic quality of the many illuminations ranges from mediocre to extremely fine and priceless. Yet despite the primacy of the institution that commissioned them, the Toledo collection is relatively plain in appearance and presentation. Unfortunately, too, a significant number of the books have sustained serious water damage. Some of the volumes, or parts of volumes in the case of the many composite bindings, were signed and/or dated by their respective scribes. Others are identifiable from a wealth of supporting documentation. Two types of documents in particular allow us to chart the history and preservation of the collection. The accounts of the Archivo de Obra y Fabrica contain a plethora of specific references to the scribes, illuminators, dates of production, and binding of identifiable volumes. (6) Likewise, detailed inventarios of chant books form part of episcopal visitation reports dating from (Cardinal Cisneros; Inv. 1503 in the checklist below), 1539 (Cardinal Tavera; Inv. 1539), 1580 (Cardinal Quiroga; Inv. 1580), 1600 (Cardinal Sandoval), 1649 (Cardinal Moscoso; Inv. …

Calcium and pH in north and central Swedish mire waters

Summary We present data on calcium concentrations and pH in mire waters collected from different mire types in central and northern Sweden, compiled from published literature or calculated from field determinations of electrical conductivity and pH. Measurements of electrical conductivity (after subtracting that of H+ ions) were used to calculate the most probable Ca concentrations, but only when pH was 4.7 or higher. At lower pH the possible errors become too large. The data support a continuous gradient in water chemistry, but with considerable overlap, from mineral‐poor ombrotrophic bogs and minerotrophic extremely poor fens, to moderately poor fens, intermediate fens, moderately rich fens and finally to extremely rich fens, rather than a discrete division. However, for hydrological reasons, we wish to retain the separation of ombrotrophy (bog) from minerotrophy (fen). The frequency histogram of pH values from central and northern Sweden shows a bimodal tendency, although a considerable number of mires still occur close to the minimum (pH 5.3). Over‐sampling in species‐rich areas could have contributed to the depth of this apparent minimum, but not to its position along the pH scale. Changes in calcium concentrations in mire waters during the last 50 years are discussed and related to changes in pH and conductivity.

Solution and properties of age population balance models which assume discrete division ages

A solution procedure for models of the transient age distribution which employ the assumption of discrete, constant division ages is developed. The solutions for the final state of the age distribution, the solutions obtained in the limit as time goes to infinity, are found to have properties which do not make biological sense. In particular, the solutions will only approach the steady-state solution for very special initial conditions. For most initial conditions, the solution for the final state will instead exhibit an oscillatory behavior. In addition, the oscillatory solutions are unstable with respect to changes in values of the model parameters and solutions with very different periods of oscillation are found arbitrarily close to each other in the parameter space. Models which assume discrete division ages must therefore be used with caution and may be unsuitable as models of autonomous microbial oscillations.

A Checklist of the Liverworts and Hornworts of North America

A Checklist of the Liverworts and Hornworts of North America

Metrizability of locally compact vector spaces

By use of the theory of characters and the Pontryagin-van Kampen theorem, it is shown that if E E is a locally compact vector space over a discrete division ring K K of characteristic zero and if dim K E > 2 m {\dim _K}E > {2^\mathfrak {m}} , where m \mathfrak {m} is the cardinality of K K , then E E is metrizable.

Locally compact vector spaces and algebras over discrete fields

The structure of locally compact vector spaces over complete division rings topologized by a proper absolute value (or, more generally, over complete division rings of type V) is summarized in the now classical theorem that such spaces are necessarily finite-dimensional and are topologically isomorphic to the cartesian product of a finite number of copies of the scalar division ring [9, Theorems 5 and 7], [6, pp. 27-31]. Here we shall continue a study of locally compact vector spaces and algebras over infinite discrete fields that was initiated in [16]. Since any topological vector space over a topological division ring K remains a topological vector space if K is retopologized with the discrete topology, some restriction needs to be imposed in our investigation, and the most natural restriction is straightness: A topological vector space E over a topological division ring K is straight if for every nonzero a E E, fa: A -Aa is a homeomorphism from K onto the one-dimensional subspace generated by a. Thus if K is discrete, a straight K-vector space is one all of whose one-dimensional subspaces are discrete. Any Hausdorff vector space over a division ring topologized by a proper absolute value is straight [6, Proposition 2, p. 25]. In ?1 we shall prove that if E is an indiscrete straight locally compact vector space over an infinite discrete division ring K, then K is an absolutely algebraic field of prime characteristic and [E : K]> Ro. In ?2 we shall see that finitedimensional subspaces of straight locally compact vector spaces need not be discrete. In ?3 we shall see that the validity of the Open Mapping and Closed Graph theorems for straight locally compact vector spaces depends on whether those spaces are generated by compact subsets. In ?4 we shall study locally compact algebras of linear operators. In ?5 we shall obtain structure theorems for a commutative semisimple straight locally compact algebra over an infinite discrete field; such an algebra is the topological direct product of a discrete algebra and a local subdirect product of a sequence of algebras, each discrete and algebraically the cartesian product of a family of fields, relative to finite subfields.