Box Topology Research Articles

Comparing two topology transformer hysteresis models derived from DC hysteresis measurements

PurposeThe purpose of this paper is to investigate the applicability of a direct current (DC) hysteresis measurement on power transformer terminals for the subsequent hysteresis model parametrization in transformer grey box topology models.Design/methodology/approachTwo transformer topology models with two different hysteresis models are used together with a DC hysteresis measurement via the power transformer terminals to parameterize the hysteresis models by means of an optimization. The calculated current waveform with the derived model in the transformer no-load condition is compared to the measured no-load current waveforms to validate the model.FindingsThe proposed DC hysteresis measurement via the power transformer terminals is suitable to parametrize two hysteresis models implemented in transformer topology models to calculate the no-load current waveforms.Originality/valueDifferent approaches for the measurement and utilization of transformer terminal measurements for the hysteresis model parametrization are discussed in literature. The transformer topology models, derived with the presented approach, are able to reproduce the transformer no-load current waveform with acceptable accuracy.

Canal: A Flexible Interconnect Generator for Coarse-Grained Reconfigurable Arrays

The architecture of a coarse-grained reconfigurable array (CGRA) interconnect has a significant effect on not only the flexibility of the resulting accelerator, but also its power, performance, and area. Design decisions that have complex trade-offs need to be explored to maintain efficiency and performance across a variety of evolving applications. This paper presents Canal, a Python-embedded domain-specific language (eDSL) and compiler for specifying and generating reconfigurable interconnects for CGRAs. Canal uses a graph-based intermediate representation (IR) that allows for easy hardware generation and tight integration with place and route tools. We evaluate Canal by constructing both a fully static interconnect and a hybrid interconnect with ready-valid signaling, and by conducting design space exploration of the interconnect architecture by modifying the switch box topology, the number of routing tracks, and the interconnect tile connections. Through the use of a graph-based IR for CGRA interconnects, the eDSL, and the interconnect generation system, Canal enables fast design space exploration and creation of CGRA interconnects.

The (dis)connectedness of products of Hausdorff spaces in the box topology

In this paper the following two propositions are proved: (a) If $X_\alpha$, $\alpha \in A$, is an infinite system of connected spaces such that infinitely many of them are nondegenerated completely Hausdorff topological spaces then the box product $\square_{\alpha \in A} X_\alpha$ can be decomposed into continuum many disjoint nonempty open subsets, in particular, it is disconnected. (b) If $X_\alpha$, $\alpha \in A$, is an infinite system of Brown Hausdorff topological spaces then the box product $\square_{\alpha \in A} X_\alpha$ is also Brown Hausdorff, and hence, it is connected. A space is Brown if for every pair of its open nonempty subsets there exists a point common to their closures. There are many examples of countable Brown Hausdorff spaces in literature.

Максимальные сцепленные системы на семействах измеримых прямоугольников

Linked and maximal linked systems (MLS) on π -systems of measurable (in the wide sense) rectangles are considered (π-system is a family of sets closed with respect to finite intersections). Structures in the form of measurable rectangles are used in measure theory and probability theory and usually lead to semi-algebra of subsets of cartesian product. In the present article, sets-factors are supposed to be equipped with π-systems with “zero” and “unit”. This, in particular, can correspond to a standard measurable structure in the form of semialgebra, algebra, or σ-algebra of sets. In the general case, the family of measurable rectangles itself forms a π -system of set-product (the measurability is identified with belonging to a π - system) which allows to consider MLS on a given π -system (of measurable rectangles). The following principal property is established: for all considered variants of π -system of measurable rectangles, MLS on a product are exhausted by products of MLS on sets-factors. In addition, in the case of infinity product, along with traditional, the “box” variant allowing a natural analogy with the base of box topology is considered. For the case of product of two widely understood measurable spaces, one homeomorphism property concerning equipments by the Stone type topologies is established.

Second-order post-Minkowskian scattering in arbitrary dimensions

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

Dispersion approach in two-loop calculations

The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak corrections to M{\o}ller or electron-proton scattering. It is a demanding task which requires an application of various approaches where two-loop calculations can be automatized. We choose to employ dispersive sub-loop insertion approach and develop two-loop integrals using two-point functions basis. In that basis, we introduce a partial tensor reduction for many-point Passarino-Veltman functions, which later could be used in computer algebra packages. In this paper, we have considered self-energy, triangle and box sub-loop insertions into self-energy, vertex and box topology.

Diagonals of separately continuous maps with values in box products

Abstract We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such that f (x, x) = g(x) for all x ∈ X.

A few remarks on boundedness in topological modules and topological groups

Let $X$, $Y$, and $Z$ be topological modules over a topological ring $R$. In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies. We show that these spaces form again topological modules over $R$. In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

Uniform powers of compacta and the proximal game

The countable uniform power (or uniform box product) of a uniform space X is a special topology on Xω that lies between the Tychonoff topology and the box topology. We solve an open problem posed by P. Nyikos showing that if X is a compact proximal space then the countable uniform power of X is also proximal (although it is not compact). By recent results of J.R. Bell and G. Gruenhage this implies that the countable uniform power of a Corson compactum is collectionwise normal, countably paracompact and Fréchet–Urysohn. We also give some results about first countability, realcompactness in countable uniform powers of compact spaces and explore questions by P. Nyikos about semi-proximal spaces.

Noetherian type in topological products

The cardinal invariant Noetherian type Nt(X) of a topological space X was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces.We prove in Section 2: (1) There are spaces X and Y such that Nt(X×Y)< min{Nt(X), Nt(Y)}. (2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight \({\aleph _\omega }\) with the countable box topology, \({({2^{{\aleph _\omega }}})_\delta }\), is shown in Section 3 to be closely related to the combinatorics of covering collections of countable subsets of \({\aleph _\omega }\). We discuss the influence of principles like \({\square _{{\aleph _\omega }}}\) and Chang’s conjecture for \({\aleph _\omega }\) on this number and prove that it is not decidable in ZFC (relative to the consistency of ZFC with large cardinal axioms).Within PCF theory we establish the existence of an (ℵ4, ℵ1)-sparse covering family of countable subsets of \({\aleph _\omega }\) (Theorem 3.20). From this follows an absolute upper bound of ℵ4 on the Noetherian type of \({({2^{{\aleph _\omega }}})_\delta }\). The proof uses a method that was introduced by Shelah in 1993 [33].

Global residues and two-loop hepta-cuts

We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby providing additional steps towards automated computation of the full amplitude. The coefficients are obtained by assembling residues extracted through integration on linear combinations of higher-dimensional tori encircling global poles of the loop integrand. We recover all salient features of two-loop maximal unitarity, such as the existence of unique projectors for each master integral. Several explicit calculations are provided. We also establish exact equivalence of our results and master integral coefficients recently obtained via integrand-level reduction in any renormalizable gauge theory.

The box topology of infinite simplicial complexes

The box topology of infinite simplicial complexes

Maximal vector topologies

Suppose that κ is an infinite cardinal, Vκ=⊕α<κRα is a vector space of dimension κ over R, τκ is the box topology on Vκ, μκ and νκ are the maximal and maximal locally convex vector topologies on Vκ respectively. We prove that τω=μω=νω but, for every κ>ω, μκ⊃νκ⊃τκ. For every κ, the topological vector spaces (Vκ,μκ), (Vκ,νκ), (Vκ,τκ) are complete but not sequential.

The metrizablity of product spaces

Let (Xt)t∈I be a family of topological spaces and t∈I Xt be a product space. In this paper, t∈I Xt has two topology which are called product and box topology. We want to establish the metrizablity of t∈I Xt with respect to both topology and get some conclusions.

Synthesis and design of asymmetrical dual-band bandpass filters based on equivalent network simplification

Although the synthesis of symmetrical dual-band bandpass filters has been studied, little seems to be known about the general asymmetrical case. In this paper, a procedure for the synthesis of general asymmetrical dual-band bandpass filters implemented with inline dual-mode cavities is proposed. The inline architecture, as well as the asymmetrical nature of the response, lead naturally to the choice of an extended box topology or generalizations of the latter. It was recently shown that these topologies possess the property of multiple solutions, meaning that the related coupling matrix synthesis problem admits several solutions. On one hand, this multiplicity offers some flexibility to the designer, but on the other hand, working with multiple solutions may lead to ambiguities during the tuning process. Our procedure takes the best of both worlds: using the list of equivalent coupling matrices, simplifications of the original topology can be obtained by canceling some particular couplings. The locations of cancelled couplings are chosen so as to preserve the electrical response and to provide some hardware simplifications. It is also shown that the resulting simplified topology no longer has the multiple solution property, therefore solving ambiguity problems. The procedure is detailed and demonstrated on two examples.

On Prebox Module Topologies

Let R be a complete topological division ring whose topology is determined by a real-valued valuation, and let M be a vector space over R. It is proved that M admits a Hausdorff module topology preceding the box topology in the lattice of all module topologies if and only if the dimension of the vector space M over R is a measurable cardinal.

Binz-Butzmann duality versus Pontryagin duality

A convergence structure Ξ on a set G is a set of pairs (F,x) consisting of a filter F on X and an element x∈X satisfying a few simple axioms expressing the idea that F converges to x. A set with a convergence structure is a convergence space. It should be clear what continuous functions between convergence spaces are. A subset of a convergence space is compact if every ultrafilter on it converges to an element in it. If G is a group, then (G,Ξ) is called a convergence group if (x,y)↦xy−1:G×G→G is continuous. For an abelian topological group G let ΓG denote the group of continuous characters G→R/Z. Then ΓG is a convergence group with respect to a convergence structure for which a filter F converges to χ if for any filter H on G converging to g the filter basis F(H) converges to χ(g). The convergence group arising in this fashion is denoted by Γc (G). The topological character group endowed with the compact-open topology is written Gˆ. The authors establish the following theorem: Let G be a topological abelian group such that the canonical evaluation morphism G→Gˆˆ is continuous. Then ΓcG is locally compact (in the sense that every convergent filter contains a compact member), and the bidual Gˆˆ may be identified with a topological subgroup of ΓcΓc (G). Examples show that equality does not prevail in general as it does when G is locally compact. The examples are mostly taken from topological vector spaces. For a countable family of locally compact abelian groups Gn one knows from Kaplan's theorem that the character group of ∑Gn with the box topology is ∏Gnˆ. Then the continuous convergence structure on ∏Gnˆ is finer than the convergence structure of the product topology and coarser than the convergence structure of the box topology—in general properly so in both instances. It is shown that ∑Gn≅ΓcΓc (∑Gn) canonically and, similarly, for ∏Gn.

Infinite Chichilnisky rules

Topological aggregation in an infinite context depends crucially upon the type of topology. Tychonov topologies do not admit an infinite Chichilnisky rule, while box topologies based upon an appropriate topology do.

Transport and carbon exchanges in Red Sea Inverse Methodology

In this paper, we use an inverse methodology to parameterize a box model of the Red Sea to study carbon exchanges and transport. In this application, we use simultaneously the information contained in physical and biogeochemical tracer profiles such as temperature, salinity, dissolved inorganic carbon, alkalinity, oxygen, and phosphate. Since the Red Sea is subject to a seasonal monsoon regime and because we are interested in resolving exchanges from the surface to the bottom, we have decoupled the temporal regime into two seasons : winter (November to May) and summer (June to October). We present the two solutions which include advective and mixing (eddy diffusion) exchanges as well as new primary production, decomposition, carbonate formation, and dissolution. The circulation is reversed from one season to the next. The net biological exchanges (new production) of carbon, compatible with the dynamical solutions, are almost null for the organic processes (negative in summer, positive in winter); the budgets for the mineral processes are negative for both seasons. This result is consistent with the view that carbonates play an important role in the budget of carbon in Red Sea. Finally, taking advantage of richer data sets for the summer season, we present two box designs for this period. It appears that transport solutions are sensitive to the choice of box topology, whereas biochemical exchanges are roughly the same for both designs.

Locally Unbounded Topological Fields and Box Topologies on Products of Vector Spaces†

Locally Unbounded Topological Fields and Box Topologies on Products of Vector Spaces†