Generalized flatness constants, spanning lattice polytopes, and the Gromov width

In this paper we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular copy of a standard simplex. Following an argument of Eisenbrand and Shmonin, we prove that every lattice polytope contains a minimal generating set of the affine lattice spanned by its lattice points such that the number of generators (and the lattice width of their convex hull) is bounded by a constant which only depends on the dimension. We also discuss relations to recent results on spanning lattice polytopes and how our results could be viewed as the beginning of the study of generalized flatness constants. Regarding symplectic geometry, we point out how the lattice width of a Delzant polytope is related to upper and lower bounds on the Gromov width of its associated symplectic toric manifold. Throughout, we include several open questions.

Pinning Decision in Interconnected Systems with Communication Disruptions under Multi-Agent Distributed Control Topology

In this study, we propose a decision-making strategy for pinning-based distributed multi-agent (PDMA) automatic generation control (AGC) in islanded microgrids against stochastic communication disruptions. The target microgrid is construed as a cyber-physical system, wherein the physical microgrid is modeled as an inverter-interfaced autonomous grid with detailed system dynamic formulation, and the communication network topology is regarded as a cyber-system independent of its physical connection. The primal goal of the proposed method is to decide the minimum number of generators to be pinned and their identities amongst all distributed generators (DGs). The pinning-decisions are made based on complex network theories using the genetic algorithm (GA), for the purpose of synchronizing and regulating the frequencies and voltages of all generator bus-bars in a PDMA control structure, i.e., without resorting to a central AGC agent. Thereafter, the mapping of cyber-system topology and the pinning decision is constructed using deep-learning (DL) technique, so that the pinning-decision can be made nearly instantly upon detecting a new cyber-system topology after stochastic communication disruptions. The proposed decision-making approach is verified using a 10-generator, 38-bus microgrid through time-domain simulation for transient stability analysis. Simulations show that the proposed pinning decision making method can achieve robust frequency control with minimum number of active communication channels.

Graded Betti Numbers of Balanced Simplicial Complexes

We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and $I\subseteq S$ I ⊆ S is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.

p-Groups of automorphisms of compact non-orientable Riemann surfaces

We study p-groups of automorphisms of compact non-orientable Riemann surfaces of topological genus $$g\ge 3$$ g ≥ 3 . We obtain upper bounds of the order of such groups in terms of p, g and the minimal number of generators of the group. We also determine those values of g for which these bounds are sharp. Furthermore, the same kind of results are obtained when the p-group acts as the full automorphism group of the surface.

Quasi-powerful 𝑝-groups

In this paper, we introduce the notion of a quasi-powerful 𝑝-group for odd primes 𝑝. These are the finite 𝑝-groups 𝐺 such that G / Z ⁢ ( G ) G/Z(G) is powerful in the sense of Lubotzky and Mann. We show that this large family of groups shares many of the same properties as powerful 𝑝-groups. For example, we show that they have a regular power structure, and we generalise a result of Fernández-Alcober on the order of commutators in powerful 𝑝-groups to this larger family of groups. We also obtain a bound on the number of generators of a subgroup of a quasi-powerful 𝑝-group, expressed in terms of the number of generators of the group, and we give an example which demonstrates this bound is close to best possible.

ROBUST TUNING OF POWER SYSTEM STABILIZER PARAMETERS USING THE MODIFIED HARMONIC SEARCH ALGORITHM

Power System Stabilizer is used to improve power system low frequency oscillations during small disturbances. In large scale power systems involving a large number of generators, PSSs parameter tuning is very difficult because of the oscillatory modes’ low damping ratios. So, the PSS tuning procedure is a complicated process to respond to operation condition changes in the power system. Some studies have been implemented on PSS tuning procedures, but the Harmony Search algorithm is a new approach in the PSS tuning procedure. In power system dynamic studies at the first step system total statues is considered and then the existed conditions are extended to the all generators and equipment. Generators’ PSS parameter tuning is usually implemented based on a dominant operation point in which the damping ratio of the oscillation modes is maximized. In fact the PSSs are installed in the system to improve the small signal stability in the system. So, a detailed model of the system and its contents are required to understand the dynamic behaviours of the system. In this study, the first step was to linearize differential equations of the system around the operation point. Then, an approach based on the modified Harmony Search algorithm was proposed to tune the PSS parameters. ABSTRAK: Penstabil Sistem Kuasa digunakan bagi meningkatkan sistem kuasa ayunan frekuensi rendah semasa gangguan kecil. Dalam sistem kuasa berskala besar yang melibatkan sebilangan besar penjana, penalaan parameter PSS adalah sangat sukar kerana nisbah corak ayunan redaman yang rendah. Maka, langkah penalaan PSS adalah satu aliran rumit bagi mengubah keadaan operasi sistem kuasa. Beberapa kajian telah dilaksanakan pada prosedur penalaan PSS, tetapi algoritma Harmony Search merupakan pendekatan baru dalam prosedur penalaan PSS. Dalam kajian sistem kuasa dinamik ini, langkah pertama adalah dengan memastikan status total sistem dan keadaan sedia ada diperluaskan kepada semua penjana dan peralatan. Parameter penalaan generator PSS biasa dilaksanakan berdasarkan titik operasi yang dominan di mana nisbah corak ayunan redaman dimaksimumkan. Malah PSS dipasang di dalam sistem bagi meningkatkan kestabilan isyarat kecil dalam sistem. Oleh itu, model terperinci sistem dan kandungannya diperlukan bagi mengenal pasti perihal sistem dinamik. Kajian ini, dimulai dengan melinear sistem persamaan pembezaan pada titik operasi. Kemudian, pendekatan berdasarkan algoritma Harmony Search yang diubah suai telah dicadangkan bagi penalaan parameter PSS.

Jordan matrix algebras defined by generators and relations

<abstract><p>In the present paper we describe Jordan matrix algebras over a field by generators and relations. We prove that the minimun number of generators of some special Jordan matrix algebras over a field is $ 2 $.</p></abstract>

Observation and measurements of vector-boson scattering with the ATLAS detector

The scattering of electroweak bosons tests the gauge structure of the Standard Model and is sensitive to anomalous quartic gauge couplings. In this paper, we present recent results on vector-boson scattering from the ATLAS experiment using proton–proton collisions with a center-of-mass energy of 13 TeV at the LHC. This includes the observation of [Formula: see text], [Formula: see text], and same-sign [Formula: see text] production via vector-boson scattering along with a measurement of [Formula: see text] production ([Formula: see text] denotes [Formula: see text] or [Formula: see text] boson) in semileptonic final states. The results can be used to constrain new physics that manifests as anomalous electroweak-boson self-interactions. Finally, predicted cross-sections for the electroweak scattering of two same-sign [Formula: see text] bosons in association with two jets are compared for a number of generators.