Set Of Generators Research Articles

Luba: understanding the intricacies of generational set, age and identity in the Gada system, Ethiopia

ABSTRACT This study investigated the intricacies of Luba structure and its dimensions of generation set, age, and identity in the Guji society, Southern Ethiopia. The study opted for in-depth interviews, key informant interviews, and focus group discussions as techniques of data production, while the analysis was conducted thematically using qualitative descriptions. The findings indicated that Luba is a broad and multifaceted concept that has wider implications in the Gada system. It indicates the Gada parties, namely Muudana, Halchiisa, Dhallana, Harmuufa, and Roobale; fourteen generational sets ranging from Dabballee to Jaarsa Ginya, socially constructed age, and identity in the Gada system. Luba is the structural basement, on which the Gada system was built, and has been functioning. It also shapes an individual’s and social groups’ identity, access to social privileges, social status, and power, serving as the core heritage and backbone of the Gada system. Thus, collaborative efforts are strongly needed for further documentation, preservation, and promotion of Luba for the practicability and sustainability of the Gada system, one of the UNESCO-inscribed intangible heritages.

Irreducible representations of the crystallization of the quantized function algebras $C(\operatorname{SU}_{q}(n+1))$

The crystallization of the C^{*} -algebras C(\operatorname{SU}_{q}(n+1)) was introduced by Giri and Pal in [Proc. Indian Acad. Sci. Math. Sci. 134 (2024), article no. 30] as a C^{*} -algebra C(\operatorname{SU}_{0}(n+1)) given by a finite set of generators and relations. Here we study the representations of the C^{*} -algebra C(\operatorname{SU}_{0}(n+1)) and prove a factorization theorem for its irreducible representations. This leads to a complete classification of all irreducible representations of this C^{*} -algebra. As an important consequence, we prove that all the irreducible representations of C(\operatorname{SU}_{0}(n+1)) arise exactly as q\to 0+ limits of the irreducible representations of C(\operatorname{SU}_{q}(n+1)) . We also present a few other important corollaries of the classification theorem.

Enhancing activity and selectivity of palladium catalysts in ketone α-arylation by tailoring the imine chelate of pyridinium amidate (PYA) ligands.

Even though α-arylation of ketones is attractive for direct C-H functionalization of organic substrates, the method largely relies on phosphine-ligated palladium complexes. Only recently, efforts have focused on developing nitrogen-based ligands as a more sustainable alternative to phosphines, with pyridine-functionalized pyridinium amidate (pyr-PYA) N,N'-bidentate ligands displaying good selectivity and activity. Here, we report on a second generation set of catalyst precursors that feature a 5-membered N-heterocycle instead of a pyridine as chelating unit of the PYA ligand to provide less steric congestion for the rate-limiting transmetalation of the enolate. To this end, new heterocycle-functionalized PYA palladium(ii) complexes containing an oxazole (5b), N-phenyl-triazole (5c), N-methyl pyrazole (5d), N-phenyl-pyrazole, (5e), N-xylyl-pyrazole (5f), and N-isopropyl-pyrazole (5g) were synthesized compared to the parent pyr-PYA complex 5a. Less packing of the palladium coordination sphere was evidenced from solid state X-ray diffraction analysis. While the catalytic activity of the oxazole system was lower, all other complexes showed higher activity. In particular, complex 5g comprised of an electron-donating and sterically demanding iPr-pyrazole chelating PYA ligand is remarkably stable towards air and moisture and shows outstanding catalytic activity with complete selectivity (>99% yield) and turnover frequencies up to 1200 h-1, surpassing that of parent 5a by one order of magnitude and rivalling the most active phosphine-based palladium systems. Kinetic studies demonstrate a first order rate-dependence on palladium and the substrate. Some deviation of linearity together with poisoning experiments suggest a mixed homogeneous/heterogeneous pathway, though the reproducible kinetics of in situ catalyst recycling experiments strongly point to a molecularly defined active species, demonstrating the high potential of PYA-based ligands.

Exhaustive Characterization of Quantum Many-Body Scars Using Commutant Algebras

We study quantum many-body scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in models with exact QMBS, i.e., the large “thermal” subspace and the small “nonthermal” subspace, which are attributed to the existence of unconventional nonlocal conserved quantities in the commutant; hence, it unifies the study of conventional symmetries and weak ergodicity-breaking phenomena into a single framework. Furthermore, this language enables us to use the von Neumann double commutant theorem to formally write down the exhaustive algebra of Hamiltonians with a desired set of QMBS, which demonstrates that QMBS survive under large classes of local perturbations. We illustrate this using several standard examples of QMBS, including the spin-1/2 ferromagnetic, AKLT, spin-1 XY π-bimagnon, and the electronic η-pairing towers of states; in each of these cases, we explicitly write down a set of generators for the full algebra of Hamiltonians with these QMBS. Understanding this hidden structure in QMBS Hamiltonians also allows us to recover results of previous “brute-force” numerical searches for such Hamiltonians. In addition, this language clearly demonstrates the equivalence of several unified formalisms for QMBS proposed in the literature and also illustrates the connection between two apparently distinct classes of QMBS Hamiltonians—those that are captured by the so-called Shiraishi-Mori construction and those that lie beyond. Finally, we show that this framework motivates a precise definition for QMBS that automatically implies that they violate the conventional eigenstate thermalization hypothesis, and we discuss its implications to dynamics. Published by the American Physical Society 2024

Relational Proxies: Fine-Grained Relationships as Zero-Shot Discriminators.

Visual categories that largely share the same set of local parts cannot be discriminated based on part information alone, as they mostly differ in the way the local parts relate to the overall global structure of the object. We propose Relational Proxies, a novel approach that leverages the relational information between the global and local views of an object for encoding its semantic label, even for categories it has not encountered during training. Starting with a rigorous formalization of the notion of distinguishability between categories that share attributes, we prove the necessary and sufficient conditions that a model must satisfy in order to learn the underlying decision boundaries to tell them apart. We design Relational Proxies based on our theoretical findings and evaluate it on seven challenging fine-grained benchmark datasets and achieve state-of-the-art results on all of them, surpassing the performance of all existing works with a margin exceeding 4% in some cases. We additionally show that Relational Proxies also generalizes to the zero-shot setting, where it can efficiently leverage emergent relationships among attributes and image views to generalize to unseen categories, surpassing current state-of-the-art in both the non-generative and generative settings. Implementation is available at https://github.com/abhrac/relational-proxies.

Relations between Poincaré series for quasi-complete intersection homomorphisms

In this article we study base change of Poincaré series along a quasi-complete intersection homomorphism φ : Q → R \varphi \colon Q \to R , where Q Q is a local ring with maximal ideal m \mathfrak {m} . In particular, we give a precise relationship between the Poincaré series P M Q ( t ) \mathrm {P}^Q_M(t) of a finitely generated R R -module M M to P M R ( t ) \mathrm {P}^R_M(t) when the kernel of φ \varphi is contained in m a n n Q ( M ) \mathfrak {m}\,\mathrm {ann}_Q(M) . This generalizes a classical result of Shamash for complete intersection homomorphisms. Our proof goes through base change formulas for Poincaré series under the map of dg algebras Q → E Q\to E , with E E the Koszul complex on a minimal set of generators for the kernel of φ \varphi .

On the automorphisms of the Drinfeld modular groups

Let [Formula: see text] be the ring of elements in an algebraic function field [Formula: see text] over [Formula: see text] which are integral outside a fixed place [Formula: see text]. In contrast to the classical modular group [Formula: see text] and the Bianchi groups, the Drinfeld modular group [Formula: see text] is not finitely generated and its automorphism group [Formula: see text] is uncountable. Except for the simplest case [Formula: see text] not much is known about the generators of [Formula: see text] or even its structure. We find a set of generators of [Formula: see text] for a new case. On the way, we show that every automorphism of [Formula: see text] acts on both the cusps and the elliptic points of [Formula: see text]. Generalizing a result of Reiner for [Formula: see text] we describe for each cusp an uncountable subgroup of [Formula: see text] whose action on [Formula: see text] is essentially defined on the stabilizer of that cusp. In the case where [Formula: see text] (the degree of [Formula: see text]) is [Formula: see text], the elliptic points are related to the isolated vertices of the quotient graph [Formula: see text] of the Bruhat–Tits tree. We construct an infinite group of automorphisms of [Formula: see text] which fully permutes the isolated vertices with cyclic stabilizer.

On monoids of endomorphisms of a cycle graph

Abstract In this paper, we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids wEndCn and EndCn of all weak endomorphisms and all endomorphisms of an undirected cycle graph Cn with n vertices. We also describe Green’s relations and regularity of these monoids and calculate their cardinalities.

Restriction theorems and root systems for symmetric superspaces

In this paper we consider those involutions θ of a finite-dimensional Kac–Moody Lie superalgebra g, with associated decomposition g=k⊕p, for which a Cartan subspace a in p0̄ is self-centralizing in p. For such θ the restriction map Cθ from p to a is injective on the algebra P(p)k of k-invariant polynomials on p. There are five infinite families and five exceptional cases of such involutions, and for each case we explicitly determine the structure of P(p)k by giving a complete set of generators for the image of Cθ. We also determine precisely when the restriction map Rθ from P(g)g to P(p)k is surjective. Finally we introduce the notion of a generalized restricted root system, and show that in the present setting the a-roots Δ(a,g) always form such a system.

Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries.

We study quantum many-body systems in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. Based on a symmetry-twisting method and spectrum robustness, we propose that a half-integer spin chain that respects any of these two antiunitary crystalline symmetries in addition to the discrete Z_{2}×Z_{2} global spin-rotation symmetry must either be gapless or possess degenerate ground states. This explains the gaplessness of a class of chiral spin models not indicated by the Lieb-Schultz-Mattis theorem and its known extensions. Moreover, we present symmetry classes with minimal sets of generators that give nontrivial Lieb-Schultz-Mattis-type constraints, argued by the bulk-boundary correspondence in 2D symmetry-protected topological phases as well as lattice homotopy. Our results for detecting the ingappability of 1D quantum magnets from the interplay between spin-rotation symmetries and magnetic space groups are applicable to systems with a broader class of spin interactions, including Dzyaloshinskii-Moriya and triple-product interactions.

Dynamic optimization of boiler for minimizing energy consumption in the intentionally transient process operation: effect of different interval number

Abstract Certain manufacturing or industrial processes may involve variable conditions, and intentionally transient boiler operation allows optimal adaptation to these variations. This helps maintain efficiency and reduce energy consumption during different process phases. Transient operation is inherent during the start-up and intermittent phases in reaching the pressure required for boiler operation. Optimizing these transient states can reduce energy consumption. Dynamic optimization of boilers is crucial for several reasons, especially in industrial and power generation settings. Boilers are used to produce steam or hot water for various processes, and optimizing their performance can lead to increased efficiency, reduced energy consumption, and improved overall system reliability. The dynamic optimization problems were solved using the orthogonal collocation method. Three problem optimizations were considered in this study: minimize process time (P1), minimize energy consumption without optimized final time (P2), minimize energy consumption with optimized final time (P3). The control/decision variables applied were firing rate, Q, and water feed flowrate, q f. From the simulation results, the control trajectories of P3 were chosen to be the most effective control operation to achieve the minimum energy consumption for reaching target pressure, i.e., 10.2 MPa, with a reasonable intermittent unit time. In practice, the selection of the number of intervals is often determined through a combination of domain knowledge, computational resources, and the desired level of accuracy. Sensitivity analysis and testing with different interval sizes can help in understanding the impact of this parameter on the optimization results. A greater interval time will decrease energy consumption.

A numerical simulation study on the spontaneous imbibition and hydro-thermal coupling in soil using the lattice Boltzmann method

This study presents a numerical simulation of underground water spontaneous upward imbibition at high density ratios using the improved lattice Boltzmann method coupled with the P-R equation of state. Porous media was created using the Quartet Structure Generation Set (QSGS) method. The research delved into the impact of factors such as porosity, soil particle size, capillary force, gravity and temperature on spontaneous imbibition. The results indicated that the permeability coefficient of water spontaneous imbibition rises with higher porosity or larger particles. The influence of gravity on spontaneous imbibition became more significant with increased porosity. Three levels of porosity, namely 0.80, 0.65, and 0.50, were simulated to determine the prevailing force between the thermal-driven force and the gravitational hindrance. The variation of groundwater spontaneous imbibition permeability coefficient under the influence of gravity at different temperature gradients was simulated, as was the change in the permeability coefficient without the influence of gravity. The results revealed that for temperature differences above 4 K, gravity had minimal impact with temperature being the main influential factor. For example, for simulation with temperature difference of 10 K, the permeability coefficient differences were 0.006, 0.015, and 0.014 for the three different porosity levels, respectively. When the temperature difference was below 4 K, the disparity in the permeability coefficient increased significantly compared to zero-gravity conditions. Under these conditions, the influence of gravity was greater. For example, for simulation with temperature difference of 2 K or greater, the permeability coefficient differences were 0.306, 0.300, and 0.108 for the corresponding porosity values respectively.

Meso-scale investigation on the permeability of frozen soils with the lattice Boltzmann method

Complex composition and intricate pore-scale structure of frozen soils poses significant challenges in reliably and efficiently obtaining their permeability. In this study, we propose a modified quartet structure generation set (QSGS) numerical tool for generating frozen soils and present the development of a computational simulation code based on the multiple-relaxation-time lattice Boltzmann method (LBM). In the modified QSGS, the arc-shaped water-ice interface is depicted, and the influence of pore-scale geometry on freezing temperature is considered. The validity of combining the proposed QSGS model and the LBM code is proved by comparing calculated results to analytical and experimental results of porous media. Our objective was to investigate the effects of soil features, including porosity, grain diameter, shape anisotropy of soil particles, and ice content on the intrinsic permeability of frozen soil. Additionally, we examined the relationship between these features and the specific surface area and tortuosity. Numerical results show that the intrinsic permeability of frozen soils increases with increasing porosity, larger granular diameter, and anisotropy, which is identical with the pressure gradient. The presence of ice led to clogging flow pathways and drastically decreased the intrinsic permeability, which is significantly less than unfrozen soil with same effective porosity. This study provides a useful tool to investigate the intricate interplay between the pore-scale structure and the intrinsic permeability of frozen soils.

Numerical approach for the simulation of flow-induced noise around a structure with complex geometry: High-speed train bogie in a cavity

The bogie region is a significant source of aerodynamic noise on high-speed trains. Owing to its complex geometry and flow field, numerical simulations using computational fluid dynamics are especially challenging. The main challenge is to achieve a grid with adequate resolution, especially in the boundary layer, while ensuring computational affordability. This challenge is addressed here by employing a hybrid grid, integrating a structured hexahedral mesh near solid surfaces with an unstructured polyhedral mesh in the remaining volume. To limit the number of cells in the boundary layer region, the delayed detached eddy simulation method is adopted. Additionally, to achieve a further reduction in the cell count, the Reynolds number of the model is decreased by scaling down the model size and lowering the inflow speed. The hybrid grid generation and numerical settings are guided by validated simulations of flow over cylinders. A grid sensitivity study, conducted with a simplified half-width bogie model, reveals the meshing requirements for the full-width model. Aerodynamic results highlight the rear section of the cavity and bogie as primary noise sources, emphasizing the critical role of the detached shear layer from upstream components. Time-resolved surface pressure data are input into the Ffowcs Williams–Hawkings equation for far-field noise calculation. The results indicate that the sound energy is concentrated below 200 Hz in the full-scale model, with the cavity contributing more than the bogie. This study provides a practical numerical approach for simulating a structure with complex geometry, offering insights for realistic model simulations.

Symmetry analysis, optimal system, conservation laws and exact solutions of time-fractional diffusion-type equation

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation [Formula: see text] is studied by the symmetry analysis method. Liu et al. obtained two group generators [Formula: see text] [Formula: see text] and only one trivial solution [Formula: see text] for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case [Formula: see text], we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically.

Combined economic emission load dispatch solution using Cuckoo Search Algorithm

The Cuckoo Search Algorithm (CSA) has been selected to find the best optimum solution for Combined Economic and Emission Load Dispatch Network (CEELD) problems. The objective, in the (CEELD) Analysis, that operating a generator schedule is necessary with both minimum fuel costs and emission levels, together, while satisfying the load demand and operational limitations. In this paper, the objective of research is oriented to minimize the fuel cost and emission for generation sets. The numerical results captured from the suggested method are compared with other techniques such as the Gravitational Search Method, strength Pareto evolutionary algorithm and nondominated sorting genetic algorithm-II to illustrate the efficiency of suggested method.

The effective thermal conductivity of random isotropic porous media analysis and prediction

Effective thermal conductivity of porous media is a crucial parameter for heat transfer within them. Many studies have characterized various porous media by adjusting the control parameters generated through the Quartet Structure Generation Set method. The porous media effective thermal conductivity is then determined through Computational Fluid Dynamics calculations, which, however, necessitate significant computational resources and time. Thus, following an exploration of the influence of control parameters (i.e., porosity, core growth probability, and their coupling) on the effective thermal conductivity of isotropic porous media generated by the Quartet Structure Generation Set method, this study developed a multi-layer perceptron prediction model. The aim was to establish a prediction model from the porous media control parameters to effective thermal conductivity, thereby reducing the time spent on iterative calculations. The findings indicate that the effective thermal conductivity does not uniformly increase with the growth of core probability, and instead fluctuates after a certain threshold. Notably, the trained model exhibits a high prediction accuracy, with average deviations of 0.0887 and 0.0748 for the training and testing datasets, respectively.

Characterization of the absorption radical of an evolution algebra using their associated graph

In this paper, we present a method for finding the absorbing radical of a finite-dimensional evolution algebra. Such a method consists of finding the acyclic vertices of an oriented graph associated with the algebra. The set of generators associated with such vertices turn out to be the generators of the absorption radical. As an application we use the absorption radical to study the decomposability of some degenerate evolution algebras.

Complete group of central units in some group rings over Z and Z [ θ p ]

In the present work, we contribute with new results that enabled us to give an explicit description of the groups of central units of integral group rings and group rings with coefficients in Z [ θ ] , for certain groups G, where θ is a p − primitive root of unity and p is a prime number. In particular, we find a set of generators for the case where G is the Heisenberg Group.

Celestial sector in CFT: Conformally soft symmetries

We show that time intervals of width \Delta \tauΔτ in 3-dimensional conformal field theories (CFT_33) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit \Delta \tau → 0Δτ→0. The associated vector fields are approximate solutions to the conformal Killing equations in the strip labelled by a function and a conformal Killing vector on the sphere. An Inonu-Wigner contraction yields a set of symmetry generators obeying the extended BMS_44 algebra. We analyze the shadow stress tensor Ward identities in CFT_dd on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by \piπ. We demonstrate that both the leading and subleading conformally soft graviton theorems in (d-1)(d−1)-dimensional celestial CFT (CCFT_{d-1}d−1) can be recovered from the transverse traceless components of these Ward identities in the limit \Delta \tau → 0Δτ→0. A similar construction allows for the leading conformally soft gluon theorem in CCFT_{d-1}d−1 to be recovered from shadow current Ward identities in CFT_dd.