Narrow Class Research Articles

Hopping potential wells and gait switching in a fish-like robot with a bistable tail

Fish outperform current underwater robots in speed, agility, and efficiency of locomotion, in part due to their flexible appendages that are capable of rich combinations of modes of motion. In fish-like robots, actuating many different modes of oscillation of tails or fins can become a challenge. This paper presents a highly underactuated (with a single actuator) fish-like robot with a bistable tail that features a double-well elastic potential. Oscillations of such a tail depend on the frequency and amplitude of excitation, and tuning the frequency-amplitude can produce controllable oscillations in different modes leading to different gaits of the robot. This robot design is inspired by recent work on underactuated flexible swimming robots driven by a single rotor. The oscillations of the rotor can propel and steer the robot, but saturation of the rotor makes performing long turns challenging. This paper demonstrates that by adding geometric bistability to the flexible tail, turns can be performed by controllably exciting single-well oscillations in the tail, while exciting double-well oscillations of the tail produces average straight-line motion. The findings of this paper go beyond the application to a narrow class of fish-like robots. More broadly we have demonstrated the use of periodic excitation to produce bistable response that generate different gaits including a steering gait. The mechanics demonstrated here show the feasibility of applications to other mobile soft robots.

On indication, strict monotonicity, and efficiency of projections in a general class of path-based data envelopment analysis models

Data envelopment analysis (DEA) theory formulates a number of desirable properties that DEA models should satisfy. Among these, indication, strict monotonicity, and strong efficiency of projections tend to be grouped together in the sense that, in individual models, typically, either all three are satisfied or all three fail at the same time. Specifically, in slacks-based graph models, the three properties are always met; in path-based models, such as radial models, directional distance function models, and the hyperbolic function model, the three properties, with some minor exceptions, typically all fail.Motivated by this observation, the article examines relationships among indication, strict monotonicity, and strong efficiency of projections in the class of path-based models over variable returns-to-scale technology sets. Under mild assumptions, it is shown that the property of strict monotonicity and strong efficiency of projections are equivalent, and that both properties imply indication. This paper also characterises a narrow class of technology sets and path directions for which the three properties hold in path-based models.

Construcțiile incidente cu funcție expresivă: analiză cantitativă pe momentele și schițele lui I.L. Caragiale

The present work is composed of two parts: a theoretical part, in which some critical and personal considerations on the incident constructions are exposed, and the second part represents a qualitative-quantitative approach to the moments and sketches of I.L. Caragiale. In the theoretical part, the aim is to present incident constructions, especially in relation to GALR, where a complex and up-to-date classification of them is made from a semantic-functional point of view, into: allocutive incident constructions, direct speech reporting constructions, metadiscursive incident constructions, incident constructions with the role of pragmatic connectors, incident constructions with expressive function, with conative function, and verbal automatisms. However, according to the three basic features of incidents, namely the representation of an additional syntactic structure, the lack of syntactic links to the underlying utterance, and the provision of information of the type comment, explanation or direct speech reporting, it can be seen that not all the categories listed above fall into the narrow class of incidents, which is why we hypothesised that those categories that do not exhibit all three defining features of incidents belong to paranthetic constructions, a superclass of incidents. After this theoretical presentation, I carried out a quantitative and qualitative analysis of the incident constructions with expressive function in Caragiale’s moments and sketches. The analysis was carried out manually and with the software Voyant Tool. From the category of incident expressive constructions, we first considered interjections and imprecations, as these are the most representatives for Caragiale’s work. As far as interjections are concerned, we made an inventory of them according to the number of occurrences, which showed that the most frequent interjections in Caragiale’s work are the interjections: a!, as!, ei! and uf!, followed by ah!, ei aș! o! aoleu! and ehei! Taking contexts and representative examples from Caragiale’s moments and sketches, we have analysed their semantic valences, highlighting the fact that interjections known positively in Caragiale’s work receive many more semantic nuances than those known negatively. Using concrete examples, the main semantic nuances identified were admiration, determination, disappointment, disapproval, dissimulation, exaltation, hesitation, anger, irritation, irony, melancholy, satisfaction, puzzlement, dissatisfaction, disbelief, fear, hope, surprise, suspicion, confusion, disappointment, indifference, irony, joy, boldness or even suffering. The semantic analysis of the interjections identified in Caragiale’s work was followed by a quantitative and qualitative analysis of the imprecations, which produced an impressive list of imprecations that suggest the linguistic inventiveness of the Romanian prose writer and support the orality of his style. Interestingly, most of the imprecations are found in the texts "Întârziere" and "Un pedagog de școală nouă", in the speech of a female character and a teacher, characters often associated with elevated language. Taken as a whole, all these incident expressive constructions, whether interjections or imprecations, are intended not only to emphasise the characters’ feelings, but are also evidence of their attitude and relationship to the world, to other characters and to society in general. Through the variety of semantic nuances they update and the multitude of forms identified in Caragiale’s texts, they acquire a central role in the articulation of the message and meanings.

A lithium–aluminium heterobimetallic dimetallocene

Homobimetallic dimetallocenes exhibiting two identical metal atoms sandwiched between two η5 bonded cyclopentadienyl rings is a narrow class of compounds, with representative examples being dizincocene and diberyllocene. Here we report the synthesis and structural characterization of a heterobimetallic dimetallocene, accessible through heterocoupling of lithium and aluminylene fragments with pentaisopropylcyclopentadienyl ligands. The Al–Li bond features a high ionic character and profits from attractive dispersion interactions between the isopropyl groups of the cyclopentadienyl ligands. A key synthetic step is the isolation of a cyclopentadienylaluminylene monomer, which also enables the structural characterization of this species. In addition to their structural authentication by single-crystal X-ray diffraction analysis, both compounds were characterized by multinuclear NMR spectroscopy in solution and in the solid state. Furthermore, reactivity studies of the lithium–aluminium heterobimetallic dimetallocene with an N-heterocyclic carbene and different heteroallenes were performed and show that the Al–Li bond is easily cleaved.

Arithmetic of Hecke L-functions of quadratic extensions of totally real fields

Deep work by Shintani in the 1970's describes Hecke L-functions associated to narrow ray class group characters of totally real fields F in terms of what are now known as Shintani zeta functions. However, for [F:Q]=n≥3, Shintani's method was ineffective due to its crucial dependence on abstract fundamental domains for the action of totally positive units of F on R+n, so-called Shintani sets. These difficulties were recently resolved in independent work of Charollois, Dasgupta, and Greenberg and Diaz y Diaz and Friedman. For those narrow ray class group characters whose conductor is an inert rational prime in a totally real field F with narrow class number 1, we obtain a natural combinatorial description of these sets, allowing us to obtain a simple description of the associated Hecke L-functions. As a consequence, we generalize earlier work of Girstmair, Hirzebruch, and Zagier, that offer combinatorial class number formulas for imaginary quadratic fields, to real and imaginary quadratic extensions of totally real number fields F with narrow class number 1. For CM quadratic extensions of F, our work may be viewed as an effective affirmative answer to Hecke's Conjecture that the relative class number has an elementary arithmetic expression in terms of the relative discriminant.

Invariant differential operators for noncompact Lie groups: The Sp(n,1) case

In this paper, we continue the project of systematic construction of invariant differential operators (IDOs) on the example of the noncompact algebras [Formula: see text]. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which are of split rank one, of which class the other cases were studied, some long time ago. We concentrate on the case [Formula: see text]. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations (ER) for, including the necessary data for all relevant invariant differential operators. We also present explicit expressions for the singular vectors and the intertwining differential operators.

Theoretical foundations for creating a quantum photon computer

Currently, significant results have emerged in the field of creation and application of quantum computers. We are talking about the Chinese quantum photonic computers Jiuzhang, Jiuzhang-2 (Jiuzhang 2.0), Jiuzhang-3 (Jiuzhang 3.0), which appeared respectively in 2020, 2021 and 2023, as well as the Canadian quantum photonic computer Borealis, which appeared in 2022. All these computers belong to the class of so-called quantum simulators – variants of quantum computers that solve one problem or a narrow class of problems. In addition to narrow specialization, quantum simulators have another important feature. In quantum simulators, controllable quantum objects simulate and effectively predict the behavior of real quantum systems. For example, in the quantum photonic computers Jiuzhang, Jiuzhang-2, Jiuzhang-3 and Borealis, the photons supplied to the inputs of these computers imitate the behavior of a “system of non-interacting identical bosons.” The Jiuzhang, Jiuzhang-2, Jiuzhang-3, and Borealis quantum simulators solve the problem of sampling bosons from a given distribution. Together they represent a significant scientific, technical and technological breakthrough in the development and creation of quantum computers. However, beyond what has been achieved, a number of important issues that are of interest both theoretically and for the field of practical applications remain unexamined. Among them are the following: about the architecture and composition of the elements of a quantum photonic computer, their number and connection diagram, as well as setting parameters that determine the required probability distribution from which boson samples are taken. The scientific problem addressed in the article is to obtain answers to the above questions by developing the theoretical foundations for creating a quantum photonic computer that solves the problem of sampling bosons from a given distribution in the most general case without restrictions on the distribution. The following results were obtained: the theoretical basis for the creation of a quantum photon computer (called in the article the Fuzuli boson sampler, briefly bsF) was developed that solves the problem of sampling bosons from a given distribution, for use as a quantum computing subsystem of a hybrid computing system to solve the problem of estimating matrix permanents; its constituent elements have been identified and studied, their numbers have been determined, and inter-element connection diagrams have been developed; an algorithm has been developed for tuning the bsF quantum photon computer to solve the problem of estimating matrix permanents; The functioning process of bsF is described. The article assumes that physically, in each cycle of operation of the bsF computer, the process of supplying photons to the inputs of the computer, their “movement” to the detectors, as well as the registration of photons by detectors is organized in such a way that the set of these photons imitates the behavior of a system of non-interacting identical bosons. Physical and engineering issues of ensuring such behavior of photons are not considered in this work. At the same time, the feasibility of such a possibility in practice (experimentally) is assumed to be undeniable. Examples confirming this position are the already created prototypes of quantum photonic computers in China (Jiuzhang, Jiuzhang-2, Jiuzhang-3) and in Canada (Borealis).

The role of vowel and consonant onsets in neural tracking of natural speech

Objective. To investigate how the auditory system processes natural speech, models have been created to relate the electroencephalography (EEG) signal of a person listening to speech to various representations of the speech. Mainly the speech envelope has been used, but also phonetic representations. We investigated to which degree of granularity phonetic representations can be related to the EEG signal. Approach. We used recorded EEG signals from 105 subjects while they listened to fairy tale stories. We utilized speech representations, including onset of any phone, vowel–consonant onsets, broad phonetic class (BPC) onsets, and narrow phonetic class onsets, and related them to EEG using forward modeling and match–mismatch tasks. In forward modeling, we used a linear model to predict EEG from speech representations. In the match–mismatch task, we trained a long short term memory based model to determine which of two candidate speech segments matches with a given EEG segment. Main results. Our results show that vowel–consonant onsets outperform onsets of any phone in both tasks, which suggests that neural tracking of the vowel vs. consonant exists in the EEG to some degree. We also observed that vowel (syllable nucleus) onsets exhibit a more consistent representation in EEG compared to syllable onsets. Significance. Finally, our findings suggest that neural tracking previously thought to be associated with BPCs might actually originate from vowel–consonant onsets rather than the differentiation between different phonetic classes.

Explicit upper bounds on the average of Euler–Kronecker constants of narrow ray class fields

Explicit upper bounds on the average of Euler–Kronecker constants of narrow ray class fields

Composition of Bhargava’s cubes over number fields

In this paper, the composition of Bhargava’s cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields. The exclusion of the latter case arises from the nonexistence of a bijection between (classes of) binary quadratic forms and an ideal class group. This problem, together with a related mistake in another paper of the author, is addressed in the appendix.

Higher Rademacher Symbols

Certain higher Rademacher symbols are defined that give class functions on the modular group. Their basic properties are derived via a two-variable reformulation of Eichler-Shimura cohomology. This reformulation better explains the role of cycle integrals and also yields new results, about the integrality of the values of the symbols. The Rademacher symbols determine the values at non-positive integers of the zeta function for a narrow ideal class of a real quadratic field. This result is equivalent to one of Siegel, but is proven in a new way by using an identity for the value of such a zeta function at a positive integer greater than one as a sum of certain double zeta values defined for the quadratic field.

A property of extreme entropy values in critical regimes of two-phase flows

In a critical regime of vertical ascending flows, a certain part of solid particles moves with the flow, while another part settles against the flow. Entropy is a key parameter in the analysis of properties of mass systems. It can be considered as consisting of two parts ― internal entropy arising during irreversible processes within the system and external entropy depending on the system correlation with the surroundings. Here a system represents the totality of all solid particles of various sizes simultaneously present in the flow. In thermodynamics, ordinary total entropy consisting of these two components has a tendency to reach the maximum when the entire system reaches equilibrium. In this case, its internal entropy always increases. In contrast to the conventional entropy, the internal entropy in the process under study can decrease due to the peculiarities of the solid phase motion and mass exchange caused by the latter. However, in a critical regime, one can always reveal a narrow size class in a mixture of particles, whose entropy tends to maximum when this class reaches a peculiar equilibrium in the flow. The peculiarity of this equilibrium consists in an equiprobable distribution of particles of this class in both directions – upwards and downwards. For other size classes participating in the process, the internal entropy does not reach the maximum, and these classes are not equally distributed between the directions of motion. The condition of optimal mass exchange of the total granulometric set of particles in specific conditions of critical flow is connected with an equilibrium size class. Ill. 1. Ref. 2.

The values of the Dedekind–Rademacher cocycle at real multiplication points

The values of the Dedekind–Rademacher cocycle at certain real quadratic arguments are shown to be global p-units in the narrow Hilbert class field of the associated real quadratic field, as predicted by the conjectures of Darmon–Dasgupta (2006) and Darmon–Vonk (2021). The strategy for proving this result combines the approach of prior work of the authors (2021) with one crucial extra ingredient: the study of infinitesimal deformations of irregular Hilbert Eisenstein series of weight 1 in the anti-parallel direction.

Asymptotic Fermat for signature (4,2,p) over number fields

Let K be a number field. Using the modular method, we prove asymptotic results on solutions of the Diophantine equation x4−y2=zp over K, assuming some deep but standard conjectures of the Langlands programme when K has at least one complex embedding. On the other hand, we give unconditional results in the case of totally real extensions having odd narrow class number and a unique prime above 2. When modularity of elliptic curves over K is known, for example when K is real quadratic or the r-layer of the cyclotomic Z2-extension of Q, effective asymptotic results hold.

A novel computational model and OpenFOAM solver for simulating thermal energy storages based on granular phase change materials: Advantages and applicability

In this paper, we consider hydrodynamic and heat transfer processes in thermal energy storages based on granular or encapsulated phase change materials. Such heat storages can be applied in renewable and conventional energy, safety systems, civil building, and so on. A computational model, which is based on the assumption of interpenetrating interacting continua, has been developed to simulate the processes of phase transitions, heat transfer and fluid flow in the packed bed latent heat storages. To implement this model, we chose OpenFOAM – the leading free, open source software for computational fluid dynamics and heat transfer. Solver porousHeatTransferFoam, which is based on the SIMPLE algorithm, and additional libraries have been developed in the OpenFOAM framework. The solver and the libraries allow one to model granular materials with complex enthalpy-temperature diagrams during phase transitions, thus expanding the applicability of OpenFOAM. The advantage of the solver is high computational speed – its calculation time varies from a minute to a few minutes for 1D simulations and from a few minutes to a few hours for 2D simulations depending on the mesh sizes. Comparison between numerical results obtained and known experimental data has shown that the model based on the assumption of interpenetrating interacting continua adequately describes the heat transfer processes in the packed bed latent heat storages not only for the large ratio of the storage characteristic size to the particle diameter, but also for the small one (about 7–8). In contrast to many existing computational models, which applicability is usually limited to rather narrow class of the processes, our model covers a variety of hydrodynamic and heat transfer problems in the thermal energy storages based on granular phase change materials. This computational model and OpenFOAM solver developed allow one to simulate incompressible and compressible (liquid or gaseous) flows through the packed bed latent heat storages under various boundary conditions, with isothermal and non-isothermal phase transitions, with various properties of granular materials and coolant, in wide ranges of flow velocities, operating temperatures and particle sizes.

On unit signatures and narrow class groups of odd degree abelian number fields

For an abelian number field of odd degree, we study the structure of its 2 2 -Selmer group as a bilinear space and as a Galois module. We prove structural results and make predictions for the distribution of unit signature ranks and narrow class groups in families where the degree and Galois group are fixed.

On simple left-symmetric algebras

We prove that the multiplication algebra M(A) of any simple finite-dimensional left-symmetric nonassociative algebra A over a field of characteristic zero coincides with the right multiplication algebra R(A). In particular, A does not contain any proper right ideal. These results immediately give a description of simple finite-dimensional Novikov algebras over an algebraically closed field of characteristic zero [29].The structure of finite-dimensional simple left-symmetric nonassociative algebras from a very narrow class A of algebras with the identities [[x,y],[z,t]]=[x,y]([z,t]u)=0 is studied in detail. We prove that every such algebra A admits a Z2-grading A=A0⊕A1 with an associative and commutative A0. Simple algebras are described in the following cases: (1) A is four dimensional over an algebraically closed field of characteristic not 2, (2) A0 is an algebra with the zero product, and (3) A0 is simple; in the last two cases, the description is given in terms of root systems. A necessary and sufficient condition for A to be complete is given.

Concentration of closed geodesics in the homology of modular curves

Abstract We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line. This fits into the framework of Duke’s Theorem and can be seen as a real quadratic analogue of results of Michel and Liu–Masri–Young on supersingular reduction of CM-elliptic curves. We also study the level aspect, as well as a homological version of the sup norm problem. Finally, we present applications to group theory and modular forms

Метод точністного тарирування при реалізації математичних моделей динамічних систем в задачах моделювання та управління

One of the main qualitative indicators of computing tools is the accura-cy of the results of solving applied problems by them, in particular, prob-lems of modeling and control of dynamic systems. However, despite the widespread use of computer technology (CT), the problem of assessing the accuracy of calculations cannot be considered solved, and its relevance is growing due to the rapid development and spread of cybernetic tools for various purposes. The severity of the problem lies in the complexity of the analysis of calculation errors, which leads to the cumbersomeness of ana-lytical justifications and the large volume of calculations required to obtain specific numerical data.To solve many technical and research problems, both universal and specialized OT tools are widely used. The characteristic difference of the latter from universal tools of OT is a deliberately narrow class of algo-rithms that are implemented, oriented (class) to solving a limited range of applied problems. At the same time, it is naturally expected to achieve a number of certain (compared to universal OT tools) advantages, which usually include one or a group of factors, such as:increased speed, a non-analytical method of solving problems (for analog specialized OT tools), reduced mass-dimensional characteristics and cost, etc. It should be noted that the problem of accuracy is relevant for both universal and specialized OT tools, being somewhat transformed, depending on the type of tool and the principle of its action, for example, the originality of primary errors.

Form Class Groups and Class Fields of CM-Fields

Let F be a totally real number field of class number one, and let K be a CM-field with F as its maximal real subfield. For each positive integer N, we construct a class group of certain binary quadratic forms over F which is isomorphic to the ray class group of K modulo N. Assuming further that the narrow class number of F is one, we construct a class field of the reflex field of K in terms of the singular values of Hilbert modular functions.