Fundamental Form Research Articles

Harmonizing virtuosities in the Zhuangzi

ABSTRACT Harmony is a crucial value for resolving conflicts. Discussions on harmony in the Zhuangzi primarily focus on harmonizing ‘right and wrong’ (shifei 是非). However, it represents only a superficial understanding of Zhuangzian harmony. To explore a fundamental form of harmony would be beneficial: harmonizing ‘virtuosities’ (de 德), which can prevent conflicts and avoid domination. This paper begins by illustrating the discombobulated (zhili 支离) characteristic of virtuosities in the Zhuangzi. By comparison with harmonizing virtues in Five Conducts, we can better understand the distinctive characteristic of harmonizing virtuositiesin the Zhuangzi. Moreover, a metaphor of perfectly still water suggests that in this process, virtuosities can be internally preserved and externally unshaken. This suggests to maintain one’s own virtuosities in the transformations of eventsand avoidacquiring specific names or reputations that can lead to interpersonal conflicts and domination. These two characteristics can fundamentally avoid disputes over ‘right and wrong’.

Kα-translators of Weingarten type in Gauss curvature flow

In this paper, we consider Kα-translating solitons in R3 and give some classifications of Kα-translating solitons fulfilling some extrinsic curvature assumptions. We prove that Kα-translating solitons with constant mean curvature are either planes or circular cylinders. We also prove that planes and circular cylinders are the only Kα-translating solitons with constant squared norm of the second fundamental form.

Dependence of eigenvalues of fourth-order Sturm-Liouville problems on canonical boundary conditions

In this paper, we discuss the dependence of eigenvalues of fourth-order Sturm-Liouville (SL) problems on the fundamental canonical forms of separated, coupled and mixed self-adjoint boundary conditions. The eigenvalues depend not only continuously but smoothly on the boundary conditions and boundary points. Simultaneously, the derivative expression of the eigenvalues with respect to all the parameters in the boundary conditions are given, and thus its monotonicity with respect to some parameters is derived.

SEMANTIC FACTOR IN MODELING VERB TENSES IN UZBEK LANGUAGE

This article provides information about the role of the semantic factor in modeling verb tenses for Uzbek language corpora. Determining the relation of speech to time is important in the process of morphological analysis. It is known that space and time are the fundamental form of existence, and any information, action, situation has signs of time and space. Understanding the relationship of information to time is an important condition for understanding changes in the world. Time determines the time of occurrence of certain events and situations, and thus they are arranged in sequence in memory, as well as how long they lasted. The need to ensure the automatic implementation of analyzes of the relationship of information to time increases the practical importance of the issue of annotating grammatical forms of tense.

Abnormal suppression of thermal transport by long-range interactions in networks

Heat and electricity are two fundamental forms of energy widely utilized in our daily lives. Recently, in the study of complex networks, there is growing evidence that they behave significantly different at the micro-nanoscale. Here, we use a small-world network model to investigate the effects of reconnection probability p and decay exponent α on thermal and electrical transport within the network. Our results demonstrate that the electrical transport efficiency increases by nearly one order of magnitude, while the thermal transport efficiency falls off a cliff by three to four orders of magnitude, breaking the traditional rule that shortcuts enhance energy transport in small-world networks. Furthermore, we elucidate that phonon localization is a crucial factor in the weakening of thermal transport efficiency in small-world networks by characterizing the density of states, phonon participation ratio, and nearest-neighbor spacing distribution. These insights will pave new ways for designing thermoelectric materials with high electrical conductance and low thermal conductance.

Complete stable minimal submanifolds with a parallel unit normal section in a Euclidean space

Let Σ be an n-dimensional complete stable minimal submanifold in Rn+p admitting a parallel unit normal section ν∈Γ(NΣ). We prove that if Σ has finite L2-norm of the second fundamental form Aν with respect to ν under an additional assumption on Aη for any unit normal section η∈Γ(NΣ) such that 〈ν,η〉=0, then Σ is an affine n-plane. We also obtain an upper bound for the fundamental tone of Σ under a certain condition on the second fundamental form.

Variations in the Appearance and Interpretation of Interpersonal Eye Contact in Social Categorizations and Psychiatric Populations Worldwide: A Scoping Review with a Critical Appraisal of the Literature.

Eye contact is one of the most fundamental forms of interhuman communication. However, to date, there has been no comprehensive research comparing how eye contact is made and interpreted in all possible populations worldwide. This study presents a summary of the existing literature on these modalities stratified to social categorizations and psychiatric disorders. A scoping review with critical appraisal of the literature according to the Joanna Briggs Institute (JBI) methodology. Databases AnthroSource, Medline, CINAHL, the Psychology and Behavioral Sciences Collection (EBSCO) and PsychInfo were searched. 7068 articles were screened for both the grey literature and reference lists, of which 385 were included, 282 for social categorizations and 103 for psychiatric disorders. In total, 603 thematic clustered outcomes of variations were included. Methodological quality was generally moderate to good. There is a great degree of variation in the presentation and interpretation of eye contact between and within populations. It remains unclear why specific variations occur in populations. Additionally, no gold standard for how eye contact should be used or interpreted emerged from the studies. Further research into the reason for differences in eye contact between and within populations is recommended.

Curvature varifolds with orthogonal boundary

AbstractWe consider the class of ‐dimensional surfaces in that intersect orthogonally along the boundary. A piece of an affine ‐plane in is called an orthogonal slice. We prove estimates for the area by the integral of the second fundamental form in three cases: first, when admits no orthogonal slices, second for if all orthogonal slices are topological disks, and finally, for all if the surfaces are confined to a neighborhood of . The orthogonality constraint has a weak formulation for curvature varifolds. We classify those varifolds of vanishing curvature. As an application, we prove for any the existence of an orthogonal 2‐varifold that minimizes the curvature in the integer rectifiable class.

An Improved Eigenvalue Estimate for Embedded Minimal Hypersurfaces in the Sphere

Abstract Suppose that $\Sigma ^{n}\subset \mathbb{S}^{n+1}$ is a closed embedded minimal hypersurface. We prove that the first non-zero eigenvalue $\lambda _{1}$ of the induced Laplace–Beltrami operator on $\Sigma $ satisfies $\lambda _{1} \geq \frac{n}{2}+ a_{n}(\Lambda ^{6} + b_{n})^{-1}$, where $a_{n}$ and $b_{n}$ are explicit dimensional constants and $\Lambda $ is an upper bound for the length of the second fundamental form of $\Sigma $. This provides the first explicitly computable improvement on Choi and Wang’s lower bound $\lambda _{1} \geq \frac{n}{2}$ without any further assumptions on $\Sigma $.

Statistical Submanifolds Equipped with F-Statistical Connections

This paper deals with statistical submanifolds and a family of statistical connections on them. The geometric structures such as the second fundamental form, curvatures tensor, mean curvature, statistical Ricci curvature and the relations among them on a statistical submanifold of a statistical manifold equipped with F-statistical connections are examined. The equations of Gauss and Codazzi of F-statistical connections are obtained. Such structures when the statistical submanifolds are conjugate symmetric are discussed. We present a inequality for statistical submanifolds in real space forms with respect to F-statistical connections. Also, we obtain a basic inequality involving statistical Ricci curvature and the squared F-mean curvature of a statistical submanifold of statistical manifolds.

Right Conoids Demonstrating a Time-like Axis within Minkowski Four-Dimensional Space

In the four-dimensional Minkowski space, hypersurfaces classified as right conoids with a time-like axis are introduced and studied. The computation of matrices associated with the fundamental form, the Gauss map, and the shape operator specific to these hypersurfaces is included in our analysis. The intrinsic curvatures of these hypersurfaces are determined to provide a deeper understanding of their geometric properties. Additionally, the conditions required for these hypersurfaces to be minimal are established, and detailed calculations of the Laplace–Beltrami operator are performed. Illustrative examples are provided to enhance our comprehension of these concepts. Finally, the umbilical condition is examined to determine when these hypersurfaces become umbilic, and also the Willmore functional is explored.

Large-Strain Surface Modeling Using Plasticity.

Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. We give a new method to represent surfaces undergoing large spatially varying rotations and strains, based on differential geometry, and surface first and second fundamental forms. Methods that penalize the difference between the current shape and the rest shape produce sharp spikes under large strains, and variational methods produce wiggles, whereas our method naturally supports large strains and rotations without any special treatment. For stable and smooth results, we demonstrate that the deformed surface has to locally satisfy compatibility conditions (Gauss-Codazzi equations) on the first and second fundamental forms. We then give a method to locally modify the surface first and second fundamental forms in a compatible way. We use those fundamental forms to define surface plastic deformations, and finally recover output surface vertex positions by minimizing the surface elastic energy under the plastic deformations. We demonstrate that our method makes it possible to smoothly deform triangle meshes to large spatially varying strains and rotations, while meeting user constraints.

Postcolonial city walks in Germany at the nexus of activism, education, and tourism

Abstract In various ways, postcolonial initiatives in Germany contribute to the formation of ‘national cultures of remembrance’ and to the debate about Europe’s responsibility for the negative effects of colonial expansion that can still be felt today. One approach, which the activist groups use in their educational and activist work, is that of the guided walking tour – a method that allows them to sensitize an interested audience to colonially contoured spaces in German cities. Interestingly, the postcolonial initiatives do not see themselves as providers of tourist services, even though they use the rather fundamental touristic form of the ‘city walk’. As this discrepancy in perception allows discussions about tourism in a more general, conceptual sense, this paper examines the tours at the nexus of activism, education, and tourism. Thereby, it asks what constitutes the walks and discusses their relation to urban tourism. To do so, the article first explains relevant concepts of tourism geographies and postcolonial studies and then connects them to insights gained from the qualitative and quantitative analysis of empirical data collected in a field phase in Germany in 2022.

Recognizing Speech Emotions Using AI

Abstract: I suggest an Among the most fundamental forms of self-expression is speech, which may convey a variety of feelings, including excitement, tranquility, joy, and rage, to mention a few. It is feasible to rearrange our activities, services, and even products in order to give each person a more customized experience customer by evaluating the emotions that underlie communication. The intention of this project is to recognize and extract various human speech sound files' emotions. to use Python to accomplish something similar. Python and a number of specialist libraries, such as Librosa, Sound File, NumPy, Scikit-learn, and PyAudio, will be used to accomplish this. These initiatives provide the features required for machine learning, feature extraction, and audio processing

On minimal Lagrangian submanifolds in complex space forms with semi-parallel second fundamental form

In this paper, we study the interesting open problem of classifying the minimal Lagrangian submanifolds of dimension [Formula: see text] in complex space forms with semi-parallel second fundamental form. First, we completely solve the problem in cases [Formula: see text]. Second, supposing further that the scalar curvature is constant for [Formula: see text], we also give an answer to the problem by applying the classification theorem of [F. Dillen, H. Li, L. Vrancken and X. Wang, Lagrangian submanifolds in complex projective space with parallel second fundamental form, Pacific J. Math. 255 (2012) 79–115]. Finally, for such Lagrangian submanifolds in the above problem with [Formula: see text], we establish an inequality in terms of the traceless Ricci tensor, the squared norm of the second fundamental form and the scalar curvature. Moreover, this inequality is optimal in the sense that all the submanifolds attaining the equality are completely determined.

Projective structures and Hodge theory

AbstractEvery compact Riemann surface X admits a natural projective structure $$p_u$$ p u as a consequence of the uniformization theorem. In this work we describe the construction of another natural projective structure on X, namely the Hodge projective structure $$p_h$$ p h , related to the second fundamental form of the period map. We then describe how projective structures correspond to (1, 1)-differential forms on the moduli space of projective curves and, from this correspondence, we deduce that $$p_u$$ p u and $$p_h$$ p h are not the same structure.

A New Class of Univalent Functions Defined by Differential Operator

In the present work, we submit and study a new class $\mathcal{S}_{\lambda, \alpha, b}^{z, m, t}(\beta, \gamma, \omega, \mu)$ containing analytic univalent functions defined by new differential operator $D_{\lambda, \alpha}^{z, m, t}$ in the open unit disk $E=\{s \in \mathbb{C}:|s|<1\}$. We get some geometric properties, such as, coefficient estimate, growth and distortion theorems, convex set, radii of convexity and starlikeness, weighted mean, arithmetic mean and partial sums for functions belonging to the class $\mathcal{S}_{\lambda, \alpha, b}^{z, m, t}(\beta, \gamma, \omega, \mu)$.

Estimates and Radii of Convexity in Some Classes of Regular Functions

Estimates and Radii of Convexity in Some Classes of Regular Functions

Narrative as a Form of Applied History

Abstract Narrative is a fundamental form of historical thinking. As such, narrative is a representational framework through which real events can be ordered into simplified temporal sequences unfolding within historical settings, driven by the interaction of historical personages or collective entities such as nations or classes. These insights, however, are yet to be fully incorporated within the field of applied history, which could profit from a closer consideration of narrative as a concrete manifestation of what has been termed genealogical or processual history. Like the historical analogy, which has been the focus of much research, narrative has the potential to fruitfully make connections between past and present events, but also to misapply history for propagandistic purposes. To address these issues, this article presents a methodological model whose usefulness is demonstrated in two case studies, together with guidelines for how a narrative perspective could inspire future applied history research.

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.