Fundamental Form Research Articles

Application of the L2-orthogonal decomposition of the second fundamental form of the hypersurfaces and the ahlfors laplacian to the study of the general relativistic vacuum constraint equations

Application of the <i>L</i>²-orthogonal decomposition of the second fundamental form of the hypersurfaces and the ahlfors laplacian to the study of the general relativistic vacuum constraint equations

On the inverse mean curvature flow by parallel hypersurfaces in space forms

We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by the distance function of the parallel hypersurfaces. The solutions to the flow are obtained explicitly when the distinct principal curvatures have the same multiplicity. This is an additional assumption only for isoparametric hypersurfaces of the hyperbolic space or of the sphere with two or four distinct principal curvatures. The boundaries of the maximal interval of definition, when finite, are determined in terms of the number g g of distinct principal curvatures, their multiplicities m m and the mean curvature H H of the initial hypersurface. We describe the collapsing submanifolds of the flow at the boundaries of the interval. In particular, we show in the Euclidean space the solutions are eternal, while in the hyperbolic space there are eternal and immortal solutions. Starting with a connected isoparametric submanifold of the sphere, we show that the flow is an ancient solution, that collapses into a minimal hypersurface whose square length of its second fundamental form and its scalar curvature are constants given in terms of g g and n n . The minimal hypersurface is totally geodesic when g = 1 g=1 , it is a Clifford minimal hypersurface of the sphere when g = 2 g=2 and it is a Cartan type minimal submanifold when g ∈ { 3 , 4 , 6 } g\in \{3,4,6\} .

Certain Class of &lt;i&gt;P&lt;/i&gt;-Valent Analytic Function Associated with Derivative Operator and Their Properties

This study aims to define a new subclass of multivalent analytic functions in the open unit disk. Jackson's derivative operator has been used to generate this subclass. Before getting coefficient characterization, we look at certain needs for the functions related to this subclass. We can see several fascinating features, including coefficient estimates, growth and distortion theorem, extreme points, and the radius of starlikeness and convexity of functions belonging to the subclass are shown using this technique.

Numerical investigation on the liquid jet and the dynamics of the near-wall cavitation bubble under an acoustic field

The dynamics of the near-wall cavitation bubble in an acoustic field are the fundamental forms of acoustic cavitation, which has been associated with promising applications in ultrasonic cleaning, chemical engineering, and food processing. However, the potential physical mechanisms for acoustic cavitation-induced surface cleaning have not been fully elucidated. The dynamics of an ultrasonically driven near-wall cavitation bubble are numerically investigated by employing a compressible two-phase model implemented in OpenFOAM. The corresponding validation of the current model containing the acoustic field was performed by comparison with experimental and state-of-the-art theoretical results. Compared to the state without the acoustic field, the acoustic field can enhance the near-wall bubble collapse due to its stretching effect, causing higher jet velocities and shorter collapse intervals. The jet velocity in the acoustic field increases by 80.2%, and the collapse time reduces by 40.9% compared to those without an acoustic field for γ = 1.1. In addition, the effects of the stand-off distances (γ), acoustic pressure wave frequency (f), and initial pressure (p*) on the bubble dynamic behaviors were analyzed in depth. The results indicate that cavitation effects (e.g., pressure loads at the wall center and the maximal bubble temperature) are weakened with the increase in the frequency (f) owing to the shorter oscillation periods. Furthermore, the maximum radius of bubble expansion and the collapse time decrease with increasing f and increase with increasing p*. The bubble maximum radius reduces by 12.6% when f increases by 62.5% and increases by 20.5% when p* increases by 74%.

Chen's Inequality for CR-warped Products in Locally Metallic Riemannian Manifolds

In this paper, we study CR warped product submanifolds in locally metallic Riemannian manifolds. We provide several non-trivial examples of such submanifolds. We establish a sharp inequality known as Chen's inequality for the squared norm of the second fundamental form. We also discuss the equality case of Chen's inequality.

Sharp starlike and convex radius for the differential operator of analytic functions

UDC 517.5 Under given coefficient conditions for analytic functions f in the unit disk D , we first obtain the starlike and convex radius for the linear combination of the differential operator z f ' of analytic functions f in D . Then we obtain the starlike and convex radius for the differential operator z f ' . Furthermore, we present the starlike and convex radius for the linear combination of the differential operator z f ' and analytic functions f in D . Our results imply the related result obtained by Gavrilov [Mat. Zametki, &lt;strong&gt;7&lt;/strong&gt;, 295–298 (1970)].

Gait performance changes after ten cervical retractions

Background and Study Aim. Students are prone to spine overloading, as they often spend prolonged periods in unfavorable postures. They tend to struggle with balancing study time and leisure physical activity. The head and neck regions are particularly rich in proprioceptors. Prolonged forward head posture (protraction) can lead to balance disturbances. This, in turn, affects gait and overall body posture. The aim of this study was to examine the effects of a series of corrective active head exercises on gait, a fundamental form of movement, in a group of healthy university students. Material and Methods. Gait patterns were assessed in 10 healthy male full-time students with an average age of 22.8 years (SD = 1.1). The assessment was based on the regional distribution of plantar pressure across two measurement sessions. One session was conducted before, and one after performing 10 active head retractions. Gait changes were analyzed in ten foot regions for 200 steps of each participant. Results. After 10 cervical retractions, a decrease in pressure, ground reaction force, contact time, and area values was observed in the 1st metatarsal head (1MTH). Conversely, an increase in these quantities was found in the toes. Additionally, there was a tendency toward a decrease in the contact area of the heel and 3rd metatarsal head (3MTH), along with increased contact time in the midfoot. Performing 10 neck retractions altered gait by inducing heel supination. It also increased hallux involvement in propulsion and widened the base of toe support. Conclusions. Even a few movements that correct head protraction have an immediate effect on whole-body movement. This effect suggests potential benefits of incorporating neck retractions into physical education programs for students. Even when time-consuming forms of regular exercise are not feasible, performing just a few neck-correcting movements can positively impact overall body movement.

Sub-picosecond biphasic ultrafast all-optical switching in ultraviolet band

Abstract Ultrafast all-optical control has been a subject of wide-spread attention as a method of manipulating optical fields using light excitation on extremely short time scales. As a fundamental form of ultrafast all-optical control, all-optical switching has achieved sub-picosecond switch speeds in the visible, infrared, and terahertz spectral regions. However, due to the lack of suitable materials, ultrafast all-optical control in the ultraviolet range remains in its early stages. We demonstrate sub-picosecond all-optical switching in the ultraviolet wavelength by designing a Si3N4-ITO Fabry–Pérot resonance aligns with the edge of the interband transition region of ITO. The response time of 500 fs achieved at a pump fluence as low as 0.17 mJ/cm2. Notably, unlike conventional binary switches (0, 1), this biphasic all-optical switch enables the modulation of optical intensity with positive, zero, and negative ΔR/R (0, 1, −1) at the same wavelength, all achieved with a switching speed of 680 fs at a pump fluence of 0.45 mJ/cm2. This work establishing a new pathway for all-optical control in the ultraviolet spectrum, the biphasic switch provides an extra degree of freedom for all-optical modulation.

CNN-Based Models for Emotion and Sentiment Analysis Using Speech Data

The study aims to present an in-depth Sentiment Analysis (SA) grounded by the presence of emotions in the speech signals. Nowadays, all kinds of web-based applications ranging from social media platforms and video-sharing sites to e-commerce applications provide support for Human–Computer Interfaces (HCIs). These media applications allow users to share their experiences in all forms such as text, audio, video, GIF, and so on. The most natural and fundamental form of expressing oneself is through speech. Speech-Based Sentiment Analysis (SBSA) is the task of gaining insights into speech signals. It aims to classify the statement as neutral, negative, or positive. On the other hand, Speech Emotion Recognition (SER) categorizes speech signals into the following emotions: disgust, fear, sadness, anger, happiness, and neutral. It is necessary to recognize the sentiments along with the profoundness of the emotions in the speech signals. To cater to the above idea, a methodology is proposed defining a text-oriented SA model using the combination of CNN and Bi-LSTM techniques along with an embedding layer, applied to the text obtained from speech signals; achieving an accuracy of 84.49%. Also, the proposed methodology suggests an Emotion Analysis (EA) model based on the CNN technique highlighting the type of emotion present in the speech signal with an accuracy measure of 95.12%. The presented architecture can also be applied to different other domains like product review systems, video recommendation systems, education, health, security, and so on.

Szülői szerepvállalás pedagógusi percepciók tükrében

Parental support in children’s homework – as one of the most fundamental forms of parental involvement – could be influenced by many factors. This study reports the results of an interview-based research conducted in the village of Praid (Harghita county, Romania), analyzing teachers’ perception on parental support practices prevalent in this region.

Terrestrial life in light of the Copernican principle

Although many solar systems have been discovered, only one example of life is known. Thus, terrestrial life represents merely one data point. Consequently, extrapolating from terrestrial life to life elsewhere in the galaxy and beyond is often seen as a limitation in the search for different forms of life. Essentially, attempting to extrapolate from terrestrial life to life elsewhere implies that terrestrial life is representative of all life, reflecting a geocentric viewpoint. However, in accordance with the Copernican principle, the opposite holds true. Asserting that terrestrial life must differ from other forms of life in the universe is, in fact, the geocentric viewpoint. For if life elsewhere is not like terrestrial life, then it is ipso facto different life; more precisely, if terrestrial life does not represent general life, then that life must represent special life, which the principle states it is not. This study employs the Copernican principle as a probability assessment, addressing critiques rooted in the implicit assumption of the existence of different extraterrestrial forms of life. If various fundamental forms of life indeed exist, then differences in the probabilities of their emergence can be expected, forming a probability scale. This holds significance because it not only allows for insights into the characteristics of the majority of life elsewhere but also facilitates the establishment of boundaries for categories of life as we do not know it. Thus, the Copernican-Darwinian principle provides a valuable tool for astrobiology and the search for life in the galaxyTop of Form and beyond.

Ricci flow of Kaehlerian slant submanifolds in complex space forms and its applications

AbstractThe normalized Ricci flow converges to a constant curvature metric for a connected Kaehlerian slant submanifold in a complex space form if the squared norm of the second fundamental form satisfies certain upper bounds. These bounds include the constant sectional curvature, the slant angle, and the squared norm of the mean curvature vector. Additionally, we demonstrate that the submanifold is diffeomorphic to the sphere $$\mathbb {S}^{n_1}$$ S n 1 under some restriction on the mean curvature. We claim that some of our previous results are rare cases.

Human-Centric Virtual Museum: Redefining the Museum Experience Through Immersive and Interactive Environments

Virtual Museums present a novel approach for audiences to experience cultural content. This paper proposes two new concepts of virtual museums: Human-Centric Virtual Museum, which emphasizes audience interaction experiences, and Content-Centric Virtual Museum, which focuses more on the digitized display of real museum collections and content. With the widespread application of extended reality (XR) technology in this field, people are increasingly inclined towards experiencing highly interactive Human-Centric Virtual Museums. However, evaluating these from a user cognition perspective warrants further investigation. To address this, we design and implement three fundamental forms: Mobile Application (MA), Virtual Reality (VR), and Mixed Reality (MR), and evaluate comprehensive user experiences, including satisfaction, cognitive load, emotional involvement, presence, interactivity, degree of participation and potential negative impact. The experimental results show that in terms of satisfaction and cognitive load, users generally find the MR mode easier to understand and operate. Regarding emotional involvement, audiences in the VR and MR modes are more likely to focus on the current content. Concerning presence, the MR mode enables audiences to perceive the real spatial location, thereby increasing their immersion. Furthermore, compared to the MA mode, both MR and VR modes exhibit stronger interactivity, providing audiences with a more immersive exhibition experience. However, the VR mode may also cause users to feel discomfort during use.

Minimal motifs for habituating systems

Habituation-a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld-is universally observed in living systems from animals to unicellular organisms. Despite its prevalence, generic mechanisms for this fundamental form of learning remain poorly defined. Drawing inspiration from prior work on systems that respond adaptively to step inputs, we study habituation from a nonlinear dynamics perspective. This approach enables us to formalize classical hallmarks of habituation that have been experimentally identified in diverse organisms and stimulus scenarios. We use this framework to investigate distinct dynamical circuits capable of habituation. In particular, we show that driven linear dynamics of a memory variable with static nonlinearities acting at the input and output can implement numerous hallmarks in a mathematically interpretable manner. This work establishes a foundation for understanding the dynamical substrates of this primitive learning behavior and offers a blueprint for the identification of habituating circuits in biological systems.

ON THE GENERALIZATION OF SOME CLASSES OF CONVEX IN DIRECTION AND TYPICALLY REAL FUNCTIONS

In the article by M.O. Reade (Duke Math. Journal, 1956) using the condition |arg (f'(z)/ g'(z)) | ≤ γπ/2, where g(z) is a convex function,0≤γ≤1 , a class of functions close-to-convex (almost convex) of order γ is introduced. In our paper, we introduce a subclass of the class of close-to-convex (almost convex) order γ functions satisfying the condition |arg [(1-λzn ) f'(z)]| ≤ γπ/2, which, for different parameter values, gives a number of well-known subclasses of univalent (schlicht) functions. Based on this subclass, a class of close-to-starlike (almost star-shaped) functions is constructed, containing a number of subclasses that have been actively studied by many authors in recent years, as well as a classical class of typically real functions. For this classes exact theorems of distortion (growth) and radii of convexity (starlikeness) are obtained, generalizing previously known results. The case is also considered when the functions of the introduced classes have missing members in the power series expansion. The results obtained are accurate and not only generalize previously known results, but also reveal the properties of a number of new subclasses of univalent (schlicht) functions.

Existence and uniqueness of periodic pseudospherical surfaces emanating from Cauchy problems

We study implications and consequences of well-posed solutions of Cauchy problems of a Novikov equation describing pseudospherical surfaces. We show that if the co-frame of dual one-forms satisfies certain conditions for a given periodic initial datum, then there exist exactly two families of periodic one-forms satisfying the structural equations for a surface. Each pair then defines a metric of constant Gaussian curvature and a corresponding Levi-Civita connection form. We prove the existence of universal connection forms giving rise to second fundamental forms compatible with the metric. The main tool to prove our geometrical results is the Kato’s semi-group approach, which is used to establish well-posedness of solutions of the Cauchy problem involved and ensure C 1 regularity for the first fundamental form and the Levi-Civita connection form.

Effectiveness of a supervised group-based walking program on physical, psychological and social outcomes among older adults: a randomised controlled trial protocol

IntroductionTo minimise adverse health events among older adults, physical activity (PA) is considered one of the most fundamental and effective forms of lifestyle. Therefore, an urgent effort to promote a...

A Comprehensive Review of Coptidis Rhizoma and Magnoliae Officinalis Cortex Drug Pair and Their Chemical Composition, Pharmacological Effects and Pharmacokinetics Analysis.

Herbal pairs are unique combinations of two relatively fixed herbs that are used in clinical practice. This is the most fundamental and straightforward form of multiple herbal treatment that aims to attain specific efficacy through unique methods. Coptidis Rhizoma ("Huanglian" in Chinese) and Magnoliae Officinalis Cortex ("Houpo" in Chinese) which are commonly used in combination and could also be used as important components of other prescriptions to treat damp-heat dysentery, splenic and stomach disorders, and qi stagnation in clinical practice. However, there is currently no summary on the compatibility of Huanglian and Houpo about traditional use, phytochemistry, and pharmacological activity. It was found the combination or separate extraction of the two drugs may affect the main active components, and new components may be produced after the combined extraction. At the same time, Huanglian and Houpo herb pair exhibited antiviral, anti-inflammatory, antibacterial and other pharmacological effects. At present, research mainly focuses on the indicator components of Huanglian and Houpo, such as berberine, magnolol, and magnolol. The models used for pharmacological validation are limited, mainly including ulcerative colitis, pneumonia, bacterial infections, etc. In order to verify the pharmacological activity of the combination of Huanglian and Houpo, it is necessary to try more in vitro and in vivo models. It's still need to study the compatibility mechanism of the Huanglian and Houpo drug pair, including but not limited to the interactions between different components and the impact of compatibility on efficacy, bioequivalence studies, and the impact of different dosage forms on pharmacokinetics in the future. It's believed that the systematic review provided comprehensive information for the study of Huanglian-Houpo drug pair, which will help highlight the importance of the Huanglian-Houpo herb pair and provide some clues for future research on this herb pair.

REDD+: A fine example of worst practice

Throughout the “Age of Aid” (1944–1989)4 development has been seen as essentially economic in nature. Increasingly, however, it has become apparent that it is economic only in its consequences. It is something else - entitlements, democratization … social capital - that makes development possible. A different paradigm is therefore needed, and we begin by sketching that by way of the various “experiments” - nationalization, privatization and communitization - with Nepal's forests over the past half-century. Nationalization and privatization turned out to be abysmal failures; communitization a great, and continuing, success. We relate all this to the differing patterns of interaction between four fundamental forms of social solidarity - individualism (eg markets), hierarchy (eg governments and aid donors), egalitarianism (eg activist groups) and fatalism (eg carriers of the “double burden”: poverty and social exclusion) - and go on to show that only when each is (a) able to make its “voice” heard and (b) is following its dharma5 (acting according to its distinctive morality rather than undermining it) do we get development. REDD+6, we then show, using examples of its implementation in Africa, is unremittingly hierarchical and does not satisfy these two conditions. We conclude with some suggestions for remedying these policy defects.

Quantitative NMR Analysis of Marine Macroalgae for AGE Inhibition by Methylglyoxal Scavenging.

Reactive carbonyl species (RCS) induce a fundamental form of biological stress that has driven the evolution of diverse mechanisms for minimizing its impact on organismal health. The complications that accompany uncontrolled hyperglycemia exemplify the health implications when RCS stress exceeds the body's capacity to prevent the excessive formation of advanced glycation end-products. Presented here is a novel quantitative NMR (qNMR) technique for evaluating scavengers of the prominent sugar-derived carbonyl methylglyoxal (MGO). This tool was employed to screen the chemical diversity of marine macroalgae extracts, with a focus on species that have a history of consumption by the World's healthiest populations and are subject to global scale aquacultural production. Fucus vesiculosus demonstrated the highest capacity for inhibiting glycation and scavenging MGO. Additionally, the Chondrus cripsus, Gracilaria vermiculophyla, and Gracilaria tikvahiae extracts had a high capacity for scavenging MGO, representing the first report of this activity. This new qNMR methodology presented is highly applicable for screening extracts and compounds from diverse sources, and the results highlight the potential of macroalgae extracts to be employed as RCS and AGE targeting therapeutics and food additives.