Fundamental Form Research Articles

Certain Family of Multivalent Functions Associated With Subordination

The main objectives of this pepper are to introduce new classes. We have attempted to obtain coefficient estimates, radius of convexity, Distortion and Growth theorem and other related results for the classes

Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications

In this study, we attain some existence characterizations for warped product pointwise semi slant submanifolds in the setting of Sasakian space forms. Moreover, we investigate the estimation for the squared norm of the second fundamental form and further discuss the case of equality. By the application of attained estimation, we obtain some classifications of these warped product submanifolds in terms of Ricci soliton and Ricci curvature. Further, the formula for Dirichlet energy of involved warping function is derived. A nontrivial example of such warped product submanifolds is also constructed. Throughout the paper, we will use the following acronyms: “WP” for warped product, “WF” for warping function, “AC” for almost contact, and “WP-PSS” for the warped product pointwise semi slant.

Perceptual Space of Action of a Musical Composition

The purpose of the article is to reveal the meaning and peculiarities of the category"perceptual space" in musical art. The methodology of the research is based on theinterdisciplinary integration of the methods of modern philosophy, cultural studies and art history.Scientific novelty of the article is the substantiation of the inseparable interconnection of space andman, which makes it possible to consider this category one of the fundamental forms ofunderstanding the world and thinking about the world in musical art. For a full study of theperceptual space in music, there are means that facilitate the creation of connections of elementsboth within the composition and between objects of art and reality. Conclusions. Continuation anddeepening of the study of spatial means and principles of form formation in music createprerequisites for a deeper understanding of the nature of space in art. This process also contributesto the identification of common psychological, physical, compositional patterns, concentratesspatial perception in music. To such we attribute the following: the value of the unconscious increating conditions corresponding to the activation of sensory channels responsible for visualperception; the operation of general physical laws; the basis of the mechanism of associativity, motor modeling in music; the necessary generality of the stages of understanding is imagesensation, image-perception, image-representation; the basis of the unity of the compositionalprinciples of visual and musical arts; the general effect of the principles of formal composition (theprinciple of simplicity, the influence of geometric forms on emotional perception, the arrangementof musical marks on the plane of the score, such as the relationship between the figure and theplane and other positions in music).Key words: space, space of musical art, perceptual space, composer creativity, synaesthesia

Audiovisual Multisensory Processing in Young Adults With Attention-Deficit/Hyperactivity Disorder.

Multisensory integration is a fundamental form of sensory processing that is involved in many everyday tasks. Those with Attention-Deficit/Hyperactivity Disorder (ADHD) have characteristic alterations to various brain regions that may influence multisensory processing. The overall aim of this work was to assess how adults with ADHD process audiovisual multisensory stimuli during a complex response time task. The paradigm used was a two-alternative forced-choice discrimination task paired with continuous 64-electrode electroencephalography, allowing for the measurement of response time and accuracy to auditory, visual, and audiovisual multisensory conditions. Analysis revealed that those with ADHD ( n = 10) respond faster than neurotypical controls ( n = 12) when presented with auditory, visual, and audiovisual multisensory conditions, while also having race model violation in early response latency quantiles. Adults with ADHD also had more prominent multisensory processing over parietal-occipital brain regions at early post-stimulus latencies, indicating that altered brain structure may have important outcomes for audiovisual multisensory processing. The present study is the first to assess how those with ADHD respond to multisensory conditions during a complex response time task, and demonstrates that adults with ADHD have unique multisensory processing when assessing both behavioral response time measures and neurological measures.

Duality on generalized cuspidal edges preserving singular set images and first fundamental forms

In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call this an `isometric duality'. When the singular set image has no symmetries and does not lie in a plane, the dual cuspidal edge is not congruent to the original one. In this paper, we show that this duality extends to generalized cuspidal edges in $\boldsymbol R^3$, including cuspidal cross caps, and $5/2$-cuspidal edges. Moreover, we give several new geometric insights on this duality.

On Some Subclasses of Strongly Starlike Analytic Functions

The aim of the present article is to investigate a family of univalent analytic functions on the unit disc $D$ defined for $M \geq 1$ by $$\Re (\frac{zf'(z)}{f(z)}) > 0, |(\frac{zf'(z)}{f(z)})^2 - M|<M, z \in D.$$ Some proprieties, radius of convexity and coefficient bounds are obtained for classes in this family.

SUBCLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING POLYLOGARITHM FUNCTION

n this paper, we introduce and study a new subclass of meromorphic functions with positive coefficients involving the polylogaritham function and obtain coefficient estimates, growth and distortion theorem, radius of convexity, integral transforms, convex linear combinations and convolution properties for the class σ c,p (α, β, λ).

Conversion of Certain Stochastic Control Problems into Deterministic Control Problems

A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. A fundamental solution form is obtained where the same solution can be used for a limited variety of terminal costs without re-solution of the problem. One may convert this fundamental solution form from a stochastic control problem form to a deterministic control problem form. This yields an equivalence between certain second-order (in space) Hamilton-Jacobi partial differential equations (HJ PDEs) and associated first-order HJ PDEs. This reformulation has substantial numerical implications.

构造上正交各向异性半球形凸起凹凸板等效刚度研究

The hemispherical convex plate was periodically divided into representative unit structures. Firstly, the stiffness characteristics of representative units were studied, and the equivalent stiffness of the hemispherical convex plate was obtained by means of the deformation equivalence principle, the homogenization procedure and the stiffness combination method. Then the 3 principal stiffnesses were brought into the theoretical solution of the 4-side simple plate to solve the plate center deflection. The finite element numerical simulation solution and the theoretical solution were compared and analyzed to verify the accuracy of the theoretical principal stiffnesses. The effect of the material dimensions of the representative units on the equivalent stiffness was then discussed. As the ratio of the length of the representative unit to the convex radius increases, the accuracy of the theoretical results will improve, and the equivalent stiffness formula is applicable to hemispherical convex plates of different thicknesses. Finally, a relatively simple engineering application formula was given with the approximate range of the convex radius based on several examples.

Evolution of space curves and the special ruled surfaces with modified orthogonal frame

In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame.

Ends of immersed minimal and Willmore surfaces in asymptotically flat spaces

We study ends of an oriented, immersed, non-compact, complete Willmore surfaces, which are critical points of the integral of the square of the mean curvature, in asymptotically flat spaces of any dimension; assuming the surface has $L^2$-bounded second fundamental form and satisfies a weak power growth on the area. We give the precise asymptotic behavior of an end of such a surface. This asymptotic information is very much dependent on the way the ambient metric decays to the Euclidean one. Our results apply in particular to minimal surfaces.

Linear systems of wave equations on cosmological backgrounds with convergent asymptotics

The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised, converges. The model examples are the Kasner solutions. The main result of the article is optimal energy estimates. However, we also derive asymptotics and demonstrate that the leading order asymptotics can be specified. It is sometimes argued that if the factors multiplying the spatial derivatives decay exponentially (for a system of wave equations), then the spatial derivatives can be ignored. This line of reasoning is incorrect: we give examples of equations such that 1) the factors multiplying the spatial derivatives decay exponentially, 2) the factors multiplying the time derivatives are constants, 3) the energies of individual modes of solutions asymptotically decay exponentially, and 4) the energies of generic solutions grow as $e^{e^{t}}$ as $t\rightarrow \infty$. When the factors multiplying the spatial derivatives grow exponentially, the Fourier modes of solutions oscillate with a frequency that grows exponentially. To obtain asymptotics, we fix a mode and consider the net evolution over one period. Moreover, we replace the evolution (over one period) with a matrix multiplication. We cannot calculate the matrices, but we approximate them. To obtain the asymptotics we need to calculate a matrix product where there is no bound on the number of factors, and where each factor can only be approximated. Nevertheless, we obtain detailed asymptotics. In fact, it is possible to isolate an overall behaviour (growth/decay) from the (increasingly violent) oscillatory behaviour. Moreover, we are also in a position to specify the leading order asymptotics.

Twisted product CR-submanifolds in a locally conformal Kähler space forms

Certain twisted product CR-submanifolds in a K?hler manifold and some inequalities of the second fundamental form of these submanifolds are presented ([14]). Then the length of the second fundamental form of a twisted product CR-submanifold in a locally conformal K?hler manifold is considered (2013), ([15]). In this paper, we consider the relation of the mean curvature and the length of the second fundamental form in two twisted product CR-submanifolds in a locally conformal K?hler space forms.

Restrictions on submanifolds via focal radius bounds

We give an optimal estimate for the norm of any submanifold's second fundamental form in terms of its focal radius and the lower sectional curvature bound of the ambient manifold. This is a special case of a similar theorem for intermediate Ricci curvature, and leads to a $C^{1,\alpha}$ compactness result for submanifolds, as well as a soul-type structure theorem for manifolds with nonnegative $k^{th}$--intermediate Ricci curvature that have a closed submanifold with dimension $\geq k$ and infinite focal radius. To prove these results, we use the comparison lemma for Jacobi fields from arXiv:1603.04050 that exploits Wilking's transverse Jacobi equation. The comparison lemma also yields new information about group actions, Riemannian submersions, and submetries, including generalizations to intermediate Ricci curvature of results of Chen and Grove.

Affine rotation surfaces of elliptic type in Affine 3-space

In this paper, we classify affine rotation surfaces of elliptic type in affine 3-space satisfying some algebraic equations regarding the co-ordinate functions and the Laplacian operators in relation the first and the second affine fundamental forms of affine rotation surfaces of elliptic type. We also give explicit forms of these surfaces.

Chen’s improved inequality for pointwise hemi-slant warped products in Kaehler manifolds

Recently, B.-Y. Chen discovered a technique to find the relation between second fundamental form and the warping function of warped product submanifolds. In this paper, we extend our further study of [24] by giving non-trivial examples of warped product pointwise hemi-slant submanifolds. Finally, we establish a sharp estimation for the squared norm of the second fundamental form ||h||2 in terms of the warping function f. The equality case is also investigated.

Apperception and Pre-Reflective Self-Consciousness in Kant

Kant points to two forms of self-consciousness: the inner sense (empirical apperception) grounded in a sensory form of self-awareness and transcendental apperception. The aim of this paper is to show that a sophisticated notion of basic self-consciousness, which contains a pre-reflective self-consciousness as its first level, is provided by the notion of transcendental apperception. The necessity for a pre-reflective self-consciousness has been pointed out in phenomenological literature. According to this account, every self-ascription of any property implies a more fundamental form of self-consciousness, i.e., a kind of immediate familiarity with oneself. This pre-reflective self-consciousness is a non-relational and non-identificational form of self-consciousness and concerns an immediate acquaintance of the subject with itself. In the specific terms of transcendentalism every thought contains an implicit reference to a first-personal “givenness” or a sense of “mineness” that articulates a non-relational and non-identificational form of a pre-reflective model of self-consciousness.

Collaborating with Strangers: How Personal Values Affect Generalized Exchange

Cooperation and reciprocity are the bedrock of organizational work. They have gained renewed attention as technological advances avail new venues for collaborative work. Yet a challenge remains: While expanding possibilities, computer-mediated interaction also removes some presumed guardians of reciprocity, elevating the risk of breakdown in collaboration. How does large-scale reciprocity emerge among strangers? One mechanism is generalized exchange, a fundamental form of reciprocity. Prior work, in the social and biological sciences, has stressed its dependence on situational factors, such as reputation. We complement theory by focusing on individual factors, defining and testing a novel measure based on personal values. We test it alongside situational factors in experiments in the US and Asia, and demonstrate how individual and situational factors contribute separately but also interact to affect generalized exchange, ultimately fostering it among strangers. The findings inform diverse conversations, including those on organizational help, knowledge sharing, crowds, and open collaboration.

Period integrals in nonpositively curved manifolds

We provide an improvement of a half power of log to standard bounds on integrals of Laplace eigenfunctions over submanifolds of codimension 2 or more, where the ambient space is a compact Riemannian manifold with negative sectional curvature. We provide the same improvement for hypersurfaces whose second fundamental form differs sufficiently from that of spheres of infinite radius. This result extends previous ones obtained in the 2-dimensional setting by Chen and Sogge; Sogge, Xi, and Zhang; and the author.

Ecolinguistics in the Cultural Acculturation of the Northern Coastal Communities of Central Java

The main subject of this research is the ecological lexicon in the northern coastal communities of Central Java. The existence of ecological lexicon in the Northern coastal communities may serve as a form of language attitude of the speech community. The language attitude is not only observable by verbal messages, but Javanese people are closely integrated with the biological environment. The symbols of nature appear to be integrated with the life of the Northern coastal communities of Central Java. These symbols of nature represent the philosophy of life of the Northern Coastal communities of Java who still firmly uphold their faith and belief. The method used was a survey involving questionnaires from several informants at the observation points. Observation points in three major areas of Northern Coast of Central Java were including Demak, Pati, and Rembang. The data were collected by ecolinguistic design. The results of the research showed that the ecological lexicon of Northern coastal communities of Central Java was observable in the designation of agricultural products, especially in the biological environment. This persistence of attitude was manifested in the belief in the ecological lexicon associated with religious rituals. Ecological lexicon was chosen as a symbol of harmonization of human interaction with nature as a fundamental form of integration with their God. In addition to being observable in the ecological lexicon, the language attitude of the Northern coastal communities of Central Java was also seen in the cultural ecology of the Northern coastal communities of Central Java. Cultural ecology appeared in the humility in giving a recpect. The respect is reflected in sedekah laut, sedekah bumi rituals, and in the number of architectural ridges (gunungan) of residential building.