Fundamental Form Research Articles

Starlike Functions Associated with Cosine Functions

Let $$S_{\cos }^{*}$$ denote the class of normalized analytic functions f such that $$\frac{zf^{\prime }(z)}{f(z)}\prec \cos (z)$$ . For this class, we obtain structural formula, inclusion results, differential subordinations and some radii problems such as radius of convexity, radius for the class of Janowski starlike functions and radius for some other subclasses of starlike functions.

A Geometric Obstruction for CR-Slant Warped Products in a Nearly Cosymplectic Manifold

In the early 20th century, B.-Y. Chen introduced the concept of CR-warped products and obtained several fundamental results, such as inequality for the length of second fundamental form. In this paper, we obtain B.-Y. Chen’s inequality for CR-slant warped products in nearly cosymplectic manifolds, which are the more general classes of manifolds. The equality case of this inequality is also investigated. Furthermore, the inequality is discussed for some important subclasses of CR-slant warped products.

Degradation evaluation and toxicity profile of bilobol, a promising eco-friendly larvicide

Aedes aegypti is the main arbovirus vector transmitting chikungunya, Zika and dengue. The current vector control strategies are limited due to multiple insecticide resistance, deleterious impacts on the environment, and toxicity to non-target organisms. Bilobol, an alkylresorcinol isolated from the plant species Schinus terebinthifolia, demonstrated larvicidal activity against Aedes aegypti (LC50 7.67 mg/L in less than 24 h). To ensure that bilobol presents a viable alternative as an eco-friendly larvicide, this study aimed to explore the degradation process and acute toxicity of this alkylresorcinol in zebrafish, a non-target organism. A quantification method with validated parameters was developed and used to evaluate bilobol degradation in water over time. The Fish Embryo Toxicity (FET) test was applied to evaluate the acute toxicity of bilobol together with its degradation derivates. Results demonstrated that bilobol gradually degrades over time and almost completely disappears after 96 h, turning into small aliphatic chains which are less toxic than bilobol in its fundamental form. Therefore, it was possible to conclude that bilobol does not present significant toxicity to zebrafish embryos nor does it show signs of persistence in the environment. Additionally, bilobol can be found in high quantities not only in S. terebinthifolia, but also in cashew nut industry waste. Thus, bilobol constitutes an alternative environmentally friendly insecticide because it is not persistent, has indications of low toxicity to non-target organisms and presents a way to exploit massive quantities of material discarded by the food industry.

Case SAC 2020:35 – Supreme Administrative Court Reasserts the Prohibition to Recharacterize Transactions, Now in a Case that Deals with Group Internal Financing

The Supreme Administrative Court (SAC) held in a previous case, SAC 2014:119, that the Finnish domestic arm’s length provision (section 31 of the Act on the Tax Assessment Procedure) does not give the Finnish tax administration legal competence to recharacterize transactions as meant in paragraphs 1.64 and 1.65 of the 2010 OECD Guidelines. Case SAC 2020:35 confirms the SAC’s earlier position: there are certain fundamental private law legal forms and structures that cannot be disregarded by applying section 31 of the AAP. The SAC found that the transfer pricing analysis must depart from the fact that the Belgian subsidiary company providing intra-group financing legally owns the intra-group receivables and, thus, it has acted in the capacity of a creditor. The tax administration had the obligation to set tax consequences accordingly.

Noncommutative minimal embeddings and morphisms of pseudo-Riemannian calculi

In analogy with classical submanifold theory, we introduce morphisms of real metric calculi together with noncommutative embeddings. We show that basic concepts, such as the second fundamental form and the Weingarten map, translate into the noncommutative setting and, in particular, we prove a noncommutative analogue of Gauss’ equations for the curvature of a submanifold. Moreover, the mean curvature of an embedding is readily introduced, giving a natural definition of a noncommutative minimal embedding, and we illustrate the novel concepts by considering the noncommutative torus as a minimal surface in the noncommutative 3-sphere.

A gap theorem for complete submanifolds with parallel mean curvature in the hyperbolic space

Let M be an n(≥7)-dimensional complete submanifold with parallel mean curvature in the hyperbolic space Hn+p, whose mean curvature satisfies H2−1≤0. Denote by A˚ and BR(q) the trace free second fundamental form of M and the geodesic ball of radius R centered at q∈M, respectively. We prove that if lim supR→∞∫BR(q)|A˚|2dMR2=0, and if (∫M|A˚|ndM)2/n+2n(n−2)3n(n−1)H(∫M|A˚|n/2dM)2/n≤C(n), then M is congruent to an n-dimensional hyperbolic space or the Euclidean space Rn. Here C(n) is an explicit positive constant depending only on n. We also obtain a similar gap theorem in the case where n=5,6.

Curvature Estimates for Graphs Over Riemannian Domains

Let $$M^n$$ be a complete n-dimensional Riemannian manifold and $$\Gamma _f$$ the graph of a $$C^2$$ -function f defined on a metric ball of $$M^n$$ . In the same spirit of the estimates obtained by Heinz for the mean and Gaussian curvatures of a surface in $${\mathbb {R}}^3$$ which is a graph over an open disk in the plane, we obtain in this work upper estimates for $$\inf |R|$$ , $$\inf |A|$$ and $$\inf |H_k|$$ , where R, |A| and $$H_k$$ are, respectively, the scalar curvature, the norm of the second fundamental form and the k-th mean curvature of $$\Gamma _f$$ . From our estimates we obtain several results for graphs over complete manifolds. For example, we prove that if $$M^n,\;n\ge 3,$$ is a complete noncompact Riemannian manifold with sectional curvature bounded below by a constant c, and $$\Gamma _f$$ is a graph over M with Ricci curvature less than c, then $$\inf |A|\le 3(n-2)\sqrt{-c}$$ . This result generalizes and improves a theorem of Chern for entire graphs in $$\mathbb R^{n+1}$$ .

Isometric deformations of wave fronts at non-degenerate singular points

Cuspidal edges and swallowtails are typical non-degenerate singular points on wave fronts in the Euclidean 3-space. Their first fundamental forms belong to a class of positive semi-definite metrics called “Kossowski metrics”. A point where a Kossowski metric is not positive definite is called a singular point or a semi-definite point of the metric. Kossowski proved that real analytic Kossowski metric germs at their non-parabolic singular points (the definition of “non-parabolic singular point” is stated in the introduction here) can be realized as wave front germs (Kossowski’s realization theorem). On the other hand, in a previous work with K. Saji, the third and the fourth authors introduced the notion of “coherent tangent bundle”. Moreover, the authors, with M. Hasegawa and K. Saji, proved that a Kossowski metric canonically induces an associated coherent tangent bundle. In this paper, we shall explain Kossowski’s realization theorem from the viewpoint of coherent tangent bundles. Moreover, as refinements of it, we give a criterion that a given Kossowski metric can be realized as the induced metric of a germ of cuspidal edge (resp. swallowtail or cuspidal cross cap). Several applications of these criteria are given. Also, some remaining problems on isometric deformations of singularities of analytic maps are given at the end of this paper.

On a subclass of close-to-convex harmonic mappings

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

On the compactness of hypersurfaces with finite total curvature via mean curvature flow

Given a complete hypersurface in the Euclidean space, we assume that the second fundamental form is bounded and the mean curvature is bounded from below by a positive constant. We prove that if the Lp-norm of the trace-free second fundamental form for some p≥2 is finite, then the hypersurface is compact.

Angular momentum and rotational energy of mean flows in toroidal magnetic fields

We derive the balance equation for the Favre averaged angular momentum in toroidal not necessarily axisymmetric magnetic field equilibria. We find that the components of angular momentum are given by the covariant poloidal and toroidal components of and parallel flow velocities and we separately identify all relevant stress tensors, torques and source terms for each of these components. Our results feature the Favre stress generalisations of previously found Reynolds stresses like the diamagnetic or parallel stress, as well as the density gradient drive term. Further, we identify the magnetic shear as a source of poloidal angular momentum and discuss the mirror and the Lorentz force. Here, we find that the geodesic transfer term, the Stringer-Winsor spin-up term and the ion-orbit loss term are all part of the Lorentz force and are in fact one and the same term.Discussing the relation to angular velocity we build the inertia tensor with the help of the first fundamental form of a flux-surface. In turn, the inertia tensor is used to construct a flux-surface averaged rotational energy for surface flows of the plasma. The evolution of this rotational energy features a correction of previous results due to the inertia tensor. In particular, this correction suggests that density sources on the high-field side contribute much more to zonal flow energy generation than on the low field side.Our derivation is based on a full-F, electromagnetic, gyro-kinetic model in a long-wavelength limit. The results can be applied to gyro-kinetic as well as gyro-fluid theories and can also be compared to drift-kinetic and drift-fluid models. Simplified cases for the magnetic field geometry including the axisymmetric purely toroidal and purely poloidal magnetic fields are discussed, as are the angular momentum balance of the electromagnetic fields, the ion-orbit loss mechanism and the parallel acceleration.

Radii of starlikeness and convexity of generalized Struve functions

In this paper, it is aimed to determine the radii of starlikeness and convexity of the normalized generalized Struve functions for three different kinds of normalization and to find tight lower and upper bounds for the radius of starlikeness and convexity of these normalized Struve functions by making use of Euler-Rayleigh inequalities. The Laguerre-Polya class of entire functions has a crucial role in constructing our main results. *********************************************************************

Five-Dimensional Contact CR-Submanifolds in S 7 ( 1 )

Due to the remarkable property of the seven-dimensional unit sphere to be a Sasakian manifold with the almost contact structure (φ,ξ,η), we study its five-dimensional contact CR-submanifolds, which are the analogue of CR-submanifolds in (almost) Kählerian manifolds. In the case when the structure vector field ξ is tangent to M, the tangent bundle of contact CR-submanifold M can be decomposed as T(M)=H(M)⊕E(M)⊕Rξ, where H(M) is invariant and E(M) is anti-invariant with respect to φ. On this occasion we obtain a complete classification of five-dimensional proper contact CR-submanifolds in S7(1) whose second fundamental form restricted to H(M) and E(M) vanishes identically and we prove that they can be decomposed as (multiply) warped products of spheres.

Ancient solutions to mean curvature flow for isoparametric submanifolds

Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied in Liu and Terng (Duke Math J 147(1):157–179, 2009). In this paper, we will show that all these solutions are ancient solutions and study their limits as time goes to negative infinity. We also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the Chern’s conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres.

Matéria impressa, matéria nómada: sobre o potencial ideológico das publicações de artista

Em contextos de ditadura e repressão, o movimento adquire enorme potencial em termos da sua capacidade de disrupção e de resistência (estética). Através do exílio, da migração, da viagem ou da correspondência, corpos, ideias e objectos são permanentemente deslocados, numa procura incessante de linhas de fuga impossíveis de fixar por qualquer regime político. No campo das artes visuais, a natureza elusiva e mutável do movimento tem a capacidade de transformar objectos em eventos, criando redes afectivas de imagens, palavras, objectos, ideias e relações. O potencial ideológico do movimento encontra-se de forma bastante vívida nas publicações de artista, ou na arte em forma de matéria impressa, tal como livros de artista ou mail art, os quais conseguem contornar as limitações físicas impostas por aparelhos repressivos. Da mesma forma, o movimento activa a imaginação, impele-a a juntar elementos de uma rede de colaborações que é assim construída e posta, também, em movimento. O exercício a que nos propormos com este artigo implica olhar mais de perto certas condições materiais e históricas inerentes a certos objectos artísticos, condições essas que os impregnam de camadas ideológicas diversas. Assim, ao considerar a triangulação movimento-tempo-espaço, tenho o objectivo de investigar a forma como várias artistas, mulheres, usaram diferentes tipos de matéria impressa para rever, confrontar e pôr a nu certas narrativas totalizantes, tais como o papel das mulheres na sociedade, o capitalismo, a escravatura, o colonialismo, etc., que foram sustentadas e simultaneamente sustentaram os regimes repressivos e ditatoriais que vigoraram em Portugal e no Brasil.

Elastic thick shells in general relativity

It is shown that exact spherically symmetric solutions to Einstein's Field Equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well defined constitutive function, and are such that elastic perturbations propagate causally. Two toy-models are then built up in which a thick elastic, spherically symmetric shell with the above properties, separates two Robertson-Walker regions corresponding to different values of the curvature $k$. The junction conditions (continuity of the first and second fundamental forms) are shown to be exactly satisfied across the corresponding matching spherical surfaces.

Rigidity theorem for holomorphic curves in a hyperquadric $$Q_n$$

In this paper, we prove that two linearly full holomorphic curves in a hyperquadric $$Q_n$$ , $$n\ge 2$$ , are congruent if their first fundamental forms and all kth covariant derivatives of the second fundamental forms, $$k=0,1,\ldots ,[\frac{|n-3|}{2}]$$ , are all the same.

The singular structure and regularity of stationary varifolds

If one considers an integral varifold I^m\subseteq M with bounded mean curvature, and if S^k(I)\equiv\{x\in M: no tangent cone at x is k+1 -symmetric} is the standard stratification of the singular set, then it is well known that \mathrm {dim} S^k\leq k . In complete generality nothing else is known about the singular sets S^k(I) . In this paper we prove for a general integral varifold with bounded mean curvature, in particular a stationary varifold, that every stratum S^k(I) is k -rectifiable. In fact, we prove for k -a.e. point x\in S^k that there exists a unique k -plane V^k such that every tangent cone at x is of the form V\times C for some cone C . In the case of minimizing hypersurfaces I^{n-1}\subseteq M^n we can go further. Indeed, we can show that the singular set S(I) , which is known to satisfy \mathrm {dim} S(I)\leq n-8 , is in fact n-8 rectifiable with uniformly finite n-8 measure. An effective version of this allows us to prove that the second fundamental form A has a priori estimates in L^7_{\mathrm {weak}} on I , an estimate which is sharp as |A| is not in L^7 for the Simons cone. In fact, we prove the much stronger estimate that the regularity scale r_I has L^7_{weak} -estimates. The above results are in fact just applications of a new class of estimates we prove on the quantitative stratifications S^k_{\epsilon,r} and S^k_{\epsilon}\equiv S^k_{\epsilon,0} . Roughly, x\in S^k_{\epsilon}\subseteq I if no ball B_r(x) is \epsilon -close to being k+1 -symmetric. We show that S^k_\epsilon is k -rectifiable and satisfies the Minkowski estimate \mathrm {Vol}(B_r\,S_\epsilon^k)\leq C_\epsilon r^{n-k} . The proof requires a new L^2 -subspace approximation theorem for integral varifolds with bounded mean curvature, and a W^{1,p} -Reifenberg type theorem proved by the authors in [NVa].

Pressure drops of air-water two-phase flows in horizontal U-bends

Pressure drops in horizontally aligned U-bends were measured for air-water bubbly, plug, slug and annular flows to examine the applicability of available correlations to the data. The bend disturbed the flow and induced large pressure drops not only within the bend but also in the downstream-side straight pipe. The bend pressure drop was therefore evaluated as the sum of the pressure drop caused within the bend and the extra pressure drop caused within the re-developing region in the downstream-side straight pipe. The experimental data were well correlated using the Lockhart-Martinelli method and the Chisholm correlation gives the most reasonable evaluation for the bend pressure drop among the available correlations tested. The fundamental functional form of the Chisholm correlation was therefore used to develop an empirical correlation applicable to the present data. The empirical correlation gave reasonable evaluations for the air-water two-phase flows.

Effects of Tai Chi Yunshou on upper limb function and balance in stroke survivors: A protocol for systematic review and meta analysis.

Background:Functional disability is the most common disorder that occurs after stroke and seriously affects the quality of life of stroke survivors. Tai Chi Yunshou (TCY), a fundamental form of Tai Chi, is a simple, convenient, and economical exercise therapy from ancient China. Some clinical trials have reported that it improves upper limb function and balance during stroke rehabilitation. Thus, we plan to conduct a systematic review to investigate the effects of TCY in stroke survivors.Methods:This review will follow the Preferred Reporting Items for Systematic Reviews and Meta-analyses statement. We will search English and Chinese databases for randomized controlled trials on TCY for stroke survivors from the dates when the databases were established to 1 July 2020. The English databases will include MEDLINE (PubMed), EMBASE (embase.com), and the Cochrane Central Register of Controlled Trials (Cochrane Library). In addition, the Chinese databases will include the Chinese National Knowledge Infrastructure, the Chinese Biomedical Literature Database, the Chinese Science and Technology Periodical Database, the Wanfang database, and the Chinese Dissertation Database. The primary outcomes will include upper limb function and balance function, as measured by the Fugl-Meyer assessment and Berg balance scale, respectively. Two reviewers will independently screen the studies on the basis of the inclusion criteria and extract data. Review Manager (v5.3) will be used for data synthesis, and Cochrane Collaboration's tool will be used to assess the risk of bias. A fixed effects model or a random effects model will be selected based on the level of heterogeneity. The grading of recommendations assessment, development, and evaluation system will be used to evaluate the quality of the outcomes.Results:This systematic review results will be carried out after the completion of the protocol.Conclusions:This protocol aims to guide a systematic review and meta-analysis investigating the effects of JCY on upper limb function and body balance in stroke survivors, which will provide evidence for post-stroke rehabilitation training.PROSPERO registration number:CRD42020169549.