Conformal Change Research Articles

Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes

Within the Γ2-calculus of Bakry and Ledoux, we define the Ricci tensor induced by a diffusion operator, we deduce precise formulas for its behavior under drift transformation, time change and conformal transformation, and we derive new transformation results for the curvature-dimension conditions of Bakry–Émery as well as for those of Lott–Sturm–Villani. Our results are based on new identities and sharp estimates for the N-Ricci tensor and for the Hessian. In particular, we obtain Bochner's formula in the general setting.

The Audit of Deferred Taxes as a Signal for Tax Auditors: Tax Compliance Implications For Private and Public Firms

Using a tax compliance game, we study whether the observability of the taxpayer’s financial accounting information and the statutory auditor’s report affects the tax compliance. We find that firms’ responses differ significantly between private and public firms. Private firms compensate for the reported signals by understating both book and tax valuations. We find that introducing the informative signals does not necessarily increase efficiency. In fact, for private firms, it may also lead to lower tax revenues. For public firms, however, the positive effect of using the informative signals on tax compliance is much more pronounced. The usage of audit reports in addition to financial accounting statements always increases tax revenues from public firms. Regarding changes in book-tax conformity, we find that higher book-tax conformity can lead to higher tax revenues from public firms; however, tax revenues from private firms decrease with higher book-tax conformity.

Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann–Lemaître–Robertson–Walker spacetimes

We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz–Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.

On quaternionic complexes over unimodular quaternionic manifolds

Penrose's two-spinor notation for 4-dimensional Lorentzian manifolds is extended to two-component notation for quaternionic manifolds, which is a useful tool for calculation. We can construct a family of quaternionic complexes over unimodular quaternionic manifolds only by elementary calculation. On complex quaternionic manifolds as complexification of quaternionic Kähler manifolds, the existence of these complexes was established by Baston by using twistor transformations and spectral sequences. Unimodular quaternionic manifolds constitute a large nice class of quaternionic manifolds: there exists a very special curvature decomposition; the conformal change of a unimodular quaternionic structure is still unimodular quaternionic; the complexes over such manifolds are conformally invariant. This class of manifolds is the real version of torsion-free QCFs introduced by Bailey and Eastwood. These complexes are elliptic. We also obtain a Weitzenböck formula to establish vanishing of the cohomology groups of these complexes for quaternionic Kähler manifolds with negative scalar curvatures.

Prescribing the mixed scalar curvature of a foliated Riemann–Cartan manifold

The mixed scalar curvature is one of the simplest curvature invariants of a foliated Riemannian manifold. We explore the problem of prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibred manifold, we reduce the problem to solution of a leafwise elliptic equation, which has three stable solutions -- only one of them corresponds to the case of a foliated Riemannian manifold.

A Collaborator's Reputation Can Bias Decisions and Anxiety under Uncertainty.

Informational social influence theory posits that under conditions of uncertainty, we are inclined to look to others for advice. This leaves us remarkably vulnerable to being influenced by others' opinions or advice. Rational agents, however, do not blindly seek and act on arbitrary information, but often consider the quality of its source before committing to a course of action. Here, we ask the question of whether a collaborator's reputation can increase their social influence and, in turn, bias perception and anxiety under changing levels of uncertainty. Human male and female participants were asked to provide estimations of dot direction using the random dot motion (RDM) perceptual discrimination task and were paired with transient collaborators of high or low reputation whom provided their own estimations. The RDM varied in degrees of uncertainty and joint performance accuracy was linked to risk of an electric shock. Despite providing identical information, we show that collaborating with a high reputation compared with a low reputation partner, led to significantly more conformity during the RDM task for uncertain perceptual decisions. Consequently, high reputation partners decreased the subjects' anxiety during the anticipatory shock periods. fMRI data showed that parametric changes in conformity resulted in increased activity in the ventromedial PFC, whereas dissent was associated with increased in activity in the dorsal anterior cingulate cortex (dACC). Furthermore, the dACC and insula, regions involved in anticipatory pain, were significantly more active when collaborating with a low reputation partner. These results suggest that information about reputation can influence both cognitive and affective processes and in turn alter the neural circuits that underlie decision-making and emotion.SIGNIFICANCE STATEMENT Humans look to others for advice when making decisions under uncertainty. Rational agents, however, do not blindly seek information, but often consider the quality of its source before committing to a course of action. Here, we ask the question of whether a collaborators' reputation can increase social influence and in turn bias perception and anxiety in the context of perceptual uncertainty. We show that when subjects are partnered with collaborators with a high reputation, this leads to increased conformity during uncertain perceptual decision-making and reduces anxiety when joint performance accuracy leads to an electric shock. Furthermore, our results show that information about reputation alters the neural circuits that underlie decision-making and emotion.

Four-dimensional Conformally Flat Berwald and Landsberg Spaces

The problem of conformal transformation and conformal flatness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally flat Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space.

Conformal Changes of Odd-Dimensional Generalized Structures

In this paper, we consider the integrability of generalized almost contact and contact manifolds after conformal changes. We also study conditions under which the generalized almost contact and normal generalized contact structures, be normal after conformal changes.

Finslerian Ricci Deformation and Conformal Metrics

In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Finslerian Ricci flow on a compact manifold which preserves the conformal class of the initial metric are obtained as an application.

New conformal invariants in absolute parallelism geometry

The aim of the present paper is to investigate conformal changes in absolute parallelism geometry. We find out some new conformal invariants in terms of the Weitzenböck connection and the Levi-Civita connection of an absolute parallelism space.

Preparation of Highly Conductive Yarns by an Optimized Impregnation Process

We report the development of the electrical conductivity in textile yarns through impregnation and post-treatment of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). The conductive polymer is deposited on fibers, which fills the gap space within the hierarchical structure of the yarns. Organic nonpolar solvents act as reducing agent to increase the density of PEDOT moieties on the yarns, galvanizing increment in conductivity values. Post-treatment by ethylene glycol transforms the resonance configuration of the conductive moieties of conjugated polymer, which helps in further enhancement of electrical conductivity of the yarns. We have optimized the method in terms of loading and conformal change of the polymer to have a lesser resistance of the coated conductive yarns. The minimum resistance achieved has a value of 77 Ωcm−1. This technique of developing conductivity in conventional yarns enables retaining the flexibility of yarns and feeling of softness which would find suitable␣applications for wearable electronics.

On the phase space of free higher-spin theories and conformal transformations

We write a first order action for higher-spin fields and construct a canonical map to Fronsdal theory. The first-order description is defined over complex field configurations and has conformal invariance. We show that it is possible to push forward these transformations to a set of symmetries in Fronsdal theory that satisfies the conformal algebra but is not given by standard conformal change of coordinates.

On invariant Finsler metrics under (almost) β-changes

In this paper, we are going to study some [Formula: see text]-changes of the special class of Finsler metrics which we refer to as the (almost) [Formula: see text]-change and generalized (almost) [Formula: see text]-conformal changes. We investigate Douglas and Weyl tensors under these changes. In particular, we find the necessary and sufficient conditions for the Douglas metrics to be invariant under these type of changes.

F-Biharmonic maps and f-biharmonic submanifolds II

We continue our study [9] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian manifolds. We are able to characterize harmonic maps and minimal submanifolds by using the concept of f-biharmonic maps and prove that the set of all f-biharmonic maps from 2-dimensional domain is invariant under the conformal change of the metric on the domain. We give an improved equation for f-biharmonic hypersurfaces and use it to prove some rigidity theorems about f-biharmonic hypersurfaces in nonpositively curved manifolds, and to give some classifications of f-biharmonic hypersurfaces in Einstein spaces and in space forms. Finally, we also use the improved f-biharmonic hypersurface equation to obtain an improved equation and some classifications of biharmonic conformal immersions of surfaces into a 3-manifold.

On Asanov's Finsleroid–Finsler metrics as the solutions of a conformal rigidity problem

Finsleroid–Finsler metrics form an important class of singular (y-local) Finsler metrics. They were introduced by G.S. Asanov in 2006. As a special case of the general construction Asanov produced examples of Landsberg spaces of dimension at least three that are not of Berwald type. The so-called Asanov's unicorns (Landsberg spaces that are not of Berwald type) were startlers in Finsler geometry although the existence of regular (y-global) Landsberg metrics that are not of Berwald type is an open problem up to this day. Independently of Asanov's works, the Finsleroid–Finsler metrics appeared in 2003 related to the invariance problem of the mixed Berwald curvature under conformal changes. In the special case of vanishing curvature the problem is due to M. Matsumoto: are there conformally equivalent non-Riemannian Berwald manifolds? Although the condition of the conformal invariance of the mixed Berwald curvature turned out to be too strong to admit non-homothetic conformal changes, the proof reduced the problem to the investigation of the so-called Asanov-type Finslerian metric functions called Finsleroid–Finsler metrics by Asanov three years later in 2006. Using some weakening of the conformal invariance of the mixed Berwald curvature Finsleroid–Finsler metrics with closed Finsleroid axis 1-forms are characterized as the solutions of a conformal rigidity problem in this paper. We are looking for (non-Riemannian) Finsler metrics admitting a (non-homothetic) conformal change such that the mixed curvature tensor of the Berwald connection contracted by the derivatives of the logarithmic scale function is invariant. We prove that any solution must be locally conformal to a Finsleroid–Finsler metric with closed Finsleroid axis 1-form. Conversely, a Finsleroid Finsler metric with closed Finsleroid axis 1-form admits a local conformal change satisfying the rigidity condition.

THE INFLUENCE OF MEDIAL-LATERAL CONTACT PAIR CONFORMITY ON CONTACT STRESSES IN TOTAL KNEE REPLACEMENT

Eleven finite element models representing the medial-lateral conformity level and shape have been analyzed. From the result, we concluded that the flat-on-flat contact model of knee joint replacement was the most vulnerable to damage. Moreover, in the flat-on-flat model, the highest von Mises stress occurred at two points in a model, namely at the medial and lateral edge of the contact area. With respect to the sensitivity of the contact stresses to the conformity (frontal clearance) in the curved-on-curved model, the larger radius of the femoral indenter showed more contact stress sensitivity to the change in conformity. The von Mises stress dropped to almost half of its previous value when the frontal clearance decreased from 10 to 2 mm.

Microgramma vacciniifolia (Polypodiaceae) fronds contain a multifunctional lectin with immunomodulatory properties on human cells

In this study, we report the purification and characterization of a multifunctional lectin (MvFL) from Microgramma vacciniifolia fronds as well as its immunomodulatory properties on human peripheral blood mononuclear cells (PBMCs). MvFL (pI 4.51; 54kDa) is a glycoprotein able to inhibit trypsin activity and that has sequence similarities (32% coverage) with a plant RNA-binding protein. Hemagglutinating activity of MvFL was not altered by heating at 100°C for 30min, but was reduced in alkaline pH (8.0 and 9.0). Fluorimetric analyses showed that this lectin did not undergo marked conformational changes when heated. However, the MvFL conformation changed depending on the pH. MvFL at 6.25–25μg/mL was not cytotoxic to lymphocytes present among PBMCs. The PBMCs incubated for 24h with the lectin (12.5μg/mL) showed increased TNF-α, IFN-γ, IL-6, IL-10, and nitric oxide production. MvFL also stimulated T lymphocytes from PBMCs to differentiate into CD8+ cells. The activation (indicated by CD28 expression) of these cells was also stimulated. In conclusion, MvFL is a heat-stable and multifunctional protein, with both lectin and trypsin inhibitor activities, and capable of inducing predominantly a Th1 response in human PBMCs as well as activation and differentiation of T lymphocytes.

Vibrational spectra of buta-1,3-diene iron tricarbonyl: comparison to surface species

Butadiene potentially exhibits many different modes of bonding to a surface, the aim of this work is to fully characterise how the spectrum of the s-cis conformer changes on coordination. A model complex, C4H6Fe(CO)3 and its deuterated isotopomer, was studied with infrared, Raman and inelastic neutron scattering (INS) spectroscopies and has provided a definitive set of assignments for the ligand. These differ in many respects from previous work that was solely based on empirical correlations. The use of INS spectroscopy has allowed observation of several of the low energy modes for the first time, the most significant of which is the C1–C1′ torsion at 485 cm−1. The comparison of observed and calculated infrared spectra for butadiene on silica confirms the surprising assignment that the molecule is adsorbed as the gauche form.

Legendre Curves on Generalized Paracontact Metric Manifolds

Two different notions of almost paracontact structures (which are compatible or anti-compatible with the metric), well known in the literature, are unified and generalized here. Several formulas of paraholomorphic maps are established, and a result of Lichnerowicz type is obtained. The connection transformations which have the same system of paracontact-planar Legendre curves are characterized. Conformal changes of metrics which preserve geodesics (resp. paracontact-planar Legendre curves) are studied.

Probing the Molecular Mechanism of Human Soluble Guanylate Cyclase Activation by NO in vitro and in vivo

Soluble guanylate cyclase (sGC) is a heme-containing metalloprotein in NO-sGC-cGMP signaling. NO binds to the heme of sGC to catalyze the synthesis of the second messenger cGMP, which plays a critical role in several physiological processes. However, the molecular mechanism for sGC to mediate the NO signaling remains unclear. Here fluorophore FlAsH-EDT2 and fluorescent proteins were employed to study the NO-induced sGC activation. FlAsH-EDT2 labeling study revealed that NO binding to the H-NOX domain of sGC increased the distance between H-NOX and PAS domain and the separation between H-NOX and coiled-coil domain. The heme pocket conformation changed from “closed” to “open” upon NO binding. In addition, the NO-induced conformational change of sGC was firstly investigated in vivo through fluorescence lifetime imaging microscopy. The results both in vitro and in vivo indicated the conformational change of the catalytic domain of sGC from “open” to “closed” upon NO binding. NO binding to the heme of H-NOX domain caused breaking of Fe-N coordination bond, initiated the domain moving and conformational change, induced the allosteric effect of sGC to trigger the NO-signaling from H-NOX via PAS & coiled-coil to the catalytic domain, and ultimately stimulates the cyclase activity of sGC.