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Journal articles on the topic 'Phi-curvature'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Ingalahalli, G., and C. S. Bagewadi. "A Study on $\phi$-Symmetric $\tau$-curvature tensor in $N(k)$-contact metric manifold." Carpathian Mathematical Publications 6, no. 2 (December 25, 2014): 203–11. http://dx.doi.org/10.15330/cmp.6.2.203-211.

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In this paper we study $\tau$-curvature tensor in $N(k)$-contact metric manifold. We study $\tau$-$\phi$-recurrent,$\tau$-$\phi$-symmetric and globally $\tau$-$\phi$-symmetric $N(k)$-contact metric manifold.

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2

Caraballo, David G. "FLAT $\phi $ CURVATURE FLOW OF CONVEX SETS." Taiwanese Journal of Mathematics 16, no. 1 (January 2012): 1–12. http://dx.doi.org/10.11650/twjm/1500406525.

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3

Azami, Shahroud. "First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow." Journal of the Indonesian Mathematical Society 24, no. 1 (December 24, 2017): 51–60. http://dx.doi.org/10.22342/jims.24.1.434.51-60.

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Let $(M,g(t))$ be a compact Riemannian manifold and the metric $g(t)$ evolve by the Ricci-Bourguignon flow. We find the formula variation of the eigenvalues of geometric operator $-\Delta_{\phi}+cR$ under the Ricci-Bourguignon flow, where $\Delta_{\phi}$ is the Witten-Laplacian operator and $R$ is the scalar curvature. In the final we show that some quantities dependent to the eigenvalues of the geometric operator are nondecreasing along the Ricci-Bourguignon flow on closed manifolds with nonnegative curvature.

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4

Hou, Lanbao, Feng Du, Jing Mao, and Chuanxi Wu. "Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces." Open Mathematics 19, no. 1 (January 1, 2021): 1110–19. http://dx.doi.org/10.1515/math-2021-0100.

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Abstract In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space ( M , ⟨ , ⟩ , e − ϕ d v ) \left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v) , with nonnegative weighted Ricci curvature Ric ϕ ≥ 0 {{\rm{Ric}}}^{\phi }\ge 0 for some ϕ ∈ C 2 ( M ) \phi \in {C}^{2}\left(M) , which is uniformly bounded from above, and successfully obtain several universal inequalities of this eigenvalue problem.

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5

Dong, Jie, Pengfei Cheng, Hanjiang Wen, and Wenke Sun. "Internal co-seismic displacement and strain changes inside a homogeneous spherical Earth." Geophysical Journal International 225, no. 2 (January 25, 2021): 1378–91. http://dx.doi.org/10.1093/gji/ggab032.

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SUMMARY In this study, we devised a new set of analytical foundation solutions to compute the internal co-seismic displacement and strain changes caused by four independent point sources (strike-slip, dip-slip, horizontal tensile and vertical tensile) inside a homogeneous spherical earth model. Our model provides constraints on the deformation properties at depth and reveals that the internal co-seismic deformation is larger than that on the surface. The deformation near the source is convergent with our formulae. For the internal deformation at radial section plane, the patterns of horizontal displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{{ rr}}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by strike-slip and tensile sources appear symmetric at the equidistance above and below the source. Their amplitudes are not identical but with a small discrepancy actually. Unlike these, the patterns of radial displacements ${u_r}$ for strike-slip and tensile sources exhibit point symmetry with the equidistance from the source. Also, the corresponding amplitudes are slightly different. The displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{{ rr}}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by dip-slip also show the same properties as ${u_{ r}}$ of the strike-slip source. The magnitudes of the displacements and strain changes depend on the source types. The curvature effect on the near-field surface deformations is small, and it increases with the studied depth. However, for the far-field deformation caused by the strike-slip source (ds = 20 km), the curvature effect can be as large as 77 per cent when the epicentral distance approximates to 1778 km.

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6

Shah, Riddhi Jung. "Some Curvature Properties of D-conformal Curvature Tensor on LP-Sasakian Manifolds." Journal of Institute of Science and Technology 19, no. 1 (November 8, 2015): 30–34. http://dx.doi.org/10.3126/jist.v19i1.13823.

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This paper deals with the study of geometry of Lorentzian para-Sasakian manifolds. We investigate some properties of D-conformally flat, D-conformally semi-symmetric, Xi-D-conformally flat and Phi-D-conformally flat curvature conditions on Lorentzian para-Sasakian manifolds. Also it is proved that in each curvature condition an LP-Sasakian manifold (Mn,g)(n>3) is an eta-Einstein manifold.Journal of Institute of Science and Technology, 2014, 19(1): 30-34

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7

Arnaudon, Marc, Anton Thalmaier, and Feng-Yu Wang. "Gradient Estimates on Dirichlet and Neumann Eigenfunctions." International Mathematics Research Notices 2020, no. 20 (September 4, 2018): 7279–305. http://dx.doi.org/10.1093/imrn/rny208.

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Abstract By methods of stochastic analysis on Riemannian manifolds, we derive explicit constants $c_1(D)$ and $c_2(D)$ for a $d$-dimensional compact Riemannian manifold $D$ with boundary such that $c_1(D)\sqrt \lambda \|\phi \|_\infty \leqslant \|\nabla \phi \|_\infty \leqslant c_2(D)\sqrt \lambda \|\phi \|_\infty $ holds for any Dirichlet eigenfunction $\phi $ of $-\Delta $ with eigenvalue $\lambda $. In particular, when $D$ is convex with nonnegative Ricci curvature, the estimate holds for $c_1(D)= 1/{d\mathrm{e}}$ and $c_2(D)=\sqrt{\mathrm{e}}\left (\frac{\sqrt{2}}{\sqrt{\pi }}+\frac{\sqrt{\pi }}{4\sqrt{2}}\right ).$ Corresponding two-sided gradient estimates for Neumann eigenfunctions are derived in the second part of the paper.

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8

Sardar, Arpan. "SOME RESULTS ON (ϵ)- KENMOTSU MANIFOLDS." Facta Universitatis, Series: Mathematics and Informatics 35, no. 1 (April 6, 2020): 273. http://dx.doi.org/10.22190/fumi2001273s.

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We have studied curvature symmetries in ($\epsilon$)-Kenmotsu manifolds. Next, we have proved the non-existence of a non-zero parallel 2-form in an ($\epsilon$)-Kenmotsu manifold. Moreover, we have characterised $\phi$-Ricci symmetric ($\epsilon$)-Kenmotsu manifolds and finally, we have proved that under certain restriction on the scalar curvature $divR$=0 and $divC$=0 are equivalent, where `$div$' denotes divergence.

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9

Regen, D. M., P. Anversa, and J. M. Capasso. "Segmental calculation of left ventricular wall stresses." American Journal of Physiology-Heart and Circulatory Physiology 264, no. 5 (May 1, 1993): H1411—H1421. http://dx.doi.org/10.1152/ajpheart.1993.264.5.h1411.

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A procedure for calculating left ventricular wall stresses segmentally was devised. Rectangular coordinates of the wall surfaces as seen in longitudinal section were plotted with the long axis as the x-axis. For each cavity point, a third-order polynomial (cubic spline) was fitted to the point together with several adjacent points on either side of it; the cavity radius (normal to cavity surface) at the point was found algebraically from the spline's coefficients. Each cavity radius was matched with the most symmetrical one from the opposite cavity surface. The point of intersection of the cavity radius with the outer surface was found, and a midwall point was identified from logarithmic means of cavity and outer radial lengths. For each midwall point, a cubic spline was fitted to that point together with several adjacent points on either side of it, and the midwall radius at that point was determined algebraically from the spline's coefficients. Each midwall radius was matched to the most symmetrical one from the opposite midwall. The locus of points at equal radial distances from opposite midwalls forms the axis. The midwall radius of curvature (r theta) orthogonal to the meridian at each point was taken as the radial distance from the midwall to the axis. Midwall meridional radius of curvature (r phi) was calculated from the spline's coefficients. Thickness (h) was calculated from intersections between the midwall radius and the inner and outer surfaces. For each point, meridional tension (T phi) was calculated as T phi = Pr theta/2, and hoop tension (T theta) was calculated as T theta = (Pr theta/2)(2 - r theta/r phi) where P is transmural pressure. Stresses were calculated as tensions divided by thicknesses (sigma phi = T phi/h, sigma theta = T theta/h), or more directly as sigma phi = Pr theta/2h and sigma theta = (Pr theta/2h)(2 - r theta/r phi). This procedure was validated with simple chamber shapes, and it has been applied to left ventricles.

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10

Li, Zhu. "Algebro-Geometric Solutions of the Harry Dym Hierarchy." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 2 (April 1, 2017): 129–36. http://dx.doi.org/10.1515/ijnsns-2016-0057.

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AbstractThe Harry Dym hierarchy is derived with the help of Lenard recursion equations and zero curvature equation. Based on the Lax matrix, an algebraic curve $\mathcal{K}_{n}$ of arithmetic genus $n$ is introduced, from which the corresponding meromorphic function $\phi$ and Dubrovin-type equations are given. Further, the divisor and asymptotic properties of $\phi$ are studied. Finally, algebro-geometric solutions for the entire hierarchy are obtained according to above results and the theory of algebraic curve.

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11

Bessa, G. Pacelli, Barnabe P. Lima, and Leandro F. Pessoa. "Curvature estimates for properly immersed $$\phi _{h}$$ ϕ h -bounded submanifolds." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 1 (August 8, 2013): 109–30. http://dx.doi.org/10.1007/s10231-013-0367-1.

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12

Ching-Peng, Huang. "A model of invariant control system using mean curvature drift from Brownian motion under submersions." Quarterly of Applied Mathematics 81, no. 1 (September 30, 2022): 175–202. http://dx.doi.org/10.1090/qam/1633.

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Given a Riemannian submersion ϕ : M → N \phi : M \to N , we construct a stochastic process X X on M M such that the image Y ≔ ϕ ( X ) Y≔\phi (X) is a (reversed, scaled) mean curvature flow of the fibers of the submersion. The model example is the mapping π : G L ( n ) → G L ( n ) / O ( n ) \pi : GL(n) \to GL(n)/O(n) , whose image is equivalent to the space of n n -by- n n positive definite matrices, S + ( n , n ) \mathcal {S}_+(n,n) , and the said flow has deterministic image. We are able to compute explicitly the mean curvature (and hence the drift term) of the fibers w.r.t. this map, (i) under diagonalization and (ii) in matrix entries, writing mean curvature as the gradient of log volume of orbits. As a consequence, we are able to write down Brownian motions explicitly on several common homogeneous spaces, such as Poincaré’s upper half plane and the Bures-Wasserstein geometry on S + ( n , n ) \mathcal {S}_+(n,n) , on which we can see the eigenvalue processes of Brownian motion reminiscent of Dyson’s Brownian motion. By choosing the background metric via natural G L ( n ) GL(n) action, we arrive at an invariant control system on the G L ( n ) GL(n) -homogenous space G L ( n ) / O ( n ) GL(n)/O(n) . We investigate the feasibility of developing stochastic algorithms using the mean curvature flow.

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13

Funaki, T., and H. Spohn. "Motion by Mean Curvature from the Ginzburg-Landau $\nabla\phi$ Interface Model." Communications in Mathematical Physics 185, no. 1 (April 1, 1997): 1–36. http://dx.doi.org/10.1007/s002200050080.

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14

Shah, Riddhi Jung. "Some curvature tensors in N(k)-contact metric manifold." BIBECHANA 16 (November 22, 2018): 55–63. http://dx.doi.org/10.3126/bibechana.v16i0.19674.

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The purpose of this paper is to study W7and W9-curvature tensors on N(k)-contact metric manifolds. We prove that a N(k)-contact metric manifold satisfying the condition W7( xi,X).W9=0 is eta-Einstein manifold. We also obtain the Ricci tensor S of type (0, 2) for phi-W9flat and divW9=0 conditions on N(k)-contact metric manifolds. Finally, we give an example of 3-dimensional N(k)-contact metric manifold.BIBECHANA 16 (2019) 55-63

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15

Kumar, S., and K. K. Dube. "Semi Invariant Submanifolds of a Para Kenmotsu Manifold with Constant \phi Holomorphic Sectional Curvature." Journal of the Tensor Society 2, no. 00 (November 30, 2008): 7–16. http://dx.doi.org/10.56424/jts.v2i00.9955.

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In this Paper We have studied submanifolds para Kenmostu manifold to be semi-invarient submanifold. In particular case when it is a para Kenmostu space form of constant φ holomorphic sectional curvature

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16

Rose, David, and Randolph Blake. "Motion perception: from phi to omega." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 353, no. 1371 (June 29, 1998): 967–80. http://dx.doi.org/10.1098/rstb.1998.0261.

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When human observers view dynamic random noise, such as television ‘snow’, through a curved or annular aperture, they experience a compelling illusion that the noise is moving smoothly and coherently around the curve (‘the omega effect’). In several series of experiments, we have investigated the conditions under which this effect occurs and the possible mechanisms that might cause it. We contrast the omega effect with ‘phi motion’, seen when an object suddenly changes position. Our conclusions are that the visual scene is first segmented into objects before a coherent velocity is assigned to the texture on each object' surface. The omega effect arises because there are motion mechanisms that deal specifically with object rotation and these interact with pattern mechanisms sensitive to curvature.

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17

Ho, Pak Tung. "The structure of $${\phi}$$ -stable minimal hypersurfaces in manifolds of nonnegative P-scalar curvature." Mathematische Annalen 348, no. 2 (January 20, 2010): 319–32. http://dx.doi.org/10.1007/s00208-010-0482-x.

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18

Bessa, G. Pacelli, Leandro F. Pessoa, and Marco Rigoli. "Higher order mean curvature estimates for properly immersed $$\phi _{h}$$ ϕ h -bounded hypersurfaces." Annali di Matematica Pura ed Applicata (1923 -) 198, no. 1 (July 16, 2018): 157–75. http://dx.doi.org/10.1007/s10231-018-0767-3.

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19

Mohammed Yousif, A., and Q. S. A. Al-Zamil. "On Weyl tensor of ACR-manifolds of class $C_{12}$ with applications." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 59 (May 2022): 3–14. http://dx.doi.org/10.35634/2226-3594-2022-59-01.

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In this paper, we determine the components of the Weyl tensor of almost contact metric (ACR-) manifold of class $C_{12}$ on associated G-structure (AG-structure) space. As an application, we prove that the conformally flat ACR-manifold of class $C_{12}$ with $n>2$ is an $\eta$-Einstein manifold and conclude that it is an Einstein manifold such that the scalar curvature $r$ has provided. Also, the case when $n=2$ is discussed explicitly. Moreover, the relationships among conformally flat, conformally symmetric, $\xi$-conformally flat and $\Phi$-invariant Ricci tensor have been widely considered here and consequently we determine the value of scalar curvature $r$ explicitly with other applications. Finally, we define new classes with identities analogously to Gray identities and discuss their connections with class $C_{12}$ of ACR-manifold.

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20

Wang, Zhenguo, and Qiuying Li. "Multiple periodic solutions for discrete boundary value problem involving the mean curvature operator." Open Mathematics 20, no. 1 (January 1, 2022): 1195–202. http://dx.doi.org/10.1515/math-2022-0509.

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Abstract In this article, by using critical point theory, we prove the existence of multiple T T -periodic solutions for difference equations with the mean curvature operator: − Δ ( ϕ c ( Δ u ( t − 1 ) ) ) + q ( t ) u ( t ) = λ f ( t , u ( t ) ) , t ∈ Z , -\Delta ({\phi }_{c}\left(\Delta u\left(t-1)))+q\left(t)u\left(t)=\lambda f\left(t,u\left(t)),\hspace{1em}t\in {\mathbb{Z}}, where Z {\mathbb{Z}} is the set of integers. As a T T -periodic problem, it does not require the nonlinear term is unbounded or bounded, and thus, our results are supplements to some well-known periodic problems. Finally, we give one example to illustrate our main results.

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21

Sasahara, Tooru. "Submanifolds in a Sasakian manifold $ \mathbf{R}^{2n+1}(-3) $ whose $\phi$ -mean curvature vectors are eigenvectors." Journal of Geometry 75, no. 1 (December 2002): 166–78. http://dx.doi.org/10.1007/s00022-002-1604-8.

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22

Rojo, F., and M. Salas. "A DNA curvature can substitute phage phi 29 regulatory protein p4 when acting as a transcriptional repressor." EMBO Journal 10, no. 11 (November 1991): 3429–38. http://dx.doi.org/10.1002/j.1460-2075.1991.tb04907.x.

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23

Roterman, Irena, Katarzyna Stapor, and Leszek Konieczny. "Secondary Structure in Amyloids in Relation to Their Wild Type Forms." International Journal of Molecular Sciences 24, no. 1 (December 21, 2022): 154. http://dx.doi.org/10.3390/ijms24010154.

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The amyloid structures and their wild type forms, available in the PDB database, provide the basis for comparative analyses. Globular proteins are characterised by a 3D spatial structure, while a chain in any amyloid fibril has a 2D structure. Another difference lies in the structuring of the hydrogen bond network. Amyloid forms theoretically engage all the NH and C=O groups of the peptide bonds in a chain with two hydrogen bonds each. In addition, the hydrogen bond network is highly ordered—as perpendicular to the plane of the chain. The β-structure segments provide the hydrogen bond system with an anti-parallel system. The folds appearing in the rectilinear propagation of the segment with the β-structure are caused by just by one of the residues in the sequence—residues with a Rα-helical or Lα-helical conformation. The antiparallel system of the hydrogen bonds in the β-structure sections at the site of the amino acid with a Rα- or Lα-helical conformation changes into a parallel system locally. This system also ensures that the involvement of the C=O and H-N groups in the construction of the interchain hydrogen bond, while maintaining a perpendicular orientation towards the plane of the chain. Conformational analysis at the level of the Phi and Psi angles indicates the presence of the conditions for the structures observed in the amyloids. The specificity of amyloid structures with the dominant conformation expressed as |Psi| = |Phi| reveals the system of organisation present in amyloid fibrils. The Phi, Psi angles, as present in this particular structure, transformed to form |Psi| = |Phi| appear to be ordered co-linearly. Therefore, the calculation of the correlation coefficient may express the distribution around this idealised localisation on the Ramachandran map. Additionally, when the outstanding points are eliminated, the part of amyloid chain can be classified as fulfilling the defined conditions. In addition, the presentation of the chain structure using geometric parameters, V-angle—the angle between the planes of the adjacent peptide bonds (angle versus the virtual axis Cα-Cα) and the radius of the curvature R, depending on the size of the angle V, allows for a quantitative assessment of changes during amyloid transformation.

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24

Peloso, Marco M., and Silvia Secco. "BOUNDEDNESS OF FOURIER INTEGRAL OPERATORS ON HARDY SPACES." Proceedings of the Edinburgh Mathematical Society 51, no. 2 (June 2008): 443–63. http://dx.doi.org/10.1017/s001309150500012x.

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AbstractFor $0\ltp\le1$, let $h^p(\mathbb{R}^n)$ denote the local Hardy space. Let $\mathcal{F}$ be a Fourier integral operator defined by the oscillatory integral$$ \mathcal{F}f(x)=\iint_{\mathbb{R}^{2n}}\exp(2\pi\mathrm{i}(\phi(x,\xi)-y\cdot\xi))b(x,y,\xi)f(y)\,\mathrm{d} y\,\mathrm{d}\xi, $$where $\phi$ is a $\mathcal{C}^\infty$ non-degenerate real phase function, and $b$ is a symbol of order $\mu$ and type $(\rho,1-\rho)$, $\sfrac12\lt\rho\le1$, vanishing for $x$ outside a compact set of $\mathbb{R}^n$. We show that when $p\le1$ and $\mu\le-(n-1)(1/p-1/2)$ then $\mathcal{F}$ initially defined on Schwartz functions in $h^p(\mathbb{R}^n)$ extends to a bounded operator $\mathcal{F}:h^p(\mathbb{R}^n)\rightarrow h^p(\mathbb{R}^n)$. The range of $p$ and $\mu$ is sharp. This result extends to the local Hardy spaces the seminal result of Seeger \et for the $L^p$ spaces. As immediate applications we prove the boundedness of smooth Radon transforms on hypersurfaces with non-vanishing Gaussian curvature on the local Hardy spaces.Finally, we prove a local version for the boundedness of Fourier integral operators on local Hardy spaces on smooth Riemannian manifolds of bounded geometry.

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25

Chakraborty, Priyesh, and Anthony R. Pullen. "Full-sky lensing reconstruction of 21 cm intensity maps." Monthly Notices of the Royal Astronomical Society 488, no. 2 (July 3, 2019): 1828–45. http://dx.doi.org/10.1093/mnras/stz1781.

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ABSTRACT Weak gravitational lensing of the 21 cm radiation is expected to be an important cosmological probe for post-reionization physics. We investigate the reconstruction of the matter density perturbations using a quadratic minimum variance estimator. The next generation of line intensity mapping (LIM) surveys such as HIRAX and CHIME will cover a larger sky fraction, which requires one to account for the curvature in the sky. Thus, we extend the plane-parallel flat-sky formalism for lensing reconstruction to account for a full-sky survey using the spherical Fourier–Bessel (SFB) expansion. Using the HIRAX 21 cm survey as a basis, we make predictions for lensing-reconstruction noise in our formalism and compare our results with the predictions from the plane-parallel formalism. We find agreement with the plane-parallel noise power spectrum at small scales and a significant deviation at scales L ≲ ℓres − keqR, where R is the radius of the shell volume, keq is the wavenumber for matter–radiation equality, and ℓres is the angular resolution scale. Furthermore, we derive the SFB flat-sky reconstruction noise and compare it with the full-sky SFB case as well as the plane-parallel case, finding minor deviations from the full-sky noise due to sphericity. We also determine that, in the absence of non-Gaussian statistics of the intensity field but accounting for foregrounds, the signal-to-noise ratio for $C_\ell ^{\phi \phi }$ using our SFB estimator increases by over 100 per cent. This shows that accounting for the curved sky in LIM weak lensing will be crucial for large-scale cosmology.

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Reddy, G. S., Mallikarjuna N. Nadagouda, and Jainagesh A. Sekhar. "Nanostructured Surfaces that Show Antimicrobial, Anticorrosive, and Antibiofilm Properties." Key Engineering Materials 521 (August 2012): 1–33. http://dx.doi.org/10.4028/www.scientific.net/kem.521.1.

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Provided in this article are the quantitative and qualitative morphological results describing the action of several nanostructured surfaces for bactericidal and bacteriostatic action. Results are also provided to illustrate microbial corrosion and its impact. Biofilm formation is correlated to colony formation. Nanostructured surfaces, i.e. surfaces with welded nanoparticles are noted to display biocidal activity with varying efficacies. Porous nanostructures, on stainless steel and copper substrates, made of high purity Ag, Ti, Al, Cu, MoSi2, and carbon nanotubes, are tested for their efficacy against bacterial colony formation for both gram-negative, and gram-positive bacteria. Silver and Molybdenum disilicide (MoSi2) nanostructures are found to be the most effective bactericidal agents with MoSi2 being particularly effective in both low and high humidity conditions. Bacteriostatic activity is also noted. The nanostructured surfaces are tested by controlled exposures to several microbial species including (Gram+ve) bacteria such as Bacillus Cereus and (Gram-ve) bacteria such as Enterobacter Aerogenes. The resistance to simultaneous exposure from diverse bacterial species including Arthrobacter Globiformis, Bacillus Megaterium, and Cupriavidus Necator is also studied. The nanostructured surfaces were found to eliminates or delay bacterial colony formation, even with short exposure times, and even after simulated surface abrasion. The virgin 316 stainless steel and copper substrates, i.e. without the nanostructure, always displayed rapid bacterial colony evolution indicating the lack of antimicrobial action. The efficacy of the nanostructured surface against colony formation (bacterial recovery) for E-Coli (two strains) and virus Phi 6 Bacteriophage with a host Pseudomonas Syringae was also studied. Preliminary results are presented that also show possible anti-fungal properties by the nanostructured MoSi2. When comparing antimicrobial efficacy of flat polished surfaces (no curvature or nanostructure) with nanostructure containing surfaces (high curvature) of the same chemistry, shows that bacterial action results from both the nanostructure size and chemistry.

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Fabian, Piotr, Katarzyna Stapor, Mateusz Banach, Magdalena Ptak-Kaczor, Leszek Konieczny, and Irena Roterman. "Different Synergy in Amyloids and Biologically Active Forms of Proteins." International Journal of Molecular Sciences 20, no. 18 (September 9, 2019): 4436. http://dx.doi.org/10.3390/ijms20184436.

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Protein structure is the result of the high synergy of all amino acids present in the protein. This synergy is the result of an overall strategy for adapting a specific protein structure. It is a compromise between two trends: The optimization of non-binding interactions and the directing of the folding process by an external force field, whose source is the water environment. The geometric parameters of the structural form of the polypeptide chain in the form of a local radius of curvature that is dependent on the orientation of adjacent peptide bond planes (result of the respective Phi and Psi rotation) allow for a comparative analysis of protein structures. Certain levels of their geometry are the criteria for comparison. In particular, they can be used to assess the differences between the structural form of biologically active proteins and their amyloid forms. On the other hand, the application of the fuzzy oil drop model allows the assessment of the role of amino acids in the construction of tertiary structure through their participation in the construction of a hydrophobic core. The combination of these two models—the geometric structure of the backbone and the determining of the participation in the construction of the tertiary structure that is applied for the comparative analysis of biologically active and amyloid forms—is presented.

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Park, Seongjun, Chandara Koem, and Changsu Shim. "Quantitative Definition of Seismic Performance Levels for Precast Bridge Piers with Continuous Reinforcement." Advances in Civil Engineering 2020 (September 7, 2020): 1–21. http://dx.doi.org/10.1155/2020/4087532.

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For construction sites within cities, which require fast construction because of restrictions in road occupation time, or for other occasions where construction period is an important factor because of similar reasons, application of a modular construction method using precast members is efficient in terms of shortening the construction period. The substructures of bridges are normally constructed using cast-in-place, which has been a major cause of delays in construction. Application of a modular construction method could decrease the occupation time in the sites. A prime example is the Accelerated Bridge Construction (ABC) by the Texas Department of Transportation (TDOT) and Federal Highway Administration (FHWA). Precast members are the key components of ABC. The main purpose of this paper is to provide clear seismic performance standards for precast bridge piers. Current seismic design codes require force-based design checks and provide qualitative evaluation of the overall structure. They do not provide specific qualitative criteria for individual structures with particular types. Previous research has been focused on reinforced-concrete bridge piers, while lacking on research towards prefabricated bridge piers with continuous reinforcements. In order to quantitatively evaluate the seismic performance level of prefabricated bridge piers, the seismic performance was quantitatively suggested in accordance with the classification of four which are operational, immediate occupancy, life safety, and collapse prevention. These criteria are cracking of cover concrete, crushing of cover concrete, yielding of axial steels, and fracture of axial steels. Based on the given seismic performance evaluation criteria, evaluation and verification were conducted on four prefabricated bridge piers with continuous reinforcement that have undergone quasistatic cyclic experiments. The moment-curvature analysis model was constructed for the parametric study and verified through experimental results. Based on the developed M-Phi model, prefabricated bridge piers with continuous reinforcement, which were designed force-based using response correction factor, were evaluated. In addition, parametric study was also conducted focusing on concrete strength, magnitude of prestress, and transverse reinforcement. Depending on the level of individual performance produced by ranges of these variables within possible runs on actual piers, the impact of 3 variables was analyzed. Furthermore, in response to changes in each variable, the impact on the relevant seismic performance level was verified through response spectrum analysis.

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29

Cecchi, Mariella, Zuzana Došlá, and Mauro Marini. "Oscillation of a class of differential equations with generalized phi-Laplacian." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143, no. 3 (May 22, 2013): 493–506. http://dx.doi.org/10.1017/s0308210511001156.

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The oscillation of the nonlinear differential equationwhere Φ is an increasing odd homeomorphism, is considered when the weight b is not summable near infinity. We extend previous results, stated for equations with the classical p-Laplacian, by obtaining necessary and sufficient conditions of integral type for the oscillation. The role of the boundedness of Im Φ [Dom Φ] is analysed in detail. Our results includes the case Φ* ◦ F linear near zero or near infinity, where Φ* is the inverse of Φ. Several examples, concerning the curvature or relativity operator, illustrate our results.

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30

Abass, Mohammed Y., and Habeeb M. Abood. "Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type." Communications in Mathematics Volume 32 (2024), Issue 1 (February 7, 2023). http://dx.doi.org/10.46298/cm.10869.

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This paper determined the components of the generalized curvature tensor for the class of Kenmotsu type and established the mentioned class is {\eta}-Einstein manifold when the generalized curvature tensor is flat; the converse holds true under suitable conditions. It also introduced the notion of generalized {\Phi}-holomorphic sectional (G{\Phi}SH-) curvature tensor and thus found the necessary and sufficient conditions for the class of Kenmotsu type to be of constant G{\Phi}SH-curvature. In addition, the notion of {\Phi}-generalized semi-symmetric was introduced and its relationship with the class of Kenmotsu type and {\eta}-Einstein manifold established. Furthermore, this paper generalized the notion of the manifold of constant curvature and deduced its relationship with the aforementioned ideas. It finally showed that the class of Kenmotsu type exists as a hypersurface of the Hermitian manifold and derived a relation between the components of the Riemannian curvature tensors of the almost Hermitian manifold and its hypersurfaces.

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31

Bueno, Antonio, and Irene Ortiz. "Surfaces of prescribed linear Weingarten curvature in." Proceedings of the Royal Society of Edinburgh: Section A Mathematics, July 22, 2022, 1–24. http://dx.doi.org/10.1017/prm.2022.48.

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Given $a,\,b\in \mathbb {R}$ and $\Phi \in C^{1}(\mathbb {S}^{2})$ , we study immersed oriented surfaces $\Sigma$ in the Euclidean 3-space $\mathbb {R}^{3}$ whose mean curvature $H$ and Gauss curvature $K$ satisfy $2aH+bK=\Phi (N)$ , where $N:\Sigma \rightarrow \mathbb {S}^{2}$ is the Gauss map. This theory widely generalizes some of paramount importance such as the ones constant mean and Gauss curvature surfaces, linear Weingarten surfaces and self-translating solitons of the mean curvature flow. Under mild assumptions on the prescribed function $\Phi$ , we exhibit a classification result for rotational surfaces in the case that the underlying fully nonlinear PDE that governs these surfaces is elliptic or hyperbolic.

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32

Cora, Gabriele, and Roberta Musina. "Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space." Calculus of Variations and Partial Differential Equations 60, no. 6 (September 16, 2021). http://dx.doi.org/10.1007/s00526-021-01932-8.

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AbstractGiven a constant $$k>1$$ k > 1 , let Z be the family of round spheres of radius $${{\,\mathrm{artanh}\,}}(k^{-1})$$ artanh ( k - 1 ) in the hyperbolic space $${\mathbb {H}}^3$$ H 3 , so that any sphere in Z has mean curvature k. We prove a crucial nondegeneracy result involving the manifold Z. As an application, we provide sufficient conditions on a prescribed function $$\phi $$ ϕ on $${\mathbb {H}}^3$$ H 3 , which ensure the existence of a $$\mathcal{C}^1$$ C 1 -curve, parametrized by $$\varepsilon \approx 0$$ ε ≈ 0 , of embedded spheres in $${\mathbb {H}}^3$$ H 3 having mean curvature $$k +\varepsilon \phi $$ k + ε ϕ at each point.

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33

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Regularity of Dirac-harmonic maps with $$\lambda $$-curvature term in higher dimensions." Calculus of Variations and Partial Differential Equations 58, no. 6 (October 13, 2019). http://dx.doi.org/10.1007/s00526-019-1632-y.

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Abstract In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with $$\lambda $$λ-curvature term. For a weakly stationary Dirac-harmonic map with $$\lambda $$λ-curvature term $$(\phi ,\psi )$$(ϕ,ψ) from a smooth bounded open domain $$\Omega \subset {\mathbb {R}}^m$$Ω⊂Rm with $$m\ge 2$$m≥2 to a compact Riemannian manifold N, if $$\psi \in W^{1,p}(\Omega )$$ψ∈W1,p(Ω) for some $$p>\frac{2m}{3}$$p>2m3, we prove that $$(\phi , \psi )$$(ϕ,ψ) is smooth outside a closed singular set whose $$(m-2)$$(m-2)-dimensional Hausdorff measure is zero. Furthermore, if the target manifold N does not admit any harmonic sphere $$S^l$$Sl, $$l=2,\ldots , m-1$$l=2,…,m-1, then $$(\phi ,\psi )$$(ϕ,ψ) is smooth.

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34

Bagher Kazemi Balgeshir, Mohammad, and Fatemeh Raei. "Recurrent and $\phi$-recurrent curvature on mixed 3-Sasakian manifolds." Novi Sad Journal of Mathematics Accepted (January 21, 2023). http://dx.doi.org/10.30755/nsjom.10764.

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35

"Design of slit loaded Planar and Curved Patch Antenna." Regular Issue 6, no. 1 (August 15, 2019): 11–14. http://dx.doi.org/10.35940/ijisme.a1139.086119.

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Slit loaded circularly polarized patch antenna embedded on planar structure and curvature structure were investigated. The curvature effect on slit loaded patch antenna determines the limiting value of radius of curvature to obtain circular polarization. At a certain radius of curvature (ROC) around 131.3 mm, circular polarization have been obtained with axial ratio band width around 15 MHz and return loss bandwidth around 56 MHz compared with 17 MHz and 65 MHz as that of planar structure. The beam width responsible for coverage of planar patch are 104 and 107 degree with respect to 84 degree and 124 degree of curved patch at phi = 0 and 90 degree respectively

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36

Li, Yanlin, Fatemah Mofarreh, Ravi P. Agrawal, and Akram Ali. "Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms." Journal of Inequalities and Applications 2022, no. 1 (August 4, 2022). http://dx.doi.org/10.1186/s13660-022-02838-5.

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AbstractThis paper aims to establish new upper bounds for the first positive eigenvalue of the Φ-Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the Φ-Laplacian operator on closed oriented m-dimensional semislant submanifolds in a Sasakian space form M ˜ 2 k + 1 ( ϵ ) is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the Φ-Laplacian on semislant submanifolds in a sphere S 2 n + 1 with $\epsilon =1$ ϵ = 1 and $\Phi =2$ Φ = 2 .

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37

Gálvez, José A., and Pablo Mira. "Rotational symmetry of Weingarten spheres in homogeneous three-manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal), October 8, 2020. http://dx.doi.org/10.1515/crelle-2020-0031.

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AbstractLet M be a simply connected homogeneous three-manifold with isometry group of dimension 4, and let Σ be any compact surface of genus zero immersed in M whose mean, extrinsic and Gauss curvatures satisfy a smooth elliptic relation {\Phi(H,K_{e},K)=0}. In this paper we prove that Σ is a sphere of revolution, provided that the unique inextendible rotational surface S in M that satisfies this equation and touches its rotation axis orthogonally has bounded second fundamental form. In particular, we prove that: (i) Any elliptic Weingarten sphere immersed in {\mathbb{H}^{2}\times\mathbb{R}} is a rotational sphere. (ii) Any sphere of constant positive extrinsic curvature immersed in M is a rotational sphere. (iii) Any immersed sphere in M that satisfies an elliptic Weingarten equation {H=\phi(H^{2}-K_{e})\geq a>0} with ϕ bounded, is a rotational sphere. As a very particular case of this last result, we recover the Abresch–Rosenberg classification of constant mean curvature spheres in M.

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38

Waheed, Saira, Iqra Nawazish, and M. Zubair. "Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries." European Physical Journal C 81, no. 2 (February 2021). http://dx.doi.org/10.1140/epjc/s10052-021-08917-z.

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AbstractThe present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

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39

Solbi, Milad, and Kayoomars Karami. "Primordial black holes formation in the inflationary model with field-dependent kinetic term for quartic and natural potentials." European Physical Journal C 81, no. 10 (October 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09690-9.

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AbstractWithin the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $$G(\phi )=g_I(\phi )\big (1+g_{II}(\phi )\big )$$ G ( ϕ ) = g I ( ϕ ) ( 1 + g II ( ϕ ) ) and show that in the presence of first term $$g_I(\phi )$$ g I ( ϕ ) both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68% CL of Planck observations. Besides, the second term $$g_{II}(\phi )$$ g II ( ϕ ) can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $$k\sim 10^{12}~{\mathrm{Mpc}}^{-1}$$ k ∼ 10 12 Mpc - 1 , $$10^{8}~{\mathrm{Mpc}}^{-1}$$ 10 8 Mpc - 1 , and $$10^{5}~{\mathrm{Mpc}}^{-1}$$ 10 5 Mpc - 1 , which causes PBHs production in mass scales around $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ , $$10^{-5}M_{\odot }$$ 10 - 5 M ⊙ , and $$10 M_{\odot }$$ 10 M ⊙ , respectively. Observational constraints confirm that PBHs with a mass scale of $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $$\Omega _{\mathrm{GW}}\sim (f/f_c)^n$$ Ω GW ∼ ( f / f c ) n , where the power index equals $$n=3-2/\ln (f_c/f)$$ n = 3 - 2 / ln ( f c / f ) in the infrared limit $$f\ll f_{c}$$ f ≪ f c .

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40

Wang, Fei, and Rui Wang. "Q-Balls formation and the production of gravitational waves with non-minimal gravitational coupling." European Physical Journal C 82, no. 4 (April 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10291-3.

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AbstractWe propose to introduce non-minimal couplings of Affleck–Dine (AD) field to gravity by adding the coupling of AD field to the Ricci scalar curvature. As the Jordan frame supergravity always predict $$|\Phi |^2 {{\mathcal {R}}}/6$$ | Φ | 2 R / 6 type coupling for scalars with canonical kinetic terms, we propose a way to realize the required $$c_0|\Phi |^2 {{\mathcal {R}}}$$ c 0 | Φ | 2 R -type couplings with generic $$c_0$$ c 0 for canonical complex scalar fields after SUSY breaking. The impacts of such non-minimal gravitational couplings for AD field is shown, especially on the Q-balls formation and the associated gravitational wave (GW) productions. New form of scalar potential for AD field in the Einstein frame is obtained. By numerical simulations, we find that, with non-minimal gravitational coupling to AD field, Q-balls can successfully form even with the choice of non-negative K parameter for $$\xi >0$$ ξ > 0 . The associated GW productions as well as their dependences on the $$\xi $$ ξ parameter are also discussed.

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41

Bazrafshan, A., and A. R. Olamaei. "Surface terms of quintic quasitopological gravity and thermodynamics of quasi-topological magnetic brane coupled to nonlinear electrodynamics." European Physical Journal C 82, no. 4 (April 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10250-y.

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AbstractFor the the quintic quasitopological action which has no well-defined variational principle, we introduced a surface term that for a spacetime with flat boundaries make the action well-defined. Moreover, we investigated the numerical solutions of the above-mentioned gravity coupled to the nonlinear logarithmic and exponential electrodynamics. It has no horizon and curvature except one conical singularity at $$r=0$$ r = 0 with a deficit angle $$\delta \phi $$ δ ϕ . Also we found the counterterm which removes non-logarithmic divergences for the static quintic quasitopological gravity. Using this counterterm one can calculate a finite action and conserved quantities for the quintic quasitopological gravity.

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42

Cheng, Mengzhen, Haiou Wang, Kun Luo, and Jianren Fan. "A direct numerical simulation study on the structures and turbulence–flame interactions of a laboratory-scale lean premixed jet flame in cross-flow." Journal of Fluid Mechanics 957 (February 22, 2023). http://dx.doi.org/10.1017/jfm.2023.78.

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In the present work, direct numerical simulation of a laboratory-scale lean premixed reacting jet in cross-flow was performed to explore the flow–flame structures and turbulence–flame interactions. A jet of lean premixed ethylene–air mixtures (equivalence ratio $\phi = 0.6$ ) was injected into a hot vitiated cross-flow. Both non-reacting and reacting cases were simulated. It was found that the reacting jet penetrates deeper in the cross-flow with a weaker shear layer compared with the non-reacting one. The wake of the non-reacting and reacting jet is characterized by vertical vortices and recirculation zones, respectively. As for the flame structure of the reacting case, the reaction intensity varies considerably in different flame zones. The heat release rate on the leeward side is higher than that on the windward side, but lower than that of the corresponding laminar flame. The analysis of the turbulence–flame interactions of the reacting case showed that the large local Damköhler number ( $Da$ ) related to reaction-induced dilatations results in an increased tendency of the scalar gradient to align with the most extensive strain rate, which is more evident in the regions with high heat release rate on the leeward side. Negative dilatation regions with positive tangential strain rate and negative normal strain rate are observed on the windward side. High positive dilatations appear on the flame front of the leeward side. The tangential strain rate is negatively correlated with the normal strain rate and curvature. Regions with a high local $Da$ on the windward side correspond with high positive curvature regions.

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43

Di Cairano, Loris. "The geometric theory of phase transitions." Journal of Physics A: Mathematical and Theoretical, May 19, 2022. http://dx.doi.org/10.1088/1751-8121/ac717d.

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Abstract We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. Such a theory allows to rephrase the Bachmann's classification of PTs for finite-size systems in terms of geometric properties of the energy level sets (ELSs) associated to the Hamiltonian function. Specifically, by defining the microcanonical entropy as the logarithm of the ELS’s volume equipped with a suitable metric tensor, we obtain an exact equivalence between thermodynamics and geometry. In fact, we show that any energy-derivative of the entropy can be associated to a specific combination of geometric curvature structures of the ELSs which, in turn, are well-precise combinations of the potential function derivatives. In so doing, we establish a direct connection between the microscopic description provided by the Hamiltonian and the collective behavior which emerges in a PT. Finally, we also analyze the behavior of the ELSs' geometry in the thermodynamic limit showing that nonanalyticities of the energy-derivatives of the entropy are caused by nonanalyticities of certain geometric properties of the ELSs around the transition point. We validate the theory studying the PTs that occur in the $\phi^4$ and Ginzburg-Landau-like models.

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44

Zhang, Yanhong, and Suyun Wang. "Multiplicity of solutions for mean curvature operators with minimum and maximum in Minkowski space." Advances in Difference Equations 2019, no. 1 (December 2019). http://dx.doi.org/10.1186/s13662-019-2394-8.

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AbstractIn this paper, we study the existence and multiplicity of solutions of the quasilinear problems with minimum and maximum $$\begin{aligned}& \bigl(\phi \bigl(u'(t)\bigr)\bigr)'=(Fu) (t),\quad \mbox{a.e. }t\in (0,T), \\& \min \bigl\{ u(t) \mid t\in [0,T]\bigr\} =A, \qquad \max \bigl\{ u(t) \mid t\in [0,T]\bigr\} =B, \end{aligned}$$ (ϕ(u′(t)))′=(Fu)(t),a.e. t∈(0,T),min{u(t)∣t∈[0,T]}=A,max{u(t)∣t∈[0,T]}=B, where $\phi :(-a,a)\rightarrow \mathbb{R}$ϕ:(−a,a)→R ($0< a<\infty $0<a<∞) is an odd increasing homeomorphism, $F:C^{1}[0,T]\rightarrow L^{1}[0,T]$F:C1[0,T]→L1[0,T] is an unbounded operator, $T>1$T>1 is a constant and $A, B\in \mathbb{R}$A,B∈R satisfy $B>A$B>A. By using the Leray–Schauder degree theory and the Brosuk theorem, we prove that the above problem has at least two different solutions.

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45

Hristov, J. "Quantum theory of $$k(\phi )$$-FLRW-metrics its connection to Chern-Simons-models and the theta vacuum structure of quantum gravity." European Physical Journal C 81, no. 7 (July 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09315-1.

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AbstractWe show how a foliated 4-dimensional FLRW-metric becomes a gravitational instanton, if the spatial metric minimizes a three-dimensional Einstein–Hilbert action with positive cosmological constant, which is equal to the demand, that the scale factor satisfies the Bogomolny-equation, where the curvature parameter varies over the one-parameter family of hyperslices and takes the role of a potential depending on the scale factor. Additionally, we draw the connection to SO(4)-Chern–Simons theory and show how the established interpolating solutions describe the gradient flow between the minima of the vacuums of the Einstein–Hilbert action, as well as how they can be used to calculate tunnelling-amplitudes of gravitons and trivialize the calculations of path integrals in quantum gravity. All the calculations are carried out particularly for k admitting a $${\mathbb {Z}}_{2}$$ Z 2 -symmetry.

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