scholarly journals The anisotropic Calderón problem for singular metrics of warped product type: the borderline between uniqueness and invisibility

2020 ◽  
Vol 10 (2) ◽  
pp. 703-746
Author(s):  
Thierry Daudé ◽  
Niky Kamran ◽  
François Nicoleau
Keyword(s):  
Warped Product ◽  
Product Type ◽  
Singular Metrics ◽  
Calderón Problem

scholarly journals A Note on the Characterization of Two-Dimensional Quasi-Einstein Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2013
Author(s):  
Gabriel Bercu
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Product Type ◽  
Two Dimensional ◽  
Einstein Manifolds ◽  
Local Coordinates ◽  
Elementary Methods

In this article, we aim to introduce new classes of two-dimensional quasi-Einstein pseudo-Riemannian manifolds with constant curvature. We also give a classification of 2D quasi-Einstein manifolds of warped product type working in local coordinates. All the results are obtained by elementary methods.

scholarly journals Stability estimates for an inverse Steklov problem in a class of hollow spheres

2021 ◽  
pp. 1-55
Author(s):  
Germain Gendron
Keyword(s):  
Hollow Sphere ◽  
Continuous Dependence ◽  
Warped Product ◽  
Hollow Spheres ◽  
Stability Estimate ◽  
Warping Function ◽  
Stability Estimates ◽  
Steklov Problem ◽  
Calderón Problem ◽  
Steklov Spectrum

In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the warping function defining the warped product with respect to the Steklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, when the warping functions are symmetric with respect to 1/2, we prove a log-type stability estimate in the inverse Steklov problem. As a last result, we prove a log-type stability estimate for the corresponding Calderón problem.

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

scholarly journals On three-variable expanders over finite valuation rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Le Quang Ham ◽  
Nguyen Van The ◽  
Phuc D. Tran ◽  
Le Anh Vinh
Keyword(s):  
Valuation Ring ◽  
Product Type ◽  
Quadratic Polynomial ◽  
Valuation Rings

AbstractLet {\mathcal{R}} be a finite valuation ring of order {q^{r}}. In this paper, we prove that for any quadratic polynomial {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form {axy+R(x)+S(y)+T(z)} for some one-variable polynomials {R,S,T}, we have|f(A,B,C)|\gg\min\biggl{\{}q^{r},\frac{|A||B||C|}{q^{2r-1}}\bigg{\}}for any {A,B,C\subset\mathcal{R}}. We also study the sum-product type problems over finite valuation ring {\mathcal{R}}. More precisely, we show that for any {A\subset\mathcal{R}} with {|A|\gg q^{r-\frac{1}{3}}} then {\max\{|AA|,|A^{d}+A^{d}|\}}, {\max\{|A+A|,|A^{2}+A^{2}|\}}, {\max\{|A-A|,|AA+AA|\}\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}}, and {|f(A)+A|\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}} for any one variable quadratic polynomial f.

scholarly journals Donation or Discount: Effect of Promotion Mode on Green Consumption Behavior

2021 ◽  
Vol 18 (4) ◽  
pp. 1912
Author(s):  
Jun Zou ◽  
Yifan Tang ◽  
Ping Qing ◽  
Han Li ◽  
Amar Razzaq
Keyword(s):  
Purchase Intention ◽  
Environmental Issues ◽  
Environmental Problems ◽  
Product Type ◽  
Mediation Effect ◽  
Green Consumption ◽  
Consumption Behavior ◽  
Conceptual Fluency ◽  
Global Concern ◽  
Practical Implications

Environmental issues are still challenging and of global concern. To improve the environmental consumption behavior of consumers, this study investigates whether the match between the promotion mode and product type can improve the conceptual fluency of consumers, so as to increase their purchase intention for green products. The results of three experiments reveal that the interaction between promotion mode and product type has a certain impact on the conceptual fluency of consumers, which can, in turn, promote their purchase intention. This research theoretically contributes to the research on green consumption by introducing promotion mode and revealing the mediation effect of conceptual fluency, it also provides some practical implications for alleviating environmental problems.

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