in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

We study the 3D reconstruction of an isometric surface from point correspondences between a template and a single input image. The template shows the surface flat and fronto-parallel. We propose three new methods. The first two use a convex relaxation of isometry to inextensibility. They are formulated as Second Order Cone Programs (SOCP). The first proposed method is point-wise (it reconstruct...

Title of dissertation: TWIST-BULGE DERIVATIVES AND DEFORMATIONS OF CONVEX REAL PROJECTIVE STRUCTURES ON SURFACES Terence Dyer Long, Doctor of Philosophy, 2015 Dissertation directed by: Professor Scott Wolpert Department of Mathematics Let S be a closed orientable surface with genus g > 1 equipped with a convex RP structure. A basic example of such a convex RP structure on a surface S is the one...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

Let K be a convex body in R and B be the Euclidean unit ball in R. We show that limt→0 |K| − |Kt| |B| − |Bt| = as(K) as(B) , where as(K) respectively as(B) is the affine surface area of K respectively B and {Kt}t≥0, {Bt}t≥0 are general families of convex bodies constructed from K, B satifying certain conditions. As a corollary we get results obtained in [M-W], [Schm],[S-W] and[W]. The affine su...

We develop a Tong-step surface-following version of the method of analytic centers for the fractional-linear problem min{to [ toB(x) A ( x ) E H, B (x ) E K, x C G}, where H is a closed convex domain, K is a convex cone contained in the recessive cone of H, G is a convex domain and B (.), A (.) are affine mappings. Tracing a two-dimensional surface of analytic centers rather than the usual path...

We investigate the problem of minimizing the moment of inertia among convex surfaces in R having a specified surface area. First we prove a minimizing surface exists, and derive a necessary condition holding at points of positive curvature. Then we show that an equilateral triangular prism is the optimal triangular prism, that the cube is the optimal rectangular prism, and that the sphere is (l...

We develop a long-step surface-following version of the method of analytic centers for the fractional-linear problem min {t0 | t0B(x)−A(x) ∈ H, B(x) ∈ K, x ∈ G} , where H is a closed convex domain, K is a convex cone contained in the recessive cone of H, G is a convex domain and B(·), A(·) are affine mappings. Tracing a twodimensional surface of analytic centers rather than the usual path of ce...

Curvature measure is one of the basic notion in the theory of convex bodies. Together with surface area measures, they play fundamental roles in the study of convex bodies. They are closely related to the differential geometry and integral geometry of convex hypersurfaces. Let Ω is a bounded convex body in R with C2 boundary M , the corresponding curvature measures and surface area measures of ...

We present numerical methods to solve optimization problems on the space of convex functions or among convex bodies. Hence convexity is a constraint on the admissible objects, whereas the functionals are not required to be convex. To deal with, our method mix geometrical and numerical algorithms. We give several applications arising from classical problems in geometry and analysis: Alexandrov’s...