In this paper we derive necessary and sufficient conditions for some problems of global minimization. Our approach is based on methods of abstract convexity: we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions. We discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global min...

*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China Abstract The purpose of this paper is to establish the general theory of the direct methods to functionals I defined on the Grassmann algebra employing the classical approaches. In this paper, various notions of convexity conditions for weak lower semicontinuity of I are di...

Abstract The objective of this paper is to analyse under what well-known operations the class of quasipolyhedral convex functions, which can be regarded as an extension of that of polyhedral convex functions, is closed. The operations that will be considered are those that preserve polyhedral convexity, such that the image and the inverse image under linear transformations, right scalar multipl...

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

in this paper, we study the convexity of the integral operator

Having a prior assumption about where light originates can disambiguate perceptual scenarios. Previous studies have reported that adult observers use a "light-from-above" prior as well as a convexity prior to constrain perception of shape from shading. Such priors may reflect information acquired about the visual world, where objects tend to be convex and light tends to come from above. In the ...

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in L 2 and we give an explicit definition of the space of data on the light-cone producing a solution in H 1. The method is based on...

The present experiment was designed to examine the roles of painted linear perspective cues, and the convexity bias that are known to influence human observers' perception of three-dimensional (3D) objects and scenes. Reverse-perspective stimuli were used to elicit a depth-inversion illusion, in which far points on the stimulus appear to be closer than near points and vice versa, with a 2 (Type...

Our visual system faces the challenging task to construct integrated visual representations from the visual input projected on our retinae. Previous research has provided mixed evidence as to whether visual awareness of the stimulus parts is required for such integration to occur. Here, we address this issue by taking a novel approach in which we combine a monocular rivalry stimulus (i.e., a bi...