Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...

Abstract We show that every convex ancient solution of mean curvature flow with Type I growth is either spherical, cylindrical, or planar. then prove the corresponding statement for flows by a natural class functions which are concave in second fundamental form. Neither these results assumes interior noncollapsing.

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

The paper deals with the extraction of features for the recognition of bidimensional objects. A set of invariants that is based on the contours of the objects is proposed. The invariance to rotation is founded on the properties of the Fourier Transform, applied to a circular signature of the contour. The specific method of creating the signature allows concave objects to be described. Interior ...

In this paper we analyze the rate of local convergence of the Newton primal-dual interiorpoint method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q–quadratic when the functions associated to the binding inequality constraints are concave. In general, the q–quadratic rate is achieved provided...

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...

By introducing new definitions of φ convex and −φ concave quasioperator and V 0 quasilower and u 0 quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new to φ convex and−φ concave quasi operator, and then we apply ...

The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.