Combinatorial sutured manifold theory is used to study the effects of attaching a 2–handle to an essential simple closed curve on a genus two boundary component of a compact, orientable 3–manifold. The main results concern degenerating handle additions to a simple 3– manifold and essential surfaces in the exterior of a knot or link obtained by “boring” a split link or unknot. (Boring is an oper...

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as h -convex functions. In this paper, we aim to establish functional form of inequalities presented by prove superadditivity monotonicity properties these functionals. Furthermore, de...

The goal of this paper is to determine the asymptotic number of labelled planar graphs and to establish limit laws of random labelled planar graphs. From now on, unless stated otherwise, all graphs are labelled. Recall that a graph is planar if it admits an embedding in the sphere. We remark that we consider planar graphs as combinatorial objects, without referring to a particular topological e...

Motivated by make-to-order cable manufacturing, we describe a remnant inventory system in which orders arrive for units of raw material that are produced-to-stock. As orders are satis!ed, the partially consumed units of material, or remnants, are either scrapped or returned to inventory for future allocation to orders. We present a linear program that minimizes the long-run average scrap rate. ...

Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique address an important problem the quantum communication scenario. While transferring information through a noisy channel, utility of channel is characterized by its capacity. Quantum channels, however, display intriguing property called superad...

A function f is said to be cone superadditive if there exists a partition of R into a family of polyhedral convex cones such that f(z + x) + f(z + y) ≤ f(z) + f(z + x+ y) holds whenever x and y belong to the same cone in the family. This concept is useful in nonlinear integer programming in that, if the objective function is cone superadditive, the global minimality can be characterized by loca...

When allocating indivisible resources or tasks, an envy-free allocation equitable may not exist. We present a sufficient condition and algorithm to achieve envy-freeness equitability when monetary transfers are allowed. The approach works for any agent valuation functions (positive negative) as long they satisfy superadditivity. For the case of additive utilities, we characterization allocation...