The tool FLOW* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. FLOW* combines well-known Taylor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. FLOW* supports a wide variety of optimizations including adaptive ste...

Leighton and Rao use multicommodity flow results to design the first polynomial time approximation algorithms for well known NP-Hard optimization problems. Such problems include graph partitioning, crossing number, VLSI layout, and many more. Furthermore, Leighton and Rao are responsible for establishing the max-flow min-cut theorems on multicommodity flow problems, which lead to the algorithms...

Flexible flow shop scheduling problem (also called blended flow shop scheduling problem) is a sort of complex Job Shop Scheduling problem. For the Flexible Flow Shop scheduling problem, only in very special cases, there are polynomial optimal algorithms. In most of the other cases, the problems are NP-Hard. It is a simplification of the original problem to solve Flexible flow shop scheduling wi...

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both combinatorics and statistical physics. It contains various numerical invariants and polynomial invariants ,such as the number of spanning trees,the number of spanning forests , the number of acyclic orientations , the reliability polynomial,chromatic polynomial and flow polynomial . In this paper,we stud...

The study of Maps (X,G), the group of polynomial maps of a complex algebraic variety X into a complex algebraic group G, and its representations is only well developed in the case that X is a complex torus C. In this case Maps (X,G) is a loop group and the corresponding Lie-algebra Maps (X, ◦ G) is the loop algebra C[t, t]⊗ ◦ G. Here the representation comes to life only after one replaces Maps...

We consider the problem of pricing items so as to maximize the profit made from selling these items. An instance is given by a set E of n items and a set of m clients, where each client is specified by one subset of E (the bundle of items she/he wants to buy), and a budget (valuation), which is the maximum price she/he is willing to pay for that subset. We restrict our attention to the model wh...