We consider the classical scheduling problem on parallel identical machines to minimize the makespan. Under the exponential time hypothesis (ETH), lower bounds on the running times of exact and approximation algorithms are characterized. We achieve the following results: (1) For scheduling on a constant number m of identical machines, denoted by Pm||Cmax, a fully polynomial time approximation s...

Abstract A new higher-order accurate space-time discontinuous Galerkin (DG) method using the interior penalty flux and basis functions, both in space time, is presented fully analyzed for second-order scalar wave equation. Special attention given to definition of numerical fluxes since they are crucial stability accuracy DG method. The theoretical analysis shows that discretization stable conve...

ABSTRACT- To evaluate effects of different soil moisture conditions namely, phosphorus (P) and zinc (Zn) application, on extractable Zn and Fe, two experiments were conducted in laboratory conditions based on a completely randomized design with a factorial arrangement of treatments with two replications. The first experiment was performed with the following factors; incubation time at four leve...

Word pronunciation can be learned by inductive machine learning algorithms when it is represented as a classiication task: classify a letter within its local word context as mapping to its pronunciation. On the basis of generalization accuracy results from empirical studies, we argue that word pronunciation, particularly in complex spelling systems such as that of En-glish, should not be modell...

The paper contains a proposal for an energy and time representation. We construct modes that correspond to fuzzy distributions around discrete values of energy or time. The modes form an orthogonal and complete set in the space of square integrable functions. Energy and time are self adjoint in the space spanned by the modes. The widths of the modes are analyzed as well as their energy-time unc...

where L is the lattice parameter and p < −1. We can therefore deduce the following relations: 1. The mass density should be a constant: m/L = constant ⇒ m = O(L). 2. The energy density of the nonlinear spring should be constant: − A p+1 (un+1 − un + L) p+1 /L = − A p+1 (L + L) p+1 /L = constant ⇒ A = O(L−p) where ∼ O(1). 3. The energy density of the bistable function should be constant: βφ(un)/...