Priority rule-based heuristic for multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting

This paper presents a priority rule-based heuristic for the multi-mode resource-constrained project scheduling problem with the splitting of activities around unavailable resources allowed. All resources considered are renewable and each resource unit may not be available at all times due to resource vacations, which are known in advance. A new concept called moving resource strength is developed to help identify project situations where activity splitting is likely to be beneficial during scheduling. The moving resource strength concept is implemented in priority rule-based heuristics to control activity splitting when scheduling. Multiple comparisons of the performance of combination of activity–mode priority rules used in the heuristics are provided. Computational experiments demonstrate the effectiveness of the heuristic in reducing project makespan, and minimizing activity splitting.     

Analysis of a queueing system with a general service scheduling function,with applications to telecommunication network traffic control

In this paper we analyze a queueing system with a general service scheduling function. There are two types of customer with different service requirements. The service order for customers of each type is determined by the service scheduling function α_k(i, j) where α_k(i, j) is the probability for type-k customer to be selected when there are i type-1 and j type-2 customers. This model is motivated by traffic control to support traffic streams with different traffic characteristics in telecommunication networks (in particular, ATM networks). By using the embedded Markov chain and supplementary variable methods, we obtain the queue-length distribution as well as the loss probability and the mean waiting time for each type of customer. We also apply our model to traffic control to support diverse traffics in telecommunication networks. Finally, the performance measures of the existing diverse scheduling policies are compared. We expect to help the system designers select appropriate scheduling policy for their systems.     

Parabolic Equations with Partially BMO Coefficients and Boundary Value Problems in Sobolev Spaces with Mixed Norms

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a ¹¹) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of the other spatial variables. The coefficient a ¹¹ is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic equations defined on a half-space or on a bounded domain.     

Avian-human influenza epidemic model with diffusion

A diffusive epidemic model is investigated. This model describes the transmission of avian influenza among birds and humans. The behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by spectral analysis and by using Lyapunov functional. Our result shows that the disease-free equilibrium is globally asymptotically stable, if the contact rate for the susceptible birds and the contact rate for the susceptible humans are small. It suggests that the best policy to prevent the occurrence of a pandemic is not only to exterminate the infected birds with avian influenza but also to reduce the contact rate for susceptible humans with the individuals infected with mutant avian influenza. Numerical simulations are presented to illustrate the main results.     

Outer automorphism groups of certain 1-relator groups

Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite, whence mapping class groups of orientable surfaces are residually finite. Allenby, Kim and Tang showed that outer automorphism groups of cyclically pinched 1-relator groups are residually finite, whence mapping class groups of orientable and non-orientable surfaces are residually finite. In this paper we show that outer automorphism groups of certain conjugacy separable 1-relator groups are residually finite.     

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

In this paper, first we introduce a new notion of commuting condition that φφ ₁ A = A φ ₁ φ between the shape operator A and the structure tensors φ and φ ₁ for real hypersurfaces in G ₂(? ^m+2). Suprisingly, real hypersurfaces of type (A), that is, a tube over a totally geodesic G ₂(? ^m+1) in complex two plane Grassmannians G ₂(? ^m+2) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G ₂(? ^m+2) satisfying the commuting condition. Finally we get a characterization of Type (A) in terms of such commuting condition φφ ₁ A = A φ ₁ φ.     

On the Markus conjecture in convex case

Annals of Global Analysis and Geometry - In this paper, we show that any convex affine domain with a nonempty limit set on the boundary under the action of the identity component of the...     

Multiple homoclinic orbits for a class of the discrete p‐Laplacian with unbounded potentials

This paper is devoted to study the existence results of a sequence of infinitely many homoclinic orbits for the discrete p‐Laplacian with unbounded potentials without the Ambrosetti and Rabinowitz condition. The strategy of the proof for these results is to approach the problem using the mountain pass theorem, the fountain theorem, and dual fountain theorem.