R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings. We give some upper bounds for the volume of integrally closed lattice polytopes. We derive some inequalities for the delta-vector of integrally closed lattice polytopes. Finally we apply our results for reflexive integrally closed and order polytopes.

Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Carathéodory’s Theorem is commonly used to identify an upper bound. However, the upper bound from Carathéodory’s Theorem is relative loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical opt...

in this paper, the direct extrusion process of bimetallic rods in conical dies is analyzed by an improved upper bound method. the deformation zone is subdivided into six smaller zones and by considering a non-spherical entrance boundary to the deformation zone, a velocity field is presented which is different from velocity fields employed in previous studies. the total power consumption of the ...

we consider online scheduling of jobs with specic release time on m identical machines. each job has a weight and a size; the goal is maximizing total weight of completed jobs. at release time of a job it must immediately be scheduled on a machine or it will be rejected. it is also allowed during execution of a job to preempt it; however, it will be lost and only weight of completed jobs contr...

precision forging process is widely used for the production of spur gears due to its advantages such asimproved strength and surface finish, little waste of materials and reduction in the machining time ofthe gear. an important aspect of precision forging process is the load required to perform the processsuccessfully and design the forging tools. in this research, a new kinematically admissibl...