Geometry compression is an effective way to distribute high-volume geometry data within limited bandwidth and storage capacity. In this paper, a new time-varying 3D geometry compression method based on 4D lifted wavelet transform is presented. In this hybrid approach, geometric information and animation are compressed based volume grid values. Isosurfaces are reconstructed from decompressed gri...

This problem is a computational investigation of Pythagoras' Theorem and Fermat's Last Theorem. It involves a branch of number theory known as Diophantine problems after Diophantus of Alexandria, who is thought to have lived around AD 250 and was the first mathematician to write comprehensively about number theory. For non-technical and historical background see the "popular science" book [1] a...

Conventional data envelopment analysis (DEA) methods assume that input and output variables are continuous. However, in many real managerial cases, some inputs and/or outputs can only take integer values. Simply rounding the performance targets to the nearest integers can lead to misleading solutions and efficiency evaluation. Addressing this kind of integer-valued data, the current paper propo...

In many applications, such as inverse dithering, it is necessary to increase the pixel bit-depth of images by expanding q -bit integer values to m -bit integer values ( q m > ). This paper describes a simple and efficient method that uses bit replication, instead of conventional multiplication, to achieve this expansion. First, we show that the optimal number of repetitions is given by } / { ce...

A Sierpiński number is an odd integer k with the property that k ·2+1 is composite for all positive integer values of n. A Riesel number is defined similarly; the only difference is that k · 2 − 1 is composite for all positive integer values of n. In this paper we find Sierpiński and Riesel numbers among the terms of the wellknown Fibonacci sequence. These numbers are smaller than all previousl...

Suppose that we have a linear program max{cx : Ax ≤ b, x ≥ 0} (P) where A is an m × n matrix, c an n-dimensional row vector, b an m-dimensional column vector, and x an n-dimensional column vector of variables. Now, we add in the restriction that some of the variables in (P) must take integer values. If some but not all variables are integer, we have a Mixed Integer Program (MIP), written as max...

For any ? > 0 \varepsilon > 0 we derive effecti...

For better guiding a system, senior managers should have accurate information. Using Data Envelopment analysis (DEA) help managers in this objective. Thus, many investigations have been made in order to find the most productive scale size (MPSS) for the evaluating decision making units (DMUs). In this paper we consider this case where there exist subsets of input and output variables to be inte...

We define and study a quantitative generalization of the traditional boolean framework of model-based specification and verification. In our setting, propositions have integer values at states, and properties have integer values on traces. For example, the value of a quantitative proposition at a state may represent power consumed at the state, and the value of a quantitative property on a trac...