Tolerances are a very important property of a design. This paper presents a method for simulating tolerances in signal processing and control systems on the system level using affine arithmetic. The method is compard to simulation based on interval arithmetic or Monte-Carlo method and goes into details of the shortcomings of interval arithmetic. An introduction to affine arithmetic is given and...

Currently, nearly all methods for proving termination of imperative programs apply an unsound and incomplete abstraction by treating bitvectors and bitvector arithmetic as (unbounded) integers and integer arithmetic, respectively. This abstraction ignores the wraparound behavior caused by underand overflows in bitvector arithmetic operations. This is particularly problematic in the termination ...

This paper presents a new method of lossless data compression called LZPP, being an advanced modification of the well-known algorithm LZSS [1]. It introduces improvements of the LZ family algorithms [2, 3], such as the use of a special coding of two and three byte matches, use of an auxiliary entropy coder and new criteria of symbol exclusions. Minimization of the data compression ratio (bpc) h...

In this paper, we propose a recursive Taylor method for ray-casting algebraic surfaces. The performance of this approach is compared with four other candidate approaches to raycasting: using interval arithmetic on the power form, using interval arithmetic on centered forms, using affine arithmetic, and using modified affine arithmetic. Test results show that the recursive Taylor method compares...

Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

a phenetic analysis of the 12 taxa or operational taxonomic units (otus) belonging to the three sections; genea, neobromus, and nevskiella of the genus bromus was performed. unweighted pair-group method using arithmetic averages (upgma) and weighted pair-group method using arithmetic averages (wpgma) clustering and factoriel method analyses were used to set the taxa apart. forty-four characters...

In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across entirety of Latin America and South America. Whereas lack financial resources often predicts low measures, history educational practice teaches us that students’ poverty need not predict their outcomes – creative instructional approaches may turn tables. Here we report on an innovative,...