Addition: for each pair of real numbers a and b there exists a unique real number a + b such that • + is a commutative and associative operation; • there exists in R a zero, 0, for addition: a+ 0 = 0 + a = a for all a ∈ R; • for each a ∈ R there exists an additive inverse −a ∈ R such that a+(−a) = (−a)+a = 0. Multiplication: for each pair of real numbers a and b there exists a unique real numbe...

objectives: anticonvulsant drugs can cause various forms of skin drug reactions, ranging from exanthema to severe blistering reactions. some studies have reported an association between hla-b*1502 allele and severe skin reactions. materials and methods: fifteen patients with severe skin reactions following treatment with anticonvulsant drugs (carbamazepine, lamotrigine, phenobarbital, primidone...

in the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. in this study, we try to prove  bernoulli's inequality in fuzzy real numbers with some of its applications. also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

The following three propositions are true: (1) For all real numbers a, b, c, d such that a ≤ c and d ≤ b and c ≤ d holds [c, d] ⊆ [a, b]. (2) For all real numbers a, b, c, d such that a ≤ c and b ≤ d and c ≤ b holds [a, b] ∪ [c, d] = [a, d]. (3) For all real numbers a, b, c, d such that a ≤ c and b ≤ d and c ≤ b holds [a, b] ∩ [c, d] = [c, b]. In the sequel a, b, c, d are real numbers. We now s...

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from real vector bundles are computed. We use characteristic classes with the axioms of Milnor and Stasheff [6]. Introduction Definition (Real generator bundles). We consider a real vector bundle F → B and a complex vector bundle E → B over the same base space B. If...

Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N , there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, andwithEN+1=E( N+1) if and only if contiguous eigenvalues a...

Piecewise algebraic B-spline surfaces (ABS surfaces) are capable of modeling globally smooth shapes of arbitrary topology. These can be potentially applied in geometric modeling, scientific visualization, computer animation and mathematical illustration. However, real-time ray casting the surface is still an obstacle for interactive applications, due to the large amount of numerical root findin...