This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

The physics of charge fractionalization is studied using a simple and physical approach. The normal ordered charge is related to the Atiyah-Patodi-Singer invariant, and the physical interpretation of the spectral asymmetry is clarified in the presence of a continuous spectrum. By introducing the quantity B(E) which is a ratio of Jost-type determinants we relate the asymmetry to the phase and ze...

Collaborative fantasy play and storytelling serve an important role in preschool children’s development. Making up characters and telling stories are activities through which children make sense of and test out their hypotheses about the world. While computers are increasingly present to support young children’s collaboration in school tasks, there is a lack of computational systems to support ...

0-7803-7952-7/03/$17.00  2003 IEEE. Abstract – Human judgment is an integral part of the teleoperation process that is often heavily influenced by a single video feed returned from the remote environment. This limitation on the perceptual links to the environment leaves the operator prone to cognitive mistakes and general disorientation. These faults may be enhanced or muted, depending on the ...

Sloane’s influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community. The sequence A001611 listing the “Fibonacci numbers + 1” contains a very large number of references and links. The sequence A000071 for the “Fibonacci numbers −1” contains an even larger number. Strangely, resentment seems to prevail between the two sequ...

Training is an intentional act of creating a learning environment, after which people may apply their learning in the work field. It is no more a reactive role in organisational life, but it has become an integral part of business and line managers of the organisation, where it forms a transformational role in decision-making, strategic development, policy formulation and business management. C...

Let α = −2+ √ −1 be a root of the polynomial p(x) = x +4x+5. It is well-known that the pair (α, {0, 1, 2, 3, 4}) forms a canonical number system, i.e., that each γ ∈ Z[α] admits a finite representation of the shape γ = a0 + a1α+ · · ·+ alα with ai ∈ {0, 1, 2, 3, 4}. The set T of points with integer part 0 in this number system

Nowadays ICT is the integral part of modern teacher’s and scholar’s activity. For teachers it is reasonable to allocate two basic approach of ICT use: e-learning courses designing (to satisfaction of educational needs of students and implementation of new educational approaches) and openness in the presentation of their own research interests. For effective implementation of these approaches it...

and Applied Analysis 3 where n α 1, α denotes the integer part of number α, provided that the right side is pointwise defined on 0, ∞ . Definition 2.2 see 20 . The Riemann-Liouville fractional integral of order α > 0 of a function f : 0, ∞ → R is given by I 0 f t 1 Γ α ∫ t 0 t − s α−1f s ds, 2.2 provided that the right side is pointwise defined on 0, ∞ . From the definition of the Riemann-Liouv...