a. ‖x‖ ≥ 0 for all x ∈ IRn, and ‖x‖ = 0 if and only if x is the zero vector. b. ‖αx‖ = |α|‖x‖. c. ‖x+ y‖ ≤ ‖x‖+ ‖y‖ [called the “triangle inequality”]. While this may seem a bit esoteric, consider that if x ∈ IR1, i.e. if x is a real number, the absolute value function, | · |, satisfies all of the above properties, and therefore constitutes as a norm. Another familiar norm would be the Euclidea...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

For fast ε-similarity search, various index structures have been proposed. Yi et al. proposed a concept multimodality support and suggested inequalities by which εsimilarity search by L1, L2 and L∞ norm can be realized. We proposed an extended inequality which allows us to realize ε-similarity search by arbitrary Lp norm using an index based on Lq norm. In these investigations a search radius o...

S ince the early 2000s, research by Thomas Piketty and Emmanuel Saez (and their coauthors, including Anthony Atkinson and Gabriel Zucman) has revolutionized our understanding of income and wealth inequality. The crucial point of departure for this revolution is the extensive data they have used, based largely on administrative tax records. Piketty’s (2014) Capital in the Twenty-First Century is...

Demand for Redistribution, Support for the Welfare State, and Party Identification in Austria This paper describes subjective wage inequality and the demand for redistribution in Austria using individuals' estimates of occupational wages from the International Social Survey Program. Although these estimates differ widely across individuals, the data clearly show that most individuals would like...

New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

A natural way of viewing an inequality or a poverty measure is in terms of the vector distance between an actual (empirical) distribution of incomes and some appropriately normative distribution (reflecting a perfectly equal distribution of incomes, or a distribution with the smallest mean that is compatible with a complete absence of poverty). Real analysis offers a number of distance function...

It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper we prove a family of weaker inequalities for this kind of domains, replacing the standard L-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kon...

Triangular norms are a generalisation of the classical two-valued conjunction. They were originally introduced for definition of the probabilistic (statistical) metric spaces as a generalisation of the classical triangle inequality for ordinary metric spaces. The next investigations were related with axiomatic of these norms. In this paper, a new t-norm is proposed which is generalisation of th...