Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

A novel framework for text-independent speaker verification is proposed. The framework is based on a new interpretation of Universal Background Model. The UBM in our framework actually defines a transform which maps the variable length observation into a fixed dimensional supervector(supervector space). Each speech utterance is then mapped into a point in this supervector space. The similarity ...

This paper studies error estimations for a fully discrete, single step finite element scheme for linear parabolic partial differential equations. Convergence in the norm of the solution space is shown and various error estimates in this norm are derived. In contrast to like results in the extant literature, the error estimates are derived in a stronger norm and under minimal regularity assumpti...

Dowling et al. in 1 defined a norm in l1 which was used by Lin 2 to exhibit an equivalent norm which makes l1 into a space with the fixed point property FPP . A similar norm can be defined in every Banach spaceX with a basis. Since l1 with its usual norm does not have FPP, we asked ourselves if this norm in these spaces would also improve properties that imply the weak fixed point property WFPP...

Gabor frames {e2πinβ·xg(x− kα)}n,k∈Zd provide series representations not only of functions in L(R) but of the entire range of spaces M ν known as the modulation spaces. Membership of a function or distribution f in the modulation space is characterized by a sequence-space norm of the Gabor coefficients of f depending only on the magnitudes of those coefficients, and the Gabor series representat...

A novel framework for text-independent speaker verification is proposed. The framework is based on a new interpretation of Universal Background Model. The UBM in our framework actually defines a transform which maps the variable length observation into a fixed dimensional supervector(supervector space). Each speech utterance is then mapped into a point in this supervector space. The similarity ...

It is proved that an arbitrary infinite-dimensional Banach space with basis admits an equivalent norm such that any Borel set can be obtained from balls by taking complements and countable disjoint unions. For reflexive spaces, the new norm can be chosen arbitrarily close to the initial norm.

A convergence analysis to the weak solution is derived for interior penalty discontinuous Galerkin methods applied to the heat equation in two and three dimensions under general mixed boundary conditions. Strong convergence is established in the DG norm, as well as in the L norm, in space and in the L norm in time.

We present a new proof of the Pythagorean theorem which suggests a particular decomposition of the elements of a topological algebra in terms of an “inverse norm” addressing unital algebraic structure rather than simply vector space structure . One consequence is the unification of Euclidean norm, Minkowski norm, geometric mean, and determinant, as expressions of this entity in the context of d...

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L...