In this paper, we provide a couple of solutions for the vector variational inequality problem, adopting topological approach. We consider here more general framework, where X and Y are spaces. Topological concepts including continuity, compactness, closedness, so on used obtaining our results. The condition admissibility function space topology is found to play an important role in achieving It...

Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the computational possibility for the realization of this approach. We provide modified simpler explanation of the reconstruction formula, restricted on the practical cas...

This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi-conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced...

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R ⋊ H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H , for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable repr...

In this paper, we study the notion of admissibility in timed games. First, we show that admissible strategies may not exist in timed games with a continuous semantics of time, even for safety objectives. Second, we show that the discrete time semantics of timed games is better behaved w.r.t. admissibility: the existence of admissible strategies is guaranteed in that semantics. Third, we provide...

The concept of admissibility with respect to clustering algorithms was introduced by Fisher and Van Ness (1971). They defined types of admissibility of an algorithm and indicated the relationships between these admissibilities and popular clustering algorithms. In recent years, admissibility with respect to space distortion (See, Lance and Williams, 1967) has been proposed by Chen and Van Ness ...

where t ∈ [0, T ] for some T > 0, x ∈ T (the one-dimensional torus), and subscripts denote partial derivatives. Equation (1.1) does not admit in general classical solutions for the associated Cauchy problem, even if the initial datum is smooth. On the other hand, if f is non-linear, there exist in general infinitely many weak solutions. An admissibility condition, the so-called entropic conditi...

Attackers tend to use complex techniques such as combining multi-step, multi-stage attack with anti-forensic tools to make it difficult to find incriminating evidence and reconstruct attack scenarios that can stand up to the expected level of evidence admissibility in a court of law. As a solution, we propose to integrate the legal aspects of evidence correlation into a Prolog based reasoner to...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...