In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
My aim is to show that some properties, proved to be true for the square matrices, are true for some not necessarily linear operators on a linear space, in particular, for Hammerstein-type operators.
In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the F-partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.
We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
Senile dementia of Alzheimer´s type (AD) is commonly characterized as a neurodegenerative disorder, which exhibits gradual changes of consciousness, loss of memory, perception and orientation as well as loss of personality and intellect. AD prevalence increases dramatically with age and is the fourth cause of death in Europe and in the USA. Currently, there are no available biological markers, which gives clinicians no other alternative than to rely upon clinical diagnosis by exclusion. There is no assay of objective ante mortem biochemical phenomena that relate to the pathophysiology of this disease. The pathophysiology of AD is connected with alterations in neurotransmission, plaque formation, cytoskeletal abnormalities and disturbances of calcium homeostasis. The search for a test, which is non-invasive, simple, cheap and user-friendly, should be directed at accessible body fluids. Only abnormalities replicated in large series across different laboratories fulfilling the criteria for a biological marker are likely to be of relevance in diagnosing AD. To date, only the combination of cerebrospinal fluid t and Ab42 most closely approximate an ideal biomarker of Alzheimer´s disease. A short review on the role of biological markers in AD on the basis of the literature, contemporary knowledge and our own recent findings are presented., D. Řípová, A. Strunecká., and Obsahuje bibliografii