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
In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums $K(m, n, r; q)$. The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving Dedekind sums and generalized Kloosterman sums, and give an interesting identity.
Let $R$ be a prime ring of characteristic different from $2$, $U$ the Utumi quotient ring of $R$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$, $F$ a non-zero generalized derivation of $R$. Suppose that $[F(u),u]F(u)=0$ for all $u\in L$, then one of the following holds: (1) there exists $\alpha \in C$ such that $F(x)=\alpha x$ for all $x\in R$; (2) $R$ satisfies the standard identity $s_4$ and there exist $a\in U$ and $\alpha \in C$ such that $F(x)=ax+xa+\alpha x$ for all $x\in R$. We also extend the result to the one-sided case. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on Banach algebras.
Cryptosporidium parvum causes life-threatening diarrhoea in immunocompromized, especially AIDS patients and the efficiency of proposed anti-cryptosporidial therapies is limited or doubtful. An immunosuppressed adult rat model of C. parvum infection was developed for screening molecules candidate for curative and preventive activity in human cryptosporidiosis. Among 31 drugs tested, lasalocid (2-10 mg/kg/24 h), and sinefungin (2-10 mg/kg/24 h), exhibited some activity against C. parvum infection. Oral sinefungin therapy resulted in a dose related suppression of oocysts shedding, which correlated with oocyst disappearance from ileum sections and was also efficient in preventing infection. Relapses were observed after discontinuation of curative sinefungin therapy, which suggests that the biliary tract, a major location and parasite reservoir which sustains persisting infection, was not cleared of parasites by the drug. Improved therapeutic procedures with sinefungin (or analogues) will result from current pharmacological studies.