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.