The Search for the Maximum of a Polynomial

AbstractFor a real polynomialf(X) ofKvariables the problem of finding maxX∈RKf(X) is investigated by reducing it to that of searching for the real roots of the univariate polynomial F(z):=∏j(z−f(Λj)), where the product is extended over all the critical points Λjoff(X). Employment of the Hermite method of separation of real solutions of an algebraic equation system permits one to construct along withF(z) its Sturm series, and to restore the coordinates of the corresponding critical point. The problem of finding the maxfin the set defined by the real polynomial inequalityG(X)≥0 is also discussed

Content of total iron, copper and manganese in liver of animals during hypokinesia, muscle activity and process of recovery

It is shown that the content of total iron, copper and manganese in the liver of animals is altered depending on the intensity and duration of their swimming. Hypodynamia for 7 days does not alter the concentration of iron, but sufficiently increases the content of copper and manganese. The barometric factor effectively influences the maintenance of constancy in the content of microelements accumulated in the liver after intensive muscle activity

Somatic Integration of Single Ion Channel Responses of α7 Nicotinic Acetylcholine Receptors Enhanced by PNU-120596

Positive allosteric modulators of highly Ca2+-permeable α7 nicotinic acetylcholine receptors, such as PNU-120596, may become useful therapeutic tools supporting neuronal survival and function. However, despite promising results, the initial optimism has been tempered by the concerns for cytotoxicity. The same concentration of a given nicotinic agent can be neuroprotective, ineffective or neurotoxic due to differences in the expression of α7 receptors and susceptibility to Ca2+ influx among various subtypes of neurons. Resolution of these concerns may require an ability to reliably detect, evaluate and optimize the extent of α7 somatic ionic influx, a key determinant of the likelihood of neuronal survival and function. In the presence of PNU-120596 and physiological choline (∼10 µM), the activity of individual α7 channels can be detected in whole-cell recordings as step-like current/voltage deviations. However, the extent of α7 somatic influx remains elusive because the activity of individual α7 channels may not be integrated across the entire soma, instead affecting only specific subdomains located in the channel vicinity. Such a compartmentalization may obstruct detection and integration of α7 currents, causing an underestimation of α7 activity. By contrast, if step-like α7 currents are integrated across the soma, then a reliable quantification of α7 influx in whole-cell recordings is possible and could provide a rational basis for optimization of conditions that support survival of α7-expressing neurons. This approach can be used to directly correlate α7 single-channel activity to neuronal function. In this study, somatic dual-patch recordings were conducted using large hypothalamic and hippocampal neurons in acute coronal rat brain slices. The results demonstrate that the membrane electrotonic properties do not impede somatic signaling, allowing reliable estimates of somatic ionic and Ca2+ influx through α7 channels, while the somatic space-clamp error is minimal (∼0.01 mV/µm). These research efforts could benefit optimization of potential α7-PAM-based therapies

Determination of the number of roots of a polynomial lying in a given algebraic domain

AbstractThe problem of finding the number of roots of a polynomial ƒ(z = x + iy) satisfying a given system of algebraic inequalities g1(x, y) > 0,…,gk(x, y) > 0 is considered. The method proposed is based on elimination theory and on the Hermite approach to the problem. The algorithm uses a finite number of elementary algebraic operations on the coefficients of the polynomials involved