We study the gravitational lensing properties of a massive object in a dark matter halo, concentrating on the critical curves and caustics of the combined lens. We model the system in the simplest approximation by a point mass embedded in a spherical Navarro–Frenk–White density profile. The low number of parameters of such a model permits a systematic exploration of its parameter space. We present galleries of critical curves and caustics for different masses and positions of the point in the halo. We demonstrate the existence of a critical mass, above which the gravitational influence of the centrally positioned point is strong enough to eliminate the radial critical curve and caustic of the halo. In the point-mass parameter space we identify the boundaries at which critical-curve transitions and corresponding caustic metamorphoses occur. The number of transitions as a function of the position of the point is surprisingly high, ranging from three for higher masses to as many as eight for lower masses. On the caustics we identify the occurrence of six different types of caustic metamorphoses. We illustrate the peculiar properties of the single radial critical curve and caustic appearing in an additional unusual nonlocal metamorphosis for a critical mass positioned at the halo center. Although we construct the model primarily to study the lensing influence of individual galaxies in a galaxy cluster, it can also be used to study the lensing by dwarf satellite galaxies in the halo of a host galaxy, as well as (super)massive black holes at a general position in a galactic halo.

Ñòàá³ë³çàö³ÿ âèðîáíèöòâà êàðòîïë³ â íåîá-õ³äíèõ îáñÿãàõ ó ð³çí³ çà ìåòåîðîëîã³÷íèìè óìîâàìè ðîêè º âàaeëèâîþ íàóêîâîþ ïðîáëåìîþ. Ðîçâ'ÿçàòè ¿¿ ìîaeëèâî øëÿõîì åôåêòèâíîãî âèêîðèñòàííÿ çíà÷íîãî íàÿâíîãî àñîðòèìåíòó ðåºñòðîâàíèõ ñîðò³â, íàñàìïåðåä íîâèõ òà òèõ, ùî ïðîõîäÿòü äåðaeàâíå ñîðòîâèïðîáóâàííÿ ÷è âèâ÷åííÿ â ñåëåêö³éíèõ ðîçñàäíèêàõ. ³äîìî, ùî é äîíèí³ ãåíåòè÷íèé ïîòåíö³àë ïðîäóêòèâíîñò³ ñîðò³â, çîêðåìà é êàðòîïë³, âèêîðèñòîâóºòüñÿ íå á³ëüøå ÿê íà 50% [1-3]. Âîäíî÷àñ, äëÿ éîãî ïîâí³øîãî âèêîðèñòàííÿ âàaeëèâèì º äîñÿãíåííÿ äîì³íóâàííÿ ãåíîòèïó íàä ñåðåäîâèùåì çà ðàõóíîê âèêîðèñòàííÿ âèñîêîïðîäóêòèâíèõ òà åêîëîã³÷íî Liudmyla Tymko http://orcid.

Important physical and mechanical properties were evaluated for Douglas-fir wood produced in a non-native environment. The specimens were obtained from 15 healthy co-dominant trees growing in three different sites located in the Czech Republic; they were studied for density, shrinkage, compression, and bending strength. The average density of the wood was 562.74 ± 62.47 kg·m-3 at 12% MC. The total volumetric shrinkage was in line with the respective literature, whereas the compression strength and modulus of rupture were found to be higher than the native Douglas-fir wood as well as several European softwoods. The properties of the wood produced in the Czech forests indicate the possibility of producing Douglas-fir timber of high quality.