5 research outputs found
Ropelength of tight polygonal knots
A physical interpretation of the rope simulated by the SONO algorithm is
presented. Properties of the tight polygonal knots delivered by the algorithm
are analyzed. An algorithm for bounding the ropelength of a smooth inscribed
knot is shown. Two ways of calculating the ropelength of tight polygonal knots
are compared. An analytical calculation performed for a model knot shows that
an appropriately weighted average should provide a good estimation of the
minimum ropelength for relatively small numbers of edges.Comment: 27 pages, to appear in "Physical and Numerical Models in Knot Theory
and their Application to the Life Sciences
Continuous unitary transformation approach to the Kondo-Majorana interplay
We analyze a setup composed of a correlated quantum dot (QD) coupled to one
metallic lead and one end of topological chain hosting a Majorana zero mode
(MZM). In such a hybrid structure, a leakage of the MZM into the region of the
QD competes with the Kondo resonance appearing as a consequence of the
spin-exchange interactions between the dot and the lead. In the work, we use
the nontrivial technique called the continuous unitary transformation (CUT) to
analyze this competition. Using the CUT technique, we inspect the influence of
the coupling between the QD and the chain on effective exchange interactions
and calculate the resultant Kondo temperature.Comment: 6 Pages, 5 figure
Length of the tightest trefoil knot
The physical sense of tight knots provided by the SONO algorithm is discussed. A method allowing one to predict their length is presented. An upper bound for the minimum length of a smooth trefoil knot is determined
Mangiferin and Hesperidin Transdermal Distribution and Permeability through the Skin from Solutions and Honeybush Extracts (Cyclopia sp.)—A Comparison Ex Vivo Study
Polyphenolic compounds—mangiferin and hesperidin—are, among others, the most important secondary metabolites of African shrub Cyclopia sp. (honeybush). The aim of this study was to compare the percutaneous absorption of mangiferin and hesperidin from solutions (water, ethanol 50%, (v/v)) and extracts obtained from green and fermented honeybush (water, ethanol 50%, (v/v)). Research was performed with the Bronaugh cells, on human dorsal skin. The mangiferin and hesperidin distributions in skin layers (stratum corneum, epidermis, and dermis) and in acceptor fluid (in every 2, 4, 6, and 24 h) were evaluated by HPLC–Photodiode Array Coulometric and Coulometric Electrochemical Array Detection. The transdermal distribution of hesperidin was also demonstrated by fluorescence microscopy. Results indicated that mangiferin and hesperidin were able to cross the stratum corneum and penetrate into the epidermis and dermis. An advantage of hesperidin penetration into the skin from the water over ethanol solution was observed (451.02 ± 14.50 vs. 357.39 ± 4.51 ng/cm2), as well as in the mangiferin study (127.56 ± 9.49 vs. 97.23 ± 2.92 ng/cm2). Furthermore, mangiferin penetration was more evident from nonfermented honeybush ethanol extract (189.85 ± 4.11 ng/cm2) than from solutions. The permeation of mangiferin and hesperidin through the skin to the acceptor fluid was observed regardless of whether the solution or the honeybush extract was applied. The highest ability to permeate the skin was demonstrated for the water solution of hesperidin (250.92 ± 16.01 ng/cm2), while the hesperidin occurring in the extracts permeated in a very low capacity. Mangiferin from nonfermented honeybush ethanol extract had the highest ability to permeate to the acceptor fluid within 24 h (152.36 ± 8.57 ng/cm2)