Drawing graphs with vertices and edges in convex position

A graph has strong convex dimension $2$, if it admits a straight-line drawing in the plane such that its vertices are in convex position and the midpoints of its edges are also in convex position. Halman, Onn, and Rothblum conjectured that graphs of strong convex dimension $2$ are planar and therefore have at most $3n-6$ edges. We prove that all such graphs have at most $2n-3$ edges while on the other hand we present a class of non-planar graphs of strong convex dimension $2$. We also give lower bounds on the maximum number of edges a graph of strong convex dimension $2$ can have and discuss variants of this graph class. We apply our results to questions about large convexly independent sets in Minkowski sums of planar point sets, that have been of interest in recent years.Comment: 15 pages, 12 figures, improved expositio

Cryomilling as environmentally friendly synthesis route to prepare nanomaterials

The milling of materials at cryogenic temperature has gained importance both in academic as well as the industrial community in the last two decades, primarily because of significant advantages this technique as compared to milling at room temperature; environmental friendly nature, cost-effectiveness, rapid grain refinement, less contamination, and large scale production capability of various nanomaterials. Scientifically, milling at cryo-temperature exhibits several distinct material related phenomena; suppression of recovery and recrystallization, predominant fractures over cold welding, significantly low oxidation, and contamination, leading to rapid grain refinement. Cryomilling has extensively been used to obtain finer scale powder of spices for the preservation of aroma, medicines for effective dissolution, or amorphization. It has been considered an environmentally friendly process as it utilizes benign liquid nitrogen or argon without discharging any toxic entity to the environment, making the process attractive and sustainable. The present review is intended to provide various scientific as well as technological aspects of cryomilling, environmental impact, and future direction

Angelica archengelica extract induced perturbation of rat skin and tight junctional protein (ZO-1) of HaCaT cells

"n  Background and purpose of the study: Herbal enhancers compared to the synthetic ones have shown less toxis effects. Coumarins have been shown at concentrations inhibiting phospoliphase C-Y (Phc-Y) are able to enhance tight junction (TJ) permeability due to hyperpoalation of Zonolous Occludense-1 (ZO-1) proteins. The purpose of this study was to evaluate the influence of ethanolic extract of Angelica archengelica (AA-E) which contain coumarin on permeation of repaglinide across rat epidermis and on the tight junction plaque protein ZO-1 in HaCaT cells. "n Methods: Transepidermal water loss (TEWL) from the rat skin treated with different concentrations of AA-E was assessed by Tewameter. Scanning and Transmission Electron Microscopy (TEM) on were performed on AA-E treated rat skin portions. The possibility of AA-E influence on the architecture of tight junctions by adverse effect on the cytoplasmic ZO-1 in HaCaT cells was investigated. Finally, the systemic delivery of repaglinide from the optimized transdermal formulation was investigated in rats. "n Results: The permeation of repaglinide across excised rat epidermis was 7-fold higher in the presence of AA-E (5% w/v) as compared to propylene glycol:ethanol (7:3) mixture. The extract was found to perturb the lipid microconstituents in both excised and viable rat skin, although, the effect was less intense in the later. The enhanced permeation of repaglinide across rat epidermis excised after treatment with AA-E (5% w/v) for different periods was in concordance with the high TEWL values of similarly treated viable rat skin. Further, the observed increase in intercellular space, disordering of lipid structure and corneocyte detachment indicated considerable effect on the ultrastructure of rat epidermis. Treatment of HaCaT cell line with AA-E (0.16% w/v) for 6 hrs influenced ZO-1 as evidenced by reduced immunofluorescence of anti-TJP1 (ZO-1) antibody in Confocal Laser Scanning Microscopy studies (CLSM) studies. The plasma concentration of repaglinide from transdermal formulation was maintained higher and for longer time as compared to oral administration of repaglinide. "n Major conclusion: Results suggest the overwhelming influence of Angelica archengelica in enhancing the percutaneous permeation of repaglinide to be mediated through perturbation of skin lipids and tight junction protein (ZO-1)

Uzbuda autoionizacijskog stanja u Na udarom elektrona

Electron-impact integral cross sections for the excitation of the lowest lying autoionizing level generated by the inner-shell 1s2 2s2 2p6 3s 2S e → 1s2 2s2 2p5 3s2 2P 0 complex transition in sodium (Na) atomic system have been calculated. In the calculation, single-configuration Hartree-Fock (HF) wave functions for both initial and final states involved in the transition matrix element within the asymptotic Green function approximation (AGFA) proposed by Tiwary (1981) were employed. The calculation was done exactly in the same way as in the earlier work in the case of the lightest alkali-metal atom lithium (Tiwary (1985), Tiwary, Macek and Madison (1985)) and the heaviest alkali-metal atom caesium (Tiwary (1983)) in the bombarding energy range from the threshold to 1500 eV. For the first time, Tiwary (1983) predicted the resonance behaviour in near vicinity of the excitation threshold in Cs using AGFA. Feuerstein et al. (1998) performed the experiment and observed resonance behaviour in the neighbourhood of excitation threshold in Na. Comparison has been made with available relevant experimental observations and other theoretical predictions. Our present AGFA theoretical result is qualitatively in accord with the experimental results.Izračunali smo integralne udarne presjeke za uzbudu najnižeg autoionizacijskog stanja koje nastaje udarom elektrona te putem kompleksnog prijelaza 1s2 2s2 2p6 3s 2S e Q 1s2 2s2 2p5 3s2 2P 0 među unutarnjim ljuskama u atomima natrija. U računu smo primijenili jedno-konfiguracijske Hartree-Fockove (HF) valne funkcije za odnosna početna i konačna stanja u matričnom elementu unutar asimptotskog približenja za Greenove funkcije (AGFA), predloženog Tiwary-em (1981). Račun je proveden točno na način kao u ranijem radu za najlakši alkalijski metalni atom litij (Tiwary (1985), Tiwary, Macek and Madison (1985)) i najteži alkalijski metalni atom cezij (Tiwary (1983)), za energije elektrona od praga do 1500 eV. Tiwary (1983) je prvi predvidio rezonanciju blizu iznad uzbudnog praga u Cs primjenom AGFA-e. Feuerstein et al. (1998) izveli su mjerenja i vidjeli rezonanciju u blizini uzbudnog praga u Na. Načinili smo usporedbu poznatih eksperimentalnih podataka i drugih teorijskih predviđanja. Naši su sadašnji teorijski rezultati u skladu s eksperimentalnima

Uzbuda autoionizacijskog stanja u Na udarom elektrona

Electron-impact integral cross sections for the excitation of the lowest lying autoionizing level generated by the inner-shell 1s2 2s2 2p6 3s 2S e → 1s2 2s2 2p5 3s2 2P 0 complex transition in sodium (Na) atomic system have been calculated. In the calculation, single-configuration Hartree-Fock (HF) wave functions for both initial and final states involved in the transition matrix element within the asymptotic Green function approximation (AGFA) proposed by Tiwary (1981) were employed. The calculation was done exactly in the same way as in the earlier work in the case of the lightest alkali-metal atom lithium (Tiwary (1985), Tiwary, Macek and Madison (1985)) and the heaviest alkali-metal atom caesium (Tiwary (1983)) in the bombarding energy range from the threshold to 1500 eV. For the first time, Tiwary (1983) predicted the resonance behaviour in near vicinity of the excitation threshold in Cs using AGFA. Feuerstein et al. (1998) performed the experiment and observed resonance behaviour in the neighbourhood of excitation threshold in Na. Comparison has been made with available relevant experimental observations and other theoretical predictions. Our present AGFA theoretical result is qualitatively in accord with the experimental results.Izračunali smo integralne udarne presjeke za uzbudu najnižeg autoionizacijskog stanja koje nastaje udarom elektrona te putem kompleksnog prijelaza 1s2 2s2 2p6 3s 2S e Q 1s2 2s2 2p5 3s2 2P 0 među unutarnjim ljuskama u atomima natrija. U računu smo primijenili jedno-konfiguracijske Hartree-Fockove (HF) valne funkcije za odnosna početna i konačna stanja u matričnom elementu unutar asimptotskog približenja za Greenove funkcije (AGFA), predloženog Tiwary-em (1981). Račun je proveden točno na način kao u ranijem radu za najlakši alkalijski metalni atom litij (Tiwary (1985), Tiwary, Macek and Madison (1985)) i najteži alkalijski metalni atom cezij (Tiwary (1983)), za energije elektrona od praga do 1500 eV. Tiwary (1983) je prvi predvidio rezonanciju blizu iznad uzbudnog praga u Cs primjenom AGFA-e. Feuerstein et al. (1998) izveli su mjerenja i vidjeli rezonanciju u blizini uzbudnog praga u Na. Načinili smo usporedbu poznatih eksperimentalnih podataka i drugih teorijskih predviđanja. Naši su sadašnji teorijski rezultati u skladu s eksperimentalnima

Unleashing Enhanced Compressive Strength: 3D Printed Octopus-Inspired Suction Cups Using Topological Engineering

Nature’s intricate designs and efficient functionality have evolved over millions of years to thrive in challenging environments while minimizing energy consumption and ecological impact. Inspired by nature’s strategies, the manufacturing industry and academic research strive to develop materials and designs that exhibit high strength. The octopus, a remarkable marine creature, exemplifies a complex and adaptive design. It has eight arms aligned with numerous tactile suction cups having a specialized geometry and cavity. This study employed fused deposition modeling (FDM) printers to model and fabricate octopus-inspired suction cups. We examined different aspect ratios and shapes of cavities, such as cuboids, cylinders, and octopus suction cup cavities, while maintaining similar outer geometry. The compressive test proved that the inside cavity plays a significant role in enhancing strength due to stress distribution and is represented as a robust biomimetic design. The finite element analysis (FEA) is also developed to corroborate the experimental findings. The statistical validation of the experimental results is achieved through a multilinear regression equation. Our findings demonstrate that the naturally evolved octopus structure exhibits superior compressive strength, enhanced energy absorption, and the ability to generate negative pressure, rendering it highly suitable for gripping, suction, and shock-absorption applications

Interference effects in the photorecombination of argonlike Sc3+ ions: Storage-ring experiment and theory

Absolute total electron-ion recombination rate coefficients of argonlike Sc3+(3s2 3p6) ions have been measured for relative energies between electrons and ions ranging from 0 to 45 eV. This energy range comprises all dielectronic recombination resonances attached to 3p -> 3d and 3p -> 4s excitations. A broad resonance with an experimental width of 0.89 +- 0.07 eV due to the 3p5 3d2 2F intermediate state is found at 12.31 +- 0.03 eV with a small experimental evidence for an asymmetric line shape. From R-Matrix and perturbative calculations we infer that the asymmetric line shape may not only be due to quantum mechanical interference between direct and resonant recombination channels as predicted by Gorczyca et al. [Phys. Rev. A 56, 4742 (1997)], but may partly also be due to the interaction with an adjacent overlapping DR resonance of the same symmetry. The overall agreement between theory and experiment is poor. Differences between our experimental and our theoretical resonance positions are as large as 1.4 eV. This illustrates the difficulty to accurately describe the structure of an atomic system with an open 3d-shell with state-of-the-art theoretical methods. Furthermore, we find that a relativistic theoretical treatment of the system under study is mandatory since the existence of experimentally observed strong 3p5 3d2 2D and 3p5 3d 4s 2D resonances can only be explained when calculations beyond LS-coupling are carried out.Comment: 11 pages, 7 figures, 3 tables, Phys. Rev. A (in print), see also: http://www.strz.uni-giessen.de/~k