Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, and show that any polygon from this family cannot be convexified by pop operations. This family contains simple, as well as non-simple (i.e., self-intersecting) polygons, as desired. We thereby answer in the negative an...

The pebbling number f(G) of a graphG is the least p such that, no matter how p pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H , we have f(G × H) ≤ f(G)f(H). If the graph G satisfies the odd 2-pebbling property, we w...

the corona product $gcirc h$ of two graphs $g$ and $h$ isobtained by taking one copy of $g$ and $|v(g)|$ copies of $h$;and by joining each vertex of the $i$-th copy of $h$ to the$i$-th vertex of $g$, where $1 leq i leq |v(g)|$. in thispaper, exact formulas for the eccentric distance sum and the edgerevised szeged indices of the corona product of graphs arepresented. we also study the conditions...

The high abundance of immunoglobulins (Igs) in the plasma protein corona on poly(lactic-co-glycolic) acid (PLGA)-based vascular-targeted carriers (VTCs) has previously been shown to reduce their adhesion to activated endothelial cells (aECs) in human blood flow. However, the relative role of individual Ig classes (e.g., IgG, IgA, and IgM) in causing adhesion reduction remains largely unknown. H...

In biological environments, nanoparticles are enshrouded by a layer of biomolecules, predominantly proteins, mediating its subsequent interactions with cells. Detecting this protein corona, understanding its formation with regards to nanoparticle (NP) and protein properties, and elucidating its biological implications were central aims of bio-related nano-research throughout the past years. Her...

Corona viruses cause common cold, and infections caused by corona viruses are generally self-resolving. During the last 4 years, corona viruses have become the most important viruses worldwide because of the occurrence of several recent deaths caused by corona viruses in Saudi Arabia. Spread of the infection occurred worldwide; however, most cases of mortality have occurred in the Middle East. ...

We apply a model of magnetically dominated coronae above standard accretion discs to the low/hard state of galactic black holes. When the disc-corona coupling is accounted for self-consistently assuming that magneto-rotational instability is at work in the disc, and that the corona is generated by buoyant escape of disc magnetic structures, then the model predicts powerful, X-ray emitting coron...

Sustaining the hot solar corona requires an energy flux of up to about 10erg cm−2s−1 whose source must be the photospheric motions below. However, the precise way this energy is transferred and damped still remains an open question. Here a review of recent advances in theoretical models for coronal heating, in the light of the fundamental observational results of the last decade, will be

For almost 20 years the physical nature of globally propagating waves in the solar corona (commonly called "EIT waves") has been controversial and subject to debate. Additional theories have been proposed over the years to explain observations that did not agree with the originally proposed fast-mode wave interpretation. However, the incompatibility of observations made using the Extreme-ultrav...

We highlight 10 key aspects of coronal heating that must be understood before we can consider the problem to be solved. (1) All coronal heating is impulsive. (2) The details of coronal heating matter. (3) The corona is filled with elemental magnetic stands. (4) The corona is densely populated with current sheets. (5) The strands must reconnect to prevent an infinite build-up of stress. (6) Nano...