Evidence for energy regularity in the Mendeleev periodic table

We show that the dependence of the total energy of the atoms on their atomic number can follow a q-exponential (as proposed by C. Tsallis), for practically all elements of the periodic table. The result is qualitatively explained in terms of the way the atomic configurations are arranged to minimize energy.     

Total Synthesis of the Antiviral Peptide Antibiotic Feglymycin

An adaptable approach : The first highly convergent stereoselective synthesis of feglymycin (see structure) and its enantiomer is based on the coupling of repeating peptide fragments. The use of weakly basic conditions throughout the synthesis suppressed the epimerization of sensitive aryl glycine units. Feglymycin has strong anti‐HIV activity as well as potent (previously identified as weak) antibacterial activity against Staphylococcus aureus.

     

Enantioselective Synthesis of (+)‐Chamaecypanone C: A Novel Microtubule Inhibitor

A bicycle built for tubulin : The total synthesis of (+)‐chamaecypanone C has been achieved by using a tandem retro‐Diels–Alder/Diels–Alder cascade reaction (see scheme). Initial biological studies demonstrate that (+)‐chamaecypanone C is an inhibitor of tubulin assembly and binds at the colchicine site.

     

Total Synthesis of Ciguatoxin

Something fishy : Ciguatoxin (see structure) is one of the principal toxins involved in ciguatera poisoning and the target of a total synthesis involving the coupling of three segments. The key transformations in this synthesis feature acetylene–dicobalthexacarbonyl complexation.

     

Total Synthesis of Sporolide B

An ocean of discovery : The first total synthesis of the highly oxygenated, marine‐derived, natural product sporolide B has been achieved through a convergent strategy. The key steps involve a ruthenium‐catalyzed [2+2+2] cycloaddition to assemble the indene structural motif and a thermally induced Diels–Alder‐type reaction to forge the macrocycle (see scheme).

     

Edge irregular total labellings for graphs of linear size

As an edge variant of the well-known irregularity strength of a graph G=(V,E) we investigate edge irregular total labellings, i.e. functions f:V∪E→{1,2,…,k} such that f(u)+f(uv)+f(v)≠f(u^′)+f(u^′v^′)+f(v^′) for every pair of different edges uv,u^′v^′∈E. The smallest possible k is the total edge irregularity strength of G. Confirming a conjecture by Ivan?o and Jendrol’ for a large class of graphs we prove that the natural lower bound is tight for every graph of order n, size m and maximum degree Δ with m>111000Δ. This also implies that the probability that a random graph from G(n,p(n)) satisfies the Ivan?o-Jendrol’ Conjecture tends to 1 as n→∞ for all functions p∈[0,1]^N. Furthermore, we prove that is an upper bound for every graph G of order n and size m≥3 whose edges are not all incident to a single vertex.     

Super-vertex-antimagic total labelings of disconnected graphs

Let G=(V,E) be a finite, simple and non-empty (p,q)-graph of order p and size q. An (a,d)-vertex-antimagic total labeling is a bijection f from V(G)∪E(G) onto the set of consecutive integers 1,2,…,p+q, such that the vertex-weights form an arithmetic progression with the initial term a and the common difference d, where the vertex-weight of x is the sum of values f(xy) assigned to all edges xy incident to vertex x together with the value assigned to x itself, i.e. f(x). Such a labeling is called super if the smallest possible labels appear on the vertices.In this paper, we will study the properties of such labelings and examine their existence for disconnected graphs.     

On the behavio r of complete g raphs in $${\mathbb{R}\sp{n+1}}$$ with Lp-finite r-cu rvatu re

We study the behavior of complete graphs in with L ^p -finite r-curvature, that is, whose length of the r-th Newton transformation |P _r | is in L ^p , for some p ≥ 1. Moreover, we use a monotonicity formulae to establish an L ^p -lower bound for |P _r | in balls. As application, we prove some new Bernstein-type results.      

TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.     

Local Spectral Properties of Total Class wF（p, r, q） Operators

In this paper, by initiative research on local spectral theory of total class wF(p, r, q) operators, we get some important results. Such as total class wF(p, r,q) op-erators is normaloid operator, the local spectral subspace of total class wF(p, r, q) operators is equal to the space EλH(Eλ the Reisz idempotent, with respect to ,λ, of T), total class wF(p, r, q) operators has finite ascent, and so on.