Equivalent birational embeddings II: divisors

Two divisors in $\P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. We produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14. Then we study the special case of plane curves and rational hypersurfaces. For the latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional characterization of surfaces Cremona equivalent to a plan

Impact of Chemically Specific Interactions between Anions and Weak Polyacids on Chain Ionization, Conformations, and Solution Energetics

The presence of salts in a solution containing weak polyelectrolytes is known to modify both their titration behavior and conformations due to electrostatic screening. Instead, little is currently known about the changes induced by chemically specific interactions (e.g., charged hydrogen bonds, c-H-bonds). To investigate this aspect, we simulated the titration of weak polyacids with a primitive model and Monte Carlo methods in the presence of monovalent salts whose anions are capable of forming c-H-bonds with associated acid groups. The interaction between anions and weak polyacids (e.g., poly(acrylic acid)) substantially hampers ionization at low pH despite the somewhat limited number of coordinated anions, whereas it has a limited impact once pH > pKa + 2 due to a progressive anion decoordination. Importantly, the suppression of ionization appears extremely local in nature, with different chain segments differing in pKa by up to 1.3 units. As for chain conformations, c-H-bonds reduce the average sizes of polyacids independently of their structure as a consequence of multidentate binding or multiarm coordination in starlike species. Analyzing the length of chain segments with all monomers coordinated or uncoordinated has also evidenced that anion binding is extremely local in nature. The energetic analysis of c-H-bond formation suggests that polyacid chemical potential may be strongly lowered (up to -0.7 kcal/mol per monomer), the impact of such results on a few phenomena relevant for the physical chemistry of polyacid-containing solutions being analyzed in some detail

Coinage metal exciplexes with helium atoms: a theoretical study of M*(2L)Hen (M = Cu, Ag, Au; L = P,D)

The structure and energetics of exciplexes M*(2L)He n (M = Cu, Ag and Au; L = P and D) in their vibrational ground state are studied by employing diffusion Monte Carlo (DMC). Interaction potentials between the excited coinage metals and He atoms are built using the Diatomics-in-Molecule (DIM) approach and ab initio potential curves for the M(2L)-He dimers. Extending our previous work [Cargnoni et al., J. Phys. Chem. A, 2011, 115, 7141], we computed the dimer potential for Au in the 2P and 2D states, as well for Cu and Ag in the 2D state, employing basis set superposition error-corrected Configuration Interaction calculations. We found that the 2\u3a0 potential correlating with the 2P state of Au is substantially less binding than for Ag and Cu, a trend well supported by the M+ ionic radiuses. Conversely, the interaction potentials between a (n - 1)d 9ns2 2D metal and He present a very weak dependency on M itself or the projection of the angular momentum along the dimer axis. This is due to the screening exerted by the ns2 electrons on the hole in the (n - 1)d shell. Including the spin-orbit coupling perturbatively in the DIM energy matrix has a major effect on the lowest potential energy surface of the 2P manifold, the one for Cu allowing the formation of a "belt" of five He atoms while the one for Au being completely repulsive. Conversely, spin-orbit coupling has only a weak effect on the 2D manifold due to the nearly degenerate nature of the diatomic potentials. Structural and energetic results from DMC have been used to support experimental indications for the formation of metastable exciplexes or the opening of non-radiative depopulation channels in bulk and cold gaseous He

THE EFFECTIVENESS OF LESSON PLAN INSTRUMENTS ON DIGESTIVE SYSTEM MATERIAL THROUGH INQUIRY BASED LEARNING

Education is one form of dynamic and developing human civilization. The development of education is a must happened thing, in line with the change of cultural life. This research is aimed to evaluate the effectiveness of developed lesson plan instruments. The development research method used in this research is based on Tessmer model, which consists of: 1) self-evaluation; 2) expert review; 3) one-to-one; 4) small group; and 5) field test. The subject of the research is 24 students of VIII A grade of MTsN 1 Tanah Laut. The effectiveness is determined from cognitive study result, critical thinking skill, behavior assessment, social skill assessment, and student activity. The result of this research shows that the lesson plan instrument is effective in use based on good students’ accomplishment on cognitive learning, very well critical thinking skill, good result of behavior assessment, good social skills, and good students’ activity.  Article visualizations

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints

Tuning Knotted Copolyelectrolyte Conformations via Solution Properties

We used Langevin dynamics simulations to study coarse-grained knotted copolyelectrolytes, composed by a neutral and a charged segment, in solutions of different salt concentrations, valency, and solvent screening power. We show that the facile variation of these parameters allows for tuning the length and position of the knotted region, which in turn controls the overall metric properties. Specifically, adding either monovalent or divalent ions causes the knot to swell at the expense of the copolyelectrolyte overall size. However, the knot typically straddles the charged-neutral interface in the presence of monovalent counterions, whereas it is attracted on the charged segment with divalent ones. Notably, similar modulations of knot size and position can also be achieved by varying the dielectric constant of the solvent. Our results demonstrate the feasibility of harnessing the solution-mediated balance of electrostatics and conformational entropy toward a facile external tuning of the conformational properties of knotted polymers

Синтез ультрадисперсного кристаллического карбида кремния в гиперскоростной струе углерод-кремниевой электроразрядной плазмы

Наночастицы карбида кремния (SiC) могут использоваться для армирования материалов, создания наноструктурированной керамики, микроэлектромеханических систем. В работе представлены результаты плазмодинамического синтеза ультрадисперсных порошков карбида кремния. Этот метод был реализован путем синтеза в электроразрядной плазменной струе, создаваемой сильноточным импульсным коаксиальным магнитоплазменным ускорителем. Синтезированные продукты были проанализированы несколькими современными методами. Согласно результатам анализа, все продукты в основном состоят из кубического карбида кремния (b-SiC) с небольшим количеством непрореагировавших прекурсоров. Сравнение результатов экспериментов позволило сделать выводы о путях контроля фазового состава и дисперсности продукта.Silicon carbide (SiC) nanoparticles can be used for ceramics reinforcement, creation of nanostructured ceramics, microelectromechanical systems. The work presents the results of plasmadynamic synthesis of silicon carbide ultradipersed powders. This method was realized by the synthesis in an electrodischarge plasma jet generated by a high-current pulsed coaxial magnetoplasma accelerator. The synthesized products were analysed by several modern techniques. According to analysis results all the products mainly composed of cubic silicon carbide (b-SiC) with a small amount of unreacted precursors. Comparison of the results of experiments made it possible to draw conclusions on ways to control product phase composition and dispersion

Decomposition of homogeneous polynomials with low rank

Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^{{m+d\choose d}-1}$ but that its minimal decomposition as a sum of $d$-th powers of linear forms $M_1, ..., M_r$ is $F=M_1^d+... + M_r^d$ with $r>s$. We show that if $s+r\leq 2d+1$ then such a decomposition of $F$ can be split in two parts: one of them is made by linear forms that can be written using only two variables, the other part is uniquely determined once one has fixed the first part. We also obtain a uniqueness theorem for the minimal decomposition of $F$ if the rank is at most $d$ and a mild condition is satisfied.Comment: final version. Math. Z. (to appear