Dichlorido(η6-p-cymene)[tris(4-methoxyphenyl)phosphane]ruthenium(II)

The title compound, [RuCl2(C10H14)(C21H21O3P)], crystallizes with two complex molecules in the asymmetric unit. The RuII atom has a classical three-legged piano-stool environment being coordinated by a cymene ligand [Ru—centroid = 1.707 (2)/1.704 (2) Å], a tris(4-methoxyphenyl)phosphane ligand [Ru—P = 2.3629 (15)/2.3665 (15) Å] and two chloride atoms with the Ru—Cl bonds adopting two distinct values of 2.4068 (16)/2.4167 (16) and 2.4016 (15)/2.4244 (16) Å. The effective cone and solid angles for the phosphane ligands were calculated to be 149.5/150.2° and 25.3/25.6°, respectively. In the crystal, weak C—H...Cl/O/π interactions are observed. The crystal was refined as a two-component twin.

Mori dreamness of blowups of weighted projective planes

We consider the blowup X(a, b, c) of a weighted projective space $${\mathbb {P}}(a,b,c)$$ P ( a , b , c ) at a general nonsingular point. We give a sufficient condition for a curve to be a negative curve on X(a, b, c) in terms of $$\chi ({\mathcal {O}}_X(C))$$ χ ( O X ( C ) ) . This can be applied to find the effective cone of X(a, b, c) and can serve as a starting point to prove the Mori dreamness of blowups of many weighted projective planes. We confirm the Mori dreamness of some X(a, b, c) as examples of our method.

CPTU identification of regular, sensitive, and organic clays towards evaluating preconsolidation stress profiles

<abstract> <p>Soil classification by piezocone penetration tests (CPTU) is mainly accomplished using empirical soil behavior charts (SBT). While commonly-used SBT methods work well to separate fine-grained soils from granular coarse-grained soils, in many instances, the groupings often fail to properly identify different categories of clays, specifically: (a) "regular" clays that are inorganic and insensitive, (b) sensitive and quick clays; and (c) organic soils. Herein, a simple means of screening and sorting these three clay types is shown using three analytical CPTU expressions for evaluating the preconsolidation stress profile from net cone resistance, excess porewater pressure, and effective cone resistance. A number of case studies are utilized to convey the methodology.</p> </abstract>

Birational Geometry of Blow-ups of Projective Spaces Along Points and Lines

Consider the blow-up $X$ of ${\mathbb{P}}^3$ at $6$ points in very general position and the $15$ lines through the $6$ points. We construct an infinite-order pseudo-automorphism $\phi _X$ on $X$. The effective cone of $X$ has infinitely many extremal rays and, hence, $X$ is not a Mori Dream Space. The threefold $X$ has a unique anticanonical section, which is a Jacobian K3 Kummer surface $S$ of Picard number 17. The restriction of $\phi _X$ on $S$ realizes one of Keum’s 192 infinite-order automorphisms. We show the blow-up of ${\mathbb{P}}^n$ ($n\geq 3$) at $(n+3)$ very general points and certain $9$ lines through them is not a Mori Dream Space. As an application, for $n\geq 7$, the blow-up of $\overline{M}_{0,n}$ at a very general point has infinitely many extremal effective divisors.

The Development of Standard Agitator Conditions for Effective Performance of a Batch Crutcher in the Frame of Semi-Boiled Process

The saponification reactor, otherwise called the crutcher is a dual purpose unit operational vessel that serves for reactor and mixer in the production of soapy detergent. Little or no efforts have been made by available literatures to work on the crutcher agitation concepts and geometry which determines the rate of reaction and degree of homogeneity of reactor mixture in the crutcher as used in the currently most widely applied semi-boiled process. This paper presents for the first time the standard optimum agitation conditions for effective performance of a crutcher for semi-boiled laundry soap production. A standard reactor volume to diameter of 0.17 m3/m and height to diameter ratio of 1.2 ratios on 7 % over design, agitator speeds of 0.75 rps (paddle), motor power of 10.5 W and torque of 2.24 Nm with impeller to reactor diameter of 1/3 and teflon shaft centralizer have been developed. The introduction of “bottom scrapper” component to the agitation unit in a cone bottomed cylindrical batch reactor would enhance mixing and heat transfer, eliminate recycling unit and the application of under steam bubbling for effective cone content mixing. Also, the introduction of 4 baffles on 0.5 × 10–2 m clearance from impeller blades would promote efficient mixing and heat transfer. The overall conditions developed ensured effective mixing, heat transfer and high rate of reaction.

Finite Generation of the Algebra of Type A Conformal Blocks via Birational Geometry

We study the birational geometry of the moduli space of parabolic bundles over a projective line, in the framework of Mori’s program. We show that the moduli space is a Mori dream space. As a consequence, we obtain the finite generation of the algebra of type A conformal blocks. Furthermore, we compute the H-representation of the effective cone that was previously obtained by Belkale. For each big divisor, the associated birational model is described in terms of moduli space of parabolic bundles.

THE EFFECTIVE CONE OF MODULI SPACES OF SHEAVES ON A SMOOTH QUADRIC SURFACE

Let $\unicode[STIX]{x1D709}$ be a stable Chern character on $\mathbb{P}^{1}\times \mathbb{P}^{1}$, and let $M(\unicode[STIX]{x1D709})$ be the moduli space of Gieseker semistable sheaves on $\mathbb{P}^{1}\times \mathbb{P}^{1}$ with Chern character $\unicode[STIX]{x1D709}$. In this paper, we provide an approach to computing the effective cone of $M(\unicode[STIX]{x1D709})$. We find Brill–Noether divisors spanning extremal rays of the effective cone using resolutions of the general elements of $M(\unicode[STIX]{x1D709})$ which are found using the machinery of exceptional bundles. We use this approach to provide many examples of extremal rays in these effective cones. In particular, we completely compute the effective cone of the first fifteen Hilbert schemes of points on $\mathbb{P}^{1}\times \mathbb{P}^{1}$.

Correspondences between convex geometry and complex geometry

We present several analogies between convex geometry and the theory of holomorphic line bundles on smooth projective varieties or K\"ahler manifolds. We study the relation between positive products and mixed volumes. We define and study a Blaschke addition for divisor classes and mixed divisor classes, and prove new geometric inequalities for divisor classes. We also reinterpret several classical convex geometry results in the context of algebraic geometry: the Alexandrov body construction is the convex geometry version of divisorial Zariski decomposition; Minkowski's existence theorem is the convex geometry version of the duality between the pseudo-effective cone of divisors and the movable cone of curves. Comment: EpiGA Volume 1 (2017), Article Nr. 6