The poset of hypergraph quasirandomness

Chung and Graham began the systematic study of k‐uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung‐Graham‐Wilson on quasirandom graphs. One feature that became apparent in the early work on k‐uniform hypergraph quasirandomness is that properties that are equivalent for graphs are not equivalent for hypergraphs, and thus hypergraphs enjoy a variety of inequivalent quasirandom properties. In the past two decades, there has been an intensive study of these disparate notions of quasirandomness for hypergraphs, and an open problem that has emerged is to determine the relationship between them. Our main result is to determine the poset of implications between these quasirandom properties. This answers a recent question of Chung and continues a project begun by Chung and Graham in their first paper on hypergraph quasirandomness in the early 1990's. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,762–800, 2015     

Four-field Galerkin/least-squares formulation for viscoelastic fluids

A new Galerkin/Least-Squares (GLS) stabilized finite element method is presented for computing viscoelastic flows of complex fluids described by the conformation tensor; it extends the well-established GLS method for computing flows of incompressible Newtonian fluids. GLS methods are attractive for large-scale computations because they yield linear systems that can be solved easily with iterative solvers (e.g., the Generalized Minimum Residual method) and because they allow simple combinations of interpolation functions that can be conveniently and efficiently implemented on modern distributed-memory cache-based clusters.Like other state-of-the-art methods for computing viscoelastic flows (e.g., DEVSS-TG/SUPG), the new GLS method introduces a separate variable to represent the velocity gradient; with the aid of this variable, the conservation equations of mass, momentum, conformation, and the definition of velocity gradient are converted into a set of first-order partial differential equations in four unknown fields—pressure, velocity, conformation, and velocity gradient. The unknown fields are represented by low-order (continuous piecewise linear or bilinear) finite element basis functions.The method is applied to the Oldroyd-B constitutive equation and is tested in two benchmark problems—flow in a planar channel and flow past a cylinder in a channel. Results show that (1) the mesh-convergence rate of GLS is comparable to the DEVSS-TG/SUPG method; (2) the LS stabilization permits using equal-order basis functions for all fields; (3) GLS handles effectively the advective terms in the evolution equation of the conformation tensor; and (4) GLS yields accurate results at lower computational costs than DEVSS-type methods.     

On the Stability of a POCsp3OP‐Type Pincer Ligand in Nickel(II) Complexes

We describe the results of a study on the stabilities of pincer‐type nickel complexes relevant to catalytic hydroalkoxylation and hydroamination of olefins, C? C and C? X couplings, and fluorination of alkyl halides. Complexes [(POC_sp3OP)NiX] are stable for X=OSiMe₃, OMes (Mes=1,3,5‐Me₃C₆H₂), NPh₂, and CC? H, whereas the O(tBu) and N(SiMe₃)₂ derivatives decompose readily. The phenylacetylide derivative transforms gradually into the zero‐valent species cis‐[{κ^P,κ^C,κ^C′‐(iPr₂POCH₂CHCH₂)}Ni{η²,κ^C,κ^C′‐(iPr₂P(O)CCPh)}]. Likewise, attempts to prepare [(POC_sp3OP)NiF] gave instead the zwitterionic trinuclear species [{(η³‐allyl)Ni}₂‐{μ,κ^P,κ^O‐(iPr₂PO)₄Ni}]. Characterization of these two complexes provides concrete examples of decomposition processes that can dismantle POC_sp3OP‐type pincer ligands by facile C? O bond rupture. These results serve as a cautionary tale for the inherent structural fragility of pincer systems bearing phosphinite donor moieties, and provide guidelines on how to design more robust analogues.     

Mathematical foundations of a cultural project or Ramchandra's treatise “through the unsentimentalised light of mathematics”

The nineteenth century witnessed a number of projects of cultural rapprochement between the knowledge traditions of the East and West. This paper discusses the attempt to render elementary calculus amenable to an Indian audience in the indigenous mathematical idiom, undertaken by an Indian polymath, Ramchandra. The exercise is specifically located in his book A Treatise on the Problems of Maxima and Minima. The paper goes on to discuss the “vocation of failure” of the book within the context of encounter and the pedagogy of mathematics.     

Fast gas chromatographic/mass spectrometric determination of diuretics and masking agents in human urine: Development and validation of a productive screening protocol for antidoping analysis

An analytical procedure was developed for the fast screening of 16 diuretics (acetazolamide, althiazide, amiloride, bendroflumethiazide, bumetanide, canrenoic acid, chlorthalidone, chlorthiazide, clopamide, ethacrynic acid, furosemide, hydrochlorthiazide, hydroflumethiazide, indapamide, triamterene, trichlormethiazide) and a masking agent (probenecid) in human urine. The whole method involves three analytical steps, including (1) liquid/liquid extraction of the analytes from the matrix, (2) their reaction with methyl iodide at 70 degrees C for 2 h to form methyl derivatives, (3) analysis of the resulting mixture by fast gas chromatography/electron impact mass spectrometry (fast GC/EI-MS). The analytical method was validated by determining selectivity, linearity, accuracy, intra and inter assay precision, extraction efficiencies and signal to noise ratio (S/N) at the lowest calibration level (LCL) for all candidate analytes. The analytical performances of three extraction procedures and five combination of derivatization parameters were compared in order to probe the conditions for speeding up the sample preparation step. Limits of detection (LOD) were evaluated in both EI-MS and ECNI-MS (electron capture negative ionization mass spectrometry) modes, indicating better sensitivity for most of the analytes using the latter ionization technique. The use of short columns and high carrier gas velocity in fast GC/MS produced efficient separation of the analytes in less than 4 min, resulting in a drastic reduction of the analysis time, while a resolution comparable to that obtained from classic GC conditions is maintained. Fast quadrupole MS electronics allows high scan rates and effective data acquisition both in scan and selected ion monitoring modes.     

Enumerative geometry of elliptic curves on toric surfaces

We establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed j-invariant, refining results of Mikhalkin and Nishinou–Siebert. As an application, we determine a formula for such counts on P² and all Hirzebruch surfaces. This formula relates the count of elliptic curves with the number of rational curves on the surface satisfying a small number of tangency conditions with the toric boundary. Furthermore, the combinatorial tropical multiplicities of Kerber and Markwig for counts in P² are derived and explained algebro-geometrically, using Berkovich geometry and logarithmic Gromov–Witten theory. As a consequence, a new proof of Pandharipande’s formula for counts of elliptic curves in P² with fixed j-invariant is obtained.     

Hamilton cycles in quasirandom hypergraphs

We show that, for a natural notion of quasirandomness in k‐uniform hypergraphs, any quasirandom k‐uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(n^k‐1) contains a loose Hamilton cycle. We also give a construction to show that a k‐uniform hypergraph satisfying these conditions need not contain a Hamilton ?‐cycle if k– ? divides k. The remaining values of ? form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 363–378, 2016     

Me2AlCH2PMe2: a new, bifunctional cocatalyst for the Ni(II)-catalyzed oligomerization of PhSiH3

The role of methylaluminoxane (MAO) in the Ni-catalyzed dehydrogenative homologation of PhSiH3 has been investigated with a view to designing new cocatalysts possessing well-defined chemical compositions and structures. These studies show that species such as the bifunctional reagent (Me2PCH2AlMe2)2, 3, should act as co-catalyst for the Si-Si bond formation reactions. Thus, it was found that the combination of (1-Me-indenyl)Ni(PPh3)Me, 2a, and 3 (Ni/Al ratio of 1:1) converts PhSiH3 to cyclic oligomers (PhSiH)n with a turnover frequency (TOF) of >500 h(-1), 50 times faster than with 2a alone. Detailed NMR studies have indicated that this acceleration is due to the formation of the intermediate (1-Me-indenyl)Ni(Me)(Me2PCH2AlMe2), 4. Coordination of the PMe2 moiety in this complex to the Ni center allows the tethered AlMe2 moiety to interact with the Ni-Me moiety in such a way that promotes fairly slow Al-Me/Ni-CD3 exchange (t(1/2) ca. 12 h) but accelerates the Si-H bond activation and Si-Si bond formation reactions. The catalysis promoted by 2a/3 proceeds even faster in the presence of NEt3 or THF (TOF > 1600 h(-1)), because these Lewis bases favor the monomeric form of 3, which in turn favors the formation of 4. On the other hand, the much more nucleophilic base quinuclidine suppresses the catalysis (TOF < 300 h(-1)) by hindering the Ni.R.Al interactions. These observations point to an emerging strategy for using bifunctional reagents such as 3 to place geometrically constrained Lewis acid moieties adjacent to metal centers, thereby activating certain metal-ligand bonds.     

Structure and stability of triangle-free set systems

We define the notion of stability for a monotone property of set systems. This phenomenon encompasses some classical results in combinatorics, foremost among them the Erdos-Simonovits stability theorem. A triangle is a family of three sets such that , , are each nonempty, and . We prove the following new theorem about the stability of triangle-free set systems.

Fix . For every , there exist and such that the following holds for all : if and is a triangle-free family of -sets of containing at least members, then there exists an -set which contains fewer than members of .

This is one of the first stability theorems for a nontrivial problem in extremal set theory. Indeed, the corresponding extremal result, that for every triangle-free family of -sets of has size at most , was a longstanding conjecture of Erdos (open since 1971) that was only recently settled by Mubayi and Verstraëte (2005) for all .