Gauss–Manin Connection in Disguise: Calabi–Yau Threefolds

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi–Yau threefolds enhanced with differential forms and its relation to the Bershadsky–Cecotti–Ooguri–Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions \({{\bf F}_{g}^{\rm alg}, g \geq 1}\), which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck’s algebraic de Rham cohomology and on the algebraic Gauss–Manin connection. In this way, we recover a result of Yamaguchi–Yau and Alim–Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi–Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.     

Determination of pharmaceuticals classified as emerging pollutants using capillary electrophoresis with capacitively coupled contactless conductivity detection

A study on the simultaneous separation of 13 pharmaceutical products by capillary electrophoresis with capacitively coupled contactless conductivity detection was presented. The parameters of the background electrolyte, such as pH, organic additives as well as types and concentrations of cyclodextrins (CD) were studied. The optimal separation conditions were achieved with a background electrolyte consisting of 9 mM Tris/5 mM lactic acid at pH 8.0, containing 5% n-propanol, 0.025% gamma-CD, 0.075% hydroxyl-beta-CD and 0.15% dimethyl-beta-CD. Limits of detections ranged from 61 to 1676 microg/L (S/N=3) and the relative standard deviations for migration time and peak area were below 2 and 6%, respectively. This demonstrated the potential of the capillary electrophoresis-capacitively coupled contactless conductivity detection method for biomedical and environmental analysis, as shown in the determination of pharmaceuticals identified as emerging pollutants in water samples.     

Cytotoxic Activity of Capnellene‐8β, 10α‐Diol Derivatives from a Taiwanese Soft Coral Capnella sp.

The sesquiterpene capnellene‐8β, 10α‐diol ( 1 ) was isolated from non‐polar extract of the soft coral Capnella sp. Ten acylation products of capnellene‐8β, 10α‐diol were prepared: 10α‐hydroxy‐8β‐O‐benzoylcapnellene ( 2 ), 10α‐hydroxy‐8β‐O‐p‐toluoylcapnellene ( 3 ), 10α‐hydroxy‐8β‐O‐4‐chlorobenzoyl‐capnellene ( 4 ), 10α‐hydroxy‐8β‐O‐2‐furoylcapnellene ( 5 ), 10α‐hydroxy‐8β‐O‐2‐thiophenoylcapnellene ( 6 ), 10α‐hydroxy‐8β‐O‐4‐fluorobenzoylcapnellene ( 7 ), 10α‐hydroxy‐8β‐O‐4‐propylbenzoylcapnellene ( 8 ), 10α‐hydroxy‐8β‐O‐cinnamoylcapnellene ( 9 ), 10α‐hydroxy‐8β‐O‐4‐nitrobenzoylcapnellene ( 10 ), and 10α‐hydroxy‐8β‐O‐4‐anisoylcapnellene ( 11 ). The structures of capnellene‐8β, 10α‐diol as well as its derivatives were established through standard spectroscopic analysis. The in vitro cytotoxic activities of the eleven compounds were evaluated against Hela, KB, Daoy, and WiDr human tumor cell lines.     

Quantum diffusion of the random Schrödinger evolution in the scaling limit

We consider random Schrödinger equations on R ^d for d???3 with a homogeneous Anderson–Poisson type random potential. Denote by λ the coupling constant and \(\psi_t\) the solution with initial data \(\psi_0\). The space and time variables scale as \(x\sim\lambda ^{{ - 2 - \varkappa/2}} {\text{ and }}t\sim\lambda ^{{ - 2 - \varkappa}} {\text{ with }}0 < \varkappa < \varkappa_{0} {\left( d \right)}\). We prove that, in the limit λ?→?0, the expectation of the Wigner distribution of \(\psi_t\) converges weakly to the solution of a heat equation in the space variable x for arbitrary L ² initial data.The proof is based on analyzing the phase cancellations of multiple scatterings on the random potential by expanding the propagator into a sum of Feynman graphs. In this paper we consider the non-recollision graphs and prove that the amplitude of the non-ladder diagrams is smaller than their “naive size” by an extra λ ^c factor per non-(anti)ladder vertex for some c?>?0. This is the first rigorous result showing that the improvement over the naive estimates on the Feynman graphs grows as a power of the small parameter with the exponent depending linearly on the number of vertices. This estimate allows us to prove the convergence of the perturbation series.     

Direct alpha-oxytosylation of carbonyl compounds: one-pot synthesis of heterocycles

N-Methyl-O-tosylhydroxylamine is an effective reagent for the direct alpha-oxytosylation of carbonyl compounds. The reactions proceed smoothly at room temperature in the presence of both moisture and air and functional group tolerance in the substrate is good. With nonsymmetrical substrates regioselectivity for primary over secondary centers is observed and complete regiospecificity for primary over tertiary centers is obtained. Addition of a bis-heteronucleophile directly to the crude reaction mixture in a one-pot process leads to the corresponding heterocyclic product.     

On formulas for Dedekind sums and the number of lattice points in tetrahedra

This paper explores a simple yet powerful relationship between the problem of counting lattice points and the computation of Dedekind sums. We begin by constructing and proving a sharp upper estimate for the number of lattice points in tetrahedra with some irrational coordinates for the vertices. Besides providing a sharper estimate, this upper bound (Theorem 1.1) becomes an equality (i.e. gives the exact number of lattice points) in a tetrahedron where the lengths of the edges divide each other. This equality condition can then be applied to the explicit computation of the classical Dedekind sums, a topic that is the central focus in the second half of our paper. In this half of the paper, we come up with a number of interesting results related to Dedekind sums, based on our upper estimate (Theorem 1.1). Among these findings, Theorem 1.9 and Theorem 1.10 deserve special attention, for they successfully generalize two of Apostol's formulas in [T.M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, New York, 1997], and also directly imply the famous Reciprocity Law of Dedekind sums.     

Robust decentralized adaptive control for uncertain large-scale delayed systems with input nonlinearities

The paper is concerned with the problem of robust stabilization for uncertain large-scale time-varying delayed systems with input nonlinearities. Based on the sliding mode control, a memoryless decentralized adaptive sliding mode controller (DASMC) is developed. The proposed controller ensures the occurrence of the sliding manifold of the composite system even subjected to input nonlinearity. It shows that the uncertain nonlinear large-scale system also possesses the property of insensitivity to uncertainties and disturbances as a linear system does. A numerical example is given to verify the validity of the developed memoryless DASMC.     

Diffeomorphic types of complements of nice point arrangements in CP<Superscript><Emphasis Type="Italic">l</Emphasis></Superscript>

We use a new method to study arrangement in CP ^l , define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics, then their complements are diffeomorphic to each other. In particular, the moduli space of nice point arrangements with same combinatorics in CP ^l is connected. It generalizes the result on point arrangements in CP ³ to point arrangements in CP ^l for any l.