Half twists and the cohomology of hypersurfaces

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight , its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondence for certain cubic 4-folds. Received: 25 August 2000; in final form: 8 January 2001 / Published online: 18 January 2002     

Effects of mussel-inspired co-deposition of 2-hydroxymethyl methacrylate and poly (2-methoxyethyl acrylate) on the hydrophilicity and binding tendency of common hemodialysis membranes: Molecular dynamics simulations and molecular docking studies

Despite advances in the field, hemoincompatibility remains a critical issue for hemodialysis (HD) as interactions between various human blood constituents and the polymeric structure of HD membranes results in complications such as activation of immune system cascades. Adding hydrophilic polymer structures to the membranes is one modification approach that can decrease the extent of protein adsorption. This study conducted molecular dynamics (MD) simulations to understand the interactions between three human serum proteins (fibrinogen [FB], human serum albumin, and transferrin) and common HD membranes in untreated and modified forms. Poly(aryl ether sulfone) (PAES) and cellulose triacetate were used as the common dialyzer polymers, and membrane modifications were performed with 2-hydroxymethyl methacrylate (HEMA) and poly (2-methoxyethyl acrylate) (PMEA), using polydopamine-assisted co-deposition. The MD simulations were used as the framework for binding energy simulations, and molecular docking simulations were also performed to conduct molecular-level investigations between the two modifying polymers (HEMA and PMEA) and FB. Each of the three proteins acted differently with the membranes due to their unique nature and surface chemistry. The simulations show PMEA binds less intensively to FB with a higher number of hydrogen bonds, which reflects PMEA's superior performance compared to HEMA. The simulations suggest PAES membranes could be used in modified forms for blood-contact applications as they reflect the lowest binding energy to blood proteins.     

In Vivo Imaging of the Tumor‐Associated Enzyme NCEH1 with a Covalent PET Probe

Herein, we report the development of an ¹⁸F‐labeled, activity‐based small‐molecule probe targeting the cancer‐associated serine hydrolase NCEH1. We undertook a focused medicinal chemistry campaign to simultaneously preserve potent and specific NCEH1 labeling in live cells and animals, while permitting facile ¹⁸F radionuclide incorporation required for PET imaging. The resulting molecule, [¹⁸F]JW199, labels active NCEH1 in live cells at nanomolar concentrations and greater than 1000‐fold selectivity relative to other serine hydrolases. [¹⁸F]JW199 displays rapid, NCEH1‐dependent accumulation in mouse tissues. Finally, we demonstrate that [¹⁸F]JW199 labels aggressive cancer tumor cells in vivo, which uncovered localized NCEH1 activity at the leading edge of triple‐negative breast cancer tumors, suggesting roles for NCEH1 in tumor aggressiveness and metastasis.     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Fourth power diophantine equations in Gaussian integers

In this paper, we examine a class of fourth power diophantine equations of the form \(x^4+kx^2y^2+y^4=z^2\) and \(ax^4+by^4=cz^2\), in the Gaussian integers, where a and b are prime integers.     

Some remarks on the Hodge conjecture for abelian varieties

We show how the classical Hodge conjecture for the middle cohomology of an abelian variety is equivalent to the general Hodge conjecture for the middle cohomology of a smooth ample divisor in the abelian variety. This is best suited to abelian varieties with actions of imaginary quadratic fields.     

Unraveling the role of binder concentration on the electrochemical behavior of mesocarbon microbead anode in lithium–ion batteries: understanding the formation of the solid electrolyte interphase

Journal of Solid State Electrochemistry - Binders play a significant role in the electrochemical performance of anodes in lithium–ion batteries. In this study, mesocarbon microbead (MCMB)...