Cohen–Macaulayness of monomial ideals and symbolic powers of Stanley–Reisner ideals

We present criteria for the Cohen–Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen–Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen–Macaulayness of the second symbolic power or of all symbolic powers of a Stanley–Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen–Macaulay. In particular, all symbolic powers are Cohen–Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen–Macaulayness can pass from a symbolic power to another symbolic powers in different ways.     

New Convolutions for Quadratic-Phase Fourier Integral Operators and their Applications

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form , where A generates a strongly continuous semigroup in a Banach space , F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e ^{2π iℳ(f)}⊂e ^{2π iℳ(u)}. If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

Long‐Wavelength Fluorescent Reporters for Monitoring Protein Kinase Activity

In vivo optical imaging must contend with the limitations imposed by the optical window of tissue (600–1000 nm). Although a wide array of fluorophores are available that are visualized in the red and near‐IR region of the spectrum, with the exception of proteases, there are few long wavelength probes for enzymes. This situation poses a particular challenge for studying the intracellular biochemistry of erythrocytes, the high hemoglobin content of which optically obscures subcellular monitoring at wavelengths less than 600 nm. To address this, tunable fluorescent reporters for protein kinase activity were developed. The probing wavelength is preprogrammed by using readily available fluorophores, thereby enabling detection within the optical window of tissue, specifically in the far‐red and near‐IR region. These agents were used to monitor endogenous cAMP‐dependent protein kinase activity in erythrocyte lysates and in intact erythrocytes when using a light‐activatable reporter.     

Theoretical study of the substituent effects on the S-H bond dissociation energy and ionization energy of 3-pyridinethiol: Prediction of novel antioxidant

The S-H bond dissociation enthalpies [BDE(S-H)] of a set of 5-X- and 6-X-3-pyridinethiols (X = F, Cl, CH3, OCH3, NH2, N(CH3)2, CF3, CN, and NO2) have been computed using the density functional theory based (RO)B3LYP procedure with 6-311++G(2df,2p) basis set. The effects of substituents on the BDE(S-H), proton affinity of the pyridinethiol anion [PA(S-)] and ionization energy (IE) are analyzed and their correlations with Hammett's substituent constants are examined. Subsequently, a series of 6-substituted 3-pyridinethiols have been explored to find out their antioxidant potentials. Finally, a number of 3-pyridinethiol based compounds are theoretically proposed as novel antioxidants.     

An order-disorder transition in Sr2IrD5: Evidence for square pyramidal IrD5 units from powder neutron diffraction data

Neutron diffraction data have been collected on a powdered sample of Sr₂IrD₅ over a range of temperatures. The compound, which is cubic at room temperature, has been found to exhibit a gradual transformation to a tetragonal phase in the temperature range 200-140 K. As a result of the transition, deuterium atoms which randomly occupy sixfold positions in the cubic phase, become tetragonally ordered. A small fraction of the cubic phase remained untransformed at 4.2 K. Both the cubic and tetragonal structures are consistent with square pyramidal IrD₅ units with average Ir---D distances of 1.714 and 1.718 Å, respectively. Agreement factors, R₁, for the two structural analyses are 3.44 and 4.94%.     

New labdane-type diterpenoids from Leonurus heterophyllus SW

Five new natural labdane-type diterpenoids (5-9), designated leoheteronins A-E, together with four known diterpenoids (1-4), two phytosterols as a mixture of beta-sitosterol and stigmasterol, and the flavone genkwanin (10) were isolated from the aerial parts of Leonurus heterophyllus SW. (Lamiaceae) collected in northern Vietnam. Compound 1 was isolated for the first time from a Leonurus species, and 10 is considered to be a chemotaxonomic marker of the Leonurus genus. Their structures were determined using spectroscopic analyses.