Rational modulation of the periodicity in linear hydrogen-bonded assemblies of trimesic acid on surfaces

We demonstrate a surprising cooperative adsorption process at the liquid-solid interface, involving self-assembly in which a three-fold hydrogen-bonding unit (trimesic acid, TMA) is forced into a linear pattern by noncovalent interaction with an alcohol. Our work shows that the unexpected linear pattern formed by coadsorption of TMA and alcohols can be modulated in size by choosing alcohols with different chain lengths.     

Syntheses and quadratic optical nonlinearities of ruthenium(II) complexes with ethynyl-connected N-methylpyridinium electron acceptors

We have prepared a number of new dipolar complexes containing ethynyl or buta-1,3-diynyl units linking electron-rich {Ru(II)(NH3)5}2+, trans-{Ru(II)(NH3)4L}+ (L = pyridine or N-methylimidazole), or trans-{Ru(II)Cl(pdma)2}+ [pdma = 1,2-phenylenebis(dimethylarsine)] centers to pyridinium electron acceptors. In acetonitrile solutions at 295 K, the new complexes display unusual blue-shifting of their metal-to-ligand charge-transfer (MLCT) bands as the conjugation is extended, in a fashion similar to that of the corresponding ethenyl systems. Hyper-Rayleigh scattering (HRS) and Stark spectroscopic measurements provide direct and indirect estimates of static first hyperpolarizabilities beta0, and both the linear and nonlinear optical (NLO) properties are temperature- and medium-dependent. Thus, at 77 K in butyronitrile glasses, the MLCT bands display more normal red shifts upon conjugation extension. While the Stark-derived beta0 values generally increase as n (the number of ethynyl units) increases from 0 to 2, the HRS data show maximization at n = 1 for two of the ammine series but an increase upon moving from n = 1 to 2 for the pdma complexes. Comparisons with the analogous ethenyl chromophores show that the latter generally display larger beta0 values, whether determined via HRS or Stark data, and the inferiority of the ethynyl systems in terms of NLO response is more pronounced when n = 2. This differing behavior is attributable primarily to larger increases in the transition dipole moment mu12 (and, hence, donor-acceptor pi-electronic coupling) on elongation in the ethenyl chromophores.     

X-ray diffraction and STM study of reactive surfaces under electrochemical control: Cl and I on Cu(100)

The surface structure of Cu(100) modified by chloride and iodide has been studied in an electrochemical environment by means of in-situ scanning tunneling microscopy in combination with in-situ surface X-ray diffraction with a particular focus on adsorbate and potential dependent surface relaxation phenomena. For positive potentials close to the on-set of the copper dissolution reaction, the X-ray data disclose an extraordinarily large Cu-Cl bond length of 2.61 A for the c(2 x 2)-Cl phase. This finding points to a largely ionic character of the Cu-Cl interaction at the Cu(100) surface, with chloride particles likely to retain their full charge upon adsorption. Together with the positive surface charging at these high potentials, this ionic Cu-Cl bond drives the observed 2.2% outward relaxation between the first two copper layers. These results indicate that the bond between the first and the second copper layer is significantly weakened which appears as the crucial prerequisite for the high surface mobility of copper-chloride species under electrochemical annealing conditions at these high potentials. With 2.51 A the Cu-I bond is 4% shorter than the Cu-Cl bond implying that the nature of the Cu-I bond is mainly covalent. Accordingly, we observe a significant inward relaxation of the top Cu layers upon substituting chloride by iodide at the same electrode potential, which suggests that the iodide adsorption involves charge transfer from the halide to the copper substrate.     

A spectral countability condition for almost automorphy of solutions of differential equations

We consider the almost automorphy of bounded mild solutions to equations of the form

with (generally unbounded) -periodic and almost automorphic in a Banach space . Under the assumption that does not contain , the part of the spectrum of the monodromy operator associated with the evolutionary process generated by on the unit circle is countable. We prove that every bounded mild solution of on the real line is almost automorphic.

     

The solvability and explicit solutions of two integral equations via generalized convolutions

This paper presents the necessary and sufficient conditions for the solvability of two integral equations of convolution type; the first equation generalizes from integral equations with the Gaussian kernel, and the second one contains the Toeplitz plus Hankel kernels. Furthermore, the paper shows that the normed rings on L¹(Rd) are constructed by using the obtained convolutions, and an arbitrary Hermite function and appropriate linear combination of those functions are the weight-function of four generalized convolutions associating F and . The open question about Hermitian weight-function of generalized convolution is posed at the end of the paper.     

Convolutions for the Fourier transforms with geometric variables and applications

This paper gives a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra, constructs three convolutions for the Fourier transforms with geometric variables and four generalized convolutions for the Fourier‐cosine, Fourier‐sine transforms. With respect to applications, by using the constructed convolutions normed rings on L₁( R ⁿ) are constructed, and explicit solutions of integral equations of convolution type are obtained (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symmetry factors of Feynman diagrams for scalar fields

We calculate the symmetry factors of diagrams for real and complex scalar fields in general form using an analysis of the Wick expansion for Green’s functions. We separate two classes of symmetry factors: factors corresponding to connected diagrams and factors corresponding to vacuum diagrams. The symmetry factors of vacuum diagrams play an important role in constructing the effective action and phase transitions in cosmology. In the complex scalar field theory, diagrams with different topologies can contribute the same, and the inverse symmetry factor for the total contribution is therefore the sum of the inverse symmetry factors.     

Regularity results for fractional diffusion equations involving fractional derivative with Mittag–Leffler kernel

This paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag–Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is analyzed and considered. The fractional derivative with Mittag–Leffler kernel or also called Atangana and Baleanu fractional derivative in time is taken in the Caputo sense. We obtain results on the existence, uniqueness, and regularity of the solution.     

Real class sizes

Following Wiener, we consider the zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We show that the variance of the number of zeroes in a long horizontal rectangle [?T,T] × [a, b] is asymptotically between cT and CT², with positive constants c and C. We also supply with conditions (in terms of the spectral measure) under which the variance grows asymptotically linearly with T, as a quadratic function of T, or has intermediate growth. The results are compared with known results for real stationary Gaussian processes and other models.     

On solutions of a system of hereditary and self-referred partial-differential equations

In this paper, we present the local and global solutions of a system of hereditary and self-referred partial-differential equations. Namely, by the assumption on the Lipschitz continuity of the initial conditions u ₀, v ₀, Theorem 1 states the existence of local solutions of the problem (1.3–1.4); furthermore, under the assumption that those initial conditions are non-negative, non-decreasing, bounded, and lower semi-continuous functions, Theorem 2 gives global solution which is also a non-negative, non-decreasing, bounded, and lower semi-continuous function (in variable x of even for any time t).