Mesomorphism of Dichotomous Compounds; X-Ray Diffraction Analysis of 4-Chlorophenyl Hexadecyl Ether

Crystallography Reports - The crystal and molecular structures of Cl–C6H4–O–C16H33 (I) have been studied, and its differential scanning calorimetry (DSC) study is performed....     

Onset of quark-hadron duality in pion electroproduction

A large data set of charged-pion (pi+/-) electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark-->pion production mechanisms.     

Mesophase-Preceding Crystal Packing of 4,4'-Dialkyl-Substituted Salicylideneanilines; C10H21O–C6H3(OH)–CH=N–C6H4–С7Н13) Structure

Crystallography Reports - The crystal structure of 4,4'-substituted salicylideneaniline C10H21O–C6H3(OH)–CH=N–C6H4–C7H13 has been investigated by X-ray diffraction. A...     

On behavior of Fourier coefficients by Walsh system

The paper proves that for any ε > 0 there exists ameasurable set E ? [0, 1] with measure |E| > 1 ? ε such that for each f ∈ L¹[0, 1] there is a function \(\tilde f \in {L^1}\left[ {0,1} \right]\) coinciding with f on E whose Fourier-Walsh series converges to \(\tilde f\) in L¹[0, 1]-norm, and the sequence \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \) is monotonically decreasing, where \(\left\{ {{c_k}\left( {\tilde f} \right)} \right\}\) is the sequence of Fourier-Walsh coefficients of \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \).     

Wightman function and vacuum polarization in models with non-trivial topology in the presence of boundaries

Wightman function and the vacuum expectation value of the scalar field squared are studied in models with a compact subspace in the presence of parallel plane boundaries, on which the field obeys Robin boundary conditions. By means of the generalized Abel-Plana summation formula we have explicitly extracted from the vacuum expectation values the parts induced by the boundaries. As a simple example, a one-dimensional internal space is considered compactified on a circle.     

New measurements of high-momentum nucleons and short-range structures in nuclei

We present new measurements of electron scattering from high-momentum nucleons in nuclei. These data allow an improved determination of the strength of two-nucleon correlations for several nuclei, including light nuclei where clustering effects can, for the first time, be examined. The data also include the kinematic region where three-nucleon correlations are expected to dominate.     

Vacuum energy-momentum tensor in models with non-trivial topology in the presence of boundaries

The vacuum expectation value of the energy-momentum tensor for a scalar field in models with the compact subspace of an arbitrary geometry in the presence of parallel plates is investigated. The field operator on the plates obeys Robin boundary conditions with constant coefficients. Depending on the values of the coefficients, the vacuum energy density can be either positive or negative. As an example, the case of one-dimensional internal space is considered.     

Uniqueness Theorems for Generalized Haar Systems

A uniqueness theorem and a recovery theorem for the coefficients of series in generalized Haar systems are proved under the assumption that the series converge in measure and satisfy a certain necessary condition on the distribution function of the majorant of partial sums.     

On series by Haar system

The paper considers the series by Haar system \(\sum\limits_{n = 1}^\infty {a_n \chi _n (x)} \), satisfying the conditions \(\sum\limits_{n = 1}^\infty {a_n^2 \chi _n^2 (x)} = \infty \) and a _n χ _n (x) → 0 almost everywhere. Some theorems about correcting a function on sets of arbitrarily small measures are proved.