Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page

Separation of the Exchange-Correlation Potential into Exchange plus Correlation: an Optimized Effective Potential Approach

Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have been generated from essentially exact densities constructed using information from either quantum chemistry or quantum Monte Carlo calculations but they have not been correctly decomposed into their separate exchange and correlation components, except for two-electron systems. exchange and correlation components (except for two-electron systems). Using a recently proposed method, equivalent to the solution of an optimized effective potential problem with the corresponding orbitals replaced by the exact Kohn-Sham orbitals, we obtain the separation according to the density functional theory definition. We compare the results for the Ne and Be atoms with those obtained by the previously used approximate separation scheme

Leakage Currents Mechanism in Thin Films of Ferroelectric Hf 0.5 Zr 0.5 O 2

We study the charge transport mechanism in ferroelectric Hf 0.5 Zr 0.5 O 2 thin films. Transport properties of the leakage currents in Hf 0.5 Zr 0.5 O 2 are described by phonon-assisted tunneling between traps. Comparison with transport properties of amorphous Hf 0.5 Zr 0.5 O 2 demonstrates that the transport mechanism does not depend on the crystal structure. The thermal trap energy of 1.25 eV and optical trap energy of 2.5 eV in Hf 0.5 Zr 0.5 O 2 were determined based on comparison of experimentally measured data on transport with simulations within phonon-assisted tunneling between traps in dielectric films. We found that the trap density in ferroelectric Hf 0.5 Zr 0.5 O 2 is slightly less that one in amorphous Hf 0.5 Zr 0.5 O 2 . A hypothesis that oxygen vacancies are responsible for the charge transport in Hf 0.5 Zr 0.5 O 2 is confirmed by electronic structure ab initio simulation

Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

The negative correlation energy per particle of a uniform electron gas of density parameter $r_s$ and spin polarization $\zeta$ is well known, but its spin resolution into up-down, up-up, and down-down contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for $\zeta = 0$, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up and down contributions to the kinetic energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio

Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior

We present an exact expression for the frequency-dependent Kohn-Sham exact-exchange (EXX) kernel for periodic insulators, which can be employed for the calculation of electronic response properties within time-dependent (TD) density-functional theory. It is shown that the EXX kernel has a long-wavelength divergence behavior of the exact full exchange-correlation kernel and thus rectifies one serious shortcoming of the adiabatic local-density approximation and generalized-gradient approximations kernels. A comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation approach is also made.Comment: two column format 6 pages + 1 figure, to be publisehd in Physical Review

How Russian Rap on YouTube Advances Alternative Political Deliberation: Hegemony, Counter- Hegemony, and Emerging Resistant Publics

The late 2010s have seen the unprecedented rise of Russian rap culture on YouTube. This study delves into the unexplored area of the relationship between rap music, politics, and the Internet audience in Russia. It focuses on the analysis of the production of the most popular rap videos—their narratives, power relations, and socio-political themes, as well as the prevailing patterns in the discussion on socio-political issues by the YouTube audience. The study brings three contributions that identify the power relations in the Russian society that manifest in the field of rap music. First, the Russian-speaking users demonstrate a high level of criticality toward the pro-Kremlin rap music on YouTube and challenge the lies of propaganda rap. Second, pro-government rappers follow the Soviet authoritarian ethos and praise belonging to the collective of elites, while liberal ones adhere to the individual responsibility. Third, we demonstrate the prevalence of patriarchal gender values, including macho politics and unquestioned sexism, which are representative of gender politics in the country. This article proves the importance of socio-political commentary on YouTube and points to the rap videos as the popular hubs for the socio-political debates. Users flow to rap videos and utilize the comment section to have their say on the political context and power relations rather than the music, to engage with others, and to contribute to the emerging collective debate. The comment sections on these rap videos have a unique value for the Russian users who exploit them as the negotiation space in the void of other platforms for social dialogue in Russia

Молекулярно-генетичні характеристики аденовірусів, як збудників гострих діарей у жителів півдня України

The etiological role of adenoviruses as causative agents of acute diarrhea in the southern region of Ukraine was studied. Adenovirus DNA was detected in 10.61±1.05 % of clinical stool samples. Serotypes of two gene groups: C and F were identified during genotyping and sequencing of genetic material of detected adenovirus isolates. Gene group F (HAdV41), proves their role in the occurrence of this infectious pathology. HAdV41 isolates had a significant advantage 75.0±15.31 % and had a pronounced genetic heterogeneity, showed similarities with serotypes circulating in previous years in different regions of the world: Sweden (1978), Japan (2003, 2006), South Africa (2009–2014), Iraq (2016). The obtained results allowed to establish the geographical origin of circulating adenoviruses, as well as to predict a further increase in the intensity of the epidemic process of adenoviral infections in southern Ukraine.Вивчали етіологічну роль аденовірусів, як збудників гострі діареї у жителів південного регіону України. ДНК аденовірусів виявлені в клінічних зразках стільця хворих у 10,61±1,05 % випадків. При генотипуванні та секвенуванні генетичного матеріалу виявлених ізолятів ідентифіковано серотипи двох геногруп: С та F. У 25,0±11,69 % хворих на гостру діарею у вигляді моноінфекції було виявлено аденовіруси геногрупи С: HAdV2 і HadV5, що поряд з серотипами геногрупи F (HAdV41), доводить їх роль у виникненні даної інфекційної патології. Ізоляти HAdV41 зустрічались із суттєвою перевагою 75,0±15,31 % та мали виражену генетичну гетерогенність, виявляючи подібність з серотипами, що циркулювали у попередні роки у різних регіонах світу: в Швеції (1978 р.), Японії (2003, 2006 рр.), Південній Африці (2009–2014 рр.), в Іраку (2016 р.). Отримані результати дозволили встановити географічне походження циркулюючих аденовірусів, прогнозувати подальше зростання інтенсивності епідемічного процесу аденовірусної інфекцій на півдні України

Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Quantum chemical calculations of X-ray emission spectroscopy

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time dependent density functional theory (TDDFT) and resolution of the identity single excitation configuration interaction with second order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s or- bitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment, however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range cor- rected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B66LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, ace- tone, dimethyl sulfoxide and CF3Cl in good agreement with experiment