Multiple zeta values and the WKB method

The multiple zeta values ζ(d1, . . . , dr ) are natural generalizations of the values ζ(d) of the Riemann zeta functions at integers d. They have many applications, e.g. in knot theory and in quantum physics. It turns out that some generating functions for the multiple zeta values, like fd(x) = 1 − ζ(d)xd + ζ(d, d)x2d − . . . , are related with hypergeometric equations. More precisely, fd(x) is the value at t = 1 of some hypergeometric series dFd−1(t) = 1 − x t + . . ., a solution to a hypergeometric equation of degree d with parameter x. Our idea is to represent fd(x) as some connection coeffi- cient between certain standard bases of solutions near t = 0 and near t = 1. Moreover, we assume that |x| is large. For large complex x the above basic solutions are represented in terms of so-called WKB solutions. The series which define the WKB solutions are divergent and are subject to so-called Stokes phenomenon. Anyway it is possible to treat them rigorously. In the paper we review our results about application of the WKB method to the generating functions f x), focusing on the cases d = 2 and d = 3

Strong-field triple ionisation of atoms with p3p^{3} valence shell

The interaction of strong pulsed femtosecond laser field with atoms having three equivalent electrons in the outer shell ($p^3$ configuration, e.g. nitrogen) is studied via numerical integration of a time-dependent Schr\"{o}dinger equation on a grid approach. Single, double and triple ionization yields originating from a completely antisymmetric wave function are calculated and extracted using a restricted-geometry model with the soft-core potential and three active electrons. The direct triple ionization channel is found to produce a larger yield than the channel connected with single and then direct double ionization. Compared against earlier results investigating the $n s^ 2 n p^1$ configuration, we propose that the differences found here might in fact be accessible through electron's momentum distribution.Comment: 5 pages, 3 figure

Quantum spin models with long-range interactions and tunnelings : a quantum Monte Carlo study

We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U (1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density–density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view this is still a challenging task, as new approaches to solve the time-dependent Schr\"odinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small, one or two-electron systems. However, as the main focus of attoscience shifts towards many-electron systems, such techniques are no longer effective and need to be replaced by more approximate, but computationally efficient ones. In this paper we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals, and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5x10^13 W/cm2 to 5x10^14 W/cm2 . We also compare the results with data obtained using Gaussian basis sets proposed previously by other authors.Comment: Minor changes in Sec. 1, 2 and

Transcriptional profiles of pilocytic astrocytoma are related to their three different locations, but not to radiological tumor features

List of genes differentiating between pilocytic astrocytomas by different clinical features (DOCX 117 kb

COVID-19 — przebieg kliniczny u pacjentki przewlekle hemodializowanej — opis przypadku i przegląd piśmiennictwa

In Poland over 21,000 patients are treated with renalreplacement therapy by hemodialysis; in the PomeranianVoivodeship over 1,300 people. During the halfyear of the COVID-19 pandemic, only one patientchronically hemodialysed in the Pomeranian Voivodeshipconfirmed SARS-CoV-2 infection. The patientwas admitted to the hospital dedicated to patientsinfected with SARS-CoV-2, where hemodialysis wascontinued. Hospitalization lasted 35 days, the patientwas discharged after obtaining 3 negative results RT--PCR SARS-CoV-2. The article describes the clinicalcourse of the infection and reviews the literature.W Polsce ponad 21 000 chorych jest leczonych nerkozastępczo metodą hemodializy; w województwie pomorskim jest to ponad 1300 osób. Przez pół roku trwania pandemii COVID-19 zakażenie SARS- -CoV-2 potwierdzono tylko u jednej pacjentki przewlekle hemodializowanej w województwie pomorskim. Chora została przyjęta do jednoimiennego szpitala zakaźnego, gdzie kontynuowano zabiegi hemodializy. Hospitalizacja trwała 35 dób, chorą wypisano po uzyskaniu 3 ujemnych wyników testu RT-PCR SARS- -CoV-2. W artykule opisano przebieg kliniczny zakażenia i dokonano przeglądu piśmiennictwa

N=1/2 Global SUSY: R-Matrix Approach

R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts of appropriately twisted Euclidean superalgebras. The corresponding generalized global symmetry transformations act on deformed superspaces as the usual ones do on undeformed spaces. However, they depend on non(anti)commuting parameters satisfying (anti)commutation relations defined by relevant R matrix.Comment: 30 pages, a number of typos corrected; two references adde

Traian and the Danubian Provinces. The political, economic and religious life in the Danubian Provinces: Proceedings of the 4th International Conference on the Roman Danubian Provinces, Zagreb, 15th - 17th November 2017.

The “Department of Archaeology“ of the Faculty of Humanities and Social Sciences of the University of Zagreb gladly hosted the 4th International Conference on the Roman Danubian Provinces in 2017. The Conference was organized with the support of the Faculty of Humanities and Social Sciences of the University of Zagreb, the Croatian Archaeological Society, and the Croatian Science Foundation through the project 6505 Between the Danube and the Mediterranean. Exploring the role of Roman military in the mobility of people and goods in Croatia during the Roman Era. Since it was organized in Zagreb, the Conference remained in Pannonia, not far from Siscia, the capital of Pannonia Savia, and in the territory of the Res publica Andautoniensium. The main topic of the Conference was Traian and the Roman Danubian Provinces or, more specifically, the political, economic and religious life in the Danubian Provinces.(from the Foreword)The “Department of Archaeology“ of the Faculty of Humanities and Social Sciences of the University of Zagreb gladly hosted the 4th International Conference on the Roman Danubian Provinces in 2017. The Conference was organized with the support of the Faculty of Humanities and Social Sciences of the University of Zagreb, the Croatian Archaeological Society, and the Croatian Science Foundation through the project 6505 Between the Danube and the Mediterranean. Exploring the role of Roman military in the mobility of people and goods in Croatia during the Roman Era. Since it was organized in Zagreb, the Conference remained in Pannonia, not far from Siscia, the capital of Pannonia Savia, and in the territory of the Res publica Andautoniensium. The main topic of the Conference was Traian and the Roman Danubian Provinces or, more specifically, the political, economic and religious life in the Danubian Provinces.(from the Foreword