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Molecular arrangement in the chiral smectic phases of the glassforming (S)-4'-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[7-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]benzoate is investigated by X-ray diffraction. An increased correlation length of the positional short-range order in the supercooled state agrees with the previous assumption of the hexatic smectic phase. However, the registered X-ray diffraction patterns are not typical for the hexatic phases. Comparison of the smectic layer spacing and optical tilt angle indicates a strongly non-linear shape of molecules, which enables choice of the molecular models obtained by DFT calculations, used subsequently to interpret the infra-red spectra. The presumption of the hexatic smectic FA* or IA* phase is supported by the splitting of the absorption bands related to the C=O stretching in the supercooled state, which is absent in the smectic CA* phase above the melting temperature. The glass transition affects the temperature dependence of the smectic layer spacing but only subtly impacts the infra-red spectra. Application of the k-means cluster analysis enables distinction between the infra-red spectra below and above the glass transition temperature, but only for certain spectral ranges., Comment: 33 pages, 12 figures

We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some variations of Boshernitzan's problem involving characteristic classes are considered. As an application, we characterize sequences orthogonal to all uniquely ergodic systems whose (unique) invariant measure yields a discrete spectrum automorphism as those satisfying an averaged Chowla property., Comment: 1 figure

We study the class $Erg^\perp$ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of $Erg^\perp,$ that is, each automorphism whose every joining with an element of $Erg^{\perp}$ yields a system which is again an element of $Erg^{\perp}$, must be an identity. Despite this fact, we show that $Erg^\perp$ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in $Erg^\perp$ whose self-joinings always yield elements in $Erg^\perp$. This shows that there are non-trivial characteristic classes included in $Erg^\perp$.

The nuclear two-photon or double-gamma ($2\gamma$) decay is a second-order electromagnetic process whereby a nucleus in an excited state emits two gamma rays simultaneously. To be able to directly measure the $2\gamma$ decay rate in the low-energy regime below the electron-positron pair-creation threshold, we combined the isochronous mode of a storage ring with Schottky resonant cavities. The newly developed technique can be applied to isomers with excitation energies down to $\sim100$\,keV and half-lives as short as $\sim10$\,ms. The half-life for the $2\gamma$ decay of the first-excited $0^+$ state in bare $^{72}\mathrm{Ge}$ ions was determined to be $23.9\left(6\right)$\,ms, which strongly deviates from expectations., Comment: Submitted to Physical Review Letters, 8 pages, 3 figures, 2 tables, 7 equations

Due to its predominantly asymptomatic or mildly symptomatic progression, lung cancer is often diagnosed in advanced stages, resulting in poorer survival rates for patients. As with other cancers, early detection significantly improves the chances of successful treatment. Early diagnosis can be facilitated through screening programs designed to detect lung tissue tumors when they are still small, typically around 3mm in size. However, the analysis of extensive screening program data is hampered by limited access to medical experts. In this study, we developed a procedure for identifying potential malignant neoplastic lesions within lung parenchyma. The system leverages machine learning (ML) techniques applied to two types of measurements: low-dose Computed Tomography-based radiomics and metabolomics. Using data from two Polish screening programs, two ML algorithms were tested, along with various integration methods, to create a final model that combines both modalities to support lung cancer screening.

Segmentation of the bronchovascular bundle within the lung parenchyma is a key step for the proper analysis and planning of many pulmonary diseases. It might also be considered the preprocessing step when the goal is to segment the nodules from the lung parenchyma. We propose a segmentation pipeline for the bronchovascular bundle based on the Computed Tomography images, returning either binary or labelled masks of vessels and bronchi situated in the lung parenchyma. The method consists of two modules, modeling of the bronchial tree and vessels. The core revolves around a similar pipeline, the determination of the initial perimeter by the GMM method, skeletonization, and hierarchical analysis of the created graph. We tested our method on both low-dose CT and standard-dose CT, with various pathologies, reconstructed with various slice thicknesses, and acquired from various machines. We conclude that the method is invariant with respect to the origin and parameters of the CT series. Our pipeline is best suited for studies with healthy patients, patients with lung nodules, and patients with emphysema.

We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalized versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalized displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped generalized Langevin equations for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviors.

Diluted magnetic semiconductors (DMS) are interesting because of the interplay between the electronic and magnetic subsystems. We describe selected magnetic properties of IV-VI diluted magnetic semiconductors, looking at the similarities and differences between magnetic properties of II-VI, IV-VI, and III-V DMS. We focus on the influence of the crystalline and electronic structure of the material on its magnetic properties, especially on the exchange interactions among magnetic ions. We describe methods of determination of the exchange parameters by using different experimental techniques, such as measurements of magnetic susceptibility, magnetization, and specific heat. We follow the development in the material technology from bulk crystals to thin films and nanostructures.

We provide a review of theoretical results concerning the Havriliak-Negami (HN) and the Jurlewicz-Weron-Stanislavsky (JWS) dielectric relaxation models. We derive explicit forms of functions characterizing relaxation phenomena in the time domain - the relaxation, response and probability distribution functions. We also explain how to construct and solve relevant evolution equations within these models. These equations are usually solved by using the Schwinger parametrization and the integral transforms. Instead, in this work we replace it by the powerful Efros theorem. That allows one to relate physically admissible solutions to the memory-dependent evolution equations with phenomenologically known spectral functions and, from the other side, with the subordination mechanism emerging from a stochastic analysis of processes underpinning considered relaxation phenomena. Our approach is based on a systematic analysis of the memory-dependent evolution equations. It exploits methods of integral transforms, operational calculus and special functions theory with the completely monotone and Bernstein functions. Merging analytic and stochastic methods enables us to give a complete classification of the standard functions used to describe the large class of the relaxation phenomena and to explain their properties.

The novel technique of mean range bunching has been developed and applied at the projectile fragment separator FRS at GSI in four experiments of the FAIR phase-0 experimental program. Using a variable degrader system at the final focal plane of the FRS, the ranges of the different nuclides can be aligned, allowing to efficiently implant a large number of different nuclides simultaneously in a gas-filled stopping cell or an implantation detector. Stopping and studying a cocktail beam overcomes the present limitations of stopped-beam experiments. The conceptual idea of mean range bunching is described and illustrated using simulations. In a single setting of the FRS, 37 different nuclides were stopped in the cryogenic stopping cell and were measured in a single setting broadband mass measurement with the multiple-reflection time-of-flight mass spectrometer of the FRS Ion Catcher.

As an increasing number of academic conferences transition to the online sphere, new event paradigms must be explored and developed to better utilise the unique multimedia opportunities offered by the virtual world. With this in mind, we conducted in-depth interviews with researchers, performed a SWOT analysis of remote conferences, and developed experimental conference functionalities. We implemented these during the 9th edition of a two-day international scientific IT conference, which was attended by over 277 participants on the first day and 199 on the second. In this article, we describe how these innovative functionalities met the participants' needs based on qualitative and quantitative data. We present how the experiences of remote and in-person events differ, and offer recommendations on organising remote conferences that encourage participants to exchange knowledge and engage in activities., Comment: 8 pages, 5 figures, presented at CHI 2023, Case Studies

Various concentrations (8{\div}300 mmol/L) of NaCl, KCl and NaCl + KCl aqueous solutions were investigated using the positron annihilation lifetime spectroscopy (PALS). A strong dependence of the o-Ps intensity as a function of solution concentration was demonstrated. On this basis, the mean positron lifetime or the sum of counts in a selected time interval were proposed as reliable parameters for detecting disturbances in the ion balance of living organisms. The use of these parameters differentiating healthy and cancerous tissues is possible in a new generation of PET scanners equipped with a PALS detection module., Comment: 4 pages, 3 figures

The paper studies the exact solution of two kinds of generalized Fokker-Planck equations in which the integral kernels are given either by the distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or the distributed order Prabhakar function $k_{2}(\alpha, \gamma; \lambda; t) = \int_{0}^{1} e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t) d\mu$, where the Prabhakar function is denoted as $e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t)$. Both of these integral kernels can be called the fading memory functions and are the Stieltjes functions. It is also shown that their Stieltjes character is enough to ensure the non-negativity of the mean square values and higher even moments. The odd moments vanish. Thus, the solution of generalized Fokker-Planck equations can be called the probability density functions. We introduce also the Volterra-Prabhakar function and its generalization which are involved in the definition of $k_{2}(\alpha, \gamma; \lambda; t)$ and generated by it the probability density function $p_2(x, t)$.

Direct mass measurements of neutron-deficient nuclides around the $N=50$ shell closure below $^{100}$Sn were performed at the FRS Ion Catcher (FRS-IC) at GSI, Germany. The nuclei were produced by projectile fragmentation of $^{124}$Xe, separated in the fragment separator FRS and delivered to the FRS-IC. The masses of 14 ground states and two isomers were measured with relative mass uncertainties down to $1\times 10^{-7}$ using the multiple-reflection time-of-flight mass spectrometer of the FRS-IC, including the first direct mass measurements of $^{98}$Cd and $^{97}$Rh. A new $Q_\mathrm{EC} = 5437\pm67$ keV was obtained for $^{98}$Cd, resulting in a summed Gamow-Teller (GT) strength for the five observed transitions ($0^+\longrightarrow1^+$) as $B(\text{GT})=2.94^{+0.32}_{-0.28}$. Investigation of this result in state-of-the-art shell model approaches sheds light into a better understanding of the GT transitions in even-even isotones at $N=50$. The excitation energy of the long-lived isomeric state in $^{94}$Rh was determined for the first time to be $293\pm 21$ keV. This, together with the shell model calculations, allows the level ordering in $^{94}$Rh to be understood.

We investigate the combinatorial sequences $A(M, n)$ introduced by W. G. Brown (1964) and W. T. Tutte (1980) appearing in enumeration of convex polyhedra. Their formula is $$A(M, n) = \frac{2 (2M+3)!}{(M+2)! M!}\,\frac{(4n+2M+1)!}{n! (3n + 2M + 3)!} $$ with $n, M =0, 1, 2, \ldots$, and we conceive it as Hausdorff moments, where $M$ is a parameter and $n$ enumerates the moments. We solve exactly the corresponding Hausdorff moment problem: $A(M, n) = \int_{0}^{R} x^{n} W_{M}(x) d x$ on the natural support $(0, R)$, $R = 4^{4}/3^{3}$, using the method of inverse Mellin transform. We provide explicitly the weight functions $W_{M}(x)$ in terms of the Meijer G-functions $G_{4, 4}^{4, 0}$, or equivalently, the generalized hypergeometric functions ${_{3}F_{2}}$ (for $M=0, 1$) and ${_{4}F_{3}}$ (for $M \geq 2$). For $M = 0, 1$, we prove that $W_{M}(x)$ are non-negative and normalizable, thus they are probability distributions. For $M \geq 2$, $W_{M}(x)$ are signed functions vanishing on the extremities of the support. By rephrasing this problem entirely in terms of Meijer G representations we reveal an integral relation which directly furnishes $W_M(x)$ based on ordinary generating function of $A(M, n)$ as an input. All the results are studied analytically as well as graphically.

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are got according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent elementary functions which in turn may be analytically transformed among themselves using the Laplace transform and compared each other. This leads to the question on comparability of results got using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch-Williams-Watts approximation and get acquainted with description using the Mittag-Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects sitting in the heart of stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions which asymptotic analysis is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. Results of such done comparison are fully confirmed by calculations which use the powerful apparatus of the Mittag-Leffler functions., Comment: 14 pages, 3 figures

We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the PDF of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution. For subdiffusion we derive the PDF in Laplace space for arbitrary resetting protocol. Resetting at constant rate allows evaluation of the PDF in terms of H-function. We analyze the steady state and derive the rate function governing the relaxation behavior. For a subdiffusive process the steady state could exist even if the distribution of reset times possesses only finite mean.

Photocurrent-voltage characteristic (PC-V) is a method of determining the critical parameter in X-ray and gamma-ray detector plates, i.e., the carrier mobility - lifetime product, mt. We show on the (Cd,Mn)Te samples that the measurement results depend strongly on the surface treatment and the charge space distribution. The PC-V characteristics obtained for hv > Eg and hv ~ Eg indicated that etching with 20% HCl caused an appearance of a significant concentration of very shallow surface traps at the (Cd,Mn)Te sample surface. These traps seriously changed the measurements of PC-V characteristics and PC kinetics. We also noticed a small contribution of holes to photoconductivity in the PC kinetics. The PC-V characteristics measurements for hv > Eg may test the detector plate surface quality., Comment: 16 pages, 13 figures

The characteristic (Laplace or L\'evy) exponents uniquely characterize infinitely divisible probability distributions. Although of purely mathematical origin they appear to be uniquely associated with the memory functions present in evolution equations which govern the course of such physical phenomena like non-Debye relaxations or anomalous diffusion. Commonly accepted procedure to mimic memory effects is to make basic equations time smeared, i.e., nonlocal in time. This is modeled either through the convolution of memory functions with those describing relaxation/diffusion or, alternatively, through the time smearing of time derivatives. Intuitive expectations say that such introduced time smearings should be physically equivalent. This leads to the conclusion that both kinds of so far introduced memory functions form a "twin" structure familiar to mathematicians for a long time and known as the Sonine pair. As an illustration of the proposed scheme we consider the excess wings model of non-Debye relaxations, determine its evolution equations and discuss properties of the solutions.