A monoclinic C form of rilpivirine hydrochloride, (N6H19C22)Cl, has been obtained and characterized using solid-state 15N, 13C, and 35Cl NMR spectroscopy and multitemperature synchrotron X-ray powder diffraction. The title compound crystallizes in the monoclinic system (space group C2/c, #15) at both room (295.0(2) K) and low (100.0(2) K) temperatures. At room temperature, the following parameters are a = 19.43051(3), b = 13.09431(14), c = 17.10254(18) Å, β = 109.3937(7), V = 4104.48(9) Å3, and Z = 8. The folded molecular conformation of the cation is similar with that of free base rilpivirine with the exception of cyanovinyl group disposition. The anion links cations to infinite chains parallel to the crystallographic c axis using N–H⋯Cl bonds where both amino groups and the protonated pyrimidine ring take part in the H-bonding. The powder patterns have been submitted to the ICDD for inclusion in the Powder Diffraction File™ (PDF®).

In the past few decades world architecture has seen radical changes as the result of industrialization, standardization and mass production. For Soviet architecture this half century of scientific and technical revolution along with the growth of economic potential has been the most fruitful in its history. If we return to the past and try to form a judgment on the urbanism of our day we will no doubt see that what is offered us by new cities, modern residential zones and social amenities corresponds to our dreams of the cities of the future. From the point of view of the past, we have only to look at the zones of Yassenevo, Tropariovo, the Olympic village or the civic centers of Tashkent or Navoi.

We recently reported on the radio-frequency attenuation length of cold polar ice at Summit Station, Greenland, based on bi-static radar measurements of radio-frequency bedrock echo strengths taken during the summer of 2021. Those data also allow studies of (a) the relative contributions of coherent (such as discrete internal conducting layers with sub-centimeter transverse scale) vs incoherent (e.g. bulk volumetric) scattering, (b) the magnitude of internal layer reflection coefficients, (c) limits on signal propagation velocity asymmetries (‘birefringence’) and (d) limits on signal dispersion in-ice over a bandwidth of ~100 MHz. We find that (1) attenuation lengths approach 1 km in our band, (2) after averaging 10 000 echo triggers, reflected signals observable over the thermal floor (to depths of ~1500 m) are consistent with being entirely coherent, (3) internal layer reflectivities are ≈–60$\to$–70 dB, (4) birefringent effects for vertically propagating signals are smaller by an order of magnitude relative to South Pole and (5) within our experimental limits, glacial ice is non-dispersive over the frequency band relevant for neutrino detection experiments.

Restudy of Campyloprion annectans Eastman, 1902 from North America demonstrated that neither specimen included is diagnostic at the species level; thus, the species name is a nomen dubium. Since this species was designated as the type species of the genus, this requires suppression of the generic name also. Another species earlier assigned to Campyloprion, Campyloprion ivanovi Karpinsky, 1924 is used as a type for a newly established genus Karpinskiprion Lebedev et Itano gen. nov. The composition of the family Helicoprionidae Karpinsky, 1911 is reviewed, and a new family Helicampodontidae Itano et Lebedev fam. nov. is erected. A new specimen of Karpinskiprion ivanovi (Karpinsky, 1924) recently discovered in the Volgograd Region of Russia is the most complete Karpinskiprion specimen ever found. It unambiguously demonstrates the coiled nature of these tooth whorls and presents information on their developmental stages. During organogeny, cutting blades of the crown became reshaped, and basal spurs progressively elongated, forming a grater. Whorl growth occurred by addition of new crowns to the earlier mineralised base followed by later spur growth. In contrast to consistently uniform cutting blades, spurs are often malformed and bear traces of growth interruption. Both sides of the outer coil of the tooth whorl bear lifetime wear facets. The youngest (lingual) crowns are as yet unaffected by wear. The best-preserved facets show parallel radially directed scratch marks. The upper jaw dentition of Karpinskiprion is unknown, but we suggest that the faceted areas resulted from interaction with the antagonistic dental structures here. Three possible hypotheses for this interaction are suggested: (a) two opposing whorls acted as scissor blades, moving alternately from one side to another; (b) the lower tooth whorl fitted between paired parasymphyseal tooth whorls of the opposing jaw; or (c) the lower tooth whorl fitted into a dental pavement in the upper jaw.

Over the last 25 years, radiowave detection of neutrino-generated signals, using cold polar ice as the neutrino target, has emerged as perhaps the most promising technique for detection of extragalactic ultra-high energy neutrinos (corresponding to neutrino energies in excess of 0.01 Joules, or 1017 electron volts). During the summer of 2021 and in tandem with the initial deployment of the Radio Neutrino Observatory in Greenland (RNO-G), we conducted radioglaciological measurements at Summit Station, Greenland to refine our understanding of the ice target. We report the result of one such measurement, the radio-frequency electric field attenuation length $L_\alpha$. We find an approximately linear dependence of $L_\alpha$ on frequency with the best fit of the average field attenuation for the upper 1500 m of ice: $\langle L_\alpha \rangle = ( ( 1154 \pm 121) - ( 0.81 \pm 0.14) \, ( \nu /{\rm MHz}) ) \,{\rm m}$ for frequencies ν ∈ [145 − 350] MHz.

Given a partial action $\unicode[STIX]{x1D703}$ of a group on a set with an algebraic structure, we construct a reflector of $\unicode[STIX]{x1D703}$ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if $\unicode[STIX]{x1D703}$ is a partial action on an algebra from a variety $\mathsf{V}$, then we show that the problem reduces to the embeddability of a certain generalized amalgam of $\mathsf{V}$-algebras associated with $\unicode[STIX]{x1D703}$. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.

We present a complex analytic proof of the Pila–Wilkie theorem for subanalytic sets. In particular, we replace the use of $C^{r}$-smooth parametrizations by a variant of Weierstrass division. As a consequence we are able to apply the Bombieri–Pila determinant method directly to analytic families without limiting the order of smoothness by a $C^{r}$ parametrization. This technique provides the key inductive step for our recent proof (in a closely related preprint) of the Wilkie conjecture for sets definable using restricted elementary functions. As an illustration of our approach we prove that the rational points of height $H$ in a compact piece of a complex-analytic set of dimension $k$ in $\mathbb{C}^{m}$ are contained in $O(1)$ complex-algebraic hypersurfaces of degree $(\log H)^{k/(m-k)}$. This is a complex-analytic analog of a recent result of Cluckers, Pila, and Wilkie for real subanalytic sets.

The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.

We characterize those partially ordered sets I for which the canonical maps Mi → colim Mj into colimits of abstract sets are always injective, provided that the transition maps are injective. We also obtain some consequences for colimits of vector spaces.

We consider an optimal stopping problem for a general discrete-time process X1, X2, …, Xn, … on a common measurable space. Stopping at time n (n = 1, 2, …) yields a reward Rn(X1, …, Xn) ≥ 0, while if we do not stop, we pay cn(X1, …, Xn) ≥ 0 and keep observing the process. The problem is to characterize all the optimal stopping times τ, i.e., such that maximize the mean net gain:

$$E(R_\tau(X_1,\dots,X_\tau)-\sum_{n=1}^{\tau-1}c_n(X_1,\dots,X_n)).$$

In the particular case of Markov sequence X1, X2, … we estimate the stability of the optimal stopping problem under perturbations of transition probabilities.

The irradiation of thin films by intensive subpicosecond laser pulses with nanosecond prepulse is accompanied by a number of various physical processes. The laser beam transmissions through the film as well as the re-emission flux on both sides of the film plasma have been evaluated by simulation for Al and CH2 materials. It has been demonstrated that the thickness of the film can be chosen to cut off the long nanosecond prepulse whereas the main pulse is transmitted through the plasma. Thus, thin films can be useful for the laser contrast improvement in experiments with different targets.

Nevertheless, the laser energy transformation into the soft X-ray radiation on the back side of the shielding film plasma can reach up to 7% of the incident intensity for the Al film and result in strong preheating of the target. At the same time the re-emission flux produced by a CH2 film is an order lower than that in the case of Al film. The shielding of an Ag bulk target by Al and CH2 films is simulated and discussed.

Results of investigation of X-ray sensors on the basis of GaAs compensated with chromium (HR GaAs) are presented in this work. HR GaAs material is shown to have the following physical parameters: the resistivity about 1GOhm*cm, the nonequilibrium charge carrier lifetime – hundreds of nanoseconds. Prototypes of microstrip and array HR GaAs sensors have been manufactured and tested. It is demonstrated that the sensors provide spatial resolution according to the pixel pitch and allow obtaining high quality X-ray images.