1,2,4-Triazole-Based Hybrid Heterocyclic Carbaldehyde Hydrazones and Their Effect on DNA Methylation Level

Russian Journal of Organic Chemistry - While developing new approaches to the design of biologically active compounds based on 1,2,4-triazole, a number of new hydrazones containing...     

Calculation of Geometric Probabilities Using Covariogram of Convex Bodies

In the paper, a formula to calculate the probability that a random segment L(ω, u) in R ⁿ with a fixed direction u and length l lies entirely in the bounded convex body D ? R ⁿ (n ≥ 2) is obtained in terms of covariogram of the body D. For any dimension n ≥ 2, a relationship between the probability P(L(ω, u) ? D) and the orientation-dependent chord length distribution is also obtained. Using this formula, we obtain the explicit form of the probability P(L(ω, u) ? D) in the cases where D is an n-dimensional ball (n ≥ 2), or a regular triangle on the plane.     

Generalized Pleijel identity

A family of identities primarily associated with isoperimetric inequalities for planar convex domains was discovered by Pleijel in 1956. We call these identities classical Pleijel identities. R. V. Ambartzumian gave combinatorial proof of these identities and pointed out that they can be applied to find chord length distribution functions for convex domains. In the classical Pleijel identities integration is over the measure in the space \(\mathbb{G}\) of lines which is invariant with respect to the all Euclidean motions. In the present paper they are considered for any locally-finite measure in the space \(\mathbb{G}\). These identities are applied to find the so-called orientation-dependent chord length distribution (or density) functions for bounded convex domains.     

Kinematic measure of segments lying in a domain

The paper proves a formula for calculation of the kinematic measure K(D, l) of set of segments with constant length l, entirely contained in a bounded convex domainDof the Euclidean space. The obtained formula permits to find an explicit form for the kinematic measure K(D, l) for the domains D with known chord length distribution. In particular, application of the obtained formula gives explicit expressions for K(D, l) in the disc, regular triangle, rectangle and regular pentagon.     

Many-body exceptional points in colliding condensates

ABSTRACT

Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.     

Random copy of a segment within a convex domain

Under the assumption that S is a segment of the length l and D is a bounded, convex domain in the Euclidean plane ℝ², the paper considers the randomly moving copy L of S, under the condition that it hits D. Denote by L| the length of L ∩ D. In the paper an elementary expression for the distribution function F _L (x) of the random variable L| is obtained. Note that F _L (x) can have a jump at the point l or can be a continuous function depending on l and the domainD. In particular, a relation between chord length distribution functions of D and F _L (x) is given. Moreover, we derive explicit forms of F _L (x) for the disk and regular n-gons with n = 3÷7.     

Investigation of the Circular Waveguide Radiating Slotted Structures Using Polarization Degeneration of the Main Mode Wave

The unusual paired slotted radiating structure of a circular waveguide is investigated when the wave of main mode H₁₁ is propagating in it. This structure is constructed in such a way that the phenomenon of the polarization degeneration of wave with this mode is taken into account. In the waveguide cross-section, the centers of the paired half-wave transverse slots are spaced by an angle γ over both sides of the waveguide diametric line along the direction of polarization of the H₁₁ mode. The radiation patterns at different spaced angles γ equal to 45°, 65°, and 72° as well as at the two-tiered location of such paired slots are investigated. The second tier is located on the distance equal to the half of the waveguide wavelength along the waveguide longitudinal axis. The pair slots of both tiers have the same γ angle but they are located at the opposite sides of the waveguide. The possibility is shown of synthesizing an omnidirectional radiation pattern by combination of the two-tiered structure with the opposite frontal slots and the two-tiered structure with the oppositely paired slots.