On weakly τ-quasinormal subgroups of finite groups

Let G be a finite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that (|Q|, |H|) = 1 and (|H|, |Q ^G |) ≠ 1; (2) H is weakly τ-quasinormal in G if G has a subnormal subgroup T such that HT = G and T ∩ H ≦ H _τG , where H _τG is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. Our main result here is the following. Let ℱ be a saturated formation containing all supersoluble groups and let X ≦ E be normal subgroups of a group G such that G/E ∈ ℱ. Suppose that every non-cyclic Sylow subgroup P of X has a subgroup D such that 1 < |D| < |P| and every subgroup H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is non-Abelian) not having a supersoluble supplement in G is weakly τ-quasinormal in G. If X is either E or F* (E), then G ∈ ℱ.     

Local embeddings of some families of subgroups of finite groups

In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group.     

Method of determining the aerodynamic coefficients of asymmetric bodies with allowance for nonlinear body shape influence factors

The numerical method proposed makes it possible to determine the aerodynamic coefficients of asymmetric bodies of fairly arbitrary shape (including those with discontinuities of the transverse contour) at small solid angles of attack. The method allows an aerodynamically sound transition from the three-dimensional system of equations of gas dynamics to a two-dimensional system, which considerably simplifies the problem and reduces by an order the machine time required. The method takes into account the nonlinear body shape influence factors, which substantially improves the accuracy of the calculations. The efficiency and accuracy of the method are demonstrated by comparing the results of the calculations with the results of a numerical solution of the three-dimensional problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–128, March–April, 1992.     

Instability of the Rossby–Haurwitz wave in the invariant sets of perturbations

Stability of the Rossby–Haurwitz (RH) wave of subspace H₁H_n in an ideal incompressible fluid on a rotating sphere is analytically studied (H_n is the subspace of homogeneous spherical polynomials of degree n). It is shown that any perturbation of the RH wave evolves in such a way that its energy K(t) and enstrophy η(t) decrease, remain constant or increase simultaneously. A geometric interpretation of variations in the perturbation energy is given. A conservation law for arbitrary perturbations is obtained and used to classify all the RH-wave perturbations in four invariant sets M₋ⁿ, M₊ⁿ, H_n and M₀ⁿ−H_n depending on the value of their mean spectral number χ(t)=η(t)/K(t). The energy cascade of growing (or decaying) perturbations has opposite directions in the sets M₋ⁿ and M₊ⁿ due to a hyperbolic dependence between K(t) and χ(t). A factor space with a factor norm of the perturbations is introduced using the invariant subspace H_n of neutral perturbations as the zero factor class. While the energy norm controls the perturbation part belonging to H_n, the factor norm controls the perturbation part orthogonal to H_n. It is shown that in the set M₋ⁿ (χ(t)<n(n+1)), any nonzonal RH wave of subspace H₁H_n (n2) is Liapunov unstable in the energy norm. This instability has nothing in common with the orbital (Poincaré) instability and is caused by asynchronous oscillations of two almost coinciding RH-wave solutions. It is also shown that the exponential instability is possible only in the invariant set M₀ⁿ−H_n. A necessary condition for this instability is given. The condition states that the spectral number χ(t) of the amplitude of each unstable mode must be equal to n(n+1), where n is the RH-wave degree. The growth rate is estimated and the orthogonality of the unstable normal modes to the RH wave is shown. The instability in the invariant set M₊ⁿ of small-scale perturbations (χ(t)>n(n+1)) is still open problem.     

Use of the aerodynamic equivalence method in the determination and analysis of the aerodynamic coefficients of asymmetric bodies

In [1] the validity of the linear method of aerodynamic equivalence (AE) was demonstrated and the results of calculating the aerodynamic characteristics (ADC) of certain asymmetric (nonaxisymmetric) bodies, differing only slightly from the axisymmetric, were presented. In this paper a nonlinear AE method is proposed. This method is based on the principle of the equivalence of two bodies, one of which has a cross section of arbitrary shape while the other has a cross section described by a smooth function. This function is the sun of the first N + 1 terms of the Fourier series of the initial (discontinuous) function describing the shape of the body. The effectiveness of the AE method is illustrated with reference to certain examples of star-shaped bodies. The accuracy of the results obtained is estimated and a comparison is made with the experimental data. It is also shown that the AE method makes it possible to give a simple explanation of certain results of aerodynamics from a new standpoint.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–105, January–February, 1986.     

Aerodynamics of an asymmetrically deformed body in nonstationary supersonic motion

A method for making numerical calculations of the stationary and nonstationary aerodynamic characteristics of bodies of variable shape is considered. The results of calculations of the aerodynamic coefficents are given [1]. The results of numerical calculations are compared with the results of Newton's theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 162–167, March–April, 1980.     

Metallodrug Profiling against SARS-CoV-2 Target Proteins Identifies Highly Potent Inhibitors of the S/ACE2 interaction and the Papain-like Protease PLpro

The global spread of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has called for an urgent need for dedicated antiviral therapeutics. Metal complexes are commonly underrepresented in compound libraries that are used for screening in drug discovery campaigns, however, there is growing evidence for their role in medicinal chemistry. Based on previous results, we have selected more than 100 structurally diverse metal complexes for profiling as inhibitors of two relevant SARS-CoV-2 replication mechanisms, namely the interaction of the spike (S) protein with the ACE2 receptor and the papain-like protease PL^pro. In addition to many well-established types of mononuclear experimental metallodrugs, the pool of compounds tested was extended to approved metal-based therapeutics such as silver sulfadiazine and thiomersal, as well as polyoxometalates (POMs). Among the mononuclear metal complexes, only a small number of active inhibitors of the S/ACE2 interaction was identified, with titanocene dichloride as the only strong inhibitor. However, among the gold and silver containing complexes many turned out to be very potent inhibitors of PL^pro activity. Highly promising activity against both targets was noted for many POMs. Selected complexes were evaluated in antiviral SARS-CoV-2 assays confirming activity for gold complexes with N-heterocyclic carbene (NHC) or dithiocarbamato ligands, a silver NHC complex, titanocene dichloride as well as a POM compound. These studies might provide starting points for the design of metal-based SARS-CoV-2 antiviral agents.