Dynamics of resistant hypertension in the postoperative period of carotid endarterectomy with and without carotid body saving

Aim. To analyze the results of multicenter study on dynamics of resistant hypertension (RH) in patients after various types of carotid endarterectomy (CE) with and without carotid body savingMaterial and methods. During the period from January 2010 to December 2020, 1827 patients with hemodynamically significant stenosis of the internal carotid artery (ICA) and RH were operated on. Depending on CE type, the two groups were selected. Group 1 (n=1135; 62,2%) consisted of patients received glomus-saving surgery: 19,2% (n=351) -conventional CE with a patch repair of reconstitution point; 13,6% (n=248) — glomus-saving CE sensu R. A. Vinogradov; 7,3% (n=133) — glomus-saving CE sensu K. A. Antsupov; 11,7% (n=214) — glomus-saving CE sensu A. N. Kazantsev; 4,6% (n=84) — Chick-Chirik CE; 5,7% (n=105) — swallow tail type patch repair sensu R. I. Izhbuldin. Group 2 (n=692; 37,8%) consisted of patients received CE without glomus saving: 18,6% (n=341) — eversion CE with carotid body cutoff; 6,3% (n=115) — CE with new bifurcation plasty; 5,85% (n=107) — autoarterial reconstruction; 7,1% (n=129) ICA autotransplantation sensu E. V. Rosseikin.Results. The mortality rate, as well as the prevalence of myocardial infarction (MI) and ischemic strokes were comparable in groups. The incidence of hemorrhagic transformation (group 1: 0%; group 2: 0,6%; p=0,04; OR=0,06; 95% CI, 0,003-1,25) and composite endpoint (death+MI+ischemic stroke+hemorrhagic transformation) (group 1: 1,06%; group 2: 3,0%; p=0,004; odds ratio (OR)=0,34; 95% CI, 0,16-0,69) significantly differs between groups. After glomus-saving CE, the number of patients with the target blood pressure (BP) level reached 51,1% (p <0,0001; OR=0,0009; 95% CI, 6,05-15,9). The number of patients with grade II (31,1%; p<0,0001; OR=12,7; 95% CI, 10,4-15,52) and III (3,6%; p<0,0001; OR=10,26; 95% CI, 6,71-15,67) hypertension significantly decreased. In the group 2, the prevalence grade III hypertension increased (48,0%; p<0,0001; OR=0,23; 95% CI, 0,18-0,3), while the number of patients with grade I (0%; p<0,0001; OR=77,0; 95% CI, 4,71-12,58) and II (52%; p<0,0001; OR=3,06; 95% CI, 2,43-3,86) hypertension decreased.Conclusion. Glomus-saving CE contributes to achieving target BP in patients with RH. Its removal increases the risks of labile hypertension, postoperative hypertensive crisis, hyperperfusion syndrome and hemorrhagic transformation.

Stationary orbits of linear time-varying observation systems

In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.

Exact Solutions of Newell-Whitehead-Segel Equations Using Symmetry Transformations

In this article, Lie and discrete symmetry transformation groups of linear and nonlinear Newell-Whitehead-Segel (NWS) equations are obtained. By using these symmetry transformation groups, several group invariant solutions of considered NWS equations have been constructed. Furthermore, some more group invariant solutions are generated by using discrete symmetry transformation group. Graphical representations of some obtained solutions are also presented.

Laguerre hypersurfaces with definite Laguerre tensor

x : Mn-1 ? Rn be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. In this paper, we will study the Laguerre hypersurface with parallel Laguerre form and nonnegative or non-positive Laguerre tensor.

Maxmal Order of NG-Transformation Group

In this paper, we consider the problem that the maximal order consider the groups that consisting of transformations we called NG-Transformation on a nonempty set A has no bijection as its element. We find the order of these groups not greater that (n-1)!. In addition, we will prove our result by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.

On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane

Dynamical conditions that guarantee stability for discrete transformation group $C^*$-algebras are determined. The results are applied to the case of some discrete subgroups of $\operatorname{SL} (2,\mathbb{R} )$ acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the $C^*$-algebra associated to the horocycle flow on the corresponding compact homogeneous space of $\operatorname{SL} (2,\mathbb{R} )$.

A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

Application of Clifford Algebra in Solving the Eigen Equations of Quantum Mechanics

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.