A Criterion for Decomposabilty in QYBE

In this paper, set theoretic solutions of the Quantum Yang–Baxter Equations are considered. Etingof et al. [ 8] defined the structure group for non-degenerate solutions and gave some properties of this group. In particular, they provided a criterion for decomposability of involutive solutions based on the transitivity of the structure group. In that paper, the diagonal permutation $T$ is also introduced. It is known that this permutation is trivial exactly when the solution is square free. Rump [ 12] proved that these solutions are decomposable except in the trivial case. Later, Ramirez and Vendramin [ 11] gave some criteria for decomposability related with the diagonal permutation $T$. In this paper it was proven that an involutive solution is decomposable when the number of symbols of the solution and the order of the diagonal permutation $T$ are coprime.

Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality

In a supersymmetric compactification of Type II supergravity, preservation of $$ \mathcal{N} $$ N = 1 supersymmetry in four dimensions requires that the structure group of the generalized tangent bundle TM ⨁ T∗M of the six dimensional internal manifold M is reduced from SO(6) to SU(3) × SU(3). This topological condition on the internal manifold implies existence of two globally defined compatible pure spinors Φ1 and Φ2 of non-vanishing norm. Furthermore, these pure spinors should satisfy certain first order differential equations. In this paper, we show that non-Abelian T-duality (NATD) is a solution generating transformation for these pure spinor equations. We first show that the pure spinor equations are covariant under Pin(d, d) transformations. Then, we use the fact NATD is generated by a coordinate dependent Pin(d, d) transformation. The key point is that the flux produced by this transformation is the same as the geometric flux associated with the isometry group, with respect to which one implements NATD. We demonstrate our method by studying NATD of certain solutions of Type IIB supergravity with SU(2) isometry and SU(3) structure.

A New Bioreactor to Promote Follicular Growth With or Without Activin A

Background: The aim of the present study was to evaluate the effect of Activin A on the activation of in vitro folliculogenesis of human ovarian tissues with or without our new three-dimensional structure (3D-structure). Methods: Five fresh ovarian human tissues were cultured in vitro in 4 groups with 100ng/mL Activin A or without Activine A and within or without a 3D-structure for 20 or 22 days of in vitro culture. Follicular density and quality were evaluated, and follicular diameters were measured. Estradiol secretion was quantified. Proliferation and apoptosis through immunostaining were performed.Results: The proportion of primordial follicles was significantly reduced, and the proportion of primary and secondary follicles was significantly increased in all four groups (p<0.001). Antral cavities were observed in the four culture groups. Activin A supplementation did not significantly affect the follicular density, follicular quality, follicular growth, or estradiol secretion (p>0.05). The 3D-structure increased the density of primary follicles and decreased the estradiol secretion (p<0.001). Tissular proliferation was significantly lower in the 3D-structure group compared to the non-3D-structure group (p=0.008). Regarding tissular apoptosis, it was significantly higher in the Activin group compared to the non-Activin group (0.006). Conclusion: The presence of Activin A did not seem to play a key role in in vitro folliculogenesis activation. However, the results may indicate that the 3D-structure could be more physiological and could prevent a pejorative in vitro folliculogenesis flare-up.

On the Tits–Weiss conjecture and the Kneser–Tits conjecture for and (With an Appendix by R. M. Weiss)

We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits–Weiss conjecture for Albert algebras and the Kneser–Tits conjecture for isotropic groups of type $\mathrm {E}_{7,1}^{78}, \mathrm {E}_{8,2}^{78}$ . As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type $^1\mathrm {E}_6$ .

Dynamic characteristics of pilot boards of structures

This work is devoted to studying the issues of vibrations of pile foundations, taking into account soil conditions for various types of fastening of piles to structures and the development of rational methods for choosing the parameters of piles and their number in earthquake-resistant construction. Based on the results of theoretical studies, resonance curves were constructed for three types of fastening of the "structure-group of piles" system. A special technique was proposed, and a series of field tests were carried out to determine the amplitude-frequency characteristics of the system.

Cervical Spine Immobilization in Patients With a Geriatric Facial Structure: The Influence of a Geriatric Mandible Structure on the Immobilization Quality Using a Cervical Collar

Introduction: Demographic changes have resulted in an increase in injuries among geriatric patients. For these patients, a rigid cervical collar is crucial for immobilizing the cervical spine. However, evidence suggests that patients with a geriatric facial structure require a different means of immobilization than patients with an adult facial structure. This study aimed to analyze the remaining motion of the immobilized cervical spine based on facial structure. Materials and Methods: This study was performed on 8 fresh human cadavers. Facial structure was evaluated via ascertaining the mandibular angle by computer tomography. A mandibular angle below 130°, belongs to the adult facial structure group ( n = 4) and a mandibular angle above 130°, belongs to the geriatric facial structure group ( n = 4). The flexion and lateral bending of the immobilized cervical spine were analyzed in both groups using a wireless motion tracker system. Results: A flexion of up to 19.0° was measured in the adult facial structure group. The mean flexion in the adult vs. geriatric facial structure groups were 14.5° vs. 6.5° (ranges: 9.0-19.0 vs. 5.0-7.0°), respectively. Thus, cervical spine motion was ( p = 0.0286) significantly more reduced in the adult facial structure group. No ( p = 0.0571) significant difference was oberserved in the mean lateral bending of the adult facial structure group (14.5°) compared to the geriatric facial structure group (7.5°). Conclusion: Emergency medical service personnel should therefore follow current guidelines and recommendations and perform cervical spine immobilization with a cervical collar, including in patients with a geriatric facial structure.