Maximal Torsion Research Articles

Semi-generalized co-Bassian groups

As a common nontrivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically, we give a complete characterization of these groups in the cases of [Formula: see text]-torsion groups and groups of finite torsion-free rank by showing that these groups can be completely determined in terms of generalized finite [Formula: see text]-ranks and also depends on their quotients modulo the maximal torsion subgroup. Surprisingly, for [Formula: see text]-primary groups, the concept of a semi-generalized co-Bassian group is closely related to that of a generalized co-Bassian group.

A bound for the torsion on subvarieties of abelian varieties

We give a uniform bound on the degree of the maximal torsion cosets for subvarieties of an abelian variety. The proof combines algebraic interpolation and a theorem of Serre on homotheties in the Galois representation associated to the torsion subgroup of an abelian variety.

A BRICK VERSION OF A THEOREM OF AUSLANDER

AbstractWe prove that a finite-dimensional algebra $ \Lambda $ is $ \tau $ -tilting finite if and only if all the bricks over $ \Lambda $ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes for $ \tau $ -tilting infinite algebras.

Torsion points on isogenous abelian varieties

Investigating a conjecture of Zannier, we study irreducible subvarieties of abelian schemes that dominate the base and contain a Zariski dense set of torsion points that lie on pairwise isogenous fibers. If everything is defined over the algebraic numbers and the abelian scheme has maximal variation, we prove that the geometric generic fiber of such a subvariety is a union of torsion cosets. We go on to prove fully or partially explicit versions of this result in fibered powers of the Legendre family of elliptic curves. Finally, we apply a recent result of Galateau and Martínez to obtain uniform bounds on the number of maximal torsion cosets in the Manin–Mumford problem across a given isogeny class. For the proofs, we adapt the strategy, due to Lang, Serre, Tate, and Hindry, of using Galois automorphisms that act on the torsion as homotheties to the family setting.

Comparison of Mechanical Resistance to Maximal Torsion Stress in Original and Nonoriginal or Compatible Prosthetic Implant Screws: An In Vitro Study.

Micromovements of the implant-abutment connection influence peri-implant bone preservation. The maximal torque after a cycle of implant prosthetic screw tightening using original components of different manufacturers and replicas produced by other companies is evaluated and quantified in this study. A total of 30 Mis Seven® standard platform implants and 30 interfaces were used, and 30 standard platform screws were tested, 10 Mis®, 10 Iconekt®, and 10 Exaktus®. The screws were tightened with an MIS® torquemeter until their respective fracture, and the fracture point was measured through the equipment's load cell, CS-Dental Testing Machine®. The screws were analyzed under an Olympus® SZ61 microscope. The fracture points were recorded and compared among all samples. To compare the mean values of the fracture torques, t-tests were performed using the reference values associated with each brand and the sample results. The variable “Place of Fracture” between the original Mis® brand and the Exaktus® replica compared to the Iconekt® replica presented a statistically significant difference (p < 0.001). When analyzing the variable “Fracture Torque,” although it was verified that the replica screws (Iconekt® and Exaktus®) had a lower maximum torque, 65.11 Nm and 62.89 Nm, respectively, compared to the original Mis® brand (70 Nm and 69 Nm), there were no statistically significant differences p > 0.05. Nonoriginal screws did not present different fracture resistances compared to the original Mis® brand screws. The fracture site of Iconekt® screws showed a different pattern compared to the other brands.

Convergence of a periodic orbit family close to asteroids during a continuation

In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total geometric perspective to understanding the evolution of the dynamic characteristics from a global perspective. Based on the polyhedron model, convergence is derived via a series of theoretical analyses and derivations, which shows that a periodic orbit will evolve into a nearly circular orbit with a normal periodic ratio (e.g., 2:1, 3:2, and 4:3) and almost zero torsion under proper circumstances. As an application of the results developed here, three asteroids, (216) Kleopatra, (22) Kalliope and (433) Eros, are studied, and several representative periodic orbit families are detected, with convergence in three different cases: bidirectional, increasing-directional and decreasing-directional continuation. At the same time, four commonalities among these numerical examples are concluded. First, a (pseudo) tangent bifurcation arises at the cuspidal points during the variations in the periodic ratios in a single periodic orbit family. In addition, these cuspidal points in the periodic ratio coincide with the turning points during the variations in the average radius, the maximal torsion and the maximal radius of curvature. Furthermore, the periodic ratio increases (or decreases) with an increase (or decrease) in the Jacobian constant overall. We find the relationship between periodic ratio and Jacobian constant. The results implies that the periodic ratios for a fixed resonant status have an infimum and a supremum. Finally, if the periodic orbit converges to a point, it can be an unstable equilibrium point of the asteroid.

Application of logistic regression equation analysis using derivatives for optimal cutoff discriminative criterion estimation

Background: Sigmoid curve function is frequently applied for modeling in clinical studies. The main task of scientific research relevant to medicine is to find rational cutoff criterion for decision making rather than finding just equation for probability calculation. The objective of this study is to analyze the specific features of logistic regression curves in order to evaluate critical points and to assess their implication for continuous predictor variable dichotomization in order to provide optimal cutoff criterion for decision making. Methods: Second order and third order derivatives were used to analyze estimated logistic regression function, critical values of independent continuous variable that correspond to zero points of second and third derivative were calculated for each logistic regression equation. Using those values continuous predictors of each logistic regression equations were converted into dichotomized scales using 1 value that correspond to second order derivative and 2 values that correspond to zero points of third derivative then receiver operating characteristics of estimated equations with dichotomized predictor were assessed. Results: Sigmoid curve of logistic regression has the same structure with inflection point corresponding probability 0.5 (zero value of second derivative) and maximal torsion (zero values of third derivative) corresponding 0.2113 and 0.7886 probability values. Thresholds accounting for predictor values that correspond to zero values of second and third derivative provide estimation of logistic regression applying dichotomized predictor with optimal ratio of sensitivity, specificity and overall accuracy with maximal area under curve. Conclusion: Analysis of logistic regression equation with continuous predictor applying derivatives help to choose optimal thresholds that provide maximally effective discriminative functions with priority sensitivity or specificity. Using this dichotomization discriminative function can be adjusted to the needs of particular task or study depending which characteristic is in priority – sensitivity or specificity.

Study of the Influence of Plant-Based Filler on the Physicomechanical Properties and Processing Parameters of a Composite Based on Secondary Polymer Raw Materials

Creating biodegradable polymer compositions is an urgent problem. In this research, the processing parameters and physicomechanical properties of materials based on secondary polypropylene and secondary polyethylene filled with plant-based fillers are studied. It is estimated that the introduction of a filler leads to an increase in the maximal torsion torque; the lowest resistance against filler introduction is observed in the use of secondary polyethylene. Similar regularities are observed during the study of the minimal torsion torque; however, in this case, the lowest resistance is observed for the sample of secondary polypropylene. It is shown that the introduction of 10–15 parts by the mass of the filler leads to an increase in the elastic modulus and an insignificant decrease in the values of rupture stress and elongation upon breaking.

On a type of maximal abelian torsion free subgroups of connected Lie groups

For an arbitrary real connected Lie group G we define $$\mathrm {p}(G)$$ as the maximal integer p such that $$\mathbb {Z}^p$$ is isomorphic to a discrete subgroup of G and $$\mathrm {q}(G)$$ is the maximal integer q such that $$\mathbb {R}^q$$ is isomorphic to a closed subgroup of G. The aim of this paper is to investigate properties of these two invariants. We will show that if G is a noncompact connected Lie group, then $$1\le \mathrm {q}(G)\le \mathrm {p}(G)\le \dim (G/K)$$ where K is a maximal compact subgroup of G. In the cases when G is an exponential Lie group or G is a connected nilpotent Lie group, we give explicit relationships between these two invariants and a well known Lie algebra invariant $$\mathcal M(\mathfrak {g})$$ , i.e. the maximum among the dimensions of abelian subalgebras of the Lie algebra $$\mathfrak {g}:=\mathrm {Lie}(G)$$ .

Splitting of Closed Subgroups of Locally Compact Abelian Groups

Let £ be the category of all locally compact abelian (LCA) groups. In this paper, we investigate the splitting of the identity component, the subgroup of all compact elements and the maximal torsion subgroup of a group £. A group £ will be called split full if every closed subgroup of G splits. In this paper, we give a necessary condition for an LCA group to be split full.&#x0D;

Left ventricular rotation and torsion in neonates and infants younger than three months with symptomatic ventricular septal defect: Acute effects from open heart surgery.

We evaluated ventricular rotation, torsion, and strain changes in infants using preoperative and postoperative M-mode echocardiography after early surgery for symptomatic ventricular septal defects (VSD). Thirty-five patients with VSD underwent vector velocity imaging echocardiography before and after open heart surgery. Their rotational variables were compared with 18 controls. All the patients (19 boys and 16 girls; median age: 44.4 days; range: 13-84 days) showed normal septal motion preoperatively; however, septal motion changed into flat septum or paradoxical septal motion after surgery. Left ventricular end-diastolic internal dimension and fractional shortening significantly decreased after surgery (P = .001 and P = .000). Patients showed significant postoperative reduction of peak systolic apical rotation and maximal torsion (P = .010 and P = .000). Peak systolic basal rotation decreased after surgery but it was not significantly (P = .106). No significant differences were found in longitudinal and circumferential systolic strains between patients and controls. Abnormal motion of the ventricular septum was confirmed by postoperative M-mode echocardiography. Decreased rotation/torsion variables may reflect postoperative changes of ventricular loading conditions. Because systolic strain was preserved, postoperative echocardiographic results should not be interpreted as abnormal or decreased ventricular function.

The number of maximal torsion cosets in subvarieties of tori

Abstract We present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus 𝔾 m n {\mathbb{G}_{\mathrm{m}}^{n}} . Our first main result gives a bound in terms of the degree of the defining polynomials. We also give a bound for the number of isolated torsion point, that is maximal torsion cosets of dimension 0, in terms of the volume of the Newton polytope of the defining polynomials. This result proves the conjectures of Ruppert and of Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.

Biomechanical effects of morphological variations of the cortical wall at the bone-cement interface.

BackgroundThe integrity of bone-cement interface is very important for the stabilization and long-term sustain of cemented prosthesis. Variations in the bone-cement interface morphology may affect the mechanical response of the shape-closed interlock.MethodsSelf-developed new reamer was used to process fresh pig reamed femoral canal, creating cortical grooves in the canal wall of experimental group. The biomechanical effects of varying the morphology with grooves of the bone-cement interface were investigated using finite element analysis (FEA) and validated using companion experimental data. Micro-CT scans were used to document interlock morphology.ResultsThe contact area of the bone-cement interface was greater (P < 0.05) for the experimental group (5470 ± 265 mm2) when compared to the specimens of control group (5289 ± 299 mm2). The mechanical responses to tensile loading and anti-torsion showed that the specimens with grooves were stronger (P < 0.05) at the bone-cement interface than the specimens without grooves. There were positively significant correlation between the contact area and the tensile force (r2 = 0.85) and the maximal torsion (r2 = 0.77) at the bone-cement interface. The volume of cement of the experimental group (7688 ± 278 mm3) was greater (P < 0.05) than of the control group (5764 ± 186 mm3). There were positively significant correlations between the volume of cement and the tensile force (r2 = 0.90) and the maximal torsion (r2 = 0.97) at the bone-cement interface. The FEA results compared favorably to the tensile and torsion relationships determined experimentally. More cracks occurred in the cement than in the bone.ConclusionsConverting the standard reaming process from a smooth bore cortical tube to the one with grooves permits the cement to interlock with the reamed bony wall. This would increase the strength of the bone-cement interface.

On Maximal Torsion Radicals, IV

It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be extended to the category σ[M] of modules subgenerated by a module M, provided that M is a Noetherian quasi-projective generator in σ[M]. Furthermore, under this hypothesis the prime M-ideals are the fully invariant submodules P of M such that M/P is semi-compressible.

Characterization of Abelian groups with a minimal generating set

We characterize Abelian groups with a minimal generating set: Let τ A denote the maximal torsion subgroup of A. An infinitely generated Abelian group A of cardinality κ has a minimal generating set iff at least one of the following conditions is satisfied:dim(A/pA) = dim(A/qA) = κ for at least two different primes p, q.dim(t A/pt A) = κ for some prime number p.Σ{dim(A/(pA + B)) ∣ dim(A/(pA + B)) < κ} = κ for every finitely generated subgroup B of A. Moreover, if the group A is uncountable, property (3) can be simplified to (3') Σ{dim(A/pA) ∣ dim(A/pA) < κ} = κ, and if the cardinality of the group A has uncountable cofinality, then A has a minimal generating set iff any of properties (1) and (2) is satisfied.

Helical vortex filament motion under the non-local Biot–Savart model

AbstractThe thin helical vortex filament is one of the fundamental exact solutions possible under the local induction approximation (LIA). The LIA is itself an approximation to the non-local Biot–Savart dynamics governing the self-induced motion of a vortex filament, and helical filaments have also been considered for the Biot–Savart dynamics, under a variety of configurations and assumptions. We study the motion of such a helical filament in the Cartesian reference frame by determining the curve defining this filament mathematically from the Biot–Savart model. In order to do so, we consider a matched approximation to the Biot–Savart dynamics, with local effects approximated by the LIA in order to avoid the logarithmic singularity inherent in the Biot–Savart formulation. This, in turn, allows us to determine the rotational and translational velocity of the filament in terms of a local contribution (which is exactly that which is found under the LIA) and a non-local contribution, each of which depends on the wavenumber, $k$, and the helix diameter, $A$. Performing our calculations in such a way, we can easily compare our results to those of the LIA. For small $k$, the transverse velocity scales as $k^{2}$, while for large $k$, the transverse velocity scales as $k$. On the other hand, the rotational velocity attains a maximum value at some finite $k$, which corresponds to the wavenumber giving the maximal torsion.

On the torsion anomalous conjecture in CM abelian varieties

The Torsion Anomalous Conjecture (TAC) states that a subvariety V of an abelian variety A has only finitely many maximal torsion anomalous subvarieties. In this work we prove, with an effective method, some cases of the TAC when the ambient variety A has CM, generalising our previous results in products of CM elliptic curves. When V is a curve, we give new results and we deduce some implications on the effective Mordell-Lang Conjecture.

The Closed Maximal Torsion Subgroup of a Locally Compact Abelian Group

The Closed Maximal Torsion Subgroup of a Locally Compact Abelian Group

Left ventricular rotation and right–left ventricular interaction in congenital heart disease: the acute effects of interventional closure of patent arterial ducts and atrial septal defects

Left ventricular rotation is physiologically affected by acute changes in preload. We investigated the acute effect of preload changes in chronically underloaded and overloaded left ventricles in children with shunt lesions. A total of 15 patients with atrial septal defects (Group A: 7.4 ± 4.7 years, 11 females) and 14 patients with patent arterial ducts (Group B: 2.7 ± 3.1 years, 10 females) were investigated using 2D speckle-tracking echocardiography before and after interventional catheterisation. The rotational parameters of the patient group were compared with those of 29 matched healthy children (Group C). Maximal torsion (A: 2.45 ± 0.9°/cm versus C: 1.8 ± 0.8°/cm, p < 0.05), apical peak systolic rotation (A: 12.6 ± 5.7° versus C: 8.7 ± 3.5°, p < 0.05), and the peak diastolic torsion rate (A: -147 ± 48°/second versus C: -110 ± 31°/second, p < 0.05) were elevated in Group A and dropped immediately to normal values after intervention (maximal torsion 1.5 ± 1.1°/cm, p < 0.05, apical peak systolic rotation 7.2 ± 4.1°, p < 0.05, and peak diastolic torsion rate -106 ± 35°/second, p < 0.05). Patients in Group B had decreased maximal torsion (B: 1.8 ± 1.1°/cm versus C: 3.8 ± 1.4°/cm, p < 0.05) and apical peak systolic rotation (B: 8.3 ± 6.1° versus C: 13.9 ± 4.3°, p < 0.05). Defect closure was followed by an increase in maximal torsion (B: 2.7 ± 1.4°/cm, p < 0.05) and the peak diastolic torsion rate (B: -133 ± 66°/second versus -176 ± 84°/second, p < 0.05). Patients with chronically underloaded left ventricles compensate with an enhanced apical peak systolic rotation, maximal torsion, and quicker diastolic untwisting to facilitate diastolic filling. In patients with left ventricular dilatation by volume overload, the peak systolic apical rotation and the maximal torsion are decreased. After normalisation of the preload, they immediately return to normal and diastolic untwisting rebounds. These mechanisms are important for understanding the remodelling processes.

Mixed Finite Element Method for a Degenerate Convex Variational Problem from Topology Optimization

The optimal design task of this paper seeks the distribution of two materials of prescribed amounts for maximal torsion stiffness of an infinite bar of a given cross section. This example of relaxation in topology optimization leads to a degenerate convex minimization problem $E\left( v \right):= \int_\Omega \varphi_0\left( \left\lvert\nabla v\right\rvert \right)\operatorname{dx} - \int_\Omega fv\operatorname{dx}\text{for } v \in V:=H^1_0( \Omega )$ with possibly multiple primal solutions u, but with unique stress $\sigma:=\varphi_0'\left( \left\lvert\nabla u\right\rvert \right)\operatorname{sign}\nabla u.$ The mixed finite element method is motivated by the smoothness of the stress variable $\sigma \in H^1_{\operatorname{loc}}( \Omega ; \mathbb R^2)$, while the primal variables are uncontrollable and possibly nonunique. The corresponding nonlinear mixed finite element method is introduced, analyzed, and implemented. The striking result of this paper is a sharp a posteriori error estimation in the dual formulation, while the a posteriori error analysis in the primal problem suffers from the reliability-efficiency gap. An empirical comparison of that primal formulation with the new mixed discretization schemes is intended for uniform and adaptive mesh refinements.