Double Bundles Research Articles

The precision of technical aspects in the minimally invasive Broström–Gould procedure: a cadaveric anatomical study

BackgroundA comprehensive understanding of the anatomy of the anterolateral ankle joint and its interrelationships is essential for advancing the development of minimally invasive Broström–Gould procedure, thereby enhancing surgical efficacy and minimizing postoperative complications.MethodsTen fresh human ankle specimens were dissected to observe the shape and trajectory of the lateral bundle of the inferior extensor retinaculum (IER) and its relationship with the deep fascia. To observe the relationship between the ankle capsule and the anterior talofibular ligament (ATFL). The center of the insertion point of ATFL at the lateral malleolus was used as the reference point. The vertical distance from the reference point to the fibula tip, the horizontal distance from the reference point to the lateral branch of the superficial peroneal nerve, the shortest distance from the reference point to IER, the narrowest width of the IER, the angle between the line connecting the shortest distance from the reference point to the IER and the longitudinal axis of the fibula were measured. The tension and elasticity of ATFL was understood. To describe the minimally invasive Broström–Gould procedure according to the anatomical characteristics of the anterolateral ankle joint.ResultsAmong the 10 cases, 8 cases (80%) had double bundles of ATFL, 2 cases (20%) had single bundle of ATFL, and no outer superior oblique bundle was observed in IER. The vertical distance from the reference point to the fibula tip was 1.2 ± 0.3 (range 1.1–1.3) mm. The shortest distance from the reference point to the level of the superficial peroneal branch was 28.2 ± 4.3 (range 24.5–32.4) mm. The shortest distance from the reference point to IER was 12.5 ± 0.6 (range 12.1–12.9) mm, and the width of IER at this point was 7.2 ± 0.3 (range 7.0–7.6) mm. The angle between the line connecting the shortest distance from the reference point to the IER and the longitudinal axis of the fibula was about 60° ± 2.8° (range 58.1°–62.1°) mm. The space between the anterolateral deep fascia of the ankle joint and the ankle capsule is very small, and only a few fat granules are separated between them. The ATFL is largely fused to the ankle capsule. The ATFL exhibited high tension and poor elasticity after traction with the probe hook.ConclusionsThe results showed that in the minimally invasive Broström–Gould technique for lateral ankle stabilization, the Broström procedure actually sutured the insertion of the ATFL together with the ankle capsule to the anterior edge of the lateral malleolus. In the Gould procedure, the deep fascia was mostly reinforced with the ankle capsule. The minimum suture span was obtained when the Gould suture needle direction was at an Angle of 60° to the longitudinal axis of the fibula.

The Influence of Glass Fiber and Copper Wire z-Binder on the Mechanical Properties of 3D Woven Polymeric Composites

AbstractThree-dimensional composites (3D) have potential applications in various fields due to their enhanced properties compared to conventional two-dimensional composites (2D). This study investigates the effect of different volumes of z-binder made from copper wire and E-glass fiber on the mechanical properties of 3D woven polymeric composites. The tensile, flexural, and fracture toughness behavior of four types of 3D orthogonal woven composites were studied in addition to a comparative 2D composite. The creation of the 3D orthogonal single-ply fabrics involved weaving z-binders using two different copper wire diameters, single fiber bundles, and double fiber bundles, each combined with four layers of woven E-glass fiber. The consolidation process for both 2D fabric and single-fabric 3D woven composites was executed using the hand lay-up technique. The results showed that most 3D woven composites outperformed 2D composites in terms of fracture toughness (stress intensity factor KIC and energy release rate GIC) and flexural strain. However, a decrease in flexural strength and tensile properties was observed for all 3D composites. The specimen with a small copper diameter had the smallest decrease of 5% in tensile strength. Furthermore, a decrease of 9% and 21% was attained by reinforcing with double and single glass fiber bundle z-binders, respectively, as compared with 2D composites. The highest enhancement of 92.5% in flexural failure strain was attained with double glass fiber bundles of z-binder. The maximum improvement in KIC fracture toughness, reaching 126% and 101.5%, was observed in specimens with a single glass fiber bundle z-binder and those with a large copper wire diameter, respectively.

A geometrisation of [formula omitted]-manifolds

This paper proposes a geometrisation of N-manifolds of degree n as n-fold vector bundles equipped with a (signed) Sn-symmetry. More precisely, it proves an equivalence between the categories of [n]-manifolds and the category of (signed) symmetric n-fold vector bundles, by finding that symmetric n-fold vector bundle cocycles and [n]-manifold cocycles are identical.This extends the already known equivalences of [1]-manifolds with vector bundles, and of [2]-manifolds with involutive double vector bundles, where the involution is understood as an S2-action.

Natural affinors and torsion of connections on Weil like functors on double vector bundles

We describe completely all natural affinors on product preserving gauge bundle functors on double vector bundles. Next, we study torsion of double-linear connections.

Modules and representations up to homotopy of Lie n-algebroids

This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general nin {mathbb {N}}. The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and coadjoint representations up to homotopy are explained. In particular, the case of Lie 2-algebroids is analysed in detail. The compatibility of a Poisson bracket with the homological vector field of a Lie n-algebroid is shown to be equivalent to a morphism from the coadjoint module to the adjoint module, leading to an alternative characterisation of non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie n-algebroid is computed explicitly in terms of splittings, and representations up to homotopy of Lie n-algebroids are used to encode decomposed VB-Lie n-algebroid structures on double vector bundles.

Description of jet like functors on double vector bundles by means of admissible systems

Description of jet like functors on double vector bundles by means of admissible systems

Quotients of double vector bundles and multigraded bundles

<p style='text-indent:20px;'>We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for weighted submanifolds, as well as for pairs of submanifolds with clean intersection.</p>

Relationship between inferior fascicle of anterior talofibular ligament and articular capsule in lateral ankle ligament complex.

The lateral ankle ligament complex (LALC) is composed of anterior talofibular (ATFL), calcaneofibular (CFL), and posterior talofibular (PTFL) ligaments, all of which have a connection/continuous fiber. However, the structural link between the LALC and the articular capsule remains unknown. The goal of our study was to determine the connection between ATFL's inferior fascicle and the articular capsule. In this study, we utilized 84 formalin-fixed ankles to elucidate the structure of LALC. Between ATFL and CFL, the bundle number of ATFL and arciform fiber was investigated. The specimens were decalcified and sectioned coronally using a freezing microtome, in the case of double bundles of ATFL, to study the connection between the inferior fascicle of ATFL and the articular capsule. ATFL had a single (25%), double (74%), and triple (1%) bundle number, respectively. The arciform fiber connecting the ATFL and the CFL was found in the superficial layer of all ankles (100%). There were two types of relationships between the inferior fascicle of ATFL and the articular capsule: 36 ankles (58%) were extracapsular, and 26 of 62 ankles (42%) were integrated with the inferior-lateral articular capsule. There are two kinds of relationships between the inferior fascicle of the ATFL and the articular capsule: extracapsular and integrated-capsular. The inferior fascicle of ATFL has a variant and integrated-capsular type is reinforced inferior-lateral articular capsule and enters the joint to form continuous fibers with PTFL, making LALC. These anatomical findings are helpful in ultrasonography diagnosis and arthroscopic ankle surgery.

Complete lifting of double-linear semi-basic tangent valued forms to Weil like functors on double vector bundles

Complete lifting of double-linear semi-basic tangent valued forms to Weil like functors on double vector bundles

Double principal bundles

We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and connections in DPBs are investigated.

Effectiveness comparison of partial versus intact posterior cruciate ligament-retaining in total knee arthroplasty with cruciate-retaining prosthesis

To compare the effectiveness of partial versus intact posterior cruciate ligament (PCL)-retaining in total knee arthroplasty (TKA) with cruciate-retaining (CR) prosthesis. A total of 200 patients with osteoarthritis, who met the selection criteria and proposed unilateral TKA with CR prosthesis, were included in the study and randomly assigned into two groups ( n=100). The patients were treated with intact retention of the double bundles of PCL in intact group and with partial resection of the anterior lateral bundle of PCL and the anterior bone island at the time of intraoperative tibial osteotomy in partial group. Patients with lost follow-up and re-fracture were excluded, and 84 cases in partial group and 88 cases in intact group were included in the final study. There was no significant difference between the two groups ( P>0.05) in terms of gender, age, body mass index, course and grade of osteoarthritis, preoperative varus deformity of knee joint, flexion contracture, range of motion, clinical and functional scores of Knee Society Score (KSS). The operation time, wound drainage volume during 24 hours after operation, visual analogue scale (VAS) score at 24 hours after operation, range of motion of knee joint, clinical and functional scores of KSS, and the anteroposterior displacement of knee joint at 30° and 90° flexion positions were compared between the two groups. There was no significant difference between the two groups in operation time, wound drainage volume during 24 hours after operation, and VAS score at 24 hours after operation ( P>0.05). Patients in both groups were followed up after operation. The follow-up time was 25-40 months (mean, 30.2 months) in intact group and 24-40 months (mean, 31.8 months) in partial group. There was no significant difference in the range of motion and clinical scores of KSS between the two groups at 6, 12, and 24 months after operation ( P>0.05). The functional scores of KSS were significantly higher in intact group than in partial group ( P<0.05). There was no significant difference between the two groups in the anteroposterior displacement of knee joints at 30° flexion position at 6, 12, and 24 months after operation ( P>0.05). When the knee was at 90° flexion position, there was no significant difference between the two groups at 6 and 12 months after operation ( P>0.05), but the intact group was significantly smaller than partial group at 24 months after operation ( P<0.05). Postoperative incision continued exudation in 4 patients (2 cases of partial group and 2 cases of intact group), and incision debridement in 2 patients (1 case of partial group and 1 case of intact group). No prosthesis loosening, excessive wear, or dislocation of gasket was found during follow-up. The double bundle of PCL plays an equally important role in maintaining the stability of the knee joint, and the integrity of PCL should be kept as much as possible when TKA is performed with CR prosthesis.

Morphological characteristics of the plantar calcaneocuboid ligaments

BackgroundThe aim of this study was to clarify the differences in morphological features between the long plantar ligament (LPL) and the short plantar ligament (SPL).MethodsThis investigation examined 50 legs from 25 Japanese cadavers. The LPL and SPL of each leg were classified into one of three types based on the shape and number of fiber bundles. Then, fiber bundle length, fiber bundle width, and fiber bundle thickness were measured.ResultsThe LPL was rectangular in shape (Type I) in 12%, hourglass shape (Type II) in 62%, and triangular in shape (Type III) in 26%. The SPL was a single fiber bundle (Type I-a) in 26%, a surface fiber bundle and a deep fiber bundle (Type I-b) in 60%, and a surface fiber bundle (medial and lateral) and a deep fiber bundle (Type II) in 14%. Regarding the morphological characteristics, there were no significant differences among the types in the LPL, but there were differences between types and between surface and deep fiber bundles in the SPL.ConclusionsFor the LPL, the hourglass shape is the most common type. However, there appeared to be no functional difference due to the difference in the shape of the LPL, since there were no significant differences among the types in the LPL. For the SPL, there were types of single, double and triple fiber bundles; there may be functional differences based on the number of fiber bundles and between superficial and deep fibers.

МІКРОМОРФОЛОГІЯ ТА АНАТОМІЯ КВІТКИ LEUCOJUM AESTIVUM L. (AMARYLLIDACEAE J. ST.-HIL.)

In the gynoecium of L. aestivum there are synascidiate, hemisynascidiate, symplicate, and asymplicate vertical zones. The longest zone is the fertile hemisynascidiate zone and the shortest is the synascidiate zone in the ovary. It was discovered that in L. aestivum the peduncle consists of 12 vascular bundles, which are reorganized into two circles of bundles, the outer with massive leading bundles, departing as dorsal bundles of perianth, traces of perianth tepals and septal bundles of carpels and inner circle of bundles over the nests are divided into three groups of ventral carpel bundles are lined up on four, which are located in the center of the ovary and providing nutrition to the ovules. Dorsal carpels bundles are double. Above the locule, ventral bundles of the carpel, as well as the double septal bundles, merge with the dorsal bundles and form a dorsal vein. The outer tepals of the simple perianth have nine vascular traces, and the inner tepals of the perianth have eight vascular traces. Traces of stamens are single-bundle, formed from traces of perianth tepals. The ovary has features of the early stages of fruit morphogenesis and adaptation to disclosure, such as differentiation of mesocarp and endocarp cells, double dorsal bundles of carpels. Structural flower features related to pollen proposal as reward pollinators. Since ovary is a structural basis of the fruit, histological ovary wall differentiation reflects the features of the subsequent morphogenesis of the fruit.

Competitive Harm from Vertical Mergers

The 2020 Vertical Merger Guidelines produced by the antitrust enforcement agencies introduce a nontechnical application of bargaining theory into the assessment of competitive effects from vertical acquisitions. The economics of such bargaining is complex and can produce skepticism among judges, who might regard its mathematics as overly technical, its game theory as excessively theoretical or speculative, or its assumptions as unrealistic. However, we have been there before. The introduction of concentration indexes in the Merger Guidelines was initially met with skepticism but gradually they were accepted as judges became more comfortable with them. The same thing very largely happened again when unilateral effects theories of mergers were introduced in the 1990s. The bargaining theory that drives much of vertical merger analysis today has much in common with the theory of unilateral effects. In any event, the value of a particular model depends not on its verisimilitude but rather on its testability. The theory that relates a concentration index to the risk of competitive harm from horizontal mergers involves as much conjecture as does the bargaining theory that the Nash model for vertical mergers contemplates. The concentration thresholds in the Horizontal Merger Guidelines capture a rough generalization about a large number of collusive or oligopolistic strategies, some of which are not consistent with each other. What they share in common is belief in a link between the number of firms in a market, the increase in concentration that results from the merger, and the extent of higher prices. Double marginalization as a vertical merger defense occurs when two bargaining firms each have market power but are unable to coordinate their output. Each takes a markup without considering the other, and aggregate markups are too high. Both firms as well as their purchasers would be better off if they could coordinate better. In the AT&T/Time-Warner case the defendants argued that after the merger TW would not coordinate with AT&T but would set its prices as if the merger had not occurred. In that case the merger would not have eliminated double marginalization either. The debate over the elimination of double marginalization bundles two themes that Ronald Coase developed in his two most well-known articles, The Nature of the Firm and The Problem of Social Cost. The first argued that the boundaries of a firm are determined by the firm’s continuous search to procure inputs in the most cost effective way. The second argued that two traders in a well-functioning market will achieve the joint-maximizing solution. This dual relationship is too often ignored. Anti-interventionists rely heavily on Coasean arguments that unless high transaction costs get in the way firms will bargain to joint maximizing results. If that is true, then double marginalization will rarely provide a defense to a vertical merger. The law of vertical mergers deals largely with firms that transact with one another routinely, in legally enforceable buy-sell relationships. By contrast, the actors who appear in The Problem of Social Cost do not bargain with each other regularly. In a well functioning vertical market durable double marginalization should be rare.

Advanced structural characterisation of agar-based hydrogels: Rheological and small angle scattering studies

Agar-based extracts from Gelidium sesquipedale were generated by heat and combined heat-sonication, with and without the application of alkali pre-treatment. Pre-treatment yielded extracts with greater agar contents; however, it produced partial degradation of the agar, reducing its molecular weight. Sonication produced extracts with lower agar contents and decreased molecular weights. A gelation mechanism is proposed based on the rheological and small angle scattering characterization of the extracts. The formation of strong hydrogels upon cooling was caused by the association of agarose chains into double helices and bundles, the sizes of which depended on the agar purity and molecular weight. These different arrangements at the molecular scale consequently affected the mechanical performance of the obtained hydrogels. Heating of the hydrogels produced a gradual disruption of the bundles; weaker or smaller bundles were formed upon subsequent cooling, suggesting that the process was not completely reversible.

The Weil Algebra of a Double Lie Algebroid

Abstract Given a double vector bundle $D\to M$, we define a bigraded bundle of algebras $W(D)\to M$ called the “Weil algebra bundle”. The space ${\mathcal{W}}(D)$ of sections of this algebra bundle ”realizes” the algebra of functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebra bundles of $D$ and those of the double vector bundles $D^{\prime},\ D^{\prime\prime}$ obtained from $D$ by duality operations. We show that ${\mathcal{V}\mathcal{B}}$-algebroid structures on $D$ are equivalent to horizontal or vertical differentials on two of the Weil algebras and a Gerstenhaber bracket on the 3rd. Furthermore, Mackenzie’s definition of a double Lie algebroid is equivalent to compatibilities between two such structures on any one of the three Weil algebras. In particular, we obtain a ”classical” version of Voronov’s result characterizing double Lie algebroid structures. In the case that $D=TA$ is the tangent prolongation of a Lie algebroid, we find that ${\mathcal{W}}(D)$ is the Weil algebra of the Lie algebroid, as defined by Mehta and Abad–Crainic. We show that the deformation complex of Lie algebroids, the theory of IM forms and IM multi-vector fields, and 2-term representations up to homotopy all have natural interpretations in terms of our Weil algebras.

Numerical study of heat transfer characteristics and friction factor for staggered circular and drop-shaped double tubes bundles

Numerical study of heat transfer characteristics and friction factor for staggered circular and drop-shaped double tubes bundles

Effect of EndoButton double-bundle reconstruction of medial patellofemoral ligament in the treatment of recurrent patellar dislocation

Objective To investigate the recovery of knee joint function in patients with recurrent patellar dislocation treated by reconstruction of medial patellofemoral ligament with EndoButton double bundles. Methods A retrospective analysis was performed for 26 patients with recurrent patellar islocation who were treated in The Second Hospital of Tangshan from February 2014 to July 2016, with a total of 26 knees, aged 14-29 years.All patients underwent medial patellofemoral ligament reconstruction with autologous semitendinosus muscle.Double tunnel technique was used in medial patella and single tunnel technique was used in femoral side.Twenty-four patients were followed up for 12 to 24 months.The recovery of knee joint function was evaluated by Kujala score, Lysholm score, patellar fitness angle and patellar tilt angle before and after treatment. Results None of the follow-up patients had dislocation again, and the fear test was negative.The preoperative Kujala score and Lysholm score were (59.67±5.28) and (61.75±5.45) respectively.The corresponding scores at the last follow-up were (87.21±4.21) and (90.13±2.47). There were significant differences between the two scores (t=-19.98, -23.24, all P <0.01). The patellar fit angle changed from (23.17±3.63)degrees before operation to (14.17±2.01)degrees after operation.There was significant difference between the two scores.(t=10.62, P<0.01); Patellar tilt angle changed from preoperative (18.33±3.92)degree to postoperative (2.45±1.10)degree, the difference was significant (t=19.10, <0.01). Conclusion EndoButton double-bundle reconstruction of medial patellofemoral ligament is effective in the treatment of patellar dislocation with satisfactory recovery of knee joint function. Key words: Recurrent patellar dislocation; Medial patellofemoral ligament; Reconstruction; Knee joint function

Lifting double linear vector fields to Weil like functors on double vector bundles

AbstractThe complete description is given of the product preserving gauge bundle functors F on the category of double vector bundles in terms of the ‐bilinear maps , where are Weil algebras and are finite dimensional (over ) ‐modules. Then the so‐called “iteration” problem is solved (i.e. by means of and is computed). That any two product preserving gauge bundle functors on commute is derived. All gauge natural operators lifting double linear vector fields to product preserving gauge bundle functors F are completely described.

From modelling of systems with constraints to generalized geometry and back to numerics

AbstractIn this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints – we recall the mathematical construction in the context of so called implicit Lagrangian systems. We explain how they can be used to produce new numerical methods, that we call Dirac integrators.On a test example of a simple pendulum in a gravity field we compare the Dirac integrators with classical explicit and implicit methods, we pay special attention to conservation of constrains. Then, on a more advanced example of the Ziegler‐type system we show that the choice of numerical methods can indeed affect the conclusions of qualitative analysis of the dynamics of mechanical systems. We also tell why we think that Dirac integrators are appropriate for this kind of systems by explaining the relation with the notions of geometric degree of non‐conservativity and kinematic structural stability.