Exact Reduction Research Articles

The competing effects of wall transpiration and stretching on Homann stagnation-point flow

The simultaneous effects of normal transpiration through a radially stretching porous plate beneath Homann stagnation-point flow are considered. The exact similarity reduction of the Navier–Stokes equations depends on the stretching parameter λ and the transpiration parameter μ. Dual solutions are found over a limited range λc<λ<−1 in the case of suction (μ>0) but unique solutions exist for blowing (μ<0). It is shown that the range of dual solutions increases with μ, but a self-similar stability analysis reveals that the lower solution branches are unstable while upper solution branches are stable.

Nonlinear waves in electromigration dispersion in a capillary

We construct exact solutions to an unusual nonlinear advection–diffusion equation arising in the study of Taylor–Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave ansatz. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.

Supervisory control for collision avoidance in vehicular networks using discrete event abstractions

We consider the problem of controlling a set of vehicles at an intersection, in the presence of uncontrolled vehicles and a bounded disturbance. We begin by discretizing the system in space and time to construct a suitable discrete event system (DES) abstraction, and formally define the problem to be solved as that of constructing a supervisor over the discrete state space that is safe (i.e., collision-free), non-deadlocking (i.e., the vehicles all cross the intersection eventually), and maximally permissive with respect to the chosen discretization. We show how to model the uncontrolled vehicles and the disturbance through uncontrollable events of the DES abstraction. We define two types of relations between systems and their abstraction: state reduction and exact state reduction. We prove that, when the abstraction is a state reduction of a continuous system, then we can obtain a safe, non-deadlocking, and maximally permissive memoryless supervisor. This is obtained by translating safety and non-deadlocking specifications to the abstract domain, synthesizing the supervisor in this domain, and finally translating the supervisor back to the concrete domain. We show that, when the abstraction is an exact state reduction, the resulting supervisor will be maximally permissive among the class of all supervisors, not merely memoryless ones. Finally, we provide a customized algorithm and demonstrate its scalability through simulation.

New techniques in the operative treatment of calcaneal fractures

The ideal treatment of displaced intra-articular calcaneal fractures is still controversially discussed. Because of the variable fracture patterns and the vulnerable soft tissue coverage an individual treatment concept is advisable. In order to minimize wound edge necrosis associated with extended lateral approaches, selected fractures may be treated percutaneously or in a less invasive manner while controlling joint reduction via a sinus tarsi approach. Fixation in these cases is achieved with screws, intramedullary locking nails or modified plates that are slid in subcutaneously. A thorough knowledge of the three dimensional calcaneal anatomy and open reduction maneuvers is a prerequisite for good results with less invasive techniques. Early functional follow-up treatment aims at early rehabilitation independent of the kind of fixation. Peripheral fractures of the talus and calcaneus frequently result from subluxation and dislocation at the subtalar and Chopart joints. They are still regularly overlooked and result in painful arthritis if left untreated. If an exact anatomical reduction of these intra-articular fractures is impossible, resection of small fragments is indicated.

Long term surgical treatment outcome of talar body fracture

lObjectiveTalar body fractures are rare and have poor treatment outcome. The purpose of this study is to report the long term surgical treatment outcome of closed talardome fractures. MethodsEight closed talar body fractures,treated by open reduction and internal fixation with small fragment cancellous screws and/or Herbert screws in our level I trauma centre were retrospectively analyzed. Preoperative and postoperative radiographs of the foot (antero-posterior, lateral and oblique views) and ankle (antero-posterior, lateral and mortise views) were obtained. The patients were followed up both radiologically and functionally (foot function index, FFI) after 3 weeks, 6 weeks, 3 months, 6 months and then annually. ResultsThere were five crush fractures and three shear fractures (two sagittal shear and one coronal shear), with average follow-up of 5 years. No early complications were noticed in these patients. Late complications included osteoarthrosis of subtalar/ankle joints in six patients and osteonecrosis of talar body in four patients. On functional assessment, mean FFI after 5 years was 104.63 points and worse outcome was noticed in crush injury and coronal shear fractures. Sagittal shear fractures had a good functional and radiological outcome. ConclusionsLate complications subsequent to surgically treated talar body fractures are inevitable, even though exact reduction and rigid fixation are achieved, thus patients are supposed to be counseled about the adverse outcome. Although crush and coronal shear fractures have poor outcome, sagittal injuries have good prognosis on long term evaluation.

Weighted G1-Multi-Degree Reduction of B´ezier Curves

In this paper, weighted G1-multi-degree reduction of B´ezier curves is considered. The degree reduction of a given B´ezier curve of degree n is used to write it as a B´ezier curve of degree m,m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 - t), t [0, 1] is used with the L2-norm in multidegree reduction with G1-continuity at the end points of the curve. Since we consider boundary conditions this weight function improves approximation in the middle of the curve. Numerical results and comparisons show that the proposed method produces fewer errors and outperform all existing methods.

EFFECT TEMPERATURE IN CHEMICAL SENSING USING TRIPLE STAGE MICRORING RESONATOR

The split-step Fourier technique is used to study the effect of temperature in triple stage microring resonating sensor (TSMRRS). The optical bright soliton beam is used as the probe pulse into the TSMRRS and the effect of temperature variations on various concentrations of glucose in deionize water is investigated. The detection of glucose is measured by intensity variations of output signals from through and drop ports of TSMRRS. The temperature variations cause an exact intensity reduction of glucose concentration in deionize water when the temperature increased by 1 oC. The performance of TSMRRS glucose sensor is improved for temperature range similar with standard room temperature which shows that TSMRRS is suitable candidate for chemical sensing application.

The Conservation of Information, Towards an Axiomatized Modular Modeling Approach to Congestion Control

We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgement rates and delays are mathematically modelled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packet-level simulations demonstrate the accuracy of the proposed model.

Tailoring the Desired Surface Chemistry in Silicon-Based Lithium-Ion Batteries with Electrolyte Additives

The design of safe, high-energy batteries exhibiting prolonged lifetime greatly depends on understanding the surface reactions occurring on the electrode surfaces and the role of the solid electrolyte interphase (SEI) film. Most of the naturally forming SEI films demonstrate undesirable characteristics, such as instability and continuous surface reaction that decrease the capacity of Si-based Li-ion batteries (LIBs). An effective and economic way to modify the surface chemistry in LIBs rather than the Si architecture is by electrolyte additives. The objective of the present study is the examination of the concentration dependence of vinylene carbonate (VC) and fluoroethylene carbonate (FEC) additives on the long-term electrochemical performance of LIBs, as well as the dependence of the SEI formation mechanism on the concentration of the VC and FEC additives. A significant improvement in the cycling performance of Si electrodes can be achieved under operation conditions of optimum VC and FEC concentration. To better understand the additive concentration effect, the reduction mechanisms of VC and FEC were investigated for both Si nanoparticle and Si(100) single crystal working electrodes. Ex-situ ATR-FTIR spectra of Si electrodes for 5% VC additive show a broad peak at a higher wavenumber (1831 cm–1) compared to the EC residual electrolyte (1799 and 1769 cm–1) (Fig. 1). Based on synthesized poly-VC standard spectra, the VC additive reduction compound is assigned to poly-VC or its oligomer, which is consistent with previous reports. However, for Si electrode and FEC additive, the original C=O stretch (1829 and 1802 cm–1) disappears or shifts to a lower wavenumber. The exact reduction product of FEC degradation has not been confirmed yet due to the lack of significant features other than the residual electrolyte. However, it is clear that FEC follows a different reduction path than VC. The reduction path of VC is polymerization with the reduction product remaining a “ring” structure (the C=O peak shifts to a higher wavenumber), whereas the reduction path of FEC is similar to that of ethylene carbonate (EC), leading to a reduction product of open “ring” structure, similar to that produced from EC reduction. More experiments are underway to confirm the different reduction paths of VC and FEC stated above. Acknowledgement This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Freedom CAR and Vehicle Technologies of the U.S. Department of Energy under contract No. DE-AC02-OSCH11231. Figure 1

Applications of Computer-Assisted Navigation for the Minimally Invasive Reduction of Isolated Zygomatic Arch Fractures

Computer-assisted navigation has been widely used in oral and maxillofacial surgery. The purpose of this study was to describe the applications of computer-assisted navigation for the minimally invasive reduction of isolated zygomatic arch fractures. All patients identified as having isolated zygomatic arch fractures presenting to the authors' department from April 2013 through November 2014 were included in this prospective study. Minimally invasive reductions of isolated zygomatic arch fractures were performed on these patients under the guidance of computer-assisted navigation. The reduction status was evaluated by postoperative computed tomography (CT) 1 week after the operation. Postoperative complications and facial contours were evaluated during follow-up. Functional recovery was evaluated by the difference between the preoperative maximum interincisal mouth opening and that at the final follow-up. Twenty-three patients were included in this case series. The operation proceeded well in all patients. Postoperatively, all patients displayed uneventful healing without postoperative complication. Postoperative CT showed exact reduction in all cases. Satisfactory facial contour and functional recovery were observed in all patients. The preoperative maximal mouth opening ranged from 8 to 25 mm, and the maximal mouth opening at the final follow-up ranged from 36 to 42 mm. Computer-assisted navigation can be used not only for guiding zygomatic arch fracture reduction, but also for assessing reduction. Computer-assisted navigation is an effective and minimally invasive technique that can be applied in the reduction of isolated zygomatic arch fractures.

Exact model reduction with delays: closed-form distributions and extensions to fully bi-directional monomolecular reactions

In order to systematically understand the qualitative and quantitative behaviour of chemical reaction networks, scientists must derive and analyse associated mathematical models. However, biochemical systems are often very large, with reactions occurring at multiple time scales, as evidenced by signalling pathways and gene expression kinetics. Owing to the associated computational costs, it is then many times impractical, if not impossible, to solve or simulate these systems with an appropriate level of detail. By consequence, there is a growing interest in developing techniques for the simplification or reduction of complex biochemical systems. Here, we extend our recently presented methodology on exact reduction of linear chains of reactions with delay distributions in two ways. First, we report that it is now possible to deal with fully bi-directional monomolecular systems, including degradations, synthesis and generalized bypass reactions. Second, we provide all derivations of associated delays in analytical, closed form. Both advances have a major impact on further reducing computational costs, while still retaining full accuracy. Thus, we expect our new methodology to respond to current simulation needs in pharmaceutical, chemical and biological research.

Finite element modelling of Coriolis mass flowmeters with arbitrary pipe geometry and unsteady flow conditions

The behaviour of Coriolis mass flowmeters (CMFs) with arbitrary pipe geometry is investigated in this paper regarding the effects of unsteady flow, geometry and damping. Timoshenko׳s beam theory, the finite element method (FEM), Mathworks Matlab and Simulink are used for creating a suitable model. Various physical quantities such as Coriolis, centrifugal and gravitational forces, mass inertia, mass flow, unsteady flow forces, damping and material parameters are considered to increase model precision. Stiffening effects due to fluid deflection are partly neglected in the model. The use of exact finite elements and model reduction via modal transformation results in fast and accurate numerical computation which corresponds well with experimental data. As a consequence, this approach allows further optimization of pipe geometries, actuation positions and concepts, actuation und flow control systems and signal processing concepts without co-simulation.

A Novel Process for Solar Hydrogen Production Based on Water Electrolysis in Alkali Molten Carbonates

High temperature water electrolysis has a tremendous potential in enabling a cost-effective and sustainable production of synthetic fuels like hydrogen by using renewable heat and electricity from concentrating solar thermal (CSP) plants [1]. Most efforts in this research area are currently directed towards investigating solid oxide electrolysis cells (SOECs) based on fuel cell technology [2,3], although this approach is not optimal for integration with CSP plants because of electrolysis temperatures (i.e., above 800°C) significantly exceeding those of most solar heat storage systems. In order to improve thermal matching with current solar thermal fluids, development of electrolysis processes within the 500-600°C range would be a desirable option. In this context, molten salts could be seen as an ideal medium to lower process temperatures with respect to solid oxide electrolyzers since overall ionic conductivity and transport numbers of liquid salts are usually higher than solid-type electrolytes. Recently, alkali molten carbonate salts have gained a return of attention as a promising and attractive electrolyte for electrochemical conversion processes of mineral ores and CO2 gas at moderate temperatures [4,5]. At the same time, water electrolysis in alkali molten carbonates has been recently mentioned as a feasible process [2], although no systematic studies on this process are available in literature. The overall electrolysis reactions can be written as: cathode, H2O+CO2 + 2e = H2+CO3 2- (1)anode, CO3 2- = CO2 +0.5O2 +2e (2) The anode gas mixture made of 33 % O2 + 67% CO2 is ideal for oxy-combustion processes. Thus, a zero CO2 emission system could be realized by integrating a molten carbonate electrolysis with an oxycombustion process. The combined process could enable a CO2 closed-loop recycling scheme with CO2 capture. Part of the post-combustion CO2 could be, in fact, re-injected to the cathode, whereas the excess CO2 could be easily captured.From a mechanistic point of view, the exact cathode reduction reaction is not well understood. Although the cathode reaction can be interpreted in terms of a conventional water reduction process (eq. (1)), there are indications in literature that bicarbonate anions are likely the reactive species rather than dissolved water according to [6]: 2HCO3 - + 2e =H2+2CO3 2- (3) The presence of bicarbonate is possible because, in presence of a water-containing atmosphere, molten carbonates cannot be considered as a pure solvent, but rather as a mixture of three anionic constituents, namely carbonate, bicarbonate and hydroxide ions, according to the following chemical equilibrium: H2O+CO3 2- = HCO3 - + OH- (4) Thermodynamic calculations indicate that bicarbonate concentration is lower than hydroxide, but it is not negligible below 600°C. Initial lab-scale work has confirmed the effective presence of hydrogen as main cathode reaction product in a electrolysis conducted in ternary alkali carbonate eutectic mixture Li2CO3-Na2CO3-K2CO3 (43.5-31.5-25.0 mol %) despite the relatively low values of steady-state current density observed within the 525-600°C range (see Fig.1). Cyclic voltammetry experiments are also underway to study in more detail kinetics and mechanisms of the cathodic reaction, which is an essential aspect for interpreting and modeling the overall electrolysis process. Detailed results of these exploratory investigations will be shown at the time of Conference.

Electrochemical Synthesis of Graphene-Metal Oxide Heterostructure for Resistive Random Access Memory

Graphene has a lot of merits for many engineering applications due to its unique physical, electrical and chemical properties [1-2]. Recently, a soft chemical reduction process of graphene oxide has been reported as a very efficient and safe method to fabricate a pure graphene film [3]. Also, the graphene-metal hybrids are fabricated by electrochemical methods in aqueous solution [4]. However, in spite of aforementioned enormous interests and efforts, the reduction mechanisms of graphene oxide and graphene-metal hybrid during electro-deposition are still unclear and controversial.In this study, the electrochemical characteristics of reduction phenomena of graphene oxide and graphen-metal oxide hybrids are investigated in detail. To investigate the exact reduction potential of graphene oxide and a variety of graphene-metal oxide hybrids in aqueous solution, the electrochemical analyses are accompanied by a cyclic voltammetry. The graphene-metal oxide hybrid film was electrochemically deposited on the conductive substrates using the cyclic co-electrodeposition method.Furthermore, we have confirmed that the electrochemically formed hybrid film could be used for a Resistive Random Access Memory(RRAM) device through the test of resistive switching behavior of this hybrid films. This novel fabrication method of switching layer will provide several advantages for nonvolatile memory, such as low-power consumption, fast switching speed, and more simple and safe fabrication process.

Finite mechanical proxies for a class of reducible continuum systems

We present the exact finite reduction of a class ofnonlinearly perturbed wave equations --typically, a non-linear elastic string-- based on the Amann--Conley--Zehnder paradigm.By solving an inverse eigenvalue problem,we establish an equivalence between the spectral finite description derived from A--C--Z and a discrete mechanical model, a well definite finite spring--mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.

Reduction mechanisms of additives on Si anodes of Li-ion batteries.

Solid-electrolyte interphase (SEI) layers are films deposited on the surface of Li-ion battery electrodes during battery charge and discharge processes. They are due to electrochemical instability of the electrolyte which causes electron transfer from (to) the anode (cathode) surfaces. The films could have a protective passivating role and therefore understanding the detailed reduction (oxidation) processes is essential. Here density functional theory and ab initio molecular dynamics simulations are used to investigate the reduction mechanisms of vinylene carbonate (VC) and fluoroethylene carbonate (FEC) on lithiated silicon surfaces. These species are frequently used as "additives" to improve the SEI properties. It is found that on lithiated Si anodes (with low to intermediate degrees of lithiation) VC may be reduced via a 2e(-) mechanism yielding an opened VC(2-) anion. At higher degrees of lithiation, such a species receives two extra electrons from the surface resulting in an adsorbed CO(2-)(ads) anion and a radical anion ˙OC2H2O(2-). Additionally, in agreement with experimental observations, it is shown that CO2 can be generated from reaction of VC with the CO3(2-)anion, a product of the reduction of the main solvent, ethylene carbonate (EC). On the other hand, FEC reduction on LixSiy surfaces is found to be independent of the degree of lithiation, and occurs through three mechanisms. One of them leads to an adsorbed VC(2-) anion upon release from the FEC molecule and adsorption on the surface of F(-) and one H atom. Thus in some cases, the reduction of FEC may lead to the exact same reduction products as that of VC, which explains similarities in SEI layers formed in the presence of these additives. However, FEC may be reduced via two other multi-electron transfer mechanisms that result in formation of either CO2(2-), F(-), and ˙CH2CHO(-) or CO(2-), F(-), and ˙OCH2CHO(-). These alternative reduction products may oligomerize and form SEI layers with different components than those formed in the presence of VC. In all cases, FEC reduction also leads to formation of LiF moieties on the anode surface, in agreement with reported experimental data. The crucial role of the surface in each of these mechanisms is thoroughly explained.

Study of tension band wiring in management of fracture of patella in tertiary care hospital in Vadodara

Background: Patella is the largest sesamoid bone in the body and is situated in front of the knee joint. Patellar fractures are encountered very frequently in day to day clinical practice due to increase in accidents. Objective: Present study is carried out to know the role of tension band wiring in management of fracture of patella. Material and Methods: This study was conducted during April 2003 to July 2005. All the patients were following trauma and all were treated, followed up and studied according to a fixed protocol. History of all patients was taken and local, general as well as radiological examinations were done. After confirmation of diagnosis patients were admitted with posterior cylindrical slab. After that preoperative evaluation was done and one the patient was fit for surgery, he was operated on appropriate day. Fracture fragments were reduced and then fixed with k-wire. Reduction was confirmed on IITV (image intensification Television). Result: In the patients after tension band wire insertion, 120-130 degree flexion was present in 50% patients, quadriceps strength was equivalent to opposite limb in 90% patients, difficulty in sitting cross legged /squatting was present in 50% patients, change of work was observed in 25% patients, infection was observed in 5% patients, non union or mal union was not observed in any patient. Conclusion: Tension band wiring produces good results when there is minimal or no communication and exact reduction of articular surface is achieved. Our results are comparable with some of studies conducted in India and abroad. Key words: Tension band wiring, k-wire, fracture of patella

Syndesmotic Malreduction after Ankle ORIF; Is Radiography Sufficient?

Ankle fractures, especially those resulting from external rotation mechanisms are associated with injury to the distal tibiofibular syndesmosis. Some authors have recommended performing CT scanning after open ankle surgery to evaluate the reduction of syndesmosis. In this current study, we aimed to investigate the sensitivity of plain radiography in diagnosing syndesmosis malreduction after open reduction and internal fixation (ORIF) in patients with ankle fractures. Thirty patients with ankle fractures participated in this prospective study. ORIFs were performed with respect to all of the technical guidelines shown in orthopedic literature for exact syndesmosis reduction, such as fibular length and proper settings. In the operating room, plain radiography was performed in anteroposterior, mortise and lateral views to assess whether syndesmosis was malreduced. If malreduction was detected, the patient was revised. As the gold standard, patients underwent postoperative bilateral CT scanning to investigate the syndesmosis reduction which was then compared to the healthy side. Finally, the sensitivity of plain radiography in the diagnosis of syndesmosis malreduction was determined by comparing this method to CT scanning. In both of the methods we did not find any patient with syndesmosis malreduction. Hence, the sensitivity of plain radiography was determined 100%. Based on our findings, there is no need to perform CT scanning to evaluate syndesmosis reduction after ankle ORIF in patients with ankle fractures. Plain radiography is sufficient and has satisfactory sensitivity in these patients.

Efficient model order reduction for dynamic systems with local nonlinearities

Abstract In the nonlinear structural analysis, the nonlinear effects are commonly localized and the rest of the structure behaves in a linear manner. Considering this fact, this research work proposes a harmonic balance solution in order to determine the nonlinear response of the structures. The solution is simplified by using an exact dynamic reduction along with the modal expansion technique. This novel approach, which is applicable to both discrete and continuous systems, converts the system equations of motion in each harmonic to a small set of nonlinear algebraic equations. The full set of system equations is reduced to a discrete system with a few generalized degrees of freedom (DOFs) confined to the localized nonlinear regions. The resultant reduced order model is shown to be accurate enough for determining the periodic response. To demonstrate the capability of the proposed method, numerical case studies for continuous and discrete systems, including systems with internal resonance, have been studied and the outcomes are validated with benchmark studies. In addition, the method is applied in the identification process of an experimental test setup with unknown frictional support parameters, and the results are presented and discussed.

Characteristic and treatment of ankle fracture combined with Tillaux-Chaput and Voikmann frac-tures

Objective To explore the clinical characteristics and operative methods of the ankle fracture combined with Tillaux-Chaput and Volkmann fractures. Methods The data of 15 patients who were suffered the ankle fracture combined with the simultaneous fractures of Tillaux-Chaput and Volkmann be- tween September 2005 and January 2012 were analyzed. There were 8 males and 7 females with an average age of 27.3 years （range, 16-57 years）. All had medial malleolar and fibular fracture with Tillaux-Chaput and Volkmann tubercle avulsed fracture. X-ray film shows that there were 8 cases in which the patients had Tillaux-Chaput fracture, among whom 7 were diagnosed by CT scan. Classified by Lauge-Hansen system, an- kle fracture could be divided into pronation-external rotation type in 4 cases, and pronation-abduction type in 11 cases. The fracture of fibula and the Volkmann tubercle were treated through the posterolateral approach. The fibular fracture was fixed with plate. The medial malleolar fracture was explored from medial curve ap- proach. Tillaux-Chaput fracture was treated by the microtubule cut. All patients were assessed with the ankle hindfoot clinical rating system of the American Orthopaedic Foot and Ankle Society （AOFAS）. Results All patients were followed up for 8-20 months （average, 12.5 months）. The fracture healed 12-36 weeks later in all the 15 patients, with an average of 23.5 weeks. Twelve patients walked normally and 3 with mild claudi- cation in the last follow-up. The AOFAS score was average 85.4 points, 9 were excellent, 4 were good, 2 were fair, with the good-excellent rate being 86.7% （13/15）. The movement of ankle joint limited in 3 pa- tients, tenderness occurred when weight bearing in 3 patients. Conclusion The ankle fracture include the simultaneous fractures of Til]aux-Chaput and Volkmann were more seen in the type of pronation-abduction. It is often misdiagnosis by the photograph; CT scan should be helpful to find the fracture fragments. The exact reduction and stable fixation were needed in the treatment of the ankle fracture combined with Tillaux-Cha- put and Volkmann fractures. Inferior tibia fibular screw was not routinely used in this fracture. Key words: Ankle joint; Fractures; Fracture fixation, internal