Experimental Investigation of Rotating Instability in an Axial Compressor with a Steady Swirl Distortion Inlet

In this paper, an experimental study was carried out on the rotating instability in an axial compressor subjected to inlet steady paired swirl distortion. In order to deepen the understanding of the rotating stall mechanism under inlet steady paired swirl distortion, the dynamic-wall static pressure near the rotor tip was monitored to characterize the flow in the rotor tip region at different circumferential stations. In the experiment, the dynamic characteristics of the rotor tip flow field at a stable operating point and during the process from the stable point to complete stall were measured. The results indicated that for the compressor with a 2 mm rotor tip clearance, the inlet paired swirl distortion induced rotating instability (RI) near the stall point, causing the compressor to enter stall in advance. Compared with the RI intensity of the clean inlet, the distortion with a swirling blade stagger angle (αst) of ±20° increased the RI intensity up to 69.8%, while for αst equal to ±40°, the RI intensity increased at most by 135.8%. As the rotor tip clearance increased to 3 mm, the co-rotating swirl in the paired swirl distortion inhibited the appearance of RI, while the counter-rotating part aggravated the development of RI. At the beginning, the process of the compressor rotating stall involved the alternation of short-scale disturbance and long-scale disturbance. The co-rotating swirl weakened the perturbation propagated from the counter-rotating swirl sector. Once the inhibition was no longer present, the short-scale disturbance rapidly developed into a long-scale disturbance and then entered the rotating stall.

Dynamics analysis of a gyrostat system with intermittent forcing

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

Analysis of long-term strategies of riparian countries in transboundary river basins

Transboundary river basins give rise to complex water-sharing decision making that can be analyzed as a game in the sense of dynamic game theory, as done in this work. The sharing of transboundary water resources depends on the long-term shifting interactions between upstream and downstream countries, which has received limited research attention in the past. The water-sharing strategy of a riparian country depends on the strategies of other countries over time. This paper presents an evolutionary game method to analyze the long-term water-sharing strategies of countries encompassing transboundary river basins over time. The method analyzes the evolutionary strategies of riparian countries and investigates evolutionary stable strategies (ESSs) considering the payoff matrix. The evolutionary game method is applied to a river basin shared by three countries assuming two types of benefits and one type of cost to countries as decision variables of a game that reflects water use, economic and political gains, and socio-economic losses of countries. Numerical examples illustrate the strategies resulting from the evolutionary game processes and the role of several parameters on the interaction between riparian countries. The countries’ strategies are analyzed for several levels of benefits and costs, and the convergence of the strategies to a stable point is assessed. Results demonstrate the role that the upstream country’s potential benefits and the cost of conflict (i.e., non-cooperation) to other countries has on reaching a stable point in the game. This work’s results show the potential benefit to the upstream country under cooperative strategy must exceed its benefits from water use under non-cooperative strategy to gain the full stable cooperation of downstream countries. This work provides a method to resolve water-sharing strategies by countries sharing transboundary river basins and to evaluate the implications of cooperation or non-cooperation.

Crossed products of operator spaces and applications to Harmonic Analysis of non commutative groups

Μελετάμε τα σταυρωτά γινόμενα που προκύπτουν από δράσεις τοπικά συμπαγών ομάδων σε δυϊκούς χώρους τελεστών, τα οποία γενικεύουν την κλασική κατασκευή του σταυρωτού γινομένου για δράσεις ομάδων σε άλγεβρες von Neumann. Οι μέθοδος μας στηρίζεται στις έννοιες των αλγεβρών Hopf-von Neumann και comodules, καθώς μας παρέχουν ένα φυσιολογικό πλαίσιο μελέτης φαινομένων δυϊσμού όσον αφορά δράσεις εν γένει μη αβελιανών τοπικά συμπαγών ομάδων. Παρακάτω, ακολουθεί μια σύντομη περίληψη των κυρίων αποτελεσμάτων αυτής της διατριβής.Το πρώτο κεφάλαιο αποτελεί εισαγωγή του απαραίτητου μαθηματικού υποβάθρου για την ανάπτυξη της γενικής θεωρίας ακολούθως. Συγκεκριμένα, παραθέτουμε τους βασικούς ορισμούς και ιδιότητες αναφορικά με (δυϊκούς) χώρους τελεστών και τανυστικά γινόμενα χώρων τελεστών, την έννοια της stable point-w*-σύγκλισης και τις βασικές άλγεβρες von Neumann (και Banach) που σχετίζονται με τοπικά συμπαγείς ομάδες.Στο δεύτερο κεφάλαιο, ασχολούμαστε με άλγεβρες Hopf-von Neumann και comodules τα οποία είναι και δυϊκοί χώροι τελεστών. Συγκεκριμένα, μελετάμε τις έννοιες saturated και non-degenerate comodules μιας γενικής άλγεβρας Hopf-von Neumann, καθώς και τις μεταξύ τους σχέσεις. Για παράδειγμα, αποδεικνύουμε ότι αν κάθε comodule μιας άλγεβρας Hopf-von Neumann είναι non-degenerate, τότε κάθε comodule αυτής είναι και saturated. Επίσης, δείχνουμε ότι η τελευταία συνθήκη, δηλαδή ότι μια άλγεβρα Hopf-von Neumann έχει μόνο saturated comodules (η οποία είναι εξ ορισμού αλγεβρικού χαρακτήρα), είναι ισοδύναμη με διάφορες συνθήκες προσέγγισης. Ως εφαρμογή, αποδεικνύουμε ότι μια τοπικά συμπαγής ομάδα G έχει την προσεγγιστική ιδιότητα (AP) κατά Haagerup και Kraus αν και μόνο αν κάθε saturated comodule της άλγεβρας von Neumann L(G) της ομάδας είναι non-degenerate.Στο τρίτο κεφάλαιο, μελετώνται το χωρικό και το Fubini σταυρωτό γινόμενο για δράσεις ομάδων σε δυϊκούς χώρους τελεστών, ενώ εξετάζεται και η φυσιολογική δομή comodule (δυϊκές δράσεις) με την οποία εφοδιάζονται. Αυτά τα δύο σταυρωτά γινόμενα συμπίπτουν για δράσεις ομάδων πάνω σε άλγεβρες von Neumann από το κλασικό θεώρημα Digernes-Takesaki. Ωστόσο, ενδέχεται να διαφέρουν για αυθαίρετους δυϊκούς χώρους τελεστών. Xρησιμοποιώντας θεωρία δυϊσμού για δράσεις και την γενική θεωρία των comodules, αποδεικνύουμε ότι το Fubini σταυρωτό γινόμενο για την δράση μιας ομάδας είναι το μικρότερο saturated comodule που περιέχει το αντίστοιχο χωρικό σταυρωτό γινόμενο, ενώ το δεύτερο είναι το μεγαλύτερο non-degenerate subcomodule του πρώτου. Επομένως, από τον προηγούμενο χαρακτηρισμό των ομάδων με την AP, παίρνουμε το κεντρικό μας θεώρημα, σύμφωνα με το οποίο μια τοπικά συμπαγής ομάδα G έχει την AP αν και μόνο αν το χωρικό και το Fubini σταυρωτό γινόμενο συμπίπτουν για κάθε G-δράση σε οποιονδήποτε δυϊκό χώρο τελεστών. Αυτό βελτιώνει ένα πρόσφατο αποτέλεσμα των Crann και Neufang.Τέλος, στο τελευταίο κεφάλαιο, εφαρμόζοντας την γενική θεωρία παίρνουμε μια από εννοιολογικής άποψης καλύτερη προσέγγιση ορισμένων κλάσεων διπρότυπων πάνω από τις άλγεβρες von Neumann μιας ομάδας, τα οποία αναπαρίστανται ως σταυρωτά γινόμενα δυϊκών χώρων τελεστών που δεν είναι κατ' ανάγκη άλγεβρες von Neumann. Ως αποτέλεσμα, παίρνουμε μια λιγότερο τεχνική απόδειξη ενός θεωρήματος των Ανούση-Κτάβολου-Todorov και απαντάμε σε μια ερώτηση των ιδίων συγγραφέων αναφορικά με τα ιδεώδη της άλγεβρας Fourier. Επί πλέον, επεκτείνουμε ένα αποτέλεσμα των Crann και Neufang σχετικά με L(G)-διπρότυπα στην περίπτωση που η ομάδα G ικανοποιεί μια συνθήκη a priori ασθενέστερη της AP.

Morphology and Position of the Right Atrioventricular Valve in Relation to Right Atrial Structures

The right atrioventricular valve (RAV) is an important anatomical structure that prevents blood backflow from the right ventricle to the right atrium. The complex anatomy of the RAV has lowered the success rate of surgical and transcatheter procedures performed within the area. The aim of this study was to describe the morphology of the RAV and determine its spatial position in relation to selected structures of the right atrium. We examined 200 randomly selected human adult hearts. All leaflets and commissures were identified and measured. The position of the RAV was defined. Notably, 3-leaflet configurations were present in 67.0% of cases, whereas 4-leaflet configurations were present in 33.0%. Septal and mural leaflets were both significantly shorter and higher in 4-leaflet than in 3-leaflet RAVs. Significant domination of the muro-septal commissure in 3-leflet valves was noted. The supero-septal commissure was the most stable point within RAV circumference. In 3-leaflet valves, the muro-septal commissure was placed within the cavo-tricuspid isthmus area in 52.2% of cases, followed by the right atrial appendage vestibule region (20.9%). In 4-leaflet RAVs, the infero-septal commissure was located predominantly in the cavo-tricuspid isthmus area and infero-mural commissure was always located within the right atrial appendage vestibule region. The RAV is a highly variable structure. The supero-septal part of the RAV is the least variable component, whereas the infero-mural is the most variable. The number of detected RAV leaflets significantly influences the relative position of individual valve components in relation to right atrial structures.

Association of Morphological Characteristics of Palatal Rugae Pattern with Dental Malocclusion in Himachal Population

Introduction: Palatal rugae used for the evaluation of dental movements and as a landmark in the superimposition of dental cast for orthodontic purpose as it is a stable point. So, the aims and objectives of our study is to investigate the association of morphological characteristics of palatal rugae with dental malocclusion in Himachali population. Materials and methods: 90 subjects divided into three groups (n=30 each) on the basis of Angle’s classification. Palatal rugae were marked on dental casts and evaluated for length, pattern and orientation. Obtained measurements were then statistically analysed. Conclusion: Primary palatal rugae’s length was found more in Class II followed by Class III and Class I malocclusion. Among the pattern of the primary palatal rugae, curved pattern were more evident on both right and left sides of all malocclusion groups. Horizontal directed orientation is more predominant on the right side and posteriorly directed on the left side of the first primary palatine rugae. Keywords: Rugae, Malocclusion, orientation pattern, length, morphology.

Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

Learning Curve and Clinical Outcome of Biportal Endoscopic-Assisted Lumbar Interbody Fusion

Interbody fusion is a common surgical technique for diseases of the lumbar spine. Biportal endoscopic-assisted lumbar interbody fusion (BE-LIF) is a novel minimally invasive technique that has a long learning curve, which can be a barrier for surgeons. Therefore, we analyzed the learning curve in terms of operative time and evaluated the outcomes of BE-LIF. A retrospective study of fifty-seven consecutive patients who underwent BE-LIF for degenerative lumbar disease by a single surgeon from January 2017 to December 2018 was performed. Fifty patients underwent a single-level procedure, and 7 underwent surgery at two levels. The mean follow-up period was 24 months (range, 14–38). Total operative time, postoperative drainage volume, time to ambulation, and complications were analyzed. Clinical outcome was measured using the Oswestry Disability Index (ODI), Visual Analog Scale (VAS) score for back and leg pain, and modified Macnab criteria. The learning curve was evaluated by a nonparametric regression locally weighted scatterplot smoothing curve. Cases before the stable point on the curve were designated as group A, and those after the stable point were designated group B. Operative time decreased as the number of cases increased. A stable point was noticed on the 400th day and the 34th case after the first BE-LIF was performed. All cases showed improved ODI and VAS scores at the final follow-up. Overall mean operative time was 171.74 ± 35.1 min . Mean operative time was significantly lower in group B ( 139.7 ± 11.6 min ) compared to group A ( 193.4 ± 28.3 min ). Time to ambulation was significantly lower in group B compared to group A. VAS and ODI scores did not differ between the two groups. BE-LIF is an effective minimally invasive technique for lumbar degenerative disease. In our case series, this technique required approximately 34 cases to reach an adequate performance level.