The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories

In this paper, we investigate the main algebraic properties of the maximally superintegrable system known as "Perlick system type I". All possible values of the relevant parameters, $K$ and $\beta$, are considered. In particular, depending on the sign of the parameter $K$ entering in the metrics, the motion will take place on compact or non compact Riemannian manifolds. To perform our analysis we follow a classical variant of the so called factorization method. Accordingly, we derive the full set of constants of motion and construct their Poisson algebra. As it is expected for maximally superintegrable systems, the algebraic structure will actually shed light also on the geometric features of the trajectories, that will be depicted for different values of the initial data and of the parameters. Especially, the crucial role played by the rational parameter $\beta$ will be seen "in action".Comment: 16 pages, 7 figure

New Stratigraphic and Palaeogeographic Results from the Palaeozoic and Early Mesozoic of the Middle Pontides (Northern Turkey) in the Azdavay, Devrekani, Küre and Inebolu Areas: Implications for the Carboniferous-Early Cretaceous Geodynamic Evolution and Some Related Remarks to the Karakaya Oceanic Rift Basin

The Küre Complex of the Middle Pontides, northern Turkey, is not a remnant of the Palaeotethys but consists of three different units with differing geological history, the Küre Ridge Unit, the Küre Ocean Unit and the Çalça Unit. The Küre Ridge Unit consists of the Serveçay Group, a pre-Permian, low-grade metamorphic Variscan oceanic sequence, and the Sirçalik Group, a Lower and Middle Triassic shallow-water sequence of North Alpine facies and event succession which disconformably overlies the Serveçay Group. Following a hiatus, the Sirçalik Group is overlain by marginal parts of the Akgöl Group with olistoliths of local origin which were derived mainly from the Sirçalik Group. The Küre Ocean Unit consists mostly of the Akgöl Group (siliciclastic turbidites and olistostromes of the Karadagtepe Formation, which is a middle Carnian to Middle Jurassic accretionary complex from the southern, active margin of the Küre Ocean, and mainly Middle Jurassic molasse type shallow-water sandstones, siltstones and shales of an unnamed formation) and of thick oceanic basalts (Ipsinler Basalt). Tectonic slices of Middle Triassic to lower Carnian ophiolites and basalts are also present. The Karadagtepe Formation contains numerous Middle Triassic exotic olistoliths and blocks of shallow-water and predominantly slope and basinal limestones, ocean-floor deep-sea sediments (shales and radiolarites), basalts and small clasts of ophiolites or ophiolitic detritus. The Çalça Unit consists of deposits from the northern, passive margin of the Küre ocean with many Pelsonian to upper Norian Hallstatt Limestones and Rhaetian-Lower Jurassic (?Middle Jurassic) deep-water shales and marls. All three units are overlain following a period of non deposition by the Upper Jurassic Bürnük Formation (red conglomerate, sandstone) and Inalti Formation (shallow-water platform carbonates). The Küre Ridge Unit was split away from the Variscan Sakarya Continent by the opening of the Karakaya oceanic rift basin during latest Permian (Dorashamian) and became a continental splinter between the Karakaya oceanic rift basin and the Küre Ocean (opened during the late Scythian). Southward subduction began in the Küre Ocean during the middle Carnian (beginning of the Karadagtepe siliciclastic turbidites), whereas at the northern passive margin the deposition of Hallstatt Limestones continued until the latest Norian. The deposition of siliciclastic turbidites and olistostromes (Diskaya Unit) began in the entire Karakaya oceanic rift basin during the middle Carnian, and ocean basin deposits (radiolarites, pelagic limestones) and slope deposits form the passive margin (e.g., Hallstatt Limestones) are no more present in the Karakaya oceanic rift basin indicating that this basin was very narrow (only a few hundreds of kilometres). During the late Norian, the Karakaya oceanic rift basin closed, whereas subduction at the southern (active margin) of the Küre ocean continued. At the northern margin of the (Upper Triassic?) Jurassic-Lower Cretaceous Beykoz-Çaglayan turbidite basin (north of the Küre Complex) the accretionary complex of an older ocean, the Late Palaeozoic Paphlagonian Ocean, was exposed that yielded clasts in the Beykoz-Çaglayan turbidite basin. Among these clasts Carboniferous to Middle Permian (Capitanian) pelagic rocks (pelagic limestones, radiolarites) could be dated. A Middle to Late Permian southward-directed subduction is assumed for the Paphlagonian Ocean. Its closure occurred either at the end of the Permian or during the Scythian

Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4,2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2,1) and so(4,2).Comment: 11 pages, 5 figure

Effect of hesperidin treatment on α-Klotho/FGF-23 pathway in rats with experimentally-induced diabetes

Objective Non-alcoholic fatty liver disease, steatohepatitis and nephropathy are considered among the mostimportant complications of diabetes mellitus (DM), which recently increased due to increased frequency of DMand the prolonged life span of diabetic patients The aim of the present study was to reveal the possible effect ofhesperidin (HP) on alpha-klotho (α-KL)/fibroblast growth factor-23 (FGF-23) pathway in rats with diabetesinduced by streptozotocin (STZ).Materials and methods Thirty six male Sprague-Dawley rats were randomly divided into three groups. Therats of the control, diabetes, and treatment groups were fed with standard feed and water throughout the 2-weekstudy. In order to induce diabetes mellitus in rats, those in the diabetes group were administered a single dose of50 mg/kg STZ. For the DM + HP group, a single dose of 50 mg/kg STZ, when diabetes was induced, hesperidinwas administered orally at a dose of 100 mg/kg by gavage.Results Theα-KL levels of our study groups, both the liver and kidneyα-KL levels and serumα-KL of the STZ-induced diabetic group were statistically significantly lower than the control group (respectively, p < 0.05,p < 0.001, p < 0.05). It was observed that hesperidin administration statistically significantly increasedα-KLlevels in serum, liver and renal tissue (p < 0.001). Liver, kidney and serum FGF-23 levels of the diabetic groupincreased significantly in comparison to the control group (respectively, p < 0.05, p < 0.01, p < 0.001). FGF-23 levels that increased in kidney tissue and serum samples of the diabetic group decreased statistically sig-nificantly with hesperidin administration (respectively, p < 0.01, p < 0.001).Conclusion Theα-KL/FGF-23 pathway is a promising bio-indicator in various cases of systemic toxicity andpathology. In addition, the strong positive effects of hesperidin administration on diabetic toxicity in the liverand kidneys suggest that it may be included in the alternative treatment methods in the future.This work was supported by Coordinator of Scientific Research Projects ( 2017.M83.02.01 ) at University of Artvin Coruh

Feasibility study of intelligent autonomous determination of the bladder voiding need to treat bedwetting using ultrasound and smartphone ML techniques

Unsatisfactory cure rates for the treatment of nocturnal enuresis (NE), i.e. bed-wetting, have led to the need to explore alternative modalities. New treatment methods that focus on preventing enuretic episodes by means of a pre-void alerting system could improve outcomes for children with NE in many aspects. No such technology exists currently to monitor the bladder to alarm before bed-wetting. The aim of this study is to carry out the feasibility of building, refining and evaluating a new, safe, comfortable and non-invasive wearable autonomous intelligent electronic device to monitor the bladder using a single-element low-powered low-frequency ultrasound with the help of Machine Learning techniques and to treat NE by warning the patient at the pre-void stage, enhancing quality of life for these children starting from the first use. The sensitivity and specificity values are 0.89 and 0.93 respectively for determining imminent voiding need. The results indicate that customised imminent voiding need based on the expansion of the bladder can be determined by applying a single-element transducer on a bladder in intermittent manner. The acquired results can be improved further with a comfortable non-invasive device by adding several more features to the current features employed in this pilot study

The mechanism of force transmission at bacterial focal adhesion complexes

Various rod-shaped bacteria mysteriously glide on surfaces in the absence of appendages such as flagella or pili. In the deltaproteobacterium Myxococcus xanthus, a putative gliding motility machinery (the Agl–Glt complex) localizes to so-called focal adhesion sites (FASs) that form stationary contact points with the underlying surface. Here we show that the Agl–Glt machinery contains an inner-membrane motor complex that moves intracellularly along a right-handed helical path; when the machinery becomes stationary at FASs, the motor complex powers a left-handed rotation of the cell around its long axis. At FASs, force transmission requires cyclic interactions between the molecular motor and the adhesion proteins of the outer membrane via a periplasmic interaction platform, which presumably involves contractile activity of motor components and possible interactions with peptidoglycan. Our results provide a molecular model of bacterial gliding motility