Discontinuous Research Articles

New Accuracy Estimates for Methods for Localizing Discontinuity Lines of a Noisy Function

We consider an ill-posed problem of localizing (finding the position of) discontinuity lines of a function of two variables, provided that the function of two variables is smooth outside the discontinuity lines and has a discontinuity of the first kind at each point on the line. There is a uniform grid with a step $$\tau$$ . It is assumed that we know the average values of the perturbed function on the square $$\tau\times\tau$$ at each node of the grid. The perturbed function approximates the exact function in space $$L_2(\mathbb{R}^2)$$ . The perturbation level $$\delta$$ is assumed to be known. Earlier, the authors investigated (obtained accuracy estimates of) the global discrete regularizing algorithms for approximating a set of discontinuity lines of a noisy function. However, stringent smoothness conditions were superimposed onto the discontinuity line. The main result of the present study is the improvement of localizing the accuracy estimation methods, which allows replacing the smoothness requirement with a weaker Lipschitz condition. Also, the conditions of separability are formulated in a more general form as compared to previous studies. In particular, it is found that the proposed algorithm makes it possible to obtain the localization accuracy of the order of $$O(\delta)$$ . Estimates of other important parameters characterizing the localization algorithm are also given.

『중론송』의 팔불연기는 연속적인가, 불연속적인가

『중론송』의 팔불연기는 연속적인가, 불연속적인가

A rare case of discontinuous type splenogonadal fusion in a 13 year old boy: a case report and review of literature

Splenogonadal fusion (SGF) is a rare developmental anomaly in which an abnormal connection between the splenic tissue and gonads or mesonephric derivatives is present. This entity often presents with scrotal mass, inguinal hernia, or cryptorchidism. Less than 200 cases have been reported since it was first described in 1883. It can be of continuous and discontinuous type based on the presence of a band of connecting splenic tissue. Report a rare case of discontinuous type of SGF in an adolescent male presenting as nonpalpable testis. On evaluation, ultrasonography (USG) and magnetic resonance imaging of abdomen and pelvis, his left scrotal testis was atrophied and right intra-abdominal undescended testis. This is the first reported case of SGF from Bosnia and Herzegovina. Laparoscopy was demonstrated to be the only accurate exploratory procedure for the diagnosis and surgical treatment of SGF with non‑palpable testis.

Vortex shedding from cylinders with two step discontinuities in diameter

Abstract

Labour market trajectories and health in Catalan youth

Abstract Background Difficulties with integration and job insecurity are currently a characteristic of youth labour market trajectories (YLMT), which have been associated with negative health impacts. This study sheds light on the relationship between YLMT and current health outcomes. Methods The study has a mixed methods sequential exploratory design, focusing on young people aged 25-34 in Catalonia, Spain. In the quantitative phase, longitudinal retrospective data from the Survey to the Catalan Youth 2017 SYC-2017 (n = 1247) was used to obtain a typology of YLMT by clustering techniques. Then, the association between such career paths and health outcomes was tested. In the qualitative phase, semi-structured individual interviews were conducted to a sample (n = 12) of SCY-2017 participants, structured according to the typology, sex and rural/urban criteria. Transcriptions were analyzed by mixed generation of categories. Results Three types of YLMT were obtained: permanent (PT), temporary (TT) and discontinuous (DT). Compared to PT, TT(p < 0.01) and DT (p < 0.001) were found to be a significant risk factor for self-perceived poor health. Similarly, DT were found to be a risk factor for life dissatisfaction (p < 0.05). Trajectory type is not associated with smoking, however, alcohol (p < 0.05), cannabis(p < 0.05), cocaine (p < 0.05) and overall consumption (p < 0.05) are associated with DT. In the qualitative phase, material deprivation, hazardous working conditions, future unpredictability and the prolonged experience of unemployment, powerlessness and insecurity were identified as key explanatory mechanisms of the YLMT health relation. Conclusions YLMT has an impact on different health outcomes and quality of life through numerous causal paths and mechanisms related to the objective and subjective experience of insecurity. The precarisation of the labour market and the lack of decent employment opportunities for the young should be addressed as a primary public health concern. Key messages This study highlights the impact of labor market precariousness on the mental and physical health of Catalan youth as a public health concern. Three broad causal pathways have been identified: material deprivation, the ability to act as an organization in the construction of horizons and exposure to physical and psychosocial risks at work.

The thermodynamic formalism and exponents of singularity of invariant measure of circle maps with a single break

Let $T \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0 $, be a circle homeomorphism with one break point $x_{b}$, at which $ T'(x) $ has a discontinuity of the first kind and both one-sided derivatives at the point $x_{b} $ are strictly positive. Assume that the rotation number $\rho_{T}$ is irrational and its decomposition into a continued fraction beginning from a certain place coincides with the golden mean, i.e., $\rho_{T}=[m_{1}, m_{2}, \ldots, m_{l}, \, m_{l + 1}, \ldots] $, $ m_{s} = 1$, $s> l> 0$. Since the rotation number is irrational, the map $ T $ is strictly ergodic, that is, possesses a unique probability invariant measure $\mu_{T}$. A.A. Dzhalilov and K.M. Khanin proved that the probability invariant measure $ \mu_{G} $ of any circle homeomorphism $ G \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0$, with one break point $ x_{b} $ and the irrational rotation number $ \rho_{G} $ is singular with respect to the Lebesgue measure $ \lambda $ on the circle, i.e., there is a measurable subset of $ A \subset S^{1} $ such that $ \mu_ {G} (A) = 1 $ and $ \lambda (A) = 0$. We will construct a thermodynamic formalism for homeomorphisms $ T_{b} \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0 $, with one break at the point $ x_{b} $ and rotation number equal to the golden mean, i.e., $ \rho_{T}:= \frac {\sqrt{5} -1}{2} $. Using the constructed thermodynamic formalism, we study the exponents of singularity of the invariant measure $ \mu_{T} $ of homeomorphism $ T $.

Integrated thermal flaw detection technology of complex spatial composite structures in operation

The paper presents a complex technology of thermal flaw detection of small-size discontinuity type defects of composite structures. The integrated flaw detection technology is based on the identification of internal defects as sources of heat caused by the use of additional sources of stimulation. The use of complex technology makes it possible to identify types of defects that cannot be detected by the existing methods, for example, defects of small sizes, closed cracks, microcracks, etc. and determine their location in the material. It is shown that the error in determining the depth of defects in the material when using the proposed integrated technology does not exceed 10-15%, which is quite acceptable for practical use.

Algorithms for Brownian dynamics across discontinuities

The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are satisfied. As the number of layers increases, the solutions may become increasingly complicated. Here, we describe an alternative computational approach to multi-layer diffusion problems, which is based on the description of the overdamped Brownian motion of particles via the underdamped Langevin equation. In this approach, the probability distribution function is computed from the statistics of an ensemble of independent single particle trajectories. To allow for simulations of Langevin dynamics in layered systems, the numerical integrator must be supplemented with algorithms for the transitions across the discontinuous interfaces. Algorithms for three common types of discontinuities are presented: (i) A discontinuity in the friction coefficient, (ii) a semi-permeable membrane, and (iii) a step-function chemical potential. The general case of an interface where all three discontinuities are present (Kedem-Katchalsky boundary) is also discussed. We demonstrate the validity and accuracy of the derived algorithms by considering a simple two-layer model system and comparing the Langevin dynamics statistics with analytical solutions and alternative computational results.

Papillary Muscle Noncompaction: A Unique Mechanism for Mitral Regurgitation in Children

Background: Noncompaction Cardiomyopathy (NCCM) is a primary genetic cardiomyopathy with variable clinical and Echocardiographic (echo) features. Association with Mitral Regurgitation (MR) was reported but the mechanism of this association has not been well described in pediatric patients. Aims: To describe clinical and echo features of MR in NCCM. Methods: All pediatric patients with NCCM associated with MR and preserved ventricle function seen in one center from January 2015 to March 2020 were included. Clinical and echo features were described. Results: Twelve patients were identified (66% females), 8 (66%) presented with heart failure due to severe MR , and 4 were asymptomatic with mild-moderate MR. Echo features in all patients showed Papillary Muscle Noncompaction (PMNC). The Papillary Muscle (PM) base was discontinuous with the endocardium in 5 patients (41%) and PM were not well differentiated from the noncompacted myocardium in 3 patients (25%)There were variable degrees of chordal elongation and malcoaptation of the leaflets in all patients. Five patients (41%) had associated congenital heart disease including ventricular septal defects in 4 and patent ductus arteriosus in one patient. Conclusion: PMNC causes MV chordal abnormalities that lead to malcoaptation of the mitral leaflets resulting in MR. NCCM needs to be considered when evaluating patients with MR.

Doppler-Derived Intrarenal Venous Flow Mirrors Right-Sided Heart Hemodynamics in Patients With Cardiovascular Disease.

Interruption in Doppler intrarenal venous flow (IRVF) has been used in assessing renal congestion and in the prediction of prognosis of cardiovascular diseases. However, there is a paucity of pathophysiological knowledge, so we aimed to clarify the determinants of IRVF interruption. Intrarenal Doppler studies were performed within 24 h before right-side catheterization studies. The interruption in IRVF in 73 patients was divided into a continuous pattern, and 4 discontinuous types based on the timing of interruption. Type 1, with an interruption in early systole, was associated with a-wave elevation of right atrial pressure (RAP). Type 2, with an interruption in early diastole, was associated with v-wave elevation, tricuspid regurgitation (TR), and right ventricular dysfunction. Both Type 1 and 2 were observed even in the normal range of mean RAP. Type 3, with an interruption throughout systole, was observed in advanced right heart failure patients with markedly elevated RAP, particularly elevated x-descend and atrial fibrillation. Finally, Type 4, with limited flow at systole, was observed in 2 of the patients with pulmonary arterial hypertension. IRVF interruption was closely related to RAP elevation at each specific point of the cardiac cycle rather than to mean RAP levels, suggesting that the characteristics of IRVF mirror right-sided heart hemodynamics, not mean RAP.

X-sperm Enrichment of Bovine Semen by Percoll Density Gradient Method and Its Effect on Semen Quality, Sex Ratio and Conception Rate

In cattle, sex selection has a significant economic impact when it improves herd capacity of milk or meat production and is commonly used for the production of calves of the desired gender. New separation techniques which present both better accuracy and low costs are necessary. Density gradient centrifugation might be an approach to sexing spermatozoa because of the additional DNA content and volume of X-bearing sperm head. The present study was designed to apply the modified percoll discontinuous density gradient for X-sperm enrichment in cross bred bovine semen. We attempted to amplify the level of X-sperm enrichment by using double centrifugation in percoll gradient. In addition, effect of percoll density gradient on fertility of semen was also evaluated at three stages; before centrifugation (stage I), after 1st centrifugation (stage II) and after 2nd centrifugation (stage III) respectively and ultrasonography was carried out to confirm the sex of fetus at 60-90 days post AI. Semen was collected from two cross bred bovine bulls and 34 cows were inseminated with liquid X-sperm enriched semen after double centrifugation in percoll gradient. 22 cows were inseminated with non-sexed fresh liquid semen (control). Results showed that the volume, progressive motility, live sperms, concentration and HOST reactive sperms significantly (P is less than 0.05) decreased at stage II and stage III compared to stage I. However, no significant (P is greater than 0.05) change was observed in pH and mass motility of semen at all three stages. There was non-significant effect on per cent spermatozoa with intact acrosomal membrane and fully damaged acrosomal membrane at all three stages however, partially damaged acrosomal membrane sperms were significantly (P is less than 0.05) decreased at Stage II and Stage III compared to Stage I. The conception rate significantly (P is less than 0.05) decreased with X-enriched semen (41.17%) compared to non-sexed liquid semen (59.09%). The female sex ratio of calves significantly (P is less than 0.05) increased to 66.66% with X- sperm enriched semen compared to the male percentage of 33.33% with sexed semen and female percentage of 46.15% with non-sexed semen.

A constitutive model for sheared dense suspensions of rough particles

In a concentrated suspension, particles come into contact due to the presence of asperities on their surfaces. As a result, the contact forces and interparticle friction become one of the important factors governing the rheology of rigid particle suspensions at high concentrations. We show that a load-dependent friction model can be used to reproduce the experimentally observed shear thickening [ST—continuous and discontinuous (DST)] behavior with an increase in the asperity size. Increasing the particle surface roughness size leads to a decrease in the critical shear rate above which shear-thickening takes place, a reduction in the critical volume fraction for DST and an increase in the viscosity jump across non-shear-thickened to shear-thickened regime. In this paper, we propose a constitutive model to quantify the effect of increasing the roughness size on the rheology of dense ST suspensions as well as on the critical shear rate for ST and the critical volume fraction for DST. We fit this model to our simulation data for stress controlled shear flow of dense rough particle suspensions. Once the fitting is complete, these equations are used to predict exact volume fractions and shear stress values for transitions between three regimes on the shear stress-shear rate flow state diagram for different roughness values. The results of this study can be used to tune the particle surface roughness for manipulating the dense suspension rheology according to different applications.

A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations

Trefftz methods are known to be very efficient to reduce the numerical pollution when associated to plane wave basis. However, these local basis functions are not adapted to the computation of evanescent modes or corner singularities. In this article, we consider a two dimensional time-harmonic Maxwell system and we propose a formulation which allows to design an electromagnetic Trefftz formulation associated to local Galerkin basis computed thanks to an auxiliary Nedelec finite element method. The results are illustrated with numerous numerical examples. The considered test cases reveal that the short range and long range propagation phenomena are both well taken into account.

Modeling Present and Future Permafrost Distribution at the Seward Peninsula, Alaska

AbstractPermafrost, a key component of Arctic ecosystems, is currently affected by climate warming and anticipated to undergo further significant changes in this century. The most pronounced changes are expected to occur in the transition zone between the discontinuous and continuous types of permafrost. We apply a transient temperature dynamic model to investigate the spatiotemporal evolution of permafrost conditions on the Seward Peninsula, Alaska—a region currently characterized by continuous permafrost in its northern part and discontinuous permafrost in the south. We calibrate model parameters using a variational data assimilation technique exploiting historical ground temperature measurements collected across the study area. The model is then evaluated with a separate control set of the ground temperature data. Calibrated model parameters are distributed across the domain according to ecosystem types. The forcing applied to our model consists of historic monthly temperature and precipitation data and climate projections based on the Representative Concentration Pathway (RCP) 4.5 and 8.5 scenarios. Simulated near‐surface permafrost extent for the 2000–2010 decade agrees well with existing permafrost maps and previous Alaska‐wide modeling studies. Future projections suggest a significant increase (3.0°C under RCP 4.5 and 4.4°C under RCP 8.5 at the 2 m depth) in mean decadal ground temperature on average for the peninsula for the 2090–2100 decade when compared to the period of 2000–2010. Widespread degradation of the near‐surface permafrost is projected to reduce its extent at the end of the 21st century to only 43% of the peninsula's area under RCP 4.5 and 8% under RCP 8.5.

Large deformation in bi-material components by XIGA and coupled FE-IGA techniques

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems.

APPROXIMATING EXPECTED VALUE OF AN OPTION WITH NON-LIPSCHITZ PAYOFF IN FRACTIONAL HESTON-TYPE MODEL

In this paper, we consider option pricing in a framework of the fractional Heston-type model with [Formula: see text]. As it is impossible to obtain an explicit formula for the expectation [Formula: see text] in this case, where [Formula: see text] is the asset price at maturity time and [Formula: see text] is a payoff function, we provide a discretization schemes [Formula: see text] and [Formula: see text] for volatility and price processes correspondingly and study convergence [Formula: see text] as the mesh of the partition tends to zero. The rate of convergence is calculated. As we allow [Formula: see text] to be non-Lipschitz and/or to have discontinuities of the first kind which can cause errors if [Formula: see text] is replaced by [Formula: see text] under the expectation straightforwardly, we use Malliavin calculus techniques to provide an alternative formula for [Formula: see text] with smooth functional under the expectation.

Fuzzy risk analysis of dam overtopping from snowmelt floods in the nonstationarity case of the Manas River catchment, China

With the significant climate change that has occurred in the Manas River catchment, the temporal and spatial patterns of the natural changes in the regional water cycle have changed dramatically in the past 30 years, and the frequency of extreme hydrological events has increased, which has changed the overall stability of the hydrological system of the catchment. According to the annual maximum peak flow data for the period 1956–2014 in the Manas River catchment, we used variable fuzzy set theory and the Mann–Kendall test to conduct trend and change point tests, respectively, and decomposition synthesis theory was used to handle consistency correction. Combined with the flood routing results for the Kensiwate reservoir using Monte Carlo simulation, a reservoir overtopping risk model based on right-angle trapezoidal fuzzy numbers was established, and the fuzzy risk index intervals and the corresponding fuzzy risk rate intervals for the Kensiwate reservoir were considered for past and present conditions. The results show that the local tendency and jumping of the maximum flood peak series showed significant changes; the annual runoff had an obvious growth trend in the period 1985–2006 and a gradually varying qualitative change from 1975 to 2000. In particular, the characteristic parameter reached an extreme qualitative change level of − 0.0016 in 1993. Then, we used decomposition synthesis theory to process the sequence with jumping points and obtained the past and present hydrological time series. Under the present conditions, the average flood peak sequence is 58.10% higher than in the past, and the flood design value decreases with increasing design frequency; however, when the present sequence increases, the change rates of both flood design values increase. The reservoir overtopping risk increased under the current conditions of snowmelt floods, which was affected by a significant increase in catchment temperature. Moreover, the use of right-angle trapezoidal fuzzy numbers to describe the reservoir overtopping risk was more in line with the objective reality than a traditional triangular fuzzy number. The results of this study can be used for the efficient utilization of water resources in the Manas River catchment and provide a new reference for the scientific management of reservoirs.

Challenge to enhance the value of the Cameroonian coastal earth: physical tests and mechanical characterization of earth material

One of the main performances of earth material is the thermal regulation. The aim of this study is centered on the possibility of applying the grunge of the Cameroonian Coast for its suitable valorisation. Thus focusing on the parliamentary law so as to be capable of supplying, first, a material with a reduced polluting impact and secondly one with which the thermal comfort of the building would be amended; all these for the population of the Cameroonian Coast. The identification results assure the possibility of using the earth of the Cameroon coastal region for CEB with a grain size distribution even though the crater spindle contained shows a discontinuous tray type. Again, this study aims at showing the possibility of using this earth material for the manufacturing of porcelain, sanitary ware and tableware. As far as the characteristics are concerned, a convergence of the grading, mineralogical and chemical results show a medium-active kaolinite-type clay and a sandy loamy-clay earth. That's why for in-depth knowledge major elements and minerals have been identified by X-ray fluorescence and X-ray diffraction. The mechanical tests carried out on the clay show a sufficient plasticity in the wet state, even though it is also pointing out possibilities of improving these performances by using adequate stabilizers.

Effect of continuity of annealing time on the recrystallization behavior of Al-Mg-Mn-Sc-Zr alloy

Recrystallization behavior of Al-Mg-Mn-Sc-Zr alloy have been studied after two different annealing ways. The one way is keeping the cold rolling plate of the alloy in 550 °C for a continuous time (CT). The other way is putting the alloy plate into the salt bath furnace at 550 °C for 10S then quenching it into water and repeating this process. The annealing time is discontinuous (DT). Results show that grains in the CT sample grow up with the increase of annealing time but the grains in the DT sample are still very fine. The recrystallization fraction of the CT sample increases with the rise of annealing time. However, in the DT sample, the recrystallization fraction is low. Much grains are maintained in substructure state. The recrystallization result is due to the pinning effect of the Al3(Sc, Zr) particles.

A sparsity-promoting image decomposition model for depth recovery

This paper proposes a novel image decomposition model for scene depth recovery from low-quality depth measurements and its corresponding high resolution color image. Through our observation, the depth map mainly contains smooth regions separated by additive step discontinuities, and can be simultaneously decomposed into a local smooth surface and an approximately piecewise constant component. Therefore, the proposed unified model combines the least square polynomial approximation (for smooth surface) and a sparsity-promoting prior (for piecewise constant) to better portray the 2D depth signal intrinsically. As we know, the representation of the piecewise constant signal in gradient domain is extremely sparse. Previous researches using total variation filter based on L1-norm or Lp-norm (0 < p < 1) are both sub-optimal when addressing the tradeoff between enhancing the sparsity and keeping the model convex. We propose a novel non-convex penalty based on Moreau envelope, which promotes the prior sparsity and simultaneously maintains the convexity of the whole model for each variable. We prove the convexity of the proposed model and give the convergence analysis of the algorithm. We also introduce an iterative reweighted strategy applied on the sparsity prior to deal with the depth-color inconsistent problem and to locate the depth boundaries. Moreover, we provide an accelerated algorithm to deal with the problem of non-uniform down-sampling when transforming the depth observation matrix into the Fourier domain for fast processing. Experimental results demonstrate that the proposed method can handle various types of depth degradation and achieve promising performance in terms of recovery accuracy and running time.