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In this paper, the Hölder regularity of weak solutions for singular parabolic systems of p-Laplacian type is investigated. By the Poincare inequality, we show that its weak solutions within Hölder space.

This article investigates a singular case of maritime marronage from Jamaica to Cuba in the 1760s to explore the possibilities that archives present to reconstruct the mental worlds of enslaved Afr...

Fetal intracranial hemorrhage affects 1 in every 10,000 pregnancies. In most cases, the etiology of the bleeding is multifactorial, and they can be either related to the mother or the fetus. Blunt prenatal trauma was occasionally associated with these hemorrhages, nevertheless, reports of hematomas secondary to mild traumas are rare. Within the prenatal intracranial bleedings, the most frequent are the subarachnoid hematoma and intraparenchymal, scarcely ever the epidural hematoma. Treating these bleedings is challenging due to the ongoing pregnancy. Thus, the prognosis is often reserved, with a mortality rate of 43% and 25% of neurological sequelae. Here, we report a singular case of a fetal epidural hematoma secondary to a mild blunt trauma at the third trimester with a good outcome.

Author(s): Stephan, Simon; Placi, Sarah; Waldmann, Michael R. | Abstract: Most psychological studies focused on how people reason about generative causation, in which a cause produces an effect. We study the prevention of effects both on the general and singular level. A general prevention query might ask how strongly a vaccine is expected to reduce the risk of contracting COVID-19, whereas a singular prevention query might ask whether the absence of COVID-19 in a vaccinated person actually resulted from this person's vaccination. We propose a computational model answering how knowledge about the general strength of a preventive cause can be used to assess whether a preventive link is instantiated in a singular case. We also discuss how psychological models of causal strength learning relate to mathematical models of vaccination efficacy used in medical research. The results of an experiment suggest that many, but not all people differentiate between preventive strength and singular prevention queries, in line with the formal model.

In a previous work the authors presented the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three real parameters and, moreover, we obtained a closed formula for their inverse. The techniques we used allowed us to reduce the computational cost of evaluating the inverse. In this work we complete the theoretical analysis of the mentioned circulant matrices by considering complex parameters and also the singular case. In addition, we explicitely compute the group inverse of a specific kind of this class of matrices using the same techniques that the authors developed for the non singular case; that is, solving first order linear difference equations.

espanolEl concepto de curva podal esta extendido en la geometria como un metodo generativo para multitud de curvas. La definicion de curva podal esta ligada al concepto de minima distancia. Sin embargo, es posible hacer una interesante distincion en el espacios ℝ2. En este caso, la curva podal de otra curva C se define como el lugar geometrico de los pies de las perpendiculares desde un punto P a las tangentes a la curva. Esto permite generalizar la definicion de curva podal a cualquier angulo que no sea 90o. En este articulo utilizamos la generalizacion de curva podal para describir un metodo diferente de generacion de la Limacon de Pascal, que puede relacionarse como un caso particular del metodo de generacion por lugares geometricos y que no se encuentra bien descrito en la literatura. Tambien se describen algunas propiedades que pueden deducirse de estas definiciones EnglishThe concept of a pedal curve is used in geometry as a generation method for a multitude of curves. The definition of a pedal curve is linked to the concept of minimal distance. However, an interesting distinction can be made for ℝ2. In this space, the pedal curve of another curve C is defined as the locus of the foot of the perpendicular from the pedal point P to the tangent to the curve. This allows the generalization of the definition of the pedal curve for any given angle that is not 90o. In this paper, we use the generalization of the pedal curve to describe a different method to generate a limacon of Pascal, which can be seen as a singular case of the locus generation method and is not well described in the literature. Some additional properties that can be deduced from these definitions are also described

The existence of positive periodic solutions of the Rayleigh equations $ x''+f(x')+g(x) = e(t) $ with singularities is investigated in this paper. Based on the continuation theorem of coincidence degree theory and the method of upper and lower solutions, the multiple periodic solutions of the singular Rayleigh equations can be determined under the weak conditions of the term $ g $. We discuss both the repulsive singular case and the attractive singular case. Some results in the literature are generalized and improved. Moreover, some examples and numerical simulations are given to illustrate our theoretical analysis.

A number of complementary, synergistic advances are reported herein. First, we describe the ‘first-time’ synthesis of ultrathin Ru2Co1 nanowires (NWs) possessing average diameters of 2.3 ± 0.5 nm using a modified surfactant-mediated protocol. Second, we utilize a combination of quantitative EDS, EDS mapping (along with accompanying line-scan profiles), and EXAFS spectroscopy results to probe the local atomic structure of not only novel Ru2Co1 NWs but also ‘control’ samples of analogous ultrathin Ru1Pt1, Au1Ag1, Pd1Pt1, and Pd1Pt9 NWs. We demonstrate that ultrathin NWs possess an atomic-level geometry that is fundamentally dependent upon their intrinsic chemical composition. In the case of the PdPt NW series, EDS mapping data are consistent with the formation of a homogeneous alloy, a finding further corroborated by EXAFS analysis. By contrast, EXAFS analysis results for both Ru1Pt1 and Ru2Co1 imply the generation of homophilic structures in which there is a strong tendency for the clustering of ‘like’ atoms; associated EDS results for Ru1Pt1 convey the same conclusion, namely the production of a heterogeneous structure. Conversely, EDS mapping data for Ru2Co1 suggests a uniform distribution of both elements. In the singular case of Au1Ag1, EDS mapping results are suggestive of a homogeneous alloy, whereas EXAFS analysis pointed to Ag segregation at the surface and an Au-rich core, within the context of a core–shell structure. These cumulative outcomes indicate that only a combined consideration of both EDS and EXAFS results can provide for an accurate representation of the local atomic structure of ultrathin NW motifs., EDS and EXAFS spectroscopy are used as complementary techniques to investigate the local structure of bimetallic ultrathin nanowires. Results highlight the importance of using a combined approach to achieve an accurate understanding of these systems.

Objective The aim of this report is to present a singular case of early post-endovascular aneurysm repair abdominal aortic aneurysm rupture and discuss the possible etiopathogenic mechanism promoting the sudden aneurysm progression toward rupture. Methods/Results: An 84-year-old man was submitted to endovascular aneurysm repair via second-generation endograft (Cordis-Incraft Stent-graft) during which, the left occluded common iliac artery was recanalized via balloon-expandable covered-stent-graft (Atrium-Advanta-V12). The aneurysm presented a severely calcified and modestly conical-shaped aortic-neck. The post-operative course was complicated by a broncho pneumonic infiltrate and a CT scan performed two weeks postoperatively accidentally revealed a relatively small hematoma surrounding the aortic wall. No active bleeding, endoleak, or aneurysm increase in diameter was documented. Nevertheless, the patient remained closely monitored. Three days later, he suffered from abdominal aortic aneurysm rupture. A CT scan revealed an arterial wall tear at the neck level. Intra-operatively the reanalyzed common iliac artery was intact and a good endograft-sealing was confirmed. Following this event, small lumbar arteries suture saccotomy was performed. The patient eventually died of multiorgan failure one month later. Conclusions The apparently “self-limiting” post-endovascular aneurysm repair CT-scan finding of periaortic hematoma may have represented a potential trigger for abdominal aortic aneurysm rupture. The possibility of developing undetected aortic lesions during endovascular aneurysm repair, specifically in the presence of potentially “at risk” anatomical conditions, should always be considered.

We extend to the singular case the results in [El Bahja H. Regularity for anisotropic quasi-linear parabolic equations with variable growth. Electron J Differ Equ. 2019;2019(104):1–21] concerning t...

A 64-year-old cirrhotic woman was admitted for alcoholic hepatitis associated with renal failure. Subsequently, she displayed symptoms of alcohol withdrawal progressing to delirium tremens. During hospitalization, she developed acute respiratory distress. The electrocardiogram showed diffuse anteroseptal ST elevation. Transthoracic echocardiography revealed systolic left ventricular apical balloon-like dilation, hypokinesis of the left ventricular mid- and apical segments, and a left ventricular ejection fraction of 30%. Coronary angiography was normal and led to the diagnosis of Takotsubo cardiomyopathy. This report describes a singular case of Takotsubo cardiomyopathy precipitated by delirium tremens in a cirrhotic patient with acute-on-chronic liver failure.

Introduction Recent literature identifies similar failure rates such as anchor pull-out and rod breakage, but a higher unplanned revision surgery with MAGEC rods than with traditional growth rods. Besides known failure modes such as rod fracture, infection, etc., failure to noninvasively distract the rods was cited as the main cause of such unplanned surgeries. The source of these data ranges from multicenter cohort studies to singular case series. These studies included explanted implants that had undergone failure in distraction mechanism, rod fracture, or infection, or had reached their maximum length. Nevertheless, in addition to identifying the overall mode of failure, it is equally important to identify the large-scale incidence of exclusive failures in comparison with standard instrumentation failure modes in spine surgery. Methods The US Food and Drug Administration (FDA) Manufacturer and User Facility Device Experience (MAUDE) databases were searched for reports on MAGEC rods, and on standard instrumentation used for spinal fusion. The adverse events were recorded, tabulated, and analyzed. Results A search of the US FDA MAUDE database yielded reports of 163 device-related adverse events. These included distraction mechanism failure (n=129), rod fracture (n=24), and minor voluntary reports of infection and tissue discoloration (n=10). For standard instrumentation usage in spine surgery, pedicle screw breakage post surgery (n=336), set screw damage during surgery (n=257), rod breakage post surgery (n=175), interbody cage breakage during surgery (n=118), and pedicle screw breakage during surgery (n=75) were identified as the top 5 failure modes. Conclusions The study identified the distraction mechanism failure as the most common and growing complication associated with MAGEC rod usage in children with scoliosis, leading to unplanned invasive revision surgeries.

The proliferation of border walls around the world, including in European Union territory, is a fact. Their construction can have harmful and irreparable consequences for biodiversity and ecosystems. This paper analyses the construction of the border fence between Slovenia and Croatia, paying special attention to the violations of European and international law and to the harm caused to the biodiversity of the Dinaric Alps region. It will also look at the singular case of the demilitarized zone between North and South Korea, which, because it has been free of human interference for more than sixty years, has enabled wildlife to thrive and the establishment of a unique ecosystem in the world. The challenge for international law is thus twofold: to ensure the conservation and protection of biodiversity without compromising the peace process or a hypothetical reunification.

International audience; From a brief reference to the exhumation of two human bodies from a pre-Columbian cemetery in the town of Chiuchiu published in a Scottish newspaper in 1851, unravels a profound plot of unsuspected scope. The biographies of its collector, its collectionists and the bodies themselves now turned into objects, converge in a single opera organized in three acts that illustrates the trajectories of the protagonists of this complex network, with their encounters and misunderstandings. The intersection of their trajectories produced new directions and unexpected destinies in their lives, orchestrated to the rhythm of the network of collectionism that has firmly anchored Atacama to the rest of the world since at least the mid-19th century. A singular case study that will serve to reflect on a larger phenomenon involving not only to Chiuchiu but the entire Atacama Desert, to discuss the role of pre-Columbian objects in the construction of Western identity.; A partir de una breve referencia a la exhumación de dos cuerpos humanos desde un cementerio precolombino en el poblado de Chiuchiu, publicada en un periódico escocés del año 1851, se desenreda una trama profunda de alcances insospechados. Las biografías de su colector, de sus coleccionistas y de los propios cuerpos ahora convertidos en objetos, confluyen en una misma ópera organizada en tres actos que ilustra las trayectorias de los agentes protagónicos de esta compleja red, con sus encuentros y desencuentros. El cruce de sus trayectorias produjo nuevos rumbos y destinos inesperados en sus vidas, orquestados al compás de la red del coleccionismo que ancla firmemente a Atacama con el resto del mundo al menos desde mediados del siglo XIX. Un caso singular de estudio que servirá para reflexionar sobre un fenómeno mayor que involucra no sólo a Chiuchiu sino a todo el desierto de Atacama, para discutir el rol de los objetos precolombinos en la construcción de la identidad de Occidente.

Although gastrointestinal hemorrhage from aorto-enteric fistulae (AEF) secondary to previous aortic grafts are well known, a primary aorto-enteric fistula (PAEF) without aortic aneurysm is an extremely rare event resulting in poor prognosis and outcome. PAEF is a rare cause of gastro-intestinal (GI) bleeding that radiologists should consider because often its presence is not easily guessed by clinical features. It is difficult to detect at CT examination therefore PAEF might be not diagnosed until a laparotomy. We report a case of a 74-year-old Italian male who presented to our Emergency Department (ED) with brightly red rectal bleeding that occurred from some hours and a pre-syncopal episode. There was no history of analgesic abuse, peptic ulceration, alcohol excess, and weight loss. Standard resuscitation was commenced with the hope that common sources of bleeding such as peptic ulcers or varices would eventually be discovered by endoscopy and treated definitely. An upper GI endoscopy showed brightly red blood in the stomach and in the first portions of duodenum, but no source of active bleeding was found. Diagnosis of PAEF was made by CT and after confirmed during surgical intervention. Both the duodenum and the aorta were successfully repaired by direct suture and synthetic graft replacement, respectively. Diagnosis of primary aortic duodenal fistula (ADF) has been very difficult in this case especially because our patient did not have abdominal aortic aneurism (AAA) history confirmed by CT examination. Radiologist should remember that upper GI bleeding could however be determined by primary ADF also if atherosclerotic damage is severe as in this case. A technically good and complete exam is mandatory to achieve this rare and complex diagnosis. Particularly, an ultra-tardive acquisition phase (5 min after contrast administration) could be helpful to suspect the presence of PADF: the appearance of contrast into the duodenal lumen is an evocative sign useful to increase clinical and radiological suspicious of ADF. Gl bleeding should be assumed to be caused from a PAEF unless another source can be identified without delay. A timely and accurate diagnosis of primary AEF may be challenging due to insidious episodes of GI bleeding, which are frequently under diagnosed until the occurrence of massive hemorrhage.

Book review of Between Ordinary and Extraordinary. The Normativity of the Singular Case in Art and Law by Angella Condello

Summary Differentiation of pagetoid cutaneous neoplasms can be very challenging on hematoxylin and eosin-stained sections. We report a singular case of pigmented pagetoid Bowen’s disease showing transitional features between extramammary Paget’s disease and in situ squamous cell carcinoma.

We consider the stability of the equilibrium state of an oscillator with an infinitely high natural oscillation frequency under time-periodic perturbations of the oscillator. It is shown that the problem of stability in the case of general equilibrium can be solved by considering only a linear approximation of the perturbation. In the singular case, a procedure is proposed to construct a nonzero constant, if it exists, whose sign specifies whether the state of equilibrium is asymptotically stable or unstable.

We present the singular Hardy-Trudinger-Moser inequality and the existence of their extremal functions on the unit disc \begin{document}$ B $\end{document} in \begin{document}$ \mathbb{R}^2 $\end{document} . As our first main result, we show that for any \begin{document}$ 0 and \begin{document}$ u \in C_0^\infty({B}) $\end{document} satisfying \begin{document}$ \int_{{B}}|\nabla u|^2 dx- \int_{{B}}\frac{u^2}{(1-|x|^2)^2}dx\leq1, $\end{document} there exists a constant \begin{document}$ C_{0}>0 $\end{document} such that the following inequality holds \begin{document}$ \int_{{B}}\frac{e^{4\pi(1-t/2)u^2}}{|x|^t} dx\leq C_{0}. $\end{document} Furthermore, by the method of blow-up analysis, we establish the existence of extremal functions in a suitable function space. Our results extend those in Wang and Ye [ 36 ] from the non-singular case \begin{document}$ t = 0 $\end{document} to the singular case for \begin{document}$ 0 .

The flow of tourism to a region is highly dependent on its accessibility and the cost of travel represents the main economic factor explaining tourism demand. The arrival of low cost carriers (LCC), with cheaper air fares, greatly leveraged the tourist flow around the world. However, as argued by some authors, if the destination is unique the importance of accessibility could be less relevant. Using quarterly data from 2000 to 2015, the paper assesses the effect of LCC on tourism demand focusing on Brussels. The peculiarity of Brussels comes from the high concentration of European and International institutions located in the city, which makes it a very interesting and singular case of research. Results reveal that LCC per se have a smaller positive effect on tourism demand for business purpose than the specific characteristic of Brussels. Indeed, the presence of European institutions complements the higher availability of low air fares, especially for business travellers.

The Italic consonant stem ablative in -ĕ is usually regarded as an anomalous instance of locative contamination in the ablative singular case endings. This interpretation has long been recognized as problematic, given that the Italic ablative is functionally the result of syncretism with the Proto-Indo-European instrumental, rather than the locative. In addition, it is difficult to reconcile the traditional view with the early Latin epigraphic evidence, which suggests that the Latin consonant stem ending, like the ablative singular endings of all other declensions, once had a final dental (-ĕd). This paper reviews the evidence for the origin and reconstruction of the Italic consonant stem ablative within the broader context of the early development of the Italic case system. It provides further arguments against the conventional locative etymology, and concludes that the consonant reflex can plausibly be aligned with the regular reflexes in other declensions if it is instead derived from a zero-grade instrumental ending ispartof: Symbolae Osloenses vol:94 issue:1 pages:1-23 status: Published online

In this paper, the modified SSOR (MSSOR) method is further investigated for solving augmented linear systems, including both the nonsingular and singular cases. The selection of quasi-optimal iteration parameters are discussed to minimize the radius of the MSSOR iteration matrix for the nonsingular case. The obtained optimality result is unified, which includes those for some existing methods as special cases. Besides, semi-convergence analysis of the MSSOR method for singular case is given using a singular preconditioning technique, which results in much better convergence behavior than some existing nonsingular preconditioning techniques. Numerical experiments are presented to confirm the theoretical results.

Aim: To present a case of double anterior chamber after DALK and its surgical management. Case description: A 67-year-old healthy woman underwent deep anterior lamellar keratoplasty (DALK) in her right eye for keratoconus with the big-bubble technique. About 7 days after surgery a partial detachment of the Descemet membrane from the posterior corneal stroma was revealed using AS-OCT (double anterior chamber appearance). In spite of two injections in the anterior chamber of air and gas on the 7th and 9th post-operative days respectively, the double anterior chamber still persisted. Furthermore, both air and gas passed through the little perforation of the host Descemet membrane-endothelium complex and enlarged the space between the stroma and Descemet membrane. About 10 weeks after DALK, a spontaneous resolution of the double anterior chamber was observed. Conclusion: This case suggests that an injection of air or gas into the anterior chamber, to deal with a Descemet membrane detachment following perforation during DALK procedure, can enlarge the double anterior chamber by increasing the space between stroma and Descemet membrane. These cases can be managed with a “wait and see” strategy for a spontaneous resolution to Descemet membrane detachment.

Recent seismic events that hit the central part of Italy have highlighted again the high vulnerability of the historical and architectonical heritage of Italy and the importance of preserving it. However, the seismic assessment of monumental buildings is particularly complex because each historical construction is a singular case realized by specific techniques. Therefore, the first step should be the knowledge of the building even if it is a difficult task. In the present paper, the seismic behavior of an important nineteenth century astronomical observatory, constructed between 1816 and 1819, was investigated. The building, located in Naples, in the southern part of Italy, and classified by the Italian code as an area of medium seismic hazard, was analyzed in the elastic and inelastic range under seismic actions. In this study, the results of two different models were proposed and critically compared. The first one was implemented by shell elements for walls and vaults developing a linear dynamic analysis, while the second one simulates the building through &ldquo, equivalent frames&rdquo, applying a nonlinear static analysis.

Pyemotes ventricosus is a free-living mite feeding on larvae or nymphs of insects, including moths, beetles, wasps and bees, that are usually found in grain, straw and firewood. When present in great number or when its food is lacking, it could accidentally bite mammals, including humans, causing a highly pruritic self-limiting dermatitis, sometimes followed by a lymphangitis known as "comet sign".We present a singular case of mite lymphangitis that surrounds and delimitates breast prosthesis in a 30-year-old Caucasian woman. Other bite in the lower abdomen did not present comet sign. The patient got the infestation in her vacation home in the South of Italy, uninhabited for 10 months since COVID-19 confinement. We hypothesize that the previous surgery made the lymphatic vessels more prone to inflammation and we compare other insect bites that can occur vacationing in a long period uninhabited room.A delayed diagnosis of comet sign implies a retarded fumigation allowing new mite bites and, in this case, extends the patient's preoccupation about the prosthesis rejection.

In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}(\mathcal{A}(x, \nabla u))&=& \mu \quad \text{in} ~\Omega, u&=&0 \quad \text{on}~ \partial \Omega, \end{array}\right. \end{eqnarray*} where $\mu$ is a finite signed Radon measure in $\Omega$, $\Omega \subset \mathbb{R}^n$ is a bounded domain such that its complement $\mathbb{R}^n\backslash\Omega$ is uniformly $p$-thick and $\mathcal{A}$ is a Carath\'eodory vector valued function satisfying growth and monotonicity conditions for the strongly singular case $1

International audience; Minimalism is a growing consumerist approach based on deliberate detachment from one’s material needs and acquisitions. The aim of this paper is to examine a singular case of minimalism which has developed in the sports sector, based on the stylization by detachment of the practice of hiking: ultralight or lightweight backpacking. While the sports market is traditionally characterized by the accumulation and renewal of equipment, this sport subculture aims the radical reduction of equipment weight and is promoted in France by an online community of practice. Lightening one’s equipment implies adopting an original material culture of detachment (mostly by innovation through withdrawal) which goes hand in hand with an alternative subjectivation of practitioners based on a form of voluntary simplicity and asceticism. This enculturation has political consequences, contributing to reconfiguring behaviors, norms and consumer values in the light of alternative markets, partly detaching oneself from “consumer society.”

This article considers the duration and meaning of insecurity—as it is experienced over the course of a life and moves over borders—through the narrative of a Palestinian woman from Shatila now seeking asylum in Belgium. Structured around one person’s account of the asylum process, it considers what a singular case can reveal about a collective migrant condition, the inconstant line separating secure from insecure states, and the reconstitution of a secure self in conditions of chronic uncertainty.

Symmetrically, it reveals possible pitfalls. Through the study of the way the Remy Cointreau Group developed its reporting tool, the authors analyze how a company can take the opportunity of a legal obligation to deploy a strategy of non-financial reporting that comes to support and structure a responsible approach. Of course, these results are only replicable under certain conditions related to this singular case. the complexity of the corporate social responsibility (Alcouffe, Berland, Dreveton, & Essid, 2010; Ancori, 2008; Antheaume, 2007; Brichard, 1996; Buritt, 2004; Chan, 2005; Gray & Bebbington, 2001; Herborn, 2005; Savall & Zardet, 2013; Vatn, 2009); the legislator’s and stakeholders’ expectations (Ancori, 2005; Batifoulier, 2001; Caillaud & Tirole, 2007; Lewis, 1969); and the company’s expectations (Argyris & Schon, 1978; Chiapello & Gilbert, 2013; David 1998; Grimand, 2012; Moisdon, 1997; Senge, 1992; Wood, 1991).

This article explores the historical role played by female pioneers of elite sport by studying the singular case of Lilí Álvarez (1905-1998). Álvarez was a high-profile Spanish female athlete with an outstanding career characterized by remarkable achievements in various sports, including being singles finalist in Wimbledon for three consecutive years (1926&-1928). In Franco's Spain, Álvarez contributed to the promotion of sports by publishing articles and delivering public lectures on sporting topics. In her published pieces and public talks, Álvarez tried to convince Spaniards of both sexes to exercise, however minimally. Álvarez also disseminated knowledge about sports other than soccer, the national sport. Thus, Álvarez contributed not only to the development of women's sport but also of sports in general. An analysis of Álvarez's case reveals much related to the role of elite female pioneers and their contribution to the history of sport across countries

Causal queries about singular cases, which inquire whether specific events were causally connected, are prevalent in daily life and important in professional disciplines such as the law, medicine, or engineering. Because causal links cannot be directly observed, singular causation judgments require an assessment of whether a co-occurrence of two events c and e was causal or simply coincidental. How can this decision be made? Building on previous work by Cheng and Novick (2005) and Stephan and Waldmann (2018), we propose a computational model that combines information about the causal strengths of the potential causes with information about their temporal relations to derive answers to singular causation queries. The relative causal strengths of the potential cause factors are relevant because weak causes are more likely to fail to generate effects than strong causes. But even a strong cause factor does not necessarily need to be causal in a singular case because it could have been preempted by an alternative cause. We here show how information about causal strength and about two different temporal parameters, the potential causes' onset times and their causal latencies, can be formalized and integrated into a computational account of singular causation. Four experiments are presented in which we tested the validity of the model. The results showed that people integrate the different types of information as predicted by the new model.

Este artículo se interroga sobre las formas de búsqueda realizadas por las asociaciones de afectados por la desaparición sin causa aparente. La desaparición sin causa aparente es un caso novedoso y singular en España que se diferencia de otros casos de desaparición por su contexto liberal y democrático. Partiendo desde enfoques teóricos que toman la espectralidad como metáfora para reflexionar sobre la vulnerabilidad, se propone aquí el concepto de espectropolítica invertida para comprender estas formas de búsqueda. Política que se nutre de dispositivos para gestionar la búsqueda de personas desaparecidas cuyo objetivo es hacerlas aparecer. A través de un trabajo cualitativo (entrevistas y trabajo etnográfico con asociaciones de desaparecidos sin causa aparente en España, así como del uso de la App "Desaparecidos"), se muestra cómo las formas de búsqueda desarrolladas entrañan una innovación tecnológica que constituye una red cada vez más extensa de agentes que actúan como buscadores. This article focuses on the forms of search carried out by associations of persons affected by disappearance without apparent cause. Disappearance without apparent cause is a novel and singular case in Spain that differs from other cases of disappearance because of its liberal and democratic context. Starting from theoretical approaches that take spectrality as a metaphor to reflect on vulnerability, the concept of inverted spectropolitics is proposed here to understand these forms of search. Politics nourished by devices to manage the search for dissapeared persons whose aim is to make them appear. Through a qualitative work (interviews and ethnographic work with associations of disappeared persons without apparent cause in Spain, as well as the use of the App "Disappeared"), the article shows how the forms of search developed involve a technological innovation that constitutes an increasingly extensive network of agents acting as searchers.

The paper is devoted to the implicit function theorem involving singular mappings.We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to nonlinear programming and complementarity problems., Comment: 11 pages

Fenichel’s geometric singular perturbation theory and the blow-up method have been very successful in describing and explaining global non-linear phenomena in systems with multiple time-scales, such as relaxation oscillations and canards. Recently, the blow-up method has been extended to systems with flat, unbounded slow manifolds that lose normal hyperbolicity at infinity. Here, we show that transition between discrete and periodic movement captured by the Jirsa–Kelso excitator is a new example of such phenomena. We, first, derive equations of the Jirsa–Kelso excitator with explicit time scale separation and demonstrate existence of canards in the systems. Then, we combine the slow-fast analysis, blow-up method and projection onto the Poincare sphere to understand the return mechanism of the periodic orbits in the singular case, ϵ = 0.

Stable inversion was an effective method to achieve precise trajectory tracking, for which the tracking problem of periodically time-varying systems was solved in the existing literature. However, iteration techniques were required to approach stable inversion, whose explicit formulas for this tracking problem cannot be obtained. To overcome this drawback, a special kind of stable inversion, named periodic inversion, for the periodic systems is proposed in this study. By means of the lifted technique, the tracking problem of the periodic systems is reformulated to be equivalent to that of lifted systems. In order to obtain precise tracking, the periodic inversion of the periodic systems or the lifted systems is proposed, and is analysed for the non-singular case and the singular case, each of which is further analysed for three cases: the full row rank case, the full column rank case and the rank-deficient case. Thus the periodic inversion of the periodic systems is computed. Accompanied with the optimal state transition method for the time-varying systems, precise trajectory tracking is achieved. The methodology is validated through simulations.

In a previous work (Adimurthi and Yang, 2010 [2] ), Adimurthi–Yang proved a singular Trudinger–Moser inequality in the entire Euclidean space R N ( N ≥ 2 ) . Precisely, if 0 ≤ β 1 and 0 γ ≤ 1 − β , then there holds for any τ > 0 , sup u ∈ W 1 , N ( R N ) , ∫ R N ( | ∇ u | N + τ | u | N ) d x ≤ 1 ⁡ ∫ R N 1 | x | N β ( e α N γ | u | N N − 1 − ∑ k = 0 N − 2 α N k γ k | u | k N N − 1 k ! ) d x ∞ , where α N = N ω N − 1 1 / ( N − 1 ) and ω N − 1 is the area of the unit sphere in R N . The above inequality is sharp in the sense that if γ > 1 − β , all integrals are still finite but the supremum is infinity. In this paper, we concern extremal functions for these singular inequalities. The regular case β = 0 has been considered by Li and Ruf (2008) [12] and Ishiwata (2011) [11] . We shall investigate the singular case 0 β 1 and prove that for all τ > 0 , 0 β 1 and 0 γ ≤ 1 − β , extremal functions for the above inequalities exist. The proof is based on blow-up analysis.

Recently, identifiability results for VAR systems in the context of mixed frequency data have been shown in a number of papers. These results have been extended to VARMA systems, where the MA order is smaller than or equal to the AR order. Here, it is shown that in the VMA case and in the VARMA case, where the MA order exceeds the AR order, results are completely different. Then, for the case, where the innovation covariance matrix is non-singular, “typically” non-identifiability occurs – not even local identifiability. This is due to the fact that, e.g., in the VMA case, as opposed to the VAR case, the not directly observed autocovariances of the output can vary “freely”. In the singular case, i.e., when the innovation covariance matrix is singular, things may be different.

We study a linear integro-differential equation with a coefficient that has finiteorder zeros. We suggest and justify generalized versions of the collocation method based on special polynomials for the approximate solution of this equation in the space of distributions.

Let $(X, \Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. We show that there exists a constant $\delta>0$ such that $\tau(X, \Delta)_P= \tau(X, \Delta + D)_P$ for each effective $\mathbb{Q}$-Cartier divisor $D$ with $\mathrm{mult}_P(D), Comment: 21pages; v2; Proposition-Definition 2.19 of our previous version was not correct, see Remark 2.20 for details, references added, several typos fixed, to appear in Mathematische Zeitschrift

The present paper deals with a linear integral equation of the third kind with fixed singularities in its kernel. We propose and substantiate special generalized methods for its approximate solving in a space of generalized funtions.

Dynamics arising in the Hindmarsh–Rose model are considered from a novel perspective. We study qualitative changes that occur as the time scale of the slow variable increases taking the system far from the slow-fast scenario. We see how the structure of spike-adding still persists far from the singular case but the geometry of the bifurcations changes notably. Particular attention is paid to changes in the shape of the homoclinic bifurcation curves and the disappearance of Inclination-Flip codimension-two points. These transformations seem to be linked to the way in which the spike-adding takes place, the changing from fold/hom to fold/Hopf bursting behavior and also with the way in which the chaotic regions evolve as the time scale of the slow variable increases.

Summary Melanoma in individuals with oculocutaneous albinism has been reported in the literature to be rare compared with the more common occurrence of squamous cell carcinoma and basal cell carcinoma. We present a singular case of amelanotic naevoid melanoma arising from a small congenital naevus in a 16-month old albino boy, the youngest reported to date.