Singular Case Research Articles

Full-deautonomisation of a class of second-order mappings in ancillary form

We present an application of the full-deautonomisation method to a class of secondorder mappings which, using an ancillary variable, can be cast into a form that greatly facilitates the study of their singularities. The ancillary approach was originally introduced to make it possible to construct discrete Painlevé equations associated with the affine Weyl group E (1) 8 by deautonomising a QRT mapping. The full-deautonomisation method has been shown to offer a practical technique for calculating the exact dynamical degree of a mapping, whereby allowing the detection of discrete integrability using only singularity analysis. We study the confinement property for a given singularity, for a wide class of mappings that includes the autonomous limit of the standard additive Painlevé equation with E (1) 8 symmetry. This leads to a class of non-autonomous mappings, which can be integrable or not, for which we obtain their exact dynamical degrees. The case of a non-confining singularity is also analysed and again we obtain the corresponding dynamical degrees.

Multicontact formulation for non-conservative field theories

A new geometric structure inspired by multisymplectic and contact geometries, which we call multicontact structure, is developed to describe non-conservative classical field theories. Using the differential forms that define this multicontact structure as well as other geometric elements that are derived from them while assuming certain conditions, we can introduce, on the multicontact manifolds, the variational field equations which are stated using sections, multivector fields, and Ehresmann connections on the adequate fiber bundles. Furthermore, it is shown how this multicontact framework can be adapted to the jet bundle description of classical field theories; the field equations are stated in the Lagrangian and the Hamiltonian formalisms both in the regular and the singular cases.

Addressing food insecurity and intersectional health-related social needs at a federally qualified health centre during the COVID-19 pandemic: a case study

ABSTRACT The COVID-19 pandemic has exacerbated preexisting health-related social needs (HRSN) in communities already facing health disparities. Federally qualified health centres (FQHC) are well positioned to understand the unique needs of diverse communities and patients. This singular case study provides a novel look into one Massachusetts FQHC's experience addressing increased hunger and poverty in their patient population. Interviews with the FQHC staff and leadership explored perspectives on the centre's current practices to address food insecurity, barriers they face, and hopes for improving community health. Interviews were recorded, transcribed, and coded using grounded theory methods. Participants were equivocal about whether food insecurity was the largest problem patients are facing. They rather emphasised the intersectional nature HRSN, including housing instability, occupational health hazards, and unemployment. Stigma associated with utilising social services, HRSN screening disruptions, and capacity limitations were barriers to addressing the community's needs. Participants highlighted the importance of patient agency; allowing patients to choose for themselves how and where they spend money to meet their health needs. The need to invest in community-centred and culturally sensitive solutions was also emphasised. Longer-term interventions, such as application assistance to federal nutrition assistance programmes, were highly favoured over emergency aid. Addressing the root causes of poverty and health disparities was recognised as essential to improving community health both during and after the pandemic. Findings highlight the importance of fostering trust and supporting community-centred and justice-oriented interventions that go beyond emergency assistance and individualised care.

Killed distribution dependent SDE for nonlinear Dirichlet problem

To characterize nonlinear Dirichlet problems in an open domain, we investigate killed distribution dependent SDEs. By constructing the coupling by projection and using the Zvonkin/Girsanov transforms, the well-posedness is proved for three different situations:1) monotone case with distribution dependent noise (possibly degenerate);2) singular case with non-degenerate distribution dependent noise;3) singular case with non-degenerate distribution independent noise. In the first two cases the domain is $ C^2 $ smooth such that the Lipschitz continuity in initial distributions is also derived, and in the last case the domain is arbitrary.

Quality-of-life Assessment among Children with Esophageal Achalasia.

Analyze the surgical management strategy and the current effects on Quality of Life of diagnosed Esophageal Achalasia (EA) patients in our department, with an assessment of the incidence, clinical course, and related disorders. Data was based on a retrospective review of all children who received achalasia treatment at our department between 2008 and 2022. Using the Pediatric Quality of Life Inventory Generic Core (PedsQL) Scales and the Pediatric-QL Gastrointestinal Symptoms Module (GI-PedsQL), we evaluated the long-term effects of this diagnosis on our patients' quality of life. Esophageal achalasia (EA) was identified in a total of 13 cases (F: 7; M: 6). The mean patient delay was 27.90 months, and the median age was 6.5 years at diagnosis (2 months to 15 years). Regurgitation was the most frequently observed symptom, and the median follow-up was 7.32 (3- 30.7) months. There were descriptions of associations with Allgrove syndrome (n=7) and Down syndrome (n=1). All patients were treated by Open Heller myotomy (OHM) with one patient (n=1) initially treated by pneumatic dilatation (PD). In all 13 laparotomy myotomies, simultaneous fundoplication was performed using the DOR (n=12) and THAL (n=1) techniques. At follow-up, 12 patients had complete symptom relief with 1 patient exhibiting a persistence of symptoms. All 13 patients were prospectively contacted with a median time from latest check-up to date of inclusion of 2.9 (0.3-8.8) years. In comparison to data from a control group of EA patients, the overall PedsQL score of our patients was 72/100 (±17), with higher established scores in physical and emotional functioning but lower scores in social and school settings. On the other hand, when compared to a control group presenting with a gastroesophageal reflux disease (GERD), the GI-PedsQL overall score in our patients was higher with a 76/100 (±14.9), but they scored significantly lower in the dimensions: Foods and drinks limitations, difficulty swallowing, heartburn and vomiting. Our study group's characteristics join most of the published literature with 54% of our patients presenting with Allgrove syndrome but it also joins the much rarer descriptions of Achalasia and Down's syndrome association with a singular case. The clinical course of our diagnosis process mainly consisted of timed esophagram and UGI endoscopy, lacking significantly in HREM evaluations but was efficient enough in guiding the surgical management. Our findings confirm the safety and effectiveness of Open Heller's myotomy with a success rate of 92.3% However, we concede that a laparoscopic approach should be further adopted if no contradiction is found. Moreover, we presented insight on long term QoL of patients posteriori to HM which was in concordance with other global experiences where patients reported dissatisfaction with their health and limited lifestyle. This significant negative impact was prominently present in comparison to healthy control groups as well as patients with inflammatory bowel diseases and compels a much needed discussion on the major chronic repercussions of Esophageal Achalasia in children. Even when managed by interdisciplinary teams of professionals, managing esophageal achalasia in specialized institutions is still a subject of debate. Early pediatric diagnosis is best achieved with routine physiological function tests and HREM. Moreover, more research is required to assess long-term Quality of Life. Standardized lifelong follow-up and qualified resources, both human and technological, are required to improve postoperative outcomes.

A NOVEL COLLECTIVE ALGORITHM USING CUBIC UNIFORM SPLINE AND FINITE DIFFERENCE APPROACHES TO SOLVING FRACTIONAL DIFFUSION SINGULAR WAVE MODEL THROUGH DAMPING-REACTION FORCES

Uses of time-fractional diffusion wave model (TFDWM) in its singular case with damping-reaction terms are widely seen in classical physics applications, e.g. for the quantitative measurement of activity diagnoses light-mechanical waves resulting from many physical experiments. The goal and importance of this paper are to predict and build accurate and convincing numerical solutions for TFDWM in its singular version by employing the collective cubic uniform B-spline approach (CUBSA) and standard finite difference approach (SFDA). The fractional Caputo time derivative (FCTD) has been estimated and broken down using SFDT, whilst the standard splines will be utilized upon realizing spatial discretization. To study the prediction error of our approach, some convergence and bound results are given under certain constraints. We demonstrate applications of our collective algorithm to a couple of fractional singular-type models appearing in fluid dynamics and electromagnetics. Detailed analysis, delegate tables, and representative graphs are displayed and offered in different dimensions to handle the crossover meaning for several order values of FCTDs. Some conclusions, observations, recommendations, and future issues were briefly raised in the final section of this paper.

Innerization and Singular LQ Control Problem for Linear Discrete-Time Systems

In this paper, we discuss the LQ problem for discrete-time linear systems with singular weight. The interactor with all-pass property is used in order to make a given strictly proper system be proper. In our approach, the type of Riccati equation to be solved is different from the result for a square transfer function matrix case, where the input weight equals to zero. The relation between our approach and the singular weight case is discussed. Unlike the square case, the explicit solution to the problem cannot be obtained and a recursive method to solve the Riccati equation is shown. An application to the finite settling-time control is also discussed.

A singular case of embolic inferior ST-elevation myocardial infarction 40 years after surgical closure of a right coronary to right atrium fistula.

A singular case of embolic inferior ST-elevation myocardial infarction 40 years after surgical closure of a right coronary to right atrium fistula.

Recovery of Nazi Looted Books in the UCLA Library: From Prague to Los Angeles and Back

This article details the search for books from the Jewish Religious Community Library in Prague that were looted by the Nazis, and how the institution’s curators are working today to rebuild their original collection. It traces the history of the Prague Library, the Nazis’ policies of confiscating Jewish books for their proposed institutes on the ‘Jewish Question,’ and how some of these confiscated books ended up in the UCLA Library. Librarians at UCLA did not find any professional guidelines for the repatriating looted material from academic libraries, even though the museum and art worlds have dealt with these issues for decades. We share processes we developed and our quest to publicize this issue as broadly as possible. We also discuss methods that European librarians are currently using research provenance. Ours is a singular case, and institutions must understand that each question of repatriation must be considered within its own particular context. We offer some models for addressing repatriation questions and call for an organized English language forum where Judaica librarians in academic libraries and archives everywhere can discuss these issues in order to promote broader understanding, collaboration, and actions.

Omni-Joint a Comparative Study for Singularity

The methodology used in this paper is; finding the singularity case using the determinant of the Jacobian (which transforms from the joint-space to the work-space) using MATLAB. The determinant is plotted; first with respect to the variables of the joint-space, second with respect to the variables of the work-space.

Existence and regularity estimates for quasilinear equations with measure data : the case 1 < p ≤ (3n − 2)∕(2n − 1)

We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are of the form $-{\rm div} (|\nabla u|^{p-2} \nabla u)= \delta\, |\nabla u|^q +\mu$ in a bounded main $\Om\subset\RR^n$ potentially with non-smooth boundary. Here either $\delta=0$ or $\delta=1$, $\mu$ is a finite signed Radon measure in $\Omega$, and $q$ is of linear or super-linear growth, i.e., $q\geq 1$. Our main concern is to extend earlier results to the strongly singular case $1<p\leq \frac{3n-2}{2n-1}$. In particular, in the case $\delta=1$ which corresponds to a Riccati type equation, we settle the question of solvability that has been raised for some time in the literature.

Virtual mutations of weighted surface algebras

The finite-dimensional symmetric algebras over algebraically closed fields, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface algebras and their deformations were introduced and studied in [14–18], and it was shown that all these algebras, except a few singular cases, are symmetric tame periodic algebras of period 4. In this article, using the general form of a weighted surface algebra from [17], we introduce and study so called virtual mutations of weighted surface algebras, which constitute a new large class of symmetric tame periodic algebras of period 4. We prove that all these algebras are derived equivalent but not isomorphic to weighted surface algebras. The results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.

Characterization of the D-Laguerre–Hahn orthogonal polynomials of class one via the cubic decomposition

In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) . Our goal is to determine all D-Laguerre–Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre–Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence coefficients are highlighted.

Two singular problems of dual-phase-lag thermo-porous-elasticity with microtemperatures

In a recent paper the authors studied a generic problem determined by the one-dimensional porous-thermoelasticity with microtemperatures in the context of the dual-phase-lag theory. Energy decay rates for that system were obtained. However, there were several cases when the coupling between the different components defining the system of equations is weaker that were not treated. In this paper we are interested in these singular cases and we will prove the polynomial decay of the solutions depending on the relations of the relaxation parameters.

Collision avoidance and asymptotic flocking in the delayed Cucker−Smale model with singular short range communication weights

The delayed Cucker−Smale (C−S) flocking model has been widely studied, however, only when the communication weights are regular. For the singular short range communication case, collision avoidance is the key of both well-posedness and large time behavior. In this paper, by an inequality of second-order velocity-position moment, collision avoidance1 is proved for the delayed C−S with some singular short range communication weights. Then, asymptotic flocking is established for some restricted initial data.

Numerical Solutions of Volterra Integral Equations of Third Kind and Its Convergence Analysis

The current work suggests a method for the numerical solution of the third type of Volterra integral equations (VIEs), based on Lagrange polynomial, modified Lagrange polynomial, and barycentric Lagrange polynomial approximations. To do this, the interpolation of the unknown function is considered in terms of the above polynomials with unknown coefficients. By substituting this approximation into the considered equation, a system of linear algebraic equations is obtained. Then, we demonstrate the method’s convergence and error estimations. The proposed approaches retain the possible singularity of the solution. To the best of the authors’ knowledge, the singularity case has not been addressed by researchers yet. To illustrate the applicability, effectiveness, and correctness of new methods for the proposed integral equation, examples with both types of kernels, symmetric as well as non-symmetric, are provided at the end.

Late Bronze Age Pot Marks From Thyateira – Hastane Höyüğü

Various hypotheses have been formulated to explain the function and meaning of pre-post firing marks in the Late Bronze Age Anatolia. Known as "pot marks," these signs have been prominently associated with the administrative systems–central authorities or viewed as an indicator of asymmetric interregional economic relations. However, these interpretations are not suitable for Western Anatolia due to the limited number of pot marks found in a few settlements, the distinctive qualities of pottery tradition in the region, and the lack of institutionalized interregional economic connections. This article presents the first examples of pot marks found in Akhisar-Hastane Höyük/Central West Anatolia with preliminary observations on the Late Bronze Age pottery groups. It emphasizes the ambiguous nature of pot marks, their typological similarities, and differences among non-regional parallels and suggests that their appearances in the Western Anatolian LBA settlements should be considered as singular cases for now.

Ein Lesevorschlag zur lykischen Inschrift TL 106

It is proposed that the inscription be segmented at a different point to the usual, namely, immediately before ñneti. The content of the second curse is then that the perpetrator shall be defiled commensurately with the defilement of the tomb, i.e., a singular case of a talion not attested elsewhere in Lycian inscriptions, nor in Greek inscriptions from Lycia. A request to bury "my" wife and "my" children follows as an additional, third part to the inscription as originally planned, then a further addition of two persons. The verb ñneti is also attested in a non-funereal inscription, probably a treaty, and replaces here the usual verbs for "to bury". Placing the verb at the beginning of the sentence is also unusual, and this may have led the epigrapher to add it, without a word divider, onto the end of the second line.

The Picaresque and the Writing Life in Mexico

The Picaresque and the Writing Life in Mexico

Stabilities and Non-Stabilities of a New Reciprocal Functional Equation

Abstract The intention of this study is to present some stronger results by investigating Ulam-JRassias product stability and Ulam-JRassias mixed-type sum-product stability of a new reciprocal functional equation. Also, a suitable counter-example is presented to show the failure of stability result for the singular case.