Singular Case Research Articles

MATERIALS OF DIALECTOLOGICAL PRACTICE AS A SOURCE OF THE STUDY OF MODERN MIDDLE POLISSYA DIALECTS

The article confirms the status of the materials of dialectological practice as an important source for the study of Ukrainian dialects from the position of synchrony in general and the study of the modern state of Middle Polissya dialects in particular, given the possibility of recording colloquial speech with the help of various technical devices, which enables its authenticity and reliability. Records of samples of dialectal connected speech, recorded by students of Zhytomyr State University named after Ivan Franko during dialectological practice in 2022–2023 from native speakers of mostly older generations, testify to the preservation of defining dialectal features primarily at the phonetic and morphological levels, which are the most static and undergo the least changes, compared, for example, with the lexical one. The analyzed dialect texts most clearly demonstrate the presence of phonetic features in the realm of vocalism, in particular, the functioning of the sounds of heterogeneous articulation [o] and [e] both in the place of etymological counterparts, and ѣ as a reflex, the absence of [i] and its replacement by other sounds (for example, [i] – in the northern regions Zhytomyr Oblast, [иі] – a bit further south, while the last feature led to a significant number of palatalized sounds, on the one hand, and on the other hand, the presence of dispalatalization of a number of consonant sounds, which has been known in the studied area for a long time. Among the morphological features, the most obvious are the presence of full uncontracted forms of adjectives, pronouns and numerals, truncated forms of adjectives, numerals, pronouns in the masculine singular nominative case, preservation of the ancient ending -e in neuter nouns, the function of the ancient infinitive in -t, etc. At the same time, the materials of dialectological practice actualized a number of problems, which mostly due to extralinguistic factors (the Russian-Ukrainian war, the migration of people from the occupied territories or those where hostilities are ongoing to the territory of Polissya, the migration of the Poleschuks themselves from areas bordering Belarus, the decrease in the number of the autochthonous population, the presence of education in the majority of the inhabitants-speakers etc.) appear every time before dialectologists in the process of collecting speaking material and its subsequent interpretation. In general, the Middle Polissya ethnolinguistic continuum demonstrates durability and continuity in linguistic terms from the most ancient state to the present.

Multiplier ideals of plane curve singularities via Newton polygons

We give a description of the multiplier ideals and jumping numbers associated with a plane curve singularity in a smooth surface in terms of Newton polygons. Our approach is inspired by a theorem of Howald about multiplier ideals of Newton non-degenerate hypersurfaces and our results provide a generalization of it to the case of plane curve singularities. We use toroidal embedded resolutions, which can be applied to the case of quasi-ordinary hypersurface singularities.

Unilateral Posterior Spinal Cord Ischemia Due to a Floating Aortic Thrombus: A Case Report

Introduction. Spinal cord ischemia (SCI) accounts for less than 1% of all strokes, and mostly affects the anterior cord. The ascending aorta (AA) is the rarest site of localization for aortic thrombi (5%). We report a singular case of posterior SCI due to a floating thrombus in the AA. Case presentation. A 75-year-old male with acute left hemiparesis and left tactile and proprioceptive sensory loss below the C5 dermatome (NIHSS 3) is presented. Spinal cord MRI showed a C4–C6 ischemic lesion, involving the left lateral posterior hemi-cord. CT angiography showed a 6 mm floating thrombus in the AA. According to cardiovascular surgeons, dual antiplatelet therapy and high-dose statin were started. After seven days, the patient was discharged with mild left distal hemiparesis and an unchanged sensory deficit. Conclusions. Posterior SCI is rarer than anterior ischemia and potentially unilateral. Its clinical presentation is mainly sensory with possible, but not systematic, weakness of the homolateral limbs. SCI is often caused by aortic pathologies in the elderly, but the incidence rate of non-aneurysmal aortic mural thrombus is about 0.45% and the AA represents a very rare location. In similar cases, conservative medical treatment is preferred despite the high-risk rates of embolic recurrences.

Optimal Temperature Distribution for a Nonisothermal Cahn–Hilliard System with Source Term

In this note, we study the optimal control of a nonisothermal phase field system of Cahn–Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. The system couples a Cahn–Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the constitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails additional mathematical difficulties because the mass conservation of the order parameter, typical of the classic Cahn–Hilliard equation, is no longer satisfied. In this paper, we analyze the case that the double-well potential driving the evolution of the phase transition is differentiable, either (in the regular case) on the whole set of reals or (in the singular logarithmic case) on a finite open interval; nondifferentiable cases like the double obstacle potential are excluded from the analysis. We prove the Fréchet differentiability of the control-to-state operator between suitable Banach spaces for both the regular and the logarithmic cases and establish the solvability of the corresponding adjoint systems in order to derive the associated first-order necessary optimality conditions for the optimal control problem. Crucial for the whole analysis to work is the boundedness property stating that the order parameter attains its values in a compact subset of the interior of the effective domain of the nonlinearity. While this property turns out to be generally valid for regular potentials in three dimensions of space, it can be shown for the logarithmic case only in two dimensions.

On a question of Nori: Obstructions, improvements, and applications

This article concerns a question asked by M. V. Nori on homotopy of sections of projective modules defined on the polynomial algebra over a smooth affine domain R. While this question has an affirmative answer, it is known that the assertion does not hold if: (1) dim(R)=2; or (2) d≥3 but R is not smooth. We first prove that an affirmative answer can be given for dim(R)=2 when R is an F‾p-algebra. Next, for d≥3 we find the precise obstruction for the failure in the singular case. Further, we improve a result of Mandal (related to Nori's question) in the case when the ring A is an affine F‾p-algebra of dimension d. We apply this improvement to define the n-th Euler class group En(A), where 2n≥d+2. Moreover, if A is smooth, we associate to a unimodular row v of length n+1 its Euler class e(v)∈En(A) and show that the corresponding stably free module, say, P(v) has a unimodular element if and only if e(v) vanishes in En(A).

HRAS-mutated primary thyroid malignant melanoma or medullary thyroid carcinoma with melanocytic dedifferentiation? A singular case with an ontogeny-phylogeny quandary.

Melanotic pigment in the thyroid is practically synonymous with chronic minocycline therapy and rare cases of melanotic medullary thyroid carcinoma. However, primary melanoma of the thyroid has not been reported yet. We report a rare case of a 25-year-old male with a locally aggressive thyroid mass and distant metastases at presentation. Radiologically, a 8.3×7.6-cm nodule was identified in the right thyroid lobe. Fine-needle aspiration cytology (FNAC) showed discohesive atypical plasmacytoid cells with prominent nucleoli and no cytoplasmic pigmentation. Serum calcitonin levels were normal. A trucut biopsy showed a malignant tumor with a similar cytomorphology, including marked nuclear pleomorphism. In addition, intracytoplasmic melanin was seen in <1% of cells. Tumor cells were immunonegative for AE1/AE3, TTF1, synaptophysin, and chromogranin while positive for SOX10, S100P, HMB45, and Melan A, confirming the diagnosis of malignant melanoma, without any detectable MTC component in the biopsy. An HRAS G13R mutation was detected on NGS, which, intriguingly, is a known mutation in MTC, and exceedingly rare in melanocytic lesions. No other clinically or radiologically apparent primary lesion was identified elsewhere in the patient. The unusual histology and hitherto unreported molecular findings make this case of primary thyroid melanocytic neoplasm worth reporting. Abstruse origin of melanoma cells in the thyroid gland with molecular signature suggestive of MTC in our case raises a nomenclature and management conundrum, prompting us to revisit the "ontogeny recapitulates phylogeny" theory.

Non-cutaneous syncytial myoepitheliomas are identical to cutaneous counterparts: a clinicopathologic study of 24 tumors occurring at diverse locations.

Cutaneous syncytial myoepithelioma (CSM) is a rare myoepithelioma variant of skin, characterized by intradermal syncytial growth of spindle cells with a distinct immunophenotype of EMA and S100 positivity and infrequent keratin expression. While CSM was first described as a cutaneous tumor, singular non-cutaneous cases have since been reported in bone. We aimed to investigate the clinicopathological features of this variant across all anatomic sites through a large multi-institutional study. We complied a total of 24 myoepitheliomas with syncytial growth from our files. The tumors occurred in 12 male and 12 female patients (M:F = 1:1), with a median age of 31 years (range, 9-69 years). While the majority of tumors (75%, n = 18) occurred in skin, a significant subset (25%, n = 6) arose in non-cutaneous sites, including bone (n = 3), bronchus/trachea (n = 2), and interosseous membrane of tibia/fibula (n = 1). Tumor size ranged from 0.4 to 5.9 cm. Clinical follow-up (7 patients; range 14-202 months; median 56.5 months) showed a single local recurrence 8 years after incomplete skin excision but no metastases; all patients were alive at the time of last follow-up without evidence of disease. Histologically, all tumors were pink at low-power and characterized by a syncytial growth of bland ovoid, spindled, or histiocytoid cells with eosinophilic cytoplasm and prominent perivascular lymphoplasmacytic inflammation. One-third displayed adipocytic metaplasia (8/24). Rare cytologic atypia was seen but was not associated with increased mitotic activity. All tumors expressed S100, SMA, and/or EMA. Keratin expression was absent in most cases. Molecular analysis was performed in 16 cases, all showing EWSR1-rearrangments. In total, 15/15 (100%) harbored an EWSR1::PBX3 fusion, whereas 1 case EWSR1 FISH was the only molecular study performed. Syncytial myoepithelioma is a rare but recognizable morphologic variant of myoepithelioma which may have a predilection for skin but also occurs in diverse non-cutaneous sites. Our series provides evidence supporting a reappraisal of the term "cutaneous syncytial myoepithelioma," as 25% of patients in our series presented with non-cutaneous tumors; thus, we propose the term "syncytial myoepithelioma" to aid pathologist recognition and avoidance of potentially confusing terminology when referring to non-cutaneous examples. The behavior of syncytial myoepithelioma, whether it arises in cutaneous or non-cutaneous sites, is indolent and perhaps benign with a small capacity for local recurrence.

Analysis of the reduction processes at the bottom of Lake Meirama: a singular case of lake formation

The formation of natural lakes is a process that takes place over thousands of years, although the volumetric formation depends on hydrological and climatological phenomena, reaching a stationary hydraulic regime, the evolution of hydrochemistry is more complex and obeys not only phenomena of stoichiometry and chemical kinetics but also diffusion processes. Depending on the depth of the lakes, the anoxization process originating from the bottom is the first phase of the lake’s methanogenesis. For this, the course of many thousands of years is necessary, so the studies carried out in the lakes are limited to the current knowledge of the state in which they are, without being able to have real information in this process of methanogenesis. There are no data available on the generation process of a natural lake in its primary stages. In this case, taking advantage of the rehabilitation of the old open-pit mining of Meirama (Northwest Spain), consisting of the controlled flooding of the hole by groundwater, by stopping the perimeter pumping, and the derivation of the nearby streams, whose contribution was the majority with respect to the subterranean contribution, there has been the opportunity to physically and chemically monitor the complete filling of the said hole. The present study focuses on the analysis of the evolution of the different processes initiated in the methanogenesis of the lake bottom identified in the well-known Redox ladder: obtaining oxygen from the reduction of nitrogenous compounds and metallic oxides, from the reduction of the sulfate and the generation of methane from carbon compounds, the latter phase without reaching. Although the methanization process is very slow, it has had the opportunity to know the formation of a lake at its origin, from the hydrochemical point of view. It has been possible to verify that the methanization processes at the bottom, given the anoxia conditions, are in a very primitive phase with the reduction of nitrate and nitrite to ammonium and beginning a reduction of metal oxides and sulfate.

Gradient estimates of general nonlinear singular elliptic equations with measure data

We develop a global Calderón-Zygmund estimate for the gradients of renormalized solutions to the general nonlinear singular elliptic equations −divA(x,u,Du)=μ on a Reifenberg flat domain with the homogeneous Dirichlet boundary condition, while μ is a finite signed Radon measure. The associated nonlinearity behaves as the elliptic p-Laplacian with respect to Du for the singular case p∈(1,2−1/n], whose discontinuity in the x-variable is measured in terms of small BMO, and the Lipschitz continuity is required with respect to the u-variable. We prove it in two folds: the perturbation technique and the weighted Vitali type covering are first employed to establish the weighted good-λ type inequality, then such inequality is used to prove the desired global gradient estimates in weighted Lorentz spaces and Lorentz-Morrey spaces. As a direct consequence, finally we obtain a global gradient regularity in weighted Orlicz spaces.

On a class of weighted anisotropic p-Laplace equation with singular nonlinearity

We consider a class of singular weighted anisotropic p-Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ensure the existence of at least one weak solution in the purely singular case and at least two different weak solutions in the purturbed singular case.

Mid vowels at the crossroads between standard and regional Italian

Abstract The variety of Italian spoken in Bolzano (South Tyrol) represents a singular case in Italy, because it is not the result of a long-term contact between standard and Italo-Romance dialects but rather the outcome of a process of levelling and koineization. In such sociolinguistic scenario, it is interesting to study phonological variability in Bolzano Italian with the aim of understanding which language varieties have possibly played a role as models from a sociolinguistic point of view. The purpose of our exploratory study is to characterize this variety within the spectrum of variation between the standard and the regional norm. In our analysis, we will focus on the set of mid vowels as a window to understand which variety of Italian BI most closely resembles. Through a corpus-based analysis, we will investigate the phonological distribution of mid vowels (for both Italian and Tyrolean speakers), in order to explore whether it can be explained on the basis of a contextual or a lexical distribution.

A CFD-Based Methodology for Impact Assessment of Industrial Emissions and Evaluation of Mitigation Measures for Regulatory Purposes

In a context where air quality has become a global concern, modelling techniques are becoming very popular for analysing pollutant dispersion conditions. While models based on empirical formulations are most widely used for industrial scenarios, singular cases involving complex terrain or large obstacles in the vicinity of emission sources require a more robust approach to evaluate the dispersion conditions. In this research, a computational fluid dynamics (CFD) model is developed to analyse the dispersion of pollutants from an industrial facility whose location and characteristics suggest the occurrence of complex flow features that affect the dispersion patterns. In addition, the variation of the gas exit temperatures of waste heat recovery systems is proposed as a measure to mitigate the impact of the plume. The simulation results show unexpected deviations in the plume path affecting vulnerable areas in a nearby mountainside, but increasing the gas exit temperature is useful to prevent this event. Therefore, the proposed methodology can be considered a decision support tool to find a compromise between the environmental impact and the fuel consumption of the plant.

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel.

Singular matrices whose Moore-Penrose inverse is tridiagonal

A variety of characterizations of nonsingular matrices whose inverse is tridiagonal (irreducible or not) have been widely investigated in the literature. One well-known such characterization is stated in terms of semiseparable matrices. In this paper, we consider singular matrices A and give necessary and sufficient conditions for the Moore-Penrose inverse of A to be tridiagonal. Our approach is based on bordering techniques, as given by Bapat and Zheng (2003). In addition, we obtain necessary conditions on A analogous to the semiseparability conditions in the nonsingular case, though in the singular case they are not sufficient, as illustrated with examples. We apply our results to give an explicit description of all the 3×3 real singular matrices and 3×3 Hermitian matrices whose Moore-Penrose inverse is irreducible and tridiagonal.

Distribution of Kloosterman paths to high prime power moduli

We consider the distribution of polygonal paths joining the partial sums of normalized Kloosterman sums modulo an increasingly high power p n p^n of a fixed odd prime p p , a pure depth-aspect analogue of theorems of Kowalski–Sawin and Ricotta–Royer–Shparlinski. We find that this collection of Kloosterman paths naturally splits into finitely many disjoint ensembles, each of which converges in law as n → ∞ n\to \infty to a distinct complex valued random continuous function. We further find that the random series resulting from gluing together these limits for every p p converges in law as p → ∞ p\to \infty , and that paths joining partial Kloosterman sums acquire a different and universal limiting shape after a modest rearrangement of terms. As the key arithmetic input we prove, using the p p -adic method of stationary phase including highly singular cases, that complete sums of products of arbitrarily many Kloosterman sums to high prime power moduli exhibit either power savings or power alignment in shifts of arguments.

0832 ABOUT CLOCKS, SLEEP, PAIN AND THEIR INTERACTIVE ROLE IN TMJ OSTEOARTHIRIS - A CASE REPORT

Abstract Introduction As a major cause of disability among older people, Temporomandibular Joint Osteoarthritis (OA) remain a critical issue for both geriatric medicine and public health. While etiologic foundations of this condition are still unclear, it is well known that 24h-driven biological (circadian) rhythms are basic physiological requirements for the homeostatic control of peripheral tissues, such as skeletal muscle, bone and particularly cartilage. Sleep, as the most conspicuous circadian rhythm rooling health and welbeing, is also relevant for anabolic and catabolic processes within cartilage, with nocturnal sleep regulating other factors from which depend important metabolic pathways . Pain, which is chronically coupled to OA is not only impacted by both circadian rhythms and sleep but is itself a contributor to circadian misalignment and sleep disruption which therefore increase pain propensity maintaining a deleterious vicious cycle. Hence, knowledge on such interactive structural and functional composition should be of great relevance both for preventing and successfully treating this chronic, debilitating, neurodegenerative disorder. Methods Authors are reporting an interesting case of a patient in which circadian disruption, impaired sleep and exacerbated persistent pain co-ocur within OA. Sleep questionnaires (Insomnia Severity Index - ISI, STOP-BANG Results NA Conclusion From this singular case, a chronobiological approach (phototherapy) directed to circadian alignment and sleep improvement showed to be effective both for general clinical improvement and for its long-term prognosis associated to OA. Support (if any)

A Comparison Estimate for Singular p-Laplace Equations and Its Consequences

Comparison estimates are an important technical device in the study of regularity problems for quasilinear possibly degenerate elliptic and parabolic equations. Such tools have been employed indispensably in many papers of Mingione, Duzaar-Mingione, and Kuusi-Mingione, etc. on certain measure datum problems to obtain pointwise bounds for solutions and their full or fractional derivatives in terms of appropriate linear or nonlinear potentials. However, a comparison estimate for $p$-Laplace type elliptic equations with measure data is still unavailable in the strongly singular case $1< p\leq \frac{3n-2}{2n-1}$, where $n\geq 2$ is the dimension of the ambient space. This issue will be completely resolved in this work by proving a comparison estimate in a slightly larger range $1<p<3/2$. Applications include a `sublinear' Poincar\'e type inequality, pointwise bounds for solutions and their derivatives by Wolff's and Riesz's potentials, respectively. Some global pointwise and weighted estimates are also obtained for bounded domains, which enable us to treat a quasilinear Riccati type equation with possibly sublinear growth in the gradient.

Machine learning approach to the temperature gradient in the case of discontinuous temperature boundary conditions in a triangular cavity

In this study, a prediction for the temperature gradient close to the sharp corners on a right triangle having singularity is proposed utilizing statistical techniques. This singularity is a result of different Dirichlet types of boundary conditions at the corners. In most of the numerical methods, refinement on corners is done, and computational difficulty in gradient calculation is softened. However, the increased refinement results in a blow-up in the temperature gradient close to the problematic corner. A natural convection flow problem is concerned in a right isosceles triangle in two cases of singularity at the left top corner. In Case 1, the left vertical hot wall and the right inclined cold wall, and in Case 2 the left vertical cold wall and the right inclined hot wall are considered. In the present approach, input data is built from the numerical solution of the problem by cutting the region at a chosen cutting point where almost blow-up starts at the temperature gradient along the hot wall. Then, model functions are derived by using machine learning techniques either multivariate adaptive regression splines (Mars) in R project or Trilayer Neural Network (TNN) in Regression Learner Toolbox in Matlab. The obtained model function for the temperature gradient is used to predict the temperature gradient of points above the cutting point. Therefore, the temperature gradient along the hot wall is calculated by combining the temperature gradients of numerical-below and predicted-above. Average Nusselt number as an integral of the temperature gradient along the concerned hot wall is compared with a reference study, and good agreement is observed. That is, modeling of the temperature gradient on singular points is a way of approach for computing accurate results of the temperature gradient.

Treatment of avoidant-restrictive food intake disorder in an older adult: A proof-of-concept case study.

Cognitive behavioral therapy for Avoidant Restrictive Food Intake Disorder (ARFID; CBT-AR) is an emerging treatment for ARFID. However, this treatment modality has yet to be examined among older adults (e.g., older than 50 years) or with adults presenting with feeding tubes. To inform future versions of CBT-AR, we present the results of a singular case study (G) of an older male with the sensory sensitivity phenotype of ARFID who presented for treatment with a gastrostomy tube. G was a 71-year-old male who completed eight sessions of CBT-AR in a doctoral training clinic. ARFID symptom severity and comorbid eating pathology changes were examined pre- and post-treatment. Posttreatment, G reported significant decreases in ARFID symptom severity and no longer met diagnostic criteria for ARFID. Furthermore, throughout treatment, G reported significant increases in his oral food consumption (vs. calories being pushed through the feeding tube), solid food consumption, and the feeding tube was ultimately removed. This study provides proof of concept that CBT-AR is potentially effective for older adults and/or those presenting for treatment with feeding tubes. Validation of patient efforts and severity of ARFID symptoms emerged as core to treatment success and should be emphasized when training clinicians in CBT-AR. Cognitive behavior therapy for ARFID (CBT-AR) is the leading treatment for this disorder; however, it has yet to be tested among older adults or those with feeding tubes. This single-patient case study demonstrates that CBT-AR may be efficacious in reducing ARFID symptom severity among older adults with a feeding tube.

Geometrical Analysis of a Brick Vault by Slices from the Aurelian Walls in Rome

This work focuses on the analysis of a singular case of brick vault by slices from the Aurelian Walls in Rome. The study is based on an accurate survey carried out through automated photogrammetry. This analysis aims to determine the geometry of the vault and compare it with the theoretical model of its type.