Miracle-dz/UniFAR-FTUs huggingface dataset:
Stationary compressible Navier–Stokes
equations with inflow condition in domains with piecewise analytical
boundaries

We show the existence of strong solutions in Sobolev-Slobodetskii spaces to the stationary compressible Navier-Stokes equations with inflow boundary condition. Our result holds provided certain condition on the shape of the boundary around the points where characteristics of the continuity equation are tangent to the boundary, which holds in particular for piecewise analytical boundaries. The mentioned situation creates a singularity which limits regularity at such points. We show the existence and uniqueness of regular solutions in a vicinity of given laminar solutions under the assumption that the pressure is a linear function of the density. The proofs require the language of suitable fractional Sobolev spaces. In other words our result is an example where application of fractional spaces is irreplaceable, although the subject is a classical system.
Diameter, Decomposability, and Minkowski Sums of Polytopes

Abstract We investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the diameter of each summand and above by, roughly, the product between the diameter of one summand and the number of vertices of the other. We also prove that both bounds are sharp. In addition, we obtain a result on polytope decomposability. More precisely, given two polytopes $P$ and $Q$ , we show that $P$ can be written as a Minkowski sum with a summand homothetic to $Q$ if and only if $P$ has the same number of vertices as its Minkowski sum with $Q$ .
A ‘wiring diagram’ for sink strength traits impacting wheat yield potential

Abstract Identifying traits for improving sink strength is a bottleneck to increasing wheat yield. The interacting processes determining sink strength and yield potential are reviewed and visualized in a set of ‘wiring diagrams’, covering critical phases of development (and summarizing known underlying genetics). Using this framework, we reviewed and assembled the main traits determining sink strength and identified research gaps and potential hypotheses to be tested for achieving gains in sink strength. In pre-anthesis, grain number could be increased through: (i) enhanced spike growth associated with optimized floret development and/or a reduction in specific stem–internode lengths and (ii) improved fruiting efficiency through an accelerated rate of floret development, improved partitioning between spikes, or optimized spike cytokinin levels. In post-anthesis, grain, sink strength could be augmented through manipulation of grain size potential via ovary size and/or endosperm cell division and expansion. Prospects for improving spike vascular architecture to support all rapidly growing florets, enabling the improved flow of assimilate, are also discussed. Finally, we considered the prospects for enhancing grain weight realization in relation to genetic variation in stay-green traits as well as stem carbohydrate remobilization. The wiring diagrams provide a potential workspace for breeders and crop scientists to achieve yield gains in wheat and other field crops.
More Reduced Obstruction Theories

We first develop a general formalism for globally removing factors from an obstruction theory. We then apply this formalism to give a construction of a reduced obstruction theory on the moduli space of morphisms from a curve to a surface f : C → S in class β such that H(C, f∗TS) − ∪β → H2(S,OS) is surjective. This condition appears in recent work of Kool and Thomas.
Correlation between galactic HI and the cosmic microwave background

We revisit the issue of a correlation between the atomic hydrogen gas in our local galaxy and the cosmic microwave background, a detection of which has been claimed in some literature. We cross correlate the 21-cm emission of galactic atomic hydrogen as traced by the Leiden/Argentine/Bonn Galactic Hi survey with the 3-year cosmic microwave background data from the Wilkinson microwave anisotropy probe. We consider a number of angular scales, masks, and Hi velocity slices and find no statistically significant correlation.
Clinical Reasoning: A 66-Year-Old Woman With Progressive Encephalopathy and Bilateral Hearing Loss

A 66-year-old woman with no medical history presented to an outside hospital for an acute alteration in cognition described as wandering aimlessly, combative behavior, and incomprehensible speech that progressed over 3 days. On arrival, she had altered cognition, psychomotor agitation, and inability to follow commands, but no weakness, dysarthria, sensation loss, vision loss, or meningismus. Vital signs and laboratory studies including complete blood count, comprehensive metabolic panel, urinalysis, and urine drug screen were normal.
A Local Limit Theorem and Loss of Rotational Symmetry of Planar Symmetric Simple Random Walk

We use elementary methods to derive a sharp local central limit theorem for simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant from the starting point. More specifically, we give explicit asymptotic expressions in terms of n and x in dimensions one and two for P (S(n) = x), the probability that simple random walk S is at some point x at time n, that are valid for all |x| ≤ n/ log(n). We also show that the behavior of planar simple random walk differs radically from that of planar standard Brownian motion outside of the disk of radius n, where simple random walk ceases to be approximately rotationally symmetric. Indeed, if n = o(|S(n)|), S(n) is more likely to be found along the coordinate axes. This loss of rotational symmetry is not surprising, since if |S(n)| = n, there are only four possible locations for S(n). In this paper, we show how the transition from approximate rotational symmetry to complete concentration of S along the coordinate axes occurs.
Root Systems In Finite Symplectic Vector Spaces

We study realizations of root systems in possibly degenerate symplectic vector spaces over finite fields, up to symplectic isomorphisms. The main result of this article is the classification of such realizations for the field 𝔽2. Thereby, each root system requires a specific degree of degeneracy of the symplectic vector space. Our main motivation for this article is that for each such realization of a root system we can construct a Nichols algebra over a nonabelian group.
Small intracranial aneurysms of the anterior circulation: A negligible risk?

According to the International Study of Unruptured Intracranial Aneurysms, small (<7 mm) unruptured intracranial aneurysms (IAs) of the anterior circulation (aC) carry a neglectable 5‐year rupture risk. In contrast, some studies report frequencies of >20% of all ruptured IAs being small IAs of the aC. This contradiction was addressed in this study by analyzing the rates and risk factors for rupture of small IAs within the aC.
Taxonomic abundance in primary and secondary root canal infections

Abstract Aim To evaluate the root canal microbiome composition in cases of primary and secondary apical periodontitis. Methodology Thirty‐nine samples from patients with primary root canal infections obtained before root canal treatment, and 40 samples obtained during root‐end resection procedures from previously filled cases with apical periodontitis were evaluated using 16S rRNA next‐generation sequencing analysis (NGS). Demographic and clinical factors included age, sex, infection type, percussion sensitivity, and presence of pain. Differences in abundances of genera were evaluated using Kruskal‐Wallis test. Alpha and beta diversity indices were calculated using mothur. The Shannon and Chao1 indices were used to measure alpha diversity. The Bray–Curtis dissimilarity was used to measure beta diversity. Differences in community composition were evaluated using analysis of similarity (ANOSIM) with Bonferroni correction for multiple comparisons. Results Significantly fewer operational taxonomic units values were observed from samples from secondary infections (p < .0001). While no significant differences were observed in the Chao 1 index between primary and secondary infections, the Shannon alpha diversity was significantly lower in secondary relative to primary infections (p = .008). Among samples, sex, age (adult vs. older adult), percussion sensitivity, and presence of pain all showed no significant effects on community composition via an analysis of similarity (ANOSIM). However, community composition was significantly different depending on whether the sample was from a primary or secondary infection (R = .051, p = .03). Nine microbial genera comprised the predominant taxa observed among samples (>3.3%) and included Parvimonas, Fusobacterium, Campylobacter, Arachnia, Eubacterium, Prevotella, Peptostreptococcus, Fretibacterirum, and Pseudoramibacter. Significantly greater relative abundances of Prevotella, Peptostreptococcus, Veillonella, Lactucaseibacillus, and Dialister were observed in primary infections. Conclusions Primary endodontic infections are more diverse than secondary infections. The microbial composition is not associated with the clinical manifestations of apical periodontitis.
Psychometric properties of the Swedish version of the Reynolds Adolescent Depression Scale second edition (RADS-2) in a clinical sample

Abstract Objective: Observed and predicted increases in the global burden of disease caused by major depressive disorder (MDD) highlight the need for psychometrically robust multi-dimensional measures to use for clinical and research purposes. Reynolds Adolescent Depression Scale second edition (RADS-2) is an internationally well-validated scale measuring different dimensions of adolescent depression. The Swedish version has previously only been evaluated in a normative sample. Methods: We collected data from patients in child and adolescent psychiatry and primary care and performed: (1) Confirmatory factor analysis (CFA) to evaluate the established four-factor structure, (2) Analyses of reliability and measurement invariance, (3) Analyses of convergent and discriminant validity using the Montgomery–Asberg Depression Rating Scale, the depression subscales of the Beck Youth Inventories and the Revised Child Anxiety and Depression Scale, as well as the Patient Reported Outcome Measurements Information System, peer-relationships and physical activity item banks. Results: Recruited participants (n = 536, 129 male and 407 female, mean age 16.45 years, SD = 2.47, range 12 − 22 years) had a variety of psychiatric diagnoses. We found support for the four-factor structure and acceptable to good reliability for the subscale and total scores. Convergent and discriminant validity were good. Measurement invariance was demonstrated for age, sex, and between the present sample and a previously published normative sample. The RADS-2-scores were significantly higher in the present sample than in the normative sample. In this clinical study, the Swedish RADS-2 demonstrated good validity and acceptable to good reliability. Our findings support the use of RADS-2 in Swedish clinical and research contexts.
Update on 3-folds

The familiar division of compact Riemann surfaces into 3 cases g = 0, 5 = 1 and g > 2 corresponds to the well known trichotomy of spherical, Euclidean and hyper­ bolic non-Euclidean plane geometry. Classification aims to treat all projective algebraic varieties in terms of this trichotomy; the model is Castelnuovo and Enriques' treatment of surfaces around 1900 (reworked by Kodaira in the 1960s). The canonical class of a variety may not have a definite sign, so we usually have to beat it up before the trichotomy applies, by a minimal model program (MMP) using contractions, flips and fibre space decompositions. The classification of 3-folds was achieved by Mori and others during the 1980s. New results over the last 5 years have added many layers of subtlety to higher dimensional classification. The study of 3-folds also yields a rich crop of applications in several different branches of algebra, geometry and theoretical physics. My lecture surveys some of these topics.
Quorum sensing in biofilms: a key mechanism to target in ecotoxicological studies

Abstract Our environment is heavily contaminated by anthropogenic compounds, and this issue constitutes a significant threat to all life forms, including biofilm-forming microorganisms. Cell–cell interactions shape microbial community structures and functions, and pollutants that affect intercellular communications impact biofilm functions and ecological roles. There is a growing interest in environmental science fields for evaluating how anthropogenic pollutants impact cell–cell interactions. In this review, we synthesize existing literature that evaluates the impacts of quorum sensing (QS), which is a widespread density-dependent communication system occurring within many bacterial groups forming biofilms. First, we examine the perturbating effects of environmental contaminants on QS circuits; and our findings reveal that QS is an essential yet underexplored mechanism affected by pollutants. Second, our work highlights that QS is an unsuspected and key resistance mechanism that assists bacteria in dealing with environmental contamination (caused by metals or organic pollutants) and that favors bacterial growth in unfavourable environments. We emphasize the value of considering QS a critical mechanism for monitoring microbial responses in ecotoxicology. Ultimately, we determine that QS circuits constitute promising targets for innovative biotechnological approaches with major perspectives for applications in the field of environmental science.
Molecular typing of dengue virus in Mizoram, Northeast India.

INTRODUCTION Dengue is an emerging vector-borne public health threat and characterization at the molecular level is important for proper management of the disease. The aim of the study is to examine the diversity of the dengue viral serotypes from a hilly mountainous region of Northeast India. METHODOLOGY Thirty-six blood samples that were positive for dengue virus IgM antibodies identified by the enzyme-linked immunosorbent assay (ELISA) method were collected and quantified for the IL6 gene expression by using reverse transcriptase polymerase chain reaction (RT-PCR). RESULTS All the patients had dengue hemorrhagic fever (DHF); 12 samples had a monotypic infection and 14 samples had dual infection with various dengue virus (DENV) serotypes; one sample had triple infection with DENV-1, DENV-2, and DENV-3. CONCLUSIONS This study identified DENV-1 as the major serotype in the state of Mizoram and it is the first report on the molecular typing of the dengue virus from the hilly mountainous state located in the Indo-Burma region bordering Myanmar and Bangladesh.
Optical far-infrared properties of a graphene monolayer and multilayer

We analyze the features of the graphene mono- and multilayer reflectance in the far-infrared region as a function of frequency, temperature, and carrier density taking the intraband conductance and the interband electron absorption into account. The dispersion of plasmon mode of the multilayers is calculated using Maxwell's equations with the influence of retardation included. At low temperatures and high electron densities, the reflectance of multilayers as a function of frequency has the sharp downfall and the subsequent deep well due to the threshold of electron interband absorption and plasmon excitations.
On a three-layer Hele-Shaw model of enhanced oil recovery with a linear viscous profile

We present a non-standard eigenvalue problem that arises in the linear stability of a three-layer Hele-Shaw model of enhanced oil recovery. A nonlinear transformation is introduced which allows reformulation of the non-standard eigenvalue problem as a boundary value problem for Kummer's equation when the viscous profile of the middle layer is linear. Using the existing body of works on Kummer's equation, we construct an exact solution of the eigenvalue problem and provide the dispersion relation implicitly through the existence criterion for the non-trivial solution. We also discuss the convergence of the series solution. It is shown that this solution reduces to the physically relevant solutions in two asymptotic limits: (i) when the linear viscous profile approaches a constant viscous profile; or (ii) when the length of the middle layer approaches zero.
A guide to closure operations in commutative algebra

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.
Response surface methodology to investigate the comparison of two carbon-based air cathodes for bio-electrochemical systems

ABSTRACT Bio-electrochemical technologies can generate renewable electrical bioenergy from the oxidation of organic materials through the catalytic reactions of the microorganisms while treating the wastewater. In this study, the use of carbon aerogel as a novel catalyst with high porosity (the total pore volume of 1.84 cm3 g−1) and high surface area (491.7 m2/g) for improving the oxygen reduction reaction (ORR) performance was compared to that of the conventional activated carbon, employed as an air cathode catalyst in bio-electrochemical systems, with the indigenous bacterial consortium. The electrochemical studies revealed the higher power efficiency in the use of carbon aerogel (with the maximum power density and current density of a 675 mWm−2 and 33.1 mAm−2, respectively), compared to the activated carbon (with the maximum power density and current density of 668.98 mWm−2 and 23.2 mAm−2, respectively). The performance of the two materials and optimum conditions for electricity production were examined using the Response Surface Method (RSM) as an optimal design method. Statistical analysis confirmed that the carbon aerogel performed better than the activated carbon in power production and facilitated cathodic redox reactions. Comparison of two catalysts showed that the redox reactions occurred in the presence of carbon aerogel more facilitated and in a wider range, produced 1.2 times more current (the maximum 2.1 and 1.69 mA current). Carbon aerogel, with a suitable load absorbance and resistance to oxidation at urban wastewater pH, can be, therefore, coated on electrodes to facilitate the oxidation–reduction reactions and electricity transmission. GRAPHICAL ABSTRACT
Symmetry and Topology in Non-Hermitian Physics

We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, point-like and line-like vacant regions. On the basis of these concepts and K-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons.
Canonical field quantization in momentum space and quantum space-time

We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a mathematically consistent way to quantize space-time in the same way that energy and momentum are quantized in standard quantum field theories.
On the unicity of formal category theories

We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category $\mathcal K$. In order to do this, we recognize the presheaf construction of a cocomplete Yoneda structure as a relative, lax idempotent monad sending each admissible 1-cell $f :A \to B$ to an adjunction $\boldsymbol{P}_! f\dashv\boldsymbol{P}^*f$. Each cocomplete Yoneda structure on $\mathcal K$ arises in this way from a relative lax idempotent monad "with enough adjoint 1-cells", whose domain generates the ideal of admissibles, and the Kleisli category of such a monad equips its domain with proarrows. We call these structures "yosegi". Quite often, the presheaf construction associated to a yosegi generates an ambidextrous Yoneda structure; in such a setting there exists a fully formal version of Isbell duality.
Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds

ABSTRACT We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.