Miracle-dz/UniFAR-FTUs huggingface dataset:
Almost Kaehler geometry of adjoint orbits of semisimple Lie groups

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the Chern-Ricci form, the Hermitian scalar curvature and the Nijenhuis tensor in terms of root data. We also discuss when the Chern-Ricci form is a multiple of the symplectic form, and when compact quotients of these orbits are of Kaehler type.
Schrödinger spectrum generated by the Cornell potential

Abstract The eigenvalues Ednl (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > 0 are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is suffcient to know E(1, λ), and the envelope method provides analytic bounds for the equivalent complete set of coupling functions λ(E). Meanwhile the easily-implemented AIM procedure yields highly accurate numerical eigenvalues with little computational effort.
Transition of streamwise streaks in zero-pressure-gradient boundary layers

A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation (Andersson et al. 2001), the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. The main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low-speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern. The present scenario is compared with transition initiated by Tollmien–Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.
Dynamics of Newton maps

Abstract In this paper, we study the dynamics of the Newton maps for arbitrary polynomials. Let p be an arbitrary polynomial with at least three distinct roots, and f be its Newton map. It is shown that the boundary $\partial B$ of any immediate root basin B of f is locally connected. Moreover, $\partial B$ is a Jordan curve if and only if $\mathrm {deg}(f|_B)=2$ . This implies that the boundaries of all components of root basins, for the Newton maps for all polynomials, from the viewpoint of topology, are tame.
Wave functions in abelian Chern-Simons theory on the torus as modular forms of weight two

It is argued that in the context of geometric quantization holomorphic part of zero-mode wave functions in abelian Chern-Simons theory on the torus can naturally be considered as modular forms of weight 2. In the geometric quantization the zero-mode wave function can be defined as $\Psi [ a, {\bar a} ] = e^{- \frac{K(a, {\bar a})}{2}} f (a)$ where $K(a ,{\bar a} )$ denotes a K\"ahler potential for the zero-mode variable $a \in \mathbb{C}$ on the torus. We first review that $f(a)$ can be described in terms of Jacobi theta functions by imposing gauge invariance on $\Psi [ a, {\bar a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. We discuss that $f(a)$ is quantum theoretically characterized by ($i$) an operative relation in the $a$-space representation and ($ii$) an inner product of $\Psi [ a, {\bar a} ]$'s including ambiguities in the choice of $K(a ,{\bar a} )$. We then consider a similar gauge invariance condition on $\Psi [ a, {\bar a} ]$ associated with modular transformations of $a$. We choose the modular parameter $\tau = i \tau_2 $ of the torus such that the number density of the zero modes is preserved under the modular transformations of $a$. The results illustrate that we can quantum theoretically identify $f(a)$ as a modular form of weight 2. We confirm this statement by use of a specific representation of $f(a)$ in terms of the Jacobi theta function. We also indicate that the wave-function inner product gives rise to a quantum version of the Petersson inner product for the modular forms of weight 2.
Gauged twistor formulation of a massive spinning particle in four dimensions

We present a gauged twistor model of a free massive spinning particle in four-dimensional Minkowski space. This model is governed by an action, referred to here as the gauged generalized Shirafuji (GGS) action, that consists of twistor variables, auxiliary variables, and $U(1)$ and $SU(2)$ gauge fields on the one-dimensional parameter space of a particle's worldline. The GGS action remains invariant under reparametrization and the local $U(1)$ and $SU(2)$ transformations of the relevant variables, although the $SU(2)$ symmetry is nonlinearly realized. We consider the canonical Hamiltonian formalism based on the GGS action in the unitary gauge by following Dirac's recipe for constrained Hamiltonian systems. It is shown that just sufficient constraints for the twistor variables are consistently derived by virtue of the gauge symmetries of the GGS action. In the subsequent quantization procedure, these constraints turn into simultaneous differential equations for a twistor function. We perform the Penrose transform of this twistor function to define a massive spinor field of arbitrary rank, demonstrating that the spinor field satisfies generalized Dirac-Fierz-Pauli equations with $SU(2)$ indices. We also investigate the rank-one spinor fields in detail to clarify the physical meanings of the $U(1)$ and $SU(2)$ symmetries.
A threshold for cutoff in two-community random graphs

In this paper, we are interested in the impact of communities on the mixing behavior of the non-backtracking random walk. We consider sequences of sparse random graphs of size $N$ generated according to a variant of the classical configuration model which incorporates a two-community structure. The strength of communities is measured by a parameter $\alpha$ which roughly corresponds to the fraction of edges that go from one community to the other. We show that if $\alpha\gg \frac{1}{\log N}$, then the non-backtracking random walk exhibits cutoff at the same time as in the one-community case, but with a larger cutoff window, and that the distance profile inside this window converges to the Gaussian tail function. On the other hand, if $\alpha\ll \frac{1}{\log N}$, then there is no cutoff.
Diagram uniqueness of even plats

Every knot has a plat projection, obtained by closing up a braid with bridges. The plat projection is determined by the number of strands and the number of rows of twist regions in the braid, and an integer number of crossings in each twist region. In recent work, we showed that under certain restrictions, including that the number of rows is odd, a minimal width plat projection is unique. In this paper we extend the results to even plats. Using new arguments, we show that if each of their twist regions contains at least three crossings, and their length is sufficiently long with respect to their width, then the projection is unique. This essentially "doubles" the set of knots for which such diagrams classify the links.
Knot theory of Morse-Bott critical loci

We give an alternative proof of that a critical knot of a Morse-Bott function $f: S^3 \rightarrow \mathbb{R}$ is a graph knot where the critical set of $f$ is a link in $S^3$. Our proof inducts on the number of index-1 critical knots of $f$.
K\"ahler-Ricci Flow on Projective Bundles over K\"ahler-Einstein Manifolds

We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum profile, we give a criterion, characterized by the triple $(\Sigma, L, [\omega_0])$, under which the $\mathbb{P}^1$-fiber collapses along the K\"ahler-Ricci flow and the projective bundle converges to $\Sigma$ in Gromov-Hausdorff sense. Furthermore, the K\"ahler-Ricci flow must have Type I singularity and is of $(\C^n \times \mathbb{P}^1)$-type. This generalizes and extends part of Song-Weinkove's work \cite{SgWk09} on Hirzebruch surfaces.
On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means

The aim of this paper is to characterize the so-called Hardy means, i.e., those means $M\colon\bigcup_{n=1}^\infty \mathbb{R}_+^n\to\mathbb{R}_+$ that satisfy the inequality $$ \sum_{n=1}^\infty M(x_1,\dots,x_n) \le C\sum_{n=1}^\infty x_n $$ for all positive sequences $(x_n)$ with some finite positive constant $C$. The smallest constant $C$ satisfying this property is called the Hardy constant of the mean $M$. In this paper we determine the Hardy constant in the cases when the mean $M$ is either a concave quasi-arithmetic or a concave and homogeneous deviation mean.
Entire Solutions for Bistable Lattice Differential Equations with Obstacles

We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Our work generalizes to the discrete spatial setting the results obtained in a paper of Berestycki, Hamel and Matano for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.
Extensions of isometric embeddings of pseudo-Euclidean metric polyhedra

We extend the results of B. Minemyer by showing that any indefinite metric polyhedron (either compact or not) with the vertex degree bounded from above admits an isometric simplicial embedding into a Minkowski space of the lowest possible dimension. We provide a simple algorithm for constructing such embeddings. We also show that every partial simplicial isometric embedding of such space in general position extends to a simplicial isometric embedding of the whole space.
Cutting planes for families implying Frankl's conjecture

We find previously unknown families which imply Frankl’s conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non–Frankl-Complete (Non–FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non–FC-families.
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. II. Dielektrizitätskonstanten und Leitfähigkeiten von Vielkristallen der nichtregulären Systeme

Die Theorie von DK. und Lfk. der Mischkorper aus isotropen (amorphen oder regularen) Substanzen5) wird hier ausgedehnt auf die nichtregularen Systeme, wo schon der Vielkristall einer einzigen reinen Substanz den Charakter eines Mischkorpers aufweist. Die Genauigkeit der alten Formeln von Voigt und Andrade-Chalmers wird untersucht, sodann werden neue Formeln abgeleitet fur Vielkristalle und Mischkorper verschiedener Strukturen und diese am vorhandenen empirischen Material gepruft. Diese Prufung ergibt eine gute Bestatigung der neuen Theorie, wobei wiederum einzelne Widerspruche zwischen den vorliegenden Messungen aufgehoben werden.
Cauchy-Compact flat spacetimes with BTZ singularities

The zoology of singularities for Lorentzian manifold is slightly more complicated than for Riemannian manifolds. Our present work study Cauchy-compact globally hyperbolic singular flat spacetimes with extreme BTZ-like singular lines. We use the notion of BTZ-extension of a singular spacetime introduced in a previous paper to give a description of Moduli spaces of such manifolds in term of common Teichmuller spaces. This description is used to construct convex polyhedral cauchy-surface in Cauchy-compact flat spacetimes with BTZ.
Cognitive Dysfunction and Its Risk Factors in Patients Undergoing Maintenance Hemodialysis

Objective Cognitive impairment (CI) in Maintenance hemodialysis (MHD) is attracting increasing attention. This study aims to clarify the prevalence and risk factors for cognitive dysfunction in patients on MHD who have no history of stroke. Methods A total of 99 patients with no history of stroke undergoing MHD were enrolled. Global cognitive function was evaluated using the Montreal Cognitive Assessment scale. Attention and executive functions were evaluated by the Digital Span (DS) test and the Color Trail Test (CTT). The Hamilton Depression and Anxiety scales were used to assess depression and anxiety status. The effects of patient background factors, laboratory indicators, anxiety, and depression on cognitive dysfunction were examined by regression analysis. Results There were 69.70% of the patients had general CI, 65.65% had depression, and 57.57% had anxiety. The forward and backward DS in the cognitively impaired (CI) group were shorter than in the normal cognitive function (NCF) group (P<0.05). Times required for CTT–I, CTT–II, and CTT II − CTT I were longer in the CI group than in the NCF group (P<0.05). Hemoglobin levels were lower, and parathyroid hormone (PTH) and uric acid levels were higher in the CI group than in the NCF group (P<0.05). Hemoglobin levels were negatively correlated with CI in these patients (odds ratio [OR] 0.634, P<0.05) and PTH, and uric acid levels were positively correlated with CI (OR 1.028, P<0.05; and OR 1.011, P<0.05). The proportions of patients with diabetes and depression were higher in the CI group (P<0.05). Conclusion There was a high prevalence of CI with significant impairment of attention and executive ability in MHD patients who had no stroke history. Hemoglobin may protect cognitive function, while diabetes, PTH, and uric acid levels may be risk factors. Depressive and anxiety states may aggravate CI in MHD patients.
An observational study of Typhoon Khanun (2017) during intensification over the South China Sea

An observational study on the characteristics of Typhoon Khanun (2017) was conducted using lightning observations, global positioning system dropsonde observations, satellite‐derived precipitation, infrared‐derived brightness temperature and reanalysis data during its intensification stage. The characteristics of the tropical cyclone (TC) eye or eyewall have been captured for Typhoon Khanun over the South China Sea for the first time using dropsonde observations in recent years. The relationship between lightning evolution and the intensification of TCs was examined, and it was found that the lightning strokes within a 500‐km radius decreased as the typhoon intensified, while the lightning within 100 km (inner‐core) was inactive until 11 h prior to the peak intensity of Khanun. The burst of inner‐core lightning overlapped with the final intensification period of Khanun, indicating that the end of the inner‐core lightning burst may be an indicator of the termination of the intensification stage of TCs. Furthermore, a cyclonic rotation of inner‐core lightning was possibly related to the intensification of TCs influenced by the diabatic heating inside the radius of maximum wind. The dropsonde observations revealed that high water content within the mixed‐phase layer favoured the lightning activity and the convection system. Overall, this study promotes an in‐depth understanding of the linkage between lightning and the intensification of TCs along with the convection system.
Exogenous β-mannanase and Dl-methionine as feed additives to improve growth, feed efficiency and hematological indices of Nile tilapia Oreochromis nilotucs fed dietary plant protein

: The present study was done to determine the effects of exogenous β-mannanase (Hemicel® enzyme) and methionine on growth performance and blood parameters of Nile tilapia Oreochromis niloticus fed plant protein diet. Two basal diets were formulated to contain 27% CP one of them contained fishmeal (A) and other was plan protein (B). This study included six treatments were as the following: T1: (negative control) fish fed with diet A, T2: (positive control) fish fed on diet B, T3 and T4: fish fed on diet B with adding 0.025 and 0.05 % of Hemicel®, respectively, and T5: fish fed the diet B with 0.025% of Hemicel® and 5% methionine and T6: Diet B with adding 0.05 % Hemicel and 5% methionine. 120 juveniles were randomly divided into 12 plastic tanks (water size: 35 liters) with density of 10 fish/tank. Fish reared in saline of 3ppt, and fed two times daily for six days weekly with rate of 4% of body weight. Results confirmed that feed additives of Hemicel and Dl-methionine significantly improved nutritional utilization of plant protein diets. One way ANOVA analysis did not show significant differences in growth performance between fish fed with a soy-based diet containing 0.025% Hemicel® and Dl-methionine 0.5% (T5) and those fed with the diet containing fish meal (T1). Fish in T5 and T4 had highest body content of protein and the best blood indicator. Generally it can be totally replaced fish meal by soy bean with adding Hemicel® and Dl-methionine at levels of 0.025% and 0.5% respectively.
Electrode and interfacial polarization in broadband dielectric spectroscopy measurements

The accumulation of charge carriers at the sample-electrode interface in broadband dielectric spectroscopy results in large electrode polarization masking the frequency response of the sample. Additionally, heterogeneous samples exhibit frequency-dependent dielectric and conductive properties that differ from those of the constituent components, yielding so-called Maxwell–Wagner relaxation. We present here an experimental approach to extract true sample dielectric properties from the total frequency response of the electrode–sample assembly. A test case (i.e., ice) is shown to prove the correctness of the proposed method. Results also confirm that polarization due to blocking electrodes is not negligible even in the MHz frequency range.
Foliations with geometric structures

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient space. Theory of h-principle plays the central role in deriving the main results of the thesis. It is a theory rich in topological techniques to solve partial differential relations which arise in connection with topology and geometry. All the geometric structures mentioned above satisfy some differential conditions and that brings us into the realm of the h-principle theory.
Field emission of different oriented carbon nanotubes

Field emission data from aligned high-density carbon nanotubes (CNTs) with orientations parallel, 45°, and perpendicular to the substrate have been obtained. The large-area uniformly distributed CNTs were synthesized on smooth nickel substrates via dc plasma-assisted hot filament chemical vapor deposition. CNTs with diameters in the range of 100–200 nm were employed in this study. The different orientations were obtained by changing the angle between the substrate and the electrical field direction. The growth mechanism for the alignment and orientation control of CNTs has been discussed. The CNTs oriented parallel to the substrate have a lower onset applied field than those oriented perpendicular to the substrate. This result indicates that electrons can emit from the body of the CNT, which means that the CNT can be used as a linear emitter. The small radius of the tube wall and the existence of defects are suggested as the reasons for the emission of electrons from the body of the tubes.
Horocycle flow on negative variable curvature surface is standard

We provide a new proof that the horocycle flow preserving the Margulis measure on a variable negative curvature surface is standard. This was first proved by Ratner. The main purpose of this note is to provide a simplified case of the arguments for Kakutani equivalence of unipotent flows on homogeneous spaces, which have similar but more complicated structures, as well as illustrate the versatility of the method by applying it to a non-homogeneous flow.
An Example of Interaction Between Two Gasdynamic Objects: a Shock Discontinuity and a Model of Turbulence

The context of the considered interaction assumes a minimal nonlinearity in the form of a nonlinear subconscious. Consequently the interaction solution is essentially constructed as an admissible solution. The present analysis has essentially two objectives: (a) finding an explicit optimal form for the interaction solution, and (b) offering an exhaustively classifying characterization of this mentioned solution. Realising the objective (a) is connected with: (a1) considering a singular limit of the interaction solution, (a2) considering a hierarchy of (natural) partitions of the singular limit, (a3) inserting some (natural) gasdynamic factorizations at a certain level of the mentioned hierarchy and noticing a compatibility (coherence) of these factorizations, (a4) identifying some inner connections inside one of the mentioned partitions, (a5) predicting some exact details of the interaction solution, (a6) indicating some parasite singularities [= strictly depending on the method] to be compensated [= pseudosingularities], (a7) re-weighting the singular limit of the interaction solution. Realising the objective (b) is connected with finding some Lorentz arguments of criticity. The interaction solution appears essentially to (exhaustively) include a subcritical and respectively a supercritical contribution distinguished by differences of a ”relativistic” nature. Precisely: in the singular limit of the interaction solution [see (a1)] the emergent sound is singular in the subcritical contribution and it is regular in the supercritical contribution (see Fig. 1). It can be shown that this ”relativistic” discontinuity in the nature of the emergent sound, corresponding to the singular limit of the interaction solution appears to be dissembled (hidden) in the re-weighted interaction solution [mentioned in (a7)]. 2000 Mathematics Subject Classification. 35L60, 35L65, 35L67, 35L99, 76N99, 76Q05.
Nonlinear Galerkin Finite Element for Viscoelastic Fluid Flow: Optimal Error Estimate

In this article, we discuss a couple of nonlinear Galerkin method (NLG) in finite element set up for viscoelastic fluid flow, mainly equations of motion arising in the flow of 2D Oldroyd model. We obtain improved error estimate in $L^{\infty}(\bL^2)$ norm, which is optimal in nature, for linear finite element approximation, in view of the error estimate available in literature, in $L^2(\bH^1)$ norm.