Miracle-dz/UniFAR-FTUs huggingface dataset:
Differentiability and monotonicity of expected passage time in Euclidean first-passage percolation

In first-passage percolation (FPP) models, the passage time T ℓ from the origin to the point ℓe ℓ satisfies f(ℓ) := ET ℓ = μℓ + o(ℓ ½+ε), where μ ∊ (0,∞) denotes the time constant. Yet, for lattice FPP, it is not known rigorously that f(ℓ) is eventually monotonically increasing. Here, for the Poisson-based Euclidean FPP of Howard and Newman (Prob. Theory Relat. Fields 108 (1997), 153–170), we prove an explicit formula for f′(ℓ). In all dimensions, for certain values of the model's only parameter we have f′(ℓ) ≥ C > 0 for large ℓ.
Dynamics of “logamediate” inflation

A computation of the inflationary observables ${n}_{s}$ and $r$ is made for logamediate inflation where the cosmological scale factor expands as $a=\mathrm{exp}﻿(A(\mathrm{ln}﻿t{)}^{\ensuremath{\lambda}})$, and is compared to their predicted values in the intermediate inflationary theory, where $a=\mathrm{exp}﻿(B{t}^{f})$. Both versions prove to be consistent with observational measurements of the cosmic background radiation. It is shown that the dynamics of a single inflaton field can be mimicked by a system of several fields in an analogous manner to that created by the joint evolution of the fields in assisted power-law inflation.
Some remarks on marginally trapped surfaces and geodesic incompleteness

In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. However, one might wonder whether the corresponding incomplete geodesics could still be complete in a possible non-globally hyperbolic extension of spacetime. In this note, some variants of that result are given with weaker causality assumptions, thus suggesting that the answer is generically negative, at least if the putative extension has no closed timelike curves. However, unlike in the case of MOTS, on which only the outgoing family of normal geodesics is constrained, we have found it necessary in our proofs to impose also a weak convergence condition on the ingoing family of normal geodesics. In other words, we consider marginally trapped surfaces (MTS) in chronological spacetimes, introducing the natural notion of a generic MTS. In particular, a Hawking-Penrose-type singularity theorem is proven in chronological spacetimes with dimensions greater than 2 containing a generic MTS. Such surfaces naturally arise as cross-sections of quasi-local generalizations of black hole horizons, such as dynamical and trapping horizons. We end with some comments on the existence of MTS in initial data sets.
Informal Science Educators' Pedagogical Choices and Goals for Learners: The Case of Planetarium Professionals.

This study extends our understanding of the goals, beliefs, and pedagogical choices made by planetarium professionals. Interviews were conducted with planetarium professionals (N1⁄4 36) to assess their goals for audiences and beliefs about the design of the learning environment. Classification of participants, according to a six-facet framework on effective learning environment design, suggests a range of perspectives on the design of the learning environment that primarily include learner-centered, motivationally-oriented, socioculturallycentered, and physically-oriented perspectives. Results also point to the importance of considering increased opportunities for professionalism in the field of planetarium education.
Resonant Raman spectra of grades of human brain glioma tumors reveal the content of tryptophan by the 1588 cm-1 mode

RR spectra of brain normal tissue, gliomas in low grade I and II, and malignant glioma tumors in grade III and IV were measured using a confocal micro Raman spectrometer. This report focus on the relative contents of tryptophan (W) in various grades of brain glioma tumors by the intrinsic molecular resonance Raman (RR) spectroscopy method using the 1588cm-1 of tryptophan mode by 532 nm excitation. The RR spectra of key fingerprints of tryptophan, with a main vibrational mode at 1588cm-1 (W8b), were observed. It was found that tryptophan contribution was accumulated in grade I to IV gliomas and the mode of 1588cm-1 in grade III and IV malignant gliomas were enhanced by resonance.
Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria

In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some stoichiometric classes, and whose right hand side is bounded above by a quadratic nonlinearity in the positive orthant. We prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.
A METHOD FOR THE VIBRATION ANALYSIS OF BUILT-UP STRUCTURES, PART I: INTRODUCTION AND ANALYTICAL ANALYSIS OF THE PLATE-STIFFENED BEAM

This is the first of two companion papers which collectively present a method for the analysis of built-up structures. One such structure is the machinery foundation of a ship which is constructed from a collection of large beams and flexible plates. The heavy vibration sources are supported by the large stiff beams. The power injected into and the power transmitted around the structure is controlled by long-wavelength waves generated in these beams by the vibration sources. As these long waves propagate along the stiff beams they generate short-wavelength flexural waves in the attached flexible plates. The long waves transmit some of their energy to the short-wavelength waves which therefore damp the long waves. The difference between the wavelengths of the long waves in the stiff beams and the short waves in the flexible plates is often very large. In this case, the short waves present a locally reacting impedance to the long waves at the structural joints. This paper argues that such a condition allows the vibration to predicted in three steps. First, the long-wave response of the stiff beams is analyzed in isolation of the short-wave response of the flexible plates; second, the short-wave response of the flexible plates is analyzed in isolation of the long-wave response; third, the two separate responses are combined to yield the response of the complete structure due to both the long and the short waves. The method is applied to a simple plate-stiffened beam consisting of a directly excited stiff beam attached to a large flexible plate which is broadly representative of the machinery foundation. The method predicts the frequency response of the plate-stiffened beam which compares well with laboratory measurements, thereby supporting the method. In this paper, all three steps are performed analytically which restricts the method to geometrically simple structures. The companion paper presents a hybrid numerical/analytical implementation which accommodates geometrically more diverse structures.
Thick tensor ideals of right bounded derived categories

Let $R$ be a commutative noetherian ring. Denote by $D^-(R)$ the derived category of cochain complexes $X$ of finitely generated $R$-modules with $H^i(X)=0$ for $i\gg0$. Then $D^-(R)$ has the structure of a tensor triangulated category with tensor product $-\otimes_R^L-$ and unit object $R$. In this paper, we study thick tensor ideals of $D^-(R)$, i.e., thick subcategories closed under the tensor action by each object in $D^-(R)$, and investigate the Balmer spectrum $Spc\,D^-(R)$ of $D^-(R)$, i.e., the set of prime thick tensor ideals of $D^-(R)$. First, we give a complete classification of the thick tensor ideals of $D^-(R)$ generated by bounded complexes, establishing a generalized version of the Hopkins-Neeman smash nilpotence theorem. Then, we define a pair of maps between the Balmer spectrum $Spc\,D^-(R)$ and the Zariski spectrum $Spec\,R$, and study their topological properties. After that, we compare several classes of thick tensor ideals of $D^-(R)$, relating them to specialization-closed subsets of $Spec\,R$ and Thomason subsets of $Spc\,D^-(R)$, and construct a counterexample to a conjecture of Balmer. Finally, we explore thick tensor ideals of $D^-(R)$ in the case where $R$ is a discrete valuation ring.
Characteristic directions of two-dimensional biholomorphisms

We prove that for each characteristic direction $[v]$ of a tangent to the identity diffeomorphism of order $k+1$ in $(\mathbb{C}^{2},0)$ there exist either an analytic curve of fixed points tangent to $[v]$ or $k$ parabolic manifolds where all the orbits are tangent to $[v]$, and that at least one of these parabolic manifolds is or contains a parabolic curve.
Infinitely many odd zeta values are irrational. By elementary means

In this small note, we provide an elementary proof of the fact that infinitely many odd zeta values are irrational. For the first time, this celebrated theorem been proven by Rivoal and Ball--Rivoal. The original proof uses highly non-elementary methods like the saddle-point method and Nesterenko's linear independence criterion. Recently, Zudilin has re-proven a slightly weaker form of his important result that at least one of the odd zeta values $\zeta(5),\zeta(7),\zeta(9)$ and $\zeta(11)$ is irrational, by elementary means. His new main ingredient are certain 'twists by half' of hypergeometric series. Generalizing this to 'higher twists' allows us to give a purely elementary proof of the result of Rivoal and Ball--Rivoal.
ON THE DOMAIN OF SINGULAR TRACES

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are genrated by a "regular" operator, the answers change, namely such traces alway vanish on trace-class, non singularly traceable operators and are always infinite on non trace-class, non singularly traceable operators. These results are achieved on a general semifinite factor and make use of a new characterization of singular traceability (cf. [7]).
Splitting of separatrices in a family of area-preserving maps that unfolds a fixed point at the resonance of order three

We study the exponentially small splitting of separatrices in an analytic one-parameter family of area-preserving maps that generically unfolds a 1:3 resonance. Near the resonance the normal form theory predicts existence of a small triangle formed by separatrices of a period three hyperbolic point. We prove that in a generic family the separatrices split, provided that the Stokes constant of the map does not vanish. This constant describes the distance between the analytical continuations of invariant manifolds associated with the degenerate saddle of the map at the exact resonance. We provide an asymptotic formula which describes the size of the splitting. The leading term of this asymptotic formula is proportional to the Stokes constant.
Upstream motions in stratified flow

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model. Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.
$2^{\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\mathbb{N})$ via the classification of the reducts of the Henson digraphs

Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, we say that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all $\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in $\mathcal{M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\mathbb{N})$ of their automorphism groups. A consequence of the classification is that there are $2^{\aleph_0}$ pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are $2^{\aleph_0}$ pairwise non-conjugate maximal-closed subgroups of Sym$(\mathbb{N})$. By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups.
Direct Cosmological Simulations of the Growth of Black Holes and Galaxies

We investigate the coupled formation and evolution of galaxies and their embedded supermassive black holes using state-of-the-art hydrodynamic simulations of cosmological structure formation. For the first time, we self-consistently follow the dark matter dynamics, radiative gas cooling, and star formation, as well as BH growth and associated feedback processes, starting directly from initial conditions appropriate for the ΛCDM cosmology. Our modeling of the black hole physics is based on an approach that we have developed in simulations of isolated galaxy mergers. Here we examine (1) the predicted global history of BH mass assembly, (2) the evolution of the local black hole-host mass correlations, and (3) the conditions that allow rapid growth of the first quasars, and the properties of their hosts and descendants today. We find a total BH mass density in good agreement with observational estimates. The BH accretion rate density peaks at lower redshift and evolves more strongly at high redshift than the star formation rate density, but the ratio of black hole to stellar mass density shows only a moderate evolution at low redshifts. We find strong correlations between BH masses and properties of the stellar systems, agreeing well with the measured local MBH-σ and MBH-M* relationships, but also suggesting (dependent on the mass range) a weak evolution with redshift in the normalization and the slope. Our simulations also produce massive black holes at high redshift, due to extended periods of exponential growth in regions that collapse early and exhibit strong gas inflows. These first supermassive BH systems, however, are not necessarily the most massive ones today, since they are often overtaken in growth by quasars that form later.
Towers of regular self-covers and linear endomorphisms of tori

Let $M$ be a closed manifold that admits a self-cover $p:M \to M$ of degree >1. We say p is strongly regular if all its iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of $M$: We prove that $\pi_1(M)$ surjects onto a nontrivial free abelian group $A$, and the self-cover is induced by a linear endomorphism of $A$. Under further hypotheses we show that a finite cover of $M$ admits the structure of a principal torus bundle. We show that this applies when $M$ is K\"ahler and $p$ is a strongly regular, holomorphic self-cover, and prove that a finite cover splits as a product with a torus factor.
Probit Cryptographic Blockchain for Secure Data Transmission in Intelligent Transportation Systems

To address the current security challenges, Digital Twin (DT) models and strategies are to be applied to improve security, privacy, and safety in intelligent transportation systems. However, the existing algorithm was failed to address the security and privacy issues for data between the vehicles. To enhance the security of data transmission, a novel Probit Regressive Davis Mayer Kupyna Cryptographic Hash Blockchain (PRDMKCHB) technique is proposed. Initially, the source vehicle finds the nearest vehicle to transmit the data based on the trust value using the probit regression function. After finding the neighboring nodes, the Blockchain is constructed to improve the security of data transmission from the source to the destination. The Blockchain uses the Kupyna Cryptography to generate the hash value for each data. Davis Mayer compression function is to improve the security of data delivery and to minimize packet loss. The comprehensive simulation is carried out to validate the performance of the proposed PRDMKCHB technique and existing Blockchain technology in terms of packet delivery ratio, packet loss rate, and execution time. Simulation results show the performance improvement of the proposed PRDMKCHB technique compared to the previous Blockchain technology in terms of higher packet delivery ratio, minimum packet loss, and execution time with respect to the number of data packets.
On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$

In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ (for $k \in {11, 13, 14, 15, 16, 17, 18}$) by using the idea of R\u{a}sdeaconu and \c{S}uvaina (2009) and the constructions in Park, Park, and Shin (arXiv:0906.5195v2) and in Park, Park, and Shin (2009). Then, we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on the exotic smooth structures of these topological manifolds by employing the obstruction developed in Ishida (2008).
On the detectability of the gas of other solar nebulae

Velocity profiles of the 12 CO (J=1-0) and 13 CO (J=1-0) lines emitted from the solar nebula are numerically calculated by taking account of the radiative transfer of the lines. For the solar nebula, the two theoretical models of a low-mass (∼0.01 M ⊙ ) nebula (i.e., Kyoto model) and a high-mass (∼1 M ⊙ ) nebula (i.e., Cameron model) are adopted. It is shown that the calculated profiles typically have double peaks at the velocities of ± 2-5 km/s, which are separable from ambient emission, and that the profiles vary greatly depending on the complex, if the 45 m telescope of the NRO is used
Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis

A deterministic model for studying the transmission dynamics of bovine tuberculosis in a single cattle herd is presented and qualitatively analyzed. A notable feature of the model is that it allows for the importation of asymptomatically infected cattle (into the herd) because re‐stocking from outside sources. Rigorous analysis of the model shows that the model has a globally‐asymptotically stable disease‐free equilibrium whenever a certain epidemiological threshold, known as the reproduction number, is less than unity. In the absence of importation of asymptomatically infected cattle, the model has a unique endemic equilibrium whenever the reproduction number exceeds unity (this equilibrium is globally asymptotically stable for a special case). It is further shown that, for the case where asymptomatically infected cattle are imported into the herd, the model has a unique endemic equilibrium. This equilibrium is also shown to be globally asymptotically stable for a special case. Copyright © 2011 John Wiley & Sons, Ltd.
Time-evolution K–L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows

The turbulent dynamics corresponding to direct numerical simulation (DNS) data of Newtonian and viscoelastic turbulent channel flows is analyzed here through a projection of a time sequence of velocity fields into a set of Karhunen–Loeve (K–L) modes, large enough to contain, on the average, more than 90% of the fluctuating turbulence kinetic energy. Previous calculations of the K–L eigenstructure have demonstrated a dramatic decrease in the K–L dimensionality accompanying the presence of viscoelasticity in turbulent channel flows. Projection of turbulent velocity information into the most energetic K–L modes allows for a significant data reduction, most suitable for the study of the time-evolution dynamics. We exploit this feature here in analyzing the time series of the projection coefficients of the velocity field into K–L modes to gain further quantitative insights into the behavior of the overall flow dynamics. The presence of viscoelasticity induces significant changes to the turbulence dynamics as compared to the Newtonian one obtained at the same friction Reynolds number. Namely, it cuts in half the representational entropy constructed from the projection coefficients whereas it doubles the fluctuating kinetic energy. Moreover, dynamic correlation analysis of pairs of K–L coefficients showed a systematic increase in the time scales characterizing dynamic turbulent events with viscoelasticity. These correlations have distinct pulse behavior characteristic of intermittence and quasiperiodicity. Correlations between K–L modes corresponding to different wavenumbers along the principal flow direction depend sensitively on the velocity of the moving frame of reference with respect to which they are calculated, and resonate at characteristic velocities corresponding to the convective velocities of the coherent structures to which the two modes contribute. Based on that, we propose a new two-dimensional analysis of those correlations with respect to both the time and the moving frame velocity in order to detect coherent flow structures and their mean convective velocity. Those show considerable differences when they are calculated with and without the presence of viscoelasticity.
A universal characterisation of codescent objects

In this work we define a 2-dimensional analogue of extranatural transformation and use these to characterise codescent objects. They will be seen as universal objects amongst pseudo-extranatural transformations in a similar manner in which coends are universal objects amongst extranatural transformations. Some composition lemmas concerning these transformations are introduced and a Fubini theorem for codescent objects is proven using the universal characterisation description.