Miracle-dz/UniFAR-FTUs huggingface dataset:
Rogers functions and fluctuation theory

Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a class of functions closely related to Nevanlinna-Pick functions and complete Bernstein functions. The name 'Rogers functions' is proposed for this class. Under mild additional condition, for a Rogers function f, the Wiener--Hopf factors of f(z)+q, as well as their ratios, are proved to be complete Bernstein functions in both z and q. This result has a natural interpretation in fluctuation theory of L\'evy processes: for a L\'evy process X_t with completely monotone jumps, under mild additional condition, the Laplace exponents kappa(q;z), kappa*(q;z) of ladder processes are complete Bernstein functions of both z and q. Integral representation for these Wiener--Hopf factors is studied, and a semi-explicit expression for the space-only Laplace transform of the supremum and the infimum of X_t follows.
First-Overtone CO Variability in Young Stellar Objects

We have monitored the 2.3 μm Δv = 2 CO bands toward young stellar objects that are predominantly of low luminosity (L < 10,000 L☉) and show evidence of mass loss. The CO emission can be highly variable, on timescales as short as a few days. In DG Tau, the bands have been observed to disappear and reappear and may also have a periodic modulation. For the BN object, the equivalent width has varied by a factor of 3; and for V1331 Cyg, the equivalent width doubled in 9 days. Changes in equivalent width also occurred in SSV 13, AS 353A, and 1548C27, while WL 16 and S106 have not shown variations. Of the nine CO absorption sources reobserved, only the FU Ori-type star V1057 Cyg went through a significant change in equivalent width. It also presents an unusual and variable band profile.
Improved Fourier restriction estimates in higher dimensions

We consider Guth's approach to the Fourier restriction problem via polynomial partitioning. By writing out his induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms, we obtain improved bounds for the restriction conjecture, particularly in high dimensions. Consequences for the Kakeya conjecture are also considered.
HEAT TRANSFER CHARACTERISTICS OF WATER FLOWING THROUGH MICROCHANNELS

The forced-flow convection of water through rectangular microchannels having hydraulic diameters of 0.133-0.367 mm and aspect ratios of H/W = 0.333-1 was investigated experimentally. The flow friction was measured to analyze the heat transfer regimes and to explore the physical aspects of the connective heat transfer. The experimental measurements indicated that the upper bound of the laminar heat transfer regime occurred at a Reynolds number of 200-700, and fully turbulent connective heat transfer was reached at Reynolds numbers of 400-1,500. The transition Reynolds number diminished with the reduction of the microchannel dimension, and the transition range was observed to become smaller in magnitude. For the laminar heat transfer regime, the Nusselt number was found to be proportional to Re0.62while the turbulent heat transfer case exhibited a typical relationship between Nu and Re, but with a different empirical coefficient, CH,t. The geometric parameters were found to be important variables that could.
Characterizations of derivations

The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 we collect all the definitions and results regarding derivations that are essential while studying this area. In Chapter 3 we intend to show that derivations can be characterized by one single functional equation. More exactly, we study here the following problem. Let $Q$ be a commutative ring and let $P$ be a subring of $Q$. Let $\lambda, \mu\in Q\setminus\left\{0\right\}$ be arbitrary, $f\colon P\rightarrow Q$ be a function and consider the equation \[ \lambda\left[f(x+y)-f(x)-f(y)\right]+ \mu\left[f(xy)-xf(y)-yf(x)\right]=0 \quad \left(x, y\in P\right). \] In this chapter it will be proved that under some assumptions on the rings $P$ and $Q$, derivations can be characterized via the above equation. Chapter 4 is devoted to the additive solvability of a system of functional equations. Moreover, the linear dependence and independence of the additive solutions $d_{0},d_{1},\dots,d_{n} \colon\mathbb{R}\to\mathbb{R}$ of the above system of equations is characterized. Finally, the closing chapter deals with the following problem. Assume that $\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and for the additive function $f\colon \mathbb{R}\to \mathbb{R}$, the mapping \[ \varphi(x)=f\left(\xi(x)\right)-\xi'(x)f(x) \] fulfills some regularity condition on its domain. Is it true that in such a case $f$ is a sum of a derivation and a linear function?
Performance Evaluation of a Kalina Cycle using a Novel Extended Thermodynamic Analysis

This research presents a novel Extended Thermodynamic Analysis Method (ETAM) to respond to the issue of ‘which equipment holds the highest priority of receiving improvements in a thermodynamic cycle’. This novel analysis comprises three parts: extended energy, extended entropy, and extended exergy analyses. As a case study, a low-temperature geothermal Kalina cycle system-34 was analyzed. The results of Conventional Exergy Analysis Method (CEAM), Advanced Exergy Analysis Method (AEAM), and the proposed novel method were compared with each other. CEAM results indicate that the condenser, followed by the evaporator and turbine, has the most exergy destruction. In contrast, according to AEAM results, the top priority for improvement should be given to the condenser, followed by turbine and Low-Temperature Recuperator (LTR). The improvement priority using the presented novel extended analysis was also given to the condenser, turbine, and LTR, the (cid:12)nding being the same as the results of AEAM, while the proposed novel method is less complicated than the AEAM.
A variant of ${\texttt{IdentityFinder}}$ and some new identities of Rogers-Ramanujan-MacMahon type

We report on findings of a variant of ${\texttt{IdentityFinder}}$ - a Maple program that was used by two of the authors to conjecture several new identities of Rogers-Ramanujan kind. In the present search, we modify the parametrization of the search space by taking into consideration several aspects of Lepowsky and Wilson's $Z$-algebraic mechanism and its variant by Meurman and Primc. We search for identities based on forbidding the appearance of "flat" partitions as sub-partitions. Several new identities of Rogers-Ramanujan-MacMahon type are found and proved.
High-Voltage Photovoltaic Effect in Evaporated CdTe Films

The properties of CdTe films vacuum-evaporated at an oblique angle of incidence onto a substrate of glass, which are known to exhibit unusually high photovoltages, are experimentally studied. (1) The angular distribution of the intensity of light scattered by the film is asymmetric. (2) The (111) planes of the crystallites do not lie parallel to the substrate surface, as they do in the case of normal incidence. The incline of the (111) planes is determined in the main by the angle of incidence of vapor θ. (3) The photovoltage V exhibits a peculiar dependence on θ. It changes its sign at a certain value of θ, which in turn is determined by the substrate temperature. A model is proposed for the structure of the film, which will explain the experimental results.
Anomalous Transient Currents in High-Density Polyethylene around 50–70°C

Transient currents in high-density polyethylene have been investigated at various temperatures and applied fields. A distinct difference between the transient charging and discharging currents suggests that they are attributable to space charge in the sample. The charging current peak around 70°C was explained on the basis of transient SCLC theory, and the carrier mobility was estimated to be 0.5–2.0×10-10 cm2/V·sec at 70°C. Anomalous discharging currents flowing in the same direction as the charging current were observed at 50 and 70°C, and they were concluded to be caused by the injected home space charge and the partial blocking of a metalpolymer contact.
EQUILIBRIUM JOINING PROBABILITIES IN OBSERVABLE QUEUES WITH GENERAL SERVICE AND SETUP TIMES

This paper analyzes an M/G/1 queue with general setup times from an economical point of view. In such a queue whenever the system becomes empty, the server is turned off. A new customer's arrival will turn the server on after a setup period. Upon arrival, the customers decide whether to join or balk the queue based on observation of the queue length and the status of the server, along with the reward-cost structure of the system. For the observable and almost observable cases, the equilibrium joining strategies of customers who wish to maximize their expected net benefit are obtained. Two numerical examples are presented to illustrate the equilibrium joining probabilities for these cases under some specific distribution functions of service times and setup times.
Singular hermitian metrics on vector bundles

We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h. m. there is a (coherent) sheaf 0-th kernel of a certain $d''$-complex. We prove a vanishing theorem for the cohomology of this sheaf. All this generalizes to the case of higher rank known results of Nadel for the case of line bundles. We introduce a new semi-positivity notion, $t$-nefness, for vector bundles, establish some of its basic properties and prove that on curves it coincides with ordinary nefness. We particularize the results on s.h. m. to the case of vector bundles of the form $E=F \otimes L$, where $F$ is a $t$-nef vector bundle and $L$ is a positive (in the sense of currents) line bundle. As applications we generalize to the higher rank case 1) Kawamata-Viehweg Vanishing Theorem, 2) the effective results concerning the global generation of jets for the adjoint to powers of ample line bundles, and 3) Matsusaka Big Theorem made effective.
Tropical 40–50- and 25–30-Day Oscillations Appearing in Realistic and Idealized GFDL Climate Models and the ECMWF Dataset

Abstract To clarify differences between the tropical 40–50- and 25–30-day oscillations and to evaluate simulations and various theories, space-time spectrum and filter analyses were performed on a nine-year dataset taken from the nine-level R30 spectral general circulation model and the nine-year (1979–1987) ECMWF four-dimensional analysis dataset. In addition, the 40-level SKYHI model was analyzed to examine the effect of increased vertical resolution, while an ocean-surface perpetual January R30 model was analyzed to examine the effects of the absence of geographical and seasonal variations. The R30 model results indicate that the relative amplitude of the wavenumber-one component of the 40–50- and 25–30-day oscillations varies greatly from year to year. For the nine-year average, the simulated 40–50-day zonal velocity oscillations are as strong as observed, while the simulated 25–30-day zonal velocity oscillations are much stronger than observed. Although 40–50- and 25–30-day oscillations have similar .
Sierpi\' nski Gasket Graphs and Some of Their Properties

The {\it Sierpinski fractal} or {\it Sierpinski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the process that leads to $\Sigma$, and study some of its properties, including its cycle structure, domination number and pebbling number. Various open questions are posed.
Brownian Polymers in Poissonian Environment: a survey

We consider a space-time continuous directed polymer in random environment. The path is Brownian and the medium is Poissonian. We review many results obtained in the last decade, and also we present new ones. In this fundamental setup, we can make use of fine formulas and strong tools from stochastic analysis for Gaussian or Poisson measure, together with martingale techniques. These notes cover the matter of a course presented during the Jean-Morlet chair 2017 of CIRM "Random Structures in Statistical Mechanics and Mathematical Physics" in Marseille.
Constructing and Counting Number Fields

In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of fields of degree up to 4 is now almost completely solved, both in theory and in practice. The same methods also allow construction of the corresponding complete tables of number fields with discriminant up to a given bound.
Competition in periodic media: I -- Existence of pulsating fronts

This paper is concerned with the existence of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. Considering highly competitive systems, a simple "high frequency or small amplitudes" algebraic sufficient condition for the existence of pulsating fronts is stated. This condition is in fact sufficient to guarantee that all periodic coexistence states vanish and become unstable as the competition becomes large enough.
Spin-Orbit Interaction in Graphite

Abstract Recent measurements of the magnetoreflection and of the de Haas-van Alphen effect have made possible a more accurate determination of the band parameters of pyrolytic graphite. In principle, these experiments could provide a more direct measurement of the small spin-orbit interaction in graphite. This interaction lifts the degeneracy of the E3 bands everywhere along the zone edge and gives rise to a band gap near point K which could be deduced from analysis of the magnetoreflection experiment. When the degeneracy of the energy bands at point H is lifted, two extremal Fermi surface areas are obtained, thus predicting two low frequency de Haas-van Alphen oscillations.
Neutral-hydrogen observations and maps of early-type galaxies

Measurements are reported of neutral hydrogen in and around 12 elliptical, S0, and early-type spiral galaxies, as well as three spirals of later type. The observations were made with the 4 arcmin flat beam of the Arecibo Radio Telescope. Ten of the 12 early-type galaxies were detected, and show small H I masses of 4x10 to the 7th to 8x10 to the 8th solar masses (H0=100 km/s/Mpc). Very low upper limits of 3x10 to the 6th and 6x10 to the 6th solar masses of H I have been established for the S0 galaxies NGC 4382 and 7332. A faint dwarf galaxy 3 arcmin south of NGC 4382 was detected. Together with the previously detected dwarfs around NGC 2859, this suggests that H I-rich companions to H I-poor S0 galaxies may be common. In contrast to the other galaxies mapped in this program, the H I distribution in NGC 3773 is tightly concentrated to the center of the galaxy. 24 references.
On the correspondence of external angles under renormalization

Let P$P$ be a monic polynomial of degree D⩾3$D \geqslant 3$ whose filled Julia set KP$K_P$ has a non‐degenerate periodic component K$K$ of period k⩾1$k \geqslant 1$ and renormalization degree 2⩽d
Rates of divergence of non-conventional ergodic averages

Abstract We first study the rate of growth of ergodic sums along a sequence (an) of times: SNf(x)=∑ n≤Nf(Tanx). We characterize the maximal rate of growth and identify a number of sequences such as an=2n, along which the maximal rate of growth is achieved. To point out though the general character of our techniques, we then turn to Khintchine’s strong uniform distribution conjecture that the averages (1/N)∑ n≤Nf(nx mod 1) converge pointwise to ∫ f for integrable functions f. We give a simple, intuitive counterexample and prove that, in fact, divergence occurs at the maximal rate.
New High Temperature Morphotropic Phase Boundary Piezoelectrics Based on Bi(Me)O3–PbTiO3 Ceramics

New morphotropic phase boundary (MPB) piezoelectrics, with ferroelectric phase transition (Tc) exceeding that of PbZrO3–PbTiO3 (PZT), were investigated. Based on a perovskite tolerance factor-Tc relationship, new high Tc MPB systems were projected in the Bi(Me)O3–PbTiO3 system, where Me is a relatively large B+3-site cation. For the (1-x)BiScO3–(x)PbTiO3 solid solution, a MPB was found at x-0.64 separating the rhombohedral and tetragonal phases, with correspondingly enhanced dielectric and piezoelectric properties. A transition temperature Tc of ∼ 450°C was determined with evidence of Tc's on the order of ≥ 600°C in the BiInO3 and BiYbO3 analogues, though issues of perovskite stability remain for the smaller tolerance end-member systems.
Local quantum information dynamics

In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path integral approaches; 2) discuss a framework for postquantum information theories, such that quantum mechanical linearity holds only locally, while the nonlocal multi-user dynamics exhibits some similarity with general relativity. In the algebraic setting, we propose a method of incorporating nonlinear Poisson and relative entropic local dynamics, as well as local gauge and local source structures, into an effective description of local temporal evolution of quantum states by using fibrewise perturbations of liouvilleans in the fibre bundle of Hilbert spaces. In the path integral setting, we incorporate local geometry by a generalisation of the Daubechies--Klauder coherent state phase space propagator formula. Finally, we discuss the role of Bregman relative entropy in the Jaynes--Mitchell--Favretti renormalisation scheme. As a result, we show that: 1) the propagation of quantum particles (in Wigner's sense) can be naturally explained as a free fall along the trajectories locally minimising the quantum relative entropy; 2) the contribution of particular trajectories to the global path integral is weighted by the local quantum entropic prior, measuring user's lack of information; 3) the presence of nonlinear quantum control variables results in the change of the curvature of the global quantum state space; 4) the behaviour of zero-point energy under renormalisation of local entropic dynamics is maintained by local redefinition of information mass (prior), which encodes the curvature change. This leads us to a new framework for nonequilibrium quantum statistical mechanics based on quantum Orlicz spaces, quantum Bregman distances and Banach Lie algebras.
Cluster densities at 2D critical points in rectangular geometries

Making use of the complete calculation [1] of the chiral six-point correlation function with the four ϕ1, 2 operators at the corners of an arbitrary rectangle and the point z = x + i y in the interior, for arbitrary central charge (equivalently, SLE parameter κ > 0), we calculate various quantities of interest for percolation (κ = 6) and many other two-dimensional critical points. In particular, we use C to specify the density at z of critical clusters conditioned to touch either or both vertical sides of the rectangle, with these sides ‘wired’, i.e. constrained to be in a single cluster, and the horizontal sides free. These quantities probe the structure of various cluster configurations, including those that contribute to the crossing probability. We first examine the effects of boundary conditions on C for the critical O(n) loop models in both high- and low-density phases and for both Fortuin–Kasteleyn (FK) and spin clusters in the critical Q-state Potts models. A Coulomb gas analysis then allows us to calculate the cluster densities with various conditionings in terms of the conformal blocks calculated in []. Explicit formulas generalizing Cardy’s horizontal crossing probability to these models (using previously known results) are also presented. These solutions are employed to generalize previous results demonstrating factorization of higher order correlation functions to the critical systems mentioned. An explicit formula for the density of critical percolation clusters that cross a rectangle horizontally with free boundary conditions is also given. Simplifications of the hypergeometric functions in our solutions for various models are presented. High-precision simulations verify these predictions for percolation and for the Q = 2- and 3-state Potts models, including both FK and spin clusters. Our formula for the density of crossing clusters in percolation with free boundary conditions is also verified.
Vector bundles over classifying spaces of p ‐local finite groups and Benson–Carlson duality

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p ‐local finite group (S,F,L) in terms of representation rings of subgroups of S . We also prove a stable elements formula for generalized cohomological invariants of p ‐local finite groups, which is used to show the existence of unitary embeddings of p ‐local finite groups. Finally, we show that the augmentation C∗(|L|p∧;Fp)→Fp is Gorenstein in the sense of Dwyer–Greenlees–Iyengar and obtain some consequences about the cohomology ring of |L|p∧ .
Geometric transitions, topological strings, and generalized complex geometry

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heteroticmore » strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism. « less