Miracle-dz/UniFAR-FTUs huggingface dataset:
The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials

Let Ap,rm(n) be the best constant that fulfills the following inequality: for every m‐homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, ∑|α|=m|aα|r1/r≤Ap,rm(n)supz∈Bℓpn|P(z)|. For every degree m, and a wide range of values of p,r∈[1,∞] (including any r in the case p∈[1,2] , and any r and p for the 2‐homogeneous case), we give the correct asymptotic behavior of these constants as n (the number of variables) tends to infinity. Remarkably, in many cases, extremal polynomials for these inequalities are not (as traditionally expected) found using classical random unimodular polynomials, and special combinatorial configurations of monomials are needed. Namely, we show that Steiner polynomials (i.e., m‐homogeneous polynomials such that the multi‐indices corresponding to the nonzero coefficients form partial Steiner systems), do the work for certain range of values of p,r . As a byproduct, we present some applications of these estimates to the interpolation of tensor products of Banach spaces, to the study of (mixed) unconditionality in spaces of polynomials and to the multivariable von Neumann's inequality.
A resolution of quantum dynamical semigroups

We consider a class of quantum dissipative systems governed by a one parameter completely positive maps on a von-Neumann algebra. We introduce a notion of recurrent and metastable projections for the dynamics and prove that the unit operator can be decomposed into orthogonal projections where each projections are recurrent or metastable for the dynamics.
Hochschild (Co)homology of Exterior Algebras

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generators and relations.
Driving Factors of Industry 4.0 Readiness among Manufacturing SMEs in Malaysia

Industry 4.0 increases the production efficiency and competitiveness of companies. However, Industry 4.0 implementation is comparatively low in developing countries, while Malaysian manufacturing Small and Medium Enterprises (SMEs) Industry 4.0 adoption is still in its infancy stage. This quantitative study aimed to broaden the knowledge of the driving factors that significantly strengthen Malaysian manufacturing SMEs’ readiness for the digital revolution. Based on the Resource-Based View theory, the study built a research framework to govern the investigation of organizational capabilities, SME institutional support, perceived advantage, and market factors as the driving factors of Industry 4.0 readiness, while firm size as the moderating variable. The data were collected by conducting an online survey with the owners and managers of Malaysian-owned manufacturing SMEs located throughout Peninsular Malaysia, where the firms have received some form of government assistance. The analysis of the study indicated that organizational capabilities, SME institutional support, and market factors positively correlate with Industry 4.0 readiness. It was determined that firm size only moderates the relationship between SME institutional support and Industry 4.0 readiness. This study’s findings benefit industry practitioners and policymakers who wish to drive the future of Malaysia’s SMEs business ecosystem and contribute to Industry 4.0 literature.
Enumeration and Identification of Active Users for Grant-Free NOMA Using Deep Neural Networks

In next-generation mobile radio systems, multiple access schemes will support a massive number of uncoordinated devices exhibiting sporadic traffic, transmitting short packets to a base station. Grant-free non-orthogonal multiple access (NOMA) has been introduced to provide services to a large number of devices and to reduce the communication overhead in massive machine-type communication (mMTC) scenarios. In grant-free communication, there is no coordination between the device and base station (BS) before the data transmission; therefore, the challenging task of active users detection (AUD) must be conducted at the BS. For NOMA with sparse spreading, we propose a deep neural network (DNN)-based approach for AUD called active users enumeration and identification (AUEI). It consists of two phases: firstly, a DNN is used to estimate the number of active users; then in the second phase, another DNN identifies them. To speed up the training process of the DNNs, we propose a multi-stage transfer learning technique. Our numerical results show a remarkable performance improvement of AUEI in comparison to previously proposed approaches.
Dynamics of strong-field above-threshold ionization of argon: Comparison between experiment and theory

We record angle-resolved electron-momentum distributions from 800-nm short-pulse laser ionization of argon and compare our data with numerical solutions of the time-dependent Schrodinger equation. A model potential of argon and the single active electron approximation are used. The calculation shows quantitative agreement in all dominant features of the experimental results. The energy and angular distributions of the photoelectrons, together with numerical simulations, allow us to identify the multiple processes involved during the interaction, such as channel switching, multiphoton resonant and nonresonant ionization, and ac Stark splitting.
Noisy quantum gyroscope

Gyroscope for rotation sensing plays a key role in inertial navigation systems. Developing more precise gyroscopes than the conventional ones bounded by classical shot-noise limit by using quantum resources has attracted much attention. However, existing quantum gyroscope schemes suffer severe deterioration under the influence of decoherence, which is called the no-go theorem of noisy metrology. Here, by using two quantized optical fields as quantum probe, we propose a quantum gyroscope scheme breaking through the constraint of the no-go theorem. Our exact analysis of the non-Markovian noise reveals that both the evolution time as a resource in enhancing the sensitivity and the achieved super-Heisenberg limit in the noiseless case are asymptotically recoverable when each optical field forms a bound state with its environment. The result provides a guideline for realizing high-precision rotation sensing in realistic noisy environments.
The cosmic evolution of low-luminosity radio sources from the Sloan Digital Sky Survey Data Release 1

In this paper we constrain the evolution in the comoving space density for low-luminosity [typically Fanaroff-Riley type I (FRI)] radio sources as a function of cosmic epoch by matching deep radio surveys [Westerbork Northern Sky Survey (WENSS), Faint Images of the Radio Sky at Twenty-centimetres (FIRST) and NRAO VLA Sky Survey (NVSS)] with the Sloan Digital Sky Survey (SDSS). This results in 1014 matched radio sources covering an effective area of 0.217 sr, 686 with L 325 MHz < 10 25 W Hz -1 sr -1 , which is an order of magnitude larger than any previous study at these luminosities. Using the non-parametric V/V max test we show that low-luminosity radio sources evolve differently from their more powerful, predominantly Fanaroff-Riley type II (FRII), counterparts. Indeed, we find that the lower luminosity population is consistent with a constant comoving space density with redshift, as opposed to the strong positive evolution for the more powerful sources.
K–theory, LQEL manifolds and Severi varieties

We use topological K‐theory to study nonsingular varieties with quadratic entry locus. We thus obtain a new proof of Russo’s divisibility property for locally quadratic entry locus manifolds. In particular we obtain a K‐theoretic proof of Zak’s theorem that the dimension of a Severi variety must be 2, 4, 8 or 16 and so answer a question of Atiyah and Berndt. We also show how the same methods applied to dual varieties recover the Landman parity theorem. 14M22; 19L64
Algebraic independence and normality of the values of Mahler's functions

The main purpose of this article is to provide new results on algebraic independence of values of Mahler functions and their generalizations. Simultaneously, we establish new measures of algebraic independence for these values. Among the other things, we provide a measure of algebraic independence for values of Mahler's functions at complex transcendental points, a result of type which has never appeared in the literature in the past. As an example of application of our new measures of algebraic independence, we prove that a Mahler number does not belong to the class $U$ in Mahler's classification. Also, our results imply new examples, for $n\geq 1$ arbitrarily large, of sets $\left(\theta_1,\dots,\theta_n\right)\in\mathbb{R}^n$ normal in the sense of G. ~Chudnovsky (1980).
Investigating the conformal window of SU(N) gauge theories

In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05
Martingale inequalities of type Dzhaparidze and van Zanten

ABSTRACT Freedman's inequality is a supermartingale counterpart to Bennett's inequality. This result shows that the tail probabilities of a supermartingale is controlled by the quadratic characteristic and a uniform upper bound for the supermartingale difference sequence. Replacing the quadratic characteristic by , Dzhaparidze and van Zanten [On Bernstein-type inequalities for martingales. Stoch Process Appl. 2001;93:109–117] have extended Freedman's inequality to martingales with unbounded differences. In this paper, we prove that can be refined to . Moreover, we also establish two inequalities of type Dzhaparidze and van Zanten. These results extend Sason's inequality [Tightened exponential bounds for discrete-time conditionally symmetric martingales with bounded jumps. Statist Probab Lett. 2013;83:1928–1936] to martingales with possibly unbounded differences and establish the connection between Sason's inequality and De la Peña's inequality [A general class of exponential inequalities for martingales and ratios. Ann Probab. 1999;27(1):537–564]. An application to self-normalized deviations is given.
A Study on the Relationship among Dietary Fiber Intake, Type 2 Diabetes, Microbiota and Immune System

With rapid socioeconomic development and demographic changes, the global diabetes mellitus pandemic becomes an alarming problem. It is necessary to extenuate the incidence of diabetes mellitus and discover potential effective treatments. Dietary fiber (DF) takes an important place in a healthy diet and they are mainly present in plant-based foods, such as vegetables, nuts, and beans. The global dietary fiber consumption trend is projected to continuously increase as the public became aware of its importance. Recent clinical trials indicated that the amount of dietary fiber was correlated with the Type 2 Diabetes Mellitus (T2DM) rate. In the current research, an underlying mechanism will be investigated. Several groups proved that dietary fiber intake could influence the diversity of intestinal microbiota and a decrease in microbiota composition could further affect the level of inflammation in the human immune system. Other studies also reflected that both the composition of gastrointestinal microflora and inflammation level was associated with the incidence of T2DM. The finding suggested a lower level of inflammation tended to have a lower rate of T2DM. Hence, the level of dietary fiber intake could eventually have an impact on T2DM incidence.
Cyclotomic expansion and volume conjecture for superpolynomials of colored HOMFLY-PT homology and colored Kauffman homology

We first study superpolynomial associated to triply-graded reduced colored HOMFLY-PT homology. We propose conjectures of congruent relations and cyclotomic expansion for it. We prove conjecture of $N=1$ for torus knot case, through which we obtain the corresponding invariant $\alpha(T(m,n))=-(m-1)(n-1)/2$. This is closely related to the Milnor conjecture. Many examples including homologically thick knots and higher representations are also tested. Based on these examples, we further propose a conjecture that invariant $\alpha$ determined in cyclotomic expansion at $N=1$ is a lower bound for smooth 4-ball genus. According to the structure of cyclotomic expansion, we propose a volume conjecture for $SU(n)$ specialized superpolynomial associated to reduced colored HOMFLY homology. We also prove the figure eight case for this new volume conjecture. Then we study superpolynomial associated to triply-graded reduced colored Kauffman homology. We propose a conjecture of cyclotomic expansion for it. Homologically thick examples and higher representations are tested. Finally we apply the same idea to the Heegaard-Floer knot homology and also obtain an expansion formula for all the examples we tested.
Study of the numerical solutions for the Electrical Impedance Equation in the plane: A pseudoanalytic approach of the forward Dirichlet boundary value problem

Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value problem, corresponding to the Electrical Impedance Equation in the plane, when the electrical conductivity is an arbitrary non-vanishing function, fully defined within a bounded domain. The new method is studied considering a variety of examples when the bounded domain coincides with the unit circle, and it is also included a description of its behaviour in non-smooth domains, selecting special cases that do not require additional regularization techniques, for warranting the convergence of the approach at the non-smooth regions, when certain requirements are fulfilled.
Applied Multivariate Statistics for the Social Sciences

Nelder 1989 and Dobson 1990), this book presents two speci c generalized linear models before its general discussion of the family of generalized linear models. I wish the authors would give some practical examples to motivate the considerations of logistic and Poisson regression models in chapter 4, where the two speci c models are introduced. Also, it would have been helpful to have some additional interpretation of the model parameters. See the approach by Agresti (1996) for an example.
Mg doped InN and confirmation of free holes in InN

We report a systematic investigation on Mg doped InN epilayers grown by radio-frequency plasma-assisted molecular beam epitaxy. Electrolyte capacitance voltage (ECV) combined with thermopower measurements find p-type conduction over an Mg concentration range. For InN:Mg in this p-type “window” the Seebeck coefficients dramatically change their signs from negative to positive when the thickness of undoped InN interlayer decreases to zero. This notable sign change of Seebeck coefficient explains the previous inconsistency between ECV and thermopower results and confirms the existence of mobile holes in the InN:Mg. Taking into account the undoped InN interlayer, the hole density and mobility are extracted.
Wave propagation in incompressible MHD wave guides: the twisted magnetic Annulus

The propagation of MHD waves in a structured magnetic flux tube embedded within a straight vertical magnetic environment is studied analytically. The motivation of this analysis comes from the observations of damped loop oscillations showing that possibly only part of the loop is homogeneous in the radial direction. The general dispersion relation of longitudinal wave propagation is derived for a fully magnetically twisted configuration consisting of a core, annulus and external region each with magnetic field of uniform, yet distinct, twist. Next, a simplified case representing coronal loops is analysed in detail considering magnetic twist just in the annulus, the internal and external regions having straight magnetic field. Modes of oscillations are examined from the general dispersion relation that is suitable for obtaining information on not just oscillations but also on some instability properties of this complex tube structure. It is shown that there are purely surface (i.e. evanescent) and hybrid (spatially oscillatory in the twisted annulus, otherwise evanescent) modes. Except for small wavenumbers, the surface waves show little dispersion: a property making them more suitable for observations. The hybrid modes show a more complex character. Though the frequency range seems to be rather limited, there is a continuum band of frequencies for a given wavenumber. Both short and long wavelength approximations are considered for the symmetrical (sausage) mode and with small twist in particular.
Aspects of quantum gravity

For more than 80 years theoretical physicists have been trying to develop a theory of quantum gravity which would successfully combine the tenets of Einstein's theory of general relativity (GR) together with those of quantum field theory. At the current stage, there are various competing responses to this challenge under construction. Attacking the problem of quantum gravity from the quantum geometry perspective, where space and spacetime are discrete, the focus of this thesis lies on the application of loop quantum gravity (LQG) and group field theory (GFT). We employ these two closely related nonperturbative approaches to two areas where quantum gravity effects are broadly expected to be relevant: black holes and quantum cosmology. Concerning black holes, apart from understanding their inner structure, a pressing issue is to give a microscopic explanation for the phenomenon of black hole entropy in terms of a discrete quantum geometry and relate it to the symmetries of the horizon. Black hole models in LQG are typically constructed via the isolated horizon boundary condition which gives rise to an effective description of the horizon geometry in terms SU(2) Chern-Simons theory. In this thesis we find a reinterpretation of the statistics of the horizon degrees of freedom as those of a system of non-Abelian anyons. As regards quantum cosmology, the challenge is to understand how the initial singularity problem of GR can be resolved by means of the discreteness of geometry and how a continuum spacetime can emerge from a large assembly of geometric building blocks. Most recent research in GFT aims at deriving the effective dynamics for condensate states directly from the microscopic GFT quantum dynamics and subsequently to extract a cosmological interpretation from them. In this thesis we elaborate on aspects of this approach and study phenomenological consequences in detail.
Airy-type evolution equations on star graphs

In the present paper the Airy operator on star graphs is defined and studied. The Airy operator is a third order differential operator arising in different contexts, but our main concern is related to its role as the linear part of the Korteweg-de Vries equation, usually studied on a line or a half-line. The first problem treated and solved is its correct definition, with different characterizations, as a skew-adjoint operator on a star graph, a set of lines connecting at a common vertex representing, for example, a network of branching channels. A necessary condition turns out to be that the graph is balanced, i.e. there is the same number of ingoing and outgoing edges at the vertex. The simplest example is that of the line with a point interaction at the vertex. In these cases the Airy dynamics is given by a unitary or isometric (in the real case) group. In particular the analysis provides the complete classification of boundary conditions giving momentum (i.e., $L^2$-norm of the solution) preserving evolution on the graph. A second more general problem here solved is the characterization of conditions under which the Airy operator generates a contraction semigroup. In this case unbalanced star graphs are allowed. In both unitary and contraction dynamics, restrictions on admissible boundary conditions occur if conservation of mass (i.e., integral of the solution) is further imposed. The above well posedness results can be considered preliminary to the analysis of nonlinear wave propagation on branching structures.
Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces

This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problem div ϕ(|∇u|)∇u=a(x)f(u)inΩ,u≥0inΩ,u=∞on∂Ω,where either Ω⊂RN with N≥1 is a smooth bounded domain or Ω=RN . The function ϕ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz–Sobolev spaces.
Secondary threshold amplitudes for sinuous streak breakdown

The nonlinear stability of laminar sinuously bent streaks is studied for the plane Couette flow at Re = 500 in a nearly minimal box and for the Blasius boundary layer at Reδ*=700. The initial perturbations are nonlinearly saturated streamwise streaks of amplitude AU perturbed with sinuous perturbations of amplitude AW. The local boundary of the basin of attraction of the linearly stable laminar flow is computed by bisection and projected in the AU – AW plane providing a well defined critical curve. Different streak transition scenarios are seen to correspond to different regions of the critical curve. The modal instability of the streaks is responsible for transition for AU = 25%–27% for the considered flows, where sinuous perturbations of amplitude below AW ≈ 1%–2% are sufficient to counteract the streak viscous dissipation and induce breakdown. The critical amplitude of the sinuous perturbations increases when the streamwise streak amplitude is decreased. With secondary perturbations amplitude AW ≈ 4%, .