Miracle-dz/UniFAR-FTUs huggingface dataset:
Fock Parafermions and Self-Dual Representations of the Braid Group

We introduce and describe in second quantization a family of particle species with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally associated to the parafermionic zero-energy modes, potentially realizable in mesoscopic arrays of fractional topological insulators. Their second-quantization description entails the concept of Fock algebra, i.e., a Fock space endowed with a statistical multiplication that captures and logically correlates these anyons' exclusion and exchange statistics. As a consequence normal-ordering continues to be a well-defined operation. Because of its relevance to topological quantum information processing, we also derive families of self-dual representations of the braid group for any $p$, with the Gaussian representation being a special case. The self-dual representations can be realized in terms of local quadratic combinations of either parafermions or Fock parafermions, an important requisite for physical implementation of quantum logic gates.
Relax-and-split method for nonsmooth nonconvex problems.

We develop and analyze a new `relax-and-split' (RS) approach for compositions of separable nonconvex nonsmooth functions with linear maps. RS uses a relaxation technique together with partial minimization, and brings classic techniques including direct factorization, matrix decompositions, and fast iterative methods to bear on nonsmooth nonconvex problems. We also extend the approach to trimmed nonconvex-composite formulations; the resulting Trimmed RS (TRS) can fit models while detecting outliers in the data. We then test RS and TRS on a diverse set of applications: (1) phase retrieval, (2) stochastic shortest path problems, (3) semi-supervised classification, and (4) new clustering approaches. RS/TRS can be applied to models with very weak functional assumptions, are easy to implement, competitive with existing methods, and enable a new level of modeling formulations to be put forward to address emerging challenges in the mathematical sciences.
An Extended Pruess Method for Sturm-Liouville Problems

A new version of the piecewise approximation (Pruess) method is developed for calculating eigenvalues of Sturm-Liouville problems. The usual piecewise constant or piecewise linear potential approximations are replaced by translates of $2/cos^2(x)$, whose corresponding eigenvalue equation has elementary solutions.
The Brown-Peterson spectrum is not $E_{2(p^2+2)}$ at odd primes

Recently, Lawson has shown that the 2-primary Brown-Peterson spectrum does not admit the structure of an $E_{12}$ ring spectrum, thus answering a question of May in the negative. We extend Lawson's result to odd primes by proving that the p-primary Brown-Peterson spectrum does not admit the structure of an $E_{2(p^2+2)}$ ring spectrum. We also show that there can be no map $MU \to BP$ of $E_{2p+3}$ ring spectra at any prime.
Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably dierent from that of the continuous time Markov process. This is dierent from the behaviour of the standard M/G/1/ 1,where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueinginventory systems are dealt with in the literature previously, and are revisited here in detail.
Killing vectors of FLRW metric (in comoving coordinates) and zero modes of the scalar Laplacian

Based on an examination of the solutions to the Killing Vector equations for the FLRW-metric in co moving coordinates , it is conjectured and proved that the components(in these coordinates) of Killing Vectors, when suitably scaled by functions, are \emph{zero modes} of the corresponding \emph{scalar} Laplacian. The complete such set of zero modes(infinitely many) are explicitly constructed for the two-sphere. They are parametrised by an integer n. For $n\,\ge\,2$, all the solutions are \emph{irregular} (in the sense that they are neither well defined everywhere nor are \emph{square-integrable}). The associated 2-d vectors are also \emph{not normalisable}. The $n=0$ solutions being constants (these correspond to the zero angular momentum solutions) are regular and normalizable. Not all of the $n=1$ solutions are regular but the associated vectors are normalizable. Of course, the action of scalar Laplacian coordinate independent significance only when acting on scalars. However, our conclusions have an unambiguous meaning as long as one works in this coordinate system. As an intermediate step, the covariant Laplacians(vector Laplacians) of Killing vectors are worked out for four-manifolds in two different ways, both of which have the novelty of not explicitly needing the connections. It is further shown that for certain maximally symmetric sub-manifolds(hypersurfaces of one or more constant comoving coordinates) of the FLRW-spaces also, the scaled Killing vector components are zero modes of their corresponding scalar Laplacians. The Killing vectors for the maximally symmetric four-manifolds are worked out using the elegant embedding formalism originally due to Schr\"odinger . Some consequences of our results are worked out. Relevance to some very recent works on zero modes in AdS/CFT correspondences , as well as on braneworld scenarios is briefly commented upon.
A High-Resolution Survey of Low-Redshift QSO Absorption Lines: Statistics and Physical Conditions of O VI Absorbers

Using high-resolution ultraviolet spectra of 16 low-z QSOs obtained with the E140M echelle mode of the Space Telescope Imaging Spectrograph, we study the physical conditions and statistics of O VI absorption in the intergalactic medium (IGM) at z < 0.5. We identify 51 intervening (zabs≪ zQSO) O VI systems comprising 77 individual components, and we find 14 “proximate” systems (zabs ≈ zQSO) containing 34 components. For intervening systems (components) with rest-frame equivalent width Wr > 30 mÅ, the number of O VI absorbers per unit redshift dN/dz = 15.6−2.4+2.9 (21.0−2.8+3.2) , and this decreases to dN/dz = 0.9−0.5+1.0 (0.3−0.3+0.7) for Wr > 300 mÅ. The number per redshift increases steeply as zabs approaches zQSO; we find that dN/dz is ≈3-10 times higher within 2500 km s−1 of zQSO. The most striking difference between intervening and proximate systems is that some proximate absorbers have substantially lower H I/O VI ratios. The lower ratios in proximate systems could be partially due to ionization effects, but these proximate absorbers must also have significantly higher metallicities. We find that 37% of the intervening O VI absorbers have velocity centroids that are well aligned with corresponding H I absorption. If the O VI and the H I trace the same gas, the relatively small differences in line widths imply that the absorbers are cool, with T < 105 K. Most of these well-aligned absorbers have the characteristics of metal-enriched photoionized gas. However, the O VI in the apparently simple and cold systems could be associated with a hot phase with T ≈ 105.5 K if the metallicity is high enough to cause the associated broad Lyα absorption to be too weak to detect. We show that 53% of the intervening O VI systems are complex multiphase absorbers that can accommodate both lower metallicity collisionally ionized gas with T > 105 K and cold photoionzed gas.
Lower bound for the number of real roots of a random algebraic polynomial

Abstract Let X1, X2, …, Xn be identically distributed independent random variables belonging to the domain of attraction of the normal law, have zero means and Pr{Xr ≠ 0} > 0. Suppose a0, a1, …, an are non-zero real numbers and max and εn is such that as n → ∞, εn. If Nn be the number of real roots of the equation then for n > n0, Nn > εn log n outside an exceptional set of measure at most provided limn→∞ (kn/tn) is finite.
M. Zimmermann1 · M. A. Efremov1 · A. Roura1 · W. P. Schleich1,2 · S. A. DeSavage3 · J. P. Davis4 · A. Srinivasan5 · F. A. Narducci3 · S. A. Werner6 · E. M. Rasel7

Phases play an extraordinary role in quantum theory. On one hand, they represent the central ingredient of wave mechanics à la Schrödinger, and on the other, they build a bridge to classical mechanics à la Hamilton–Jacobi [4]. For these reasons they constitute a crucial ingredient of matter-wave interferometers [5–7] which nowadays represent standard tools for precision measurements. In this article, we propose a new type of atom interferometer whose phase scales with the cube of the time T the atom spends in the interferometer.
Quantum Shuffles and Quantum Supergroups of Basic Type

We initiate the study of several distinguished bases for the positive half of a quantum supergroup $U_q$ associated to a general super Cartan datum $(\mathrm{I}, (\cdot,\cdot))$ of basic type inside a quantum shuffle superalgebra. The combinatorics of words for an arbitrary total ordering on $\mathrm{I}$ is developed in connection with the root system associated to $\mathrm{I}$. The monomial, Lyndon, and PBW bases of $U_q$ are constructed, and moreover, a direct proof of the orthogonality of the PBW basis is provided within the framework of quantum shuffles. Consequently, the canonical basis is constructed for $U_q$ associated to the standard super Cartan datum of type $\mathfrak{gl}(n|1)$, $\mathfrak{osp}(1|2n)$, or $\mathfrak{osp}(2|2n)$ or an arbitrary non-super Cartan datum. In the non-super case, this refines Leclerc's work and provides a new self-contained construction of canonical bases. The canonical bases of $U_q$, of its polynomial modules, as well as of Kac modules in the case of quantum $\mathfrak{gl}(2|1)$ are explicitly worked out.
First‑principle study of local and electronic structures of yttrium‑doped Ba ( Zr x Ti 1 − x ) O 3

Yttrium substitution in Ba ( Zr x Ti 1 − x ) O 3 (BZT) solid solutions has been found to be an effective way to induce relaxor behavior and improve their dielectric and ferroelectric performances. However, the underlying mechanism of such enhancement is not yet well understood. Here we employ density functional theory with the generalized gradient approximation to investigate the effect of yttrium on the structural and electronic properties of BZT for x = 0.125, 0.250, and 0.375. The results will be discussed in terms of yttrium site preference, atomic pair distribution functions (PDFs), cation off-centering and electronic density of states. It was found that yttrium incorporation could occur in either A- or B-site with corresponding defect vacancies and that the effect of the sites of impurities is only to cause small changes in formation energies. The calculated PDFs and cation off-centering indicate that yttrium ions actively induce lattice distortion and increase structural disorder. This implies that the addition of yttrium in BZT suppresses the ferroelectric instabilities and may help to explain the transition from ferroelectric to relaxor state of such materials.
On the Bielliptic and Bihyperelliptic Loci

We study some particular loci inside the moduli space $\mathcal{M}_g$, namely the bielliptic locus (i.e. the locus of curves admitting a $2:1$ cover over an elliptic curve $E$) and the bihyperelliptic locus (i.e. the locus of curves admitting a $2:1$ cover over a hyperelliptic curve $C'$, $g(C') \geq 2$). We show that the bielliptic locus is not a totally geodesic subvariety of $\mathcal{A}_g$ if $g \geq 4$ (while it is for $g=3$, see [16]) and that the bihyperelliptic locus is not totally geodesic if $g \geq 3g'$. We also give a lower bound for the rank of the second gaussian map on the generic point of the bielliptic locus and an upper bound for this rank for every bielliptic curve.
Global existence of weak solutions of a model for electrolyte solutions - Part 2: Multicomponent case

This paper analytically investigates the Darcy–Poisson–Nernst–Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple suspended charged chemical species with arbitrary valencies. We prove global existence and uniqueness of weak solutions in two space dimensions.
On the limit distributions of lightly trimmed sums

Let Xnn ≥ 1, be i.i. d.r. v. 's and Sn = X1+…+Xn. Let be Sn minus the r terms of largest absoluete value. Maller proved that if coverages in distribution to N(0, 1) then so does (Sn/bn)−an, assuming that Xn have a continuous symmetric distribution. We show that his resul;t is true without these extra assumptions. Some related results are also given.
POWER RELATIONS AND GROUP AGGREGATION IN THE MULTIPLICATIVE AHP AND SMART

The relative power of the members in a group of decision makers can be incorporated in the multiplicative AHP via power coefficients in the logarithmic least squares whereby we analyse the pairwise comparison matrices. When each decision maker judges every pair of alternatives under each of the criteria, aggregation over the criteria and over the decision makers proceeds via a sequence of geometric-mean calculations which can be carried out in any order, at least with predetermined criterion weights and power coefficients. Hence, since we preserve the rank order of the alternatives, we avoid a deficiency of the original AHP. We also consider SMART, an additive method which is logarithmically related to the multiplicative AHP so that power relations can easily be incorporated in it. Finally, in order to illustrate the proposed model, we analyse a generalized version of the well-known example of Belton and Gear as well as the power relations between member countries of the European Community. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal.6: 155–165 (1997) No. of Figures: 0. No. of Tables: 6. No. of References: 23.
Existence of solution for a system involving fractional Laplacians and a Radon measure

An existence of a nontrivial solution in some `weaker' sense of the following system of equations \begin{align*} (-\Delta)^{s}u+l(x)\phi u+w(x)|u|^{k-1}u&=\mu~\text{in}~\Omega\nonumber\\ (-\Delta)^{s}\phi&= l(x)u^2~\text{in}~\Omega\nonumber\\ u=\phi&=0 ~\text{in}~\mathbb{R}^N\setminus\Omega \end{align*} has been proved. Here $s \in (0,1)$, $l,w$ are bounded nonnegative functions in $\Omega$, $\mu$ is a Radon measure and $k > 1$ belongs to a certain range.
Nonlocal Hormander's hypoellipticity theorem

Consider the following nonlocal integro-differential operator: for $\alpha\in(0,2)$, $$ \cal L^{(\alpha)}_{\sigma,b} f(x):=\mbox{p.v. } \int_{\mathbb{R}^d-\{0\}}\frac{f(x+\sigma(x)z)-f(x)}{|z|^{d+\alpha}}d z+b(x)\cdot\nabla f(x), $$ where $\sigma:\mathbb{R}^d\to\mathbb{R}^d\times\mathbb{R}^d$ and $b:\mathbb{R}^d\to\mathbb{R}^d$ are two $C^\infty_b$-functions, and p.v. stands for the Cauchy principal value. Let $B_1(x):=\sigma(x)$ and $B_{j+1}(x):=b(x)\cdot\nabla B_j(x)-\nabla b(x)\cdot B_j(x)$ for $j\in\mathbb{N}$. Under the following H\"ormander's type condition: for any $x\in\mathbb{R}^d$ and some $n=n(x)\in\mathbb{N}$, $$ \mathrm{Rank}[B_1(x), B_2(x),\cdots, B_n(x)]=d, $$ by using the Malliavin calculus, we prove the existence of the heat kernel $\rho_t(x,y)$ to the operator $\cal L^{(\alpha)}_{\sigma,b}$ as well as the continuity of $x\mapsto \rho_t(x,\cdot)$ in $L^1(\mathbb{R}^d)$ for each $t>0$. Moreover, when $\sigma(x)=\sigma$ is constant, under the following uniform H\"ormander's type condition: for some $j_0\in\mathbb{N}$, $$ \inf_{x\in\mathbb{R}^d}\inf_{|u|=1}\sum_{j=1}^{j_0}|u B_j(x)|^2>0, $$ we also prove the smoothness of $(t,x,y)\mapsto\rho_t(x,y)$ with $\rho_t(\cdot,\cdot)\in C^\infty_b(\mathbb{R}^d\times\mathbb{R}^d)$ for each $t>0$.
A microbial technology approach using bioleaching for low grade metals extraction - a review

Bioleaching is a promising technological advancement of metal refinement which arises from the application of beneficial microorganism. Low grade ores and electronic waste (e-waste) that contains significant amounts of “critical metals” such as the rare earth elements (REE) are commonly discarded in waste heaps which causes major pollution. The over mining of the primary resources of REE is becoming a major concern considering its limited supply and increasing demand. Bioleaching application is able to provide not only a simpler method of metal leaching but are also cost-effective in comparison to chemical leaching and thermo-hydrometallurgy. By applying bioleaching in major e-waste treatments, we can extract back significant amounts of REE with lower cost and better environmental impacts. This review provides studies which discuss the backgrounds of bioleaching, its methods and mechanisms, direct comparison of chemical leaching, pyrometallurgy, hydrometallurgy and bioleaching in terms of its economic and environmental aspect and lastly its future in the mining industry in Malaysia.
Fire severity and the legacy of mountain pine beetle outbreak: high-severity fire peaks with mixed live and dead vegetation

Bark beetle outbreaks and wildfires are two of the most prevalent disturbances that influence tree mortality, regeneration, and successional trajectories in western North American forests. Subboreal forests have experienced broad overlaps in these disturbances, and recent wildfires have burned through landscapes with substantial tree mortality from prior outbreaks. This study investigated how fuel conditions associated with mountain pine beetle outbreaks influence the probability of high burn severity (i.e. stand-replacing fire) across a range of fire weather conditions in subboreal forests of central interior British Columbia, Canada. We focused on three large fires that occurred in 2012, 2013, and 2014. We characterized outbreak severity, outbreak-influenced prefire vegetation, and subsequent burn severity using Landsat spectral vegetation indices, high-resolution imagery, and field observations. Substantial portions of the prefire landscape contained mixtures of live and dead vegetation created by variable beetle damage and vegetation response—spatial patterns that are related to, but distinct from, peak outbreak severity. We evaluated drivers—fuels, weather, and topography—of high-severity fire under ‘extreme,’ ‘moderate,’ and ‘benign’ fire weather conditions (i.e. burning conditions) using Boosted Regression Trees. While fire weather was a primary driver in most cases, prefire vegetation was an influential predictor variable across all burning conditions, and the probability of high-severity fire was highest when prefire vegetation was a mixture of tree mortality from bark beetles and live vegetation. Thus, while weather and drought are important drivers of wildfires in subboreal forests, bottom-up drivers of elevation and vegetation, including the fuel legacies of bark beetle outbreaks, are crucial factors influencing high-severity burning. The legacy of recent bark beetle outbreaks will continue for decades on these landscapes, affecting fuel structures, future wildfires, forest dynamics, and the broader social-ecological systems of the region.
Implementing a Digital Solution for Architectural Daylight Analysis in BIM Based Projects by developing a new plugin

To achieve a successful architectural project, it is essential for architects to truly understand and collaborate with other designers and engineers during the whole project. Regarding daylight analysis, what architects decide about the fenestration types, sizes, and their placements, interior layout design, interior or exterior materials, and finally the outer shape of the buildings may change the quantity and quality of natural light in the interiors. Moreover, such decisions about room configurations, fenestration, and materials can also directly or indirectly affect thermal comfort which is needed to be checked and confirmed by energy experts in the project. In this paper, a newly developed digital solution, and a new plugin called AftabRad is introduced. Its main goal is to export the 3D model from the BIM Modeling software to Radiance, as its daylight simulation core, and present the results back to the BIM software. This plugin can help daylight specialists to be fully or partially involved in any projects to assist architects or urban designers to easily calculate different types of static or dynamic daylight metrics by themselves. However, daylight specialists can do daylight calculations in the final stage or the project if it is needed. In such a project, since most of the daylight analyses for different types of alternatives can be done by architects, and regarding the nature of BIM-based project, by having direct dialogs with energy experts, the probability of achieving a well-daylit space, being thermally and visually comfortable, and fulfilling the daylight requirements can be much higher in comparison with doing daylight simulation just at the end of a project.
Debris flow susceptibility analysis using a bivariate statistical analysis in the Panataran River, Kg Melangkap, Sabah, Malaysia

This study area is part of the Kadamaian watershed and is located on the North-West flank of Mount Kinabalu, composed of sedimentary rock from the Crocker Formation and the Mt. Kinabalu granitic pluton. Many loose seismic materials were found on the slopes during the 2015 Sabah Earthquake with a moment magnitude of 6.0. These materials later served as the source material for rainfall-induced debris flows or shallow landslides. The community closest to the Panataran river in the Kg Melangkap area is the most affected. Therefore, the objective of this study is to study the debris flow susceptibility analysis using a bivariate statistical analysis approach, namely the Frequency Ratio (FR) model. Forty-eight landslides were identified using remote sensing interpretation. Characteristics of the research area, such as slope gradient, elevation, slope aspect, lithology, slope curvature, and topographic wetness index, were selected as the factors to evaluate the debris flow susceptibility analysis. The correlations between these factors and the occurrence of landslides were established, and the results were assessed and validated based on those results. Validation findings demonstrate that this technique provides high accuracy, with an AUC of 81.8 for success rate. As a result, it can be stated that this model accurately predicted landslide susceptibility in the research area, and that it can help local authority with future land-use planning, as well as give tools for hazard mitigation.