Miracle-dz/UniFAR-FTUs huggingface dataset:
$\mathcal{S}$-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.
Visibility of graphene flakes on a dielectric substrate

The authors model the optical visibility of monolayer and bilayer graphene deposited on a SiO2∕Si substrate or thermally annealed on the surface of SiC. Visibility is much stonger in reflection than in transmission, reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.
Infinitesimal Hilbertianity of Weighted Riemannian Manifolds

Abstract The main result of this paper is the following: any weighted Riemannian manifold $(M,g,\unicode[STIX]{x1D707})$, i.e., a Riemannian manifold $(M,g)$ endowed with a generic non-negative Radon measure $\unicode[STIX]{x1D707}$, is infinitesimally Hilbertian, which means that its associated Sobolev space $W^{1,2}(M,g,\unicode[STIX]{x1D707})$ is a Hilbert space. We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold $(M,F,\unicode[STIX]{x1D707})$ can be isometrically embedded into the space of all measurable sections of the tangent bundle of $M$ that are $2$-integrable with respect to $\unicode[STIX]{x1D707}$. By following the same approach, we also prove that all weighted (sub-Riemannian) Carnot groups are infinitesimally Hilbertian.
The entropy of dense non-commutative fermion gases

We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, Jz, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e., for such systems the number of microscopic degrees of freedom is determined by the circumference, rather than the area (size) of the system. From a commutative perspective these results can also be interpreted in terms of an effective excluded volume. Possible generalizations to three dimensions, which restore rotational symmetry, are briefly discussed.
A missed persistence property for the Euler equations and its effect on inviscid limits

We consider the problem of strong convergence, as the viscosity goes to zero, of the solutions to the three-dimensional evolutionary Navier–Stokes equations, under the Navier slip-type boundary condition (1.4), to the solution of the Euler equations under the no-penetration condition. In two dimensions, the above strong convergence holds in any smooth domain. Furthermore, in three dimensions, arbitrarily strong convergence results hold in the half-space case. In spite of the above results, recently we presented an explicit family of smooth initial data in the 3D sphere, for which the result fails. The result was proved as a by-product of the lack of time persistency for the above boundary condition under the Euler flow. Our aim here is to show a more general, and simpler proof, displayed in arbitrary, smooth domains.
On badly approximable subspaces

Given an $a$-dimensional linear subspace $\mathfrak{A}$ in $\mathbb{R}^d$ which contains a badly approximable $b$-dimensional subspace $\mathfrak{B} \subset \mathfrak{A}$. We study the badly approximability almost all $c$-dimensional linear subspaces $\mathfrak{C} \subset \mathfrak{A}$.
Analysis and Performance of the Barzilai-Borwein Step-Size Rules for Optimization Problems in Hilbert Spaces

Due to simplicity, computational cheapness, and efficiency, the Barzilai and Borwein (BB) gradient method has received a significant amount of attention in different fields of optimization. In the first part of this paper, based on spectral analysis, R-linear global convergence for the BB-method is proven for strictly convex quadratic problems posed in infinite-dimensional Hilbert spaces. Then this result is strengthened to R-linear local convergence for a class of twice continuously Fr\'echet-differentiable functions. In the second part, aiming at problems governed by partial differential equations (PDE), the mesh-independent principle is investigated for the BB-method. The applicability of these results is demonstrated for three different types of PDE-constrained optimization problems. Numerical experiments illustrate the theoretical results.
Detecting Fast solvability of equations via small powerful Galois groups

Fix an odd prime $p$, and let $F$ be a field containing a primitive $p$th root of unity. It is known that a $p$-rigid field $F$ is characterized by the property that the Galois group $G_F(p)$ of the maximal $p$-extension $F(p)/F$ is a solvable group. We give a new characterization of $p$-rigidity which says that a field $F$ is $p$-rigid precisely when two fundamental canonical quotients of the absolute Galois groups coincide. This condition is further related to analytic $p$-adic groups and to some Galois modules. When $F$ is $p$-rigid, we also show that it is possible to solve for the roots of any irreducible polynomials in $F[X]$ whose splitting field over $F$ has a $p$-power degree via non-nested radicals. We provide new direct proofs for hereditary $p$-rigidity, together with some characterizations for $G_F(p)$ -- including a complete description for such a group and for the action of it on $F(p)$ -- in the case $F$ is $p$-rigid.
Quintic threefolds with triple points

We study the geometry of quintic threefolds [Formula: see text] with only ordinary triple points as singularities. In particular, we show that if a quintic threefold [Formula: see text] has a reducible hyperplane section then [Formula: see text] has at most [Formula: see text] ordinary triple points, and that this bound is sharp. We construct various examples of quintic threefolds with triple points and discuss their defect.
T = 0 partition functions for Potts antiferromagnets on square lattice strips with (twisted) periodic boundary conditions

We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (or, equivalently, the chromatic polynomial) for two families of arbitrarily long strip graphs of the square lattice with periodic boundary conditions in the transverse direction and (i) periodic and (ii) twisted periodic boundary conditions in the longitudinal direction, so that the strip graphs are embedded on (i) a torus and (ii) a Klein bottle. In the limit of infinite length, we calculate the exponent of the entropy, W(q), show it to be the same for (i) and (ii), and determine its analytic structure.
The Parisi formula for mixed $p$-spin models

The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed $p$-spin models which also include $p$-spin interactions for odd $p$. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in [Ann. of Math. (2) 177 (2013) 383-393].
Flake Graphene as an Innovative Additive to Grease with Improved Tribological Properties

The paper presents the results of research on the use of flake graphene as an additive to plastic grease in order to improve its tribological properties. The influence of concentration (0.25–5.00 wt.%) and the form of graphene (graphene oxide, reduced graphene oxide) on selected properties of the base grease were investigated. It has been found that the addition of graphene flakes improves the anti-wear properties of the lubricant. The greatest improvement in the properties of the lubricant was achieved by using graphene at a concentration of 4.00 wt. %; the reduction in the average diameter of the wear scar was almost 70% for GO and RGO, compared to the base lubricant without the addition of graphene.
The Impact of the COVID-19 Crisis on the Practices and Mental Health of Psychologists in Belgium: Between Exhaustion and Resilience

While the COVID-19 pandemic has created psychological distress in the general population and increased the need for psychological care, little research has been done on how mental health practitioners (MHP) have been affected by the pandemic, and these health professionals have received little attention from public authorities. In this article, we focus on psychologists and the impact that the pandemic has had on their mental health and practices by exploring the adaptive and innovative responses generated. This study is based on an online survey (including multiple choice questions, several validated scales, and eight free text items) completed by 187 psychologists (86% female) one year after the beginning of the COVID-19 pandemic in Belgium (February–April 2021). Most participants considered that the crisis had an impact on their well-being and mental health. However, the prevalence of symptoms of depression and anxiety was relatively low (17%; 12%). On the other hand, the majority of psychologists (72%) suffered from a medium level of burnout (BO), 7% suffered from a high level of BO, and only 21% had low levels of BO. Psychologists working in face-to-face settings had the highest scores on the “exhaustion” subscale of the BO, and those working primarily with patients in precarious situations had significantly higher scores of BO and exhaustion. Qualitative analysis of free text items showed that MHP were resilience and developed new frameworks and modes for proactive interventions in order to reach their patients, meet the psychological and social population’s needs, and maintain their relationships with the network. In a crisis or pandemic context, public policies should take into account the psychological and social needs of the most socially precarious populations in reinforcing and supporting mental health professionals working in this sector.
Update on Dental Luting Materials

A dental luting material aids in the retention and stability of indirect restorations on the prepared tooth structure. In dentistry, clinicians are using a wide range of luting materials for the cementation of indirect restorations. Zinc oxide eugenol and non-eugenol cements, zinc phosphate cement, zinc polycarboxylate cement, glass ionomer cement and resin cements are common dental cements used in dentistry. Each luting material or cement possesses unique properties and clinical implications. An ideal luting cement should be biocompatible, insoluble, resistant to thermal and chemical assaults, antibacterial, aesthetic, simple and easy to use. It should have high strength properties under tension, shear and compression to resist stress at the restoration–tooth interface, as well as adequate working and setting times. So far, no luting material possesses all of these properties of an ideal cement. Scientists have been modifying the conventional luting cements to improve the material’s clinical performance and developing novel materials for clinical use. To achieve the best clinical outcome, clinicians should update their knowledge and gain a good understanding of the luting materials so that they can make a wise clinical decision on the material selection and obtain an insight into the development of luting cements. Therefore, the objective of this study is to provide a discussion on the physical, chemical, adhesive and aesthetic properties of common luting materials. The clinical indications of these luting materials are suggested based on their properties. In addition, overviews of the modification of the conventional luting materials and the newly developed luting materials are provided.
CCA-Based Compressive Sensing for SSVEP-Based Brain-Computer Interfaces to Command a Robotic Wheelchair

People with severe physical disabilities are not able of using standard robotic wheelchairs, which generally demand some motor skills, and therefore total usage of associate muscles. Robotic wheelchairs commanded by brain-computer interfaces (BCIs) based on electroencephalography have demonstrated to be an alternative for these end-users. In general, existing robotic wheelchairs commanded by BCIs require special platforms adapted to the EEG-BCI, and end-users need to attend a long training process to safely drive these devices. But many times these potential users do not have access to training sessions; due to mobility problems or technology access restrictions. This study proposes an EEG-based BCI with a customizable configuration to be used in cloud architectures for the remote control of robotic wheelchairs. This research explores two types of steady-state visual evoked potential (SSVEP)-based BCI by applying canonical correlation analysis (CCA) and compressive sensing (CS) as a novelty, adopting one free calibration, and the other including a calibration stage. The free-calibrated SSVEP recognition approach (CS-ncCCA) using compression ratio (CR) at 60% obtained accuracy (ACC) of 85% and information transfer rate (ITR) of 102 bits per minute (b/min), whereas the calibrated BCI (CS-wcCCA) applying also CR at 62% achieved ACC of 85% and ITR of 195 b/min. As a highlight, the proposed BCI allows a significant reduction of the transmitted file size (TFS) and improves the communication latency that may be useful in remote and cloud robotics applications, such as for users with severe motor disabilities, to train driving safely robotic wheelchairs via Internet of Things (IoT).
Word combinatorics for stochastic differential equations: Splitting integrators

We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a technique to write down systematically the expansion of the local error; this makes it possible to easily formulate the conditions that guarantee that a given integrator achieves a prescribed strong or weak order. This approach bypasses the need to use the Baker-Campbell-Hausdorff (BCH) formula and shows the existence of an order barrier of two for the attainable weak order. The paper also provides a succinct introduction to the combinatorics of words.
Knowledge, attitude, perception, and factors associated with the risk perception of COVID‐19 among nursing college students in Japanese universities: A cross‐sectional study

The spread of coronavirus disease 2019 (COVID‐19) in the world has brought different attitudes and perceptions among social strata. Nursing students being future first‐line healthcare workers are more at risk of being infected and exposed to various stressors from shared information. The objectives of this study were to evaluate the knowledge, attitude, and perception of COVID‐19 among nursing students and to estimate predictors of their risk perception.
On a generalized Wirtinger inequality

Let $\alpha( p,q,r) =$inf{$\frac{|| u'||_p}{||u||_q}:u\in W_{p e r}^{1,p}( -1,1) $\{$ 0$}, $\int_{-1}^1|u|^{r-2} u=0$} . We show that $\alpha( p,q,r )=\alpha ( p,q,q)$ if $q\leq rp+r-1$ $\alpha( p,q,r) ( 2r-1) p$ generalizing results of Dacorogna-Gangbo-Subia and others.
Scalable Multi-Stage CMOS OTAs With a Wide CL-Drivability Range Using Low-Frequency Zeros

This work introduces a multi-stage CMOS OTA design technique that allows cascading identical gain stages (for arbitrarily scalable high DC gain) while driving an ultra-wide range of capacitive loads (<inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L}}\text{s}$ </tex-math></inline-formula>). At the heart of the proposed design is a new frequency compensation technique (FCT) that relies on low-frequency left-half-plane zeros to allow the proposed OTA to operate for a desired closed-loop behavior. In this work, classical gain-stages (i.e., differential pair and common source transistors) are used to design fully-differential 2-, 3-, 4- and 5-stage CMOS OTAs. The proposed 2-to-4-stage designs have been fabricated in TSMC 65 nm CMOS process and the measurement results show that the 2-stage OTA is achieving a DC gain of 50 dB with a <inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L}}$ </tex-math></inline-formula>-drivability ratio (i.e., <inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L,max}}/\text{C}_{\text {L,min}}$ </tex-math></inline-formula>) of <inline-formula> <tex-math notation="LaTeX">$10,000\times $ </tex-math></inline-formula>, the 3-stage OTA is achieving a DC gain of 70 dB with a <inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L}}$ </tex-math></inline-formula>-drivability of <inline-formula> <tex-math notation="LaTeX">$1,000,000\times $ </tex-math></inline-formula>, and the 4-stage OTA is achieving a DC gain of 90 dB with a <inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L}}$ </tex-math></inline-formula>-drivability of <inline-formula> <tex-math notation="LaTeX">$1,000,000\times $ </tex-math></inline-formula>. This is a 10-to-1000-time improvement in the state-of-the-art, as the highest <inline-formula> <tex-math notation="LaTeX">$\text{C}_{\text {L}}$ </tex-math></inline-formula>-drivability reported to date is <inline-formula> <tex-math notation="LaTeX">$1000\times $ </tex-math></inline-formula>. Accordingly, the proposed OTAs can cover a wider range of applications than any other reported works.
Auto-Segment Control System With High Spatially Average Power for Dynamic Inductive Power Transfer

This work proposes an auto-segment control system with multiple transmitters and dual receivers for dynamic inductive power transfer (DIPT) charging. The current of the transmitting coil precisely coupled with the receiver can be enhanced automatically, while the transmitting current will be suppressed when the transmitter is uncoupled with the receiver. Therefore, the electromagnetic interference (EMI) and power loss generated by uncoupled transmitters can be reduced without position detection and switching control. Each receiver includes a power coil and an impedance coil. When the vehicle moves along the road, the impedance coils are utilized to adjust the resonant state of the transmitter, and the power coils operate alternately to maintain a high spatially average power. The relative position and size between transmitters and receivers directly impact the power transfer performance. Therefore, several critical parameters of the magnetic coupler are analyzed and designed to obtain a considerable output power. An around 300 W experimental prototype is established to verify the feasibility of the proposed magnetic coupler and design method. Compared to the auto-segment control system with a single receiver, the spatially average power of the proposed system is improved by twice, and the maximum efficiency is 84.9% in a moving period.
Fluctuations around Hartree states in the mean-field regime

We consider the dynamics of a large system of $N$ interacting bosons in the mean-field regime where the interaction is of order $1/N$. We prove that the fluctuations around the nonlinear Hartree state are generated by an effective quadratic Hamiltonian in Fock space, which is derived from Bogoliubov's approximation. We use a direct method in the $N$-particle space, which is different from the one based on coherent states in Fock space.
Some dynamical properties of pseudo-automorphisms in dimension 3

Let $X$ be a compact K\"ahler manifold of dimension 3 and let $f:X\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\lambda_1(f)^2>\lambda_2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$ currents, and we also discuss the (still open) problem of intersection of such currents. We prove a weak equidistribution result (which is essentially known in the literature) for Green $(1,1)$ currents of meromorphic selfmaps, not necessarily 1-algebraic stable, of a compact K\"ahler manifold of arbitrary dimension; and discuss how a stronger equidistribution result may be proved for pseudo-automorphisms in dimension 3. As a byproduct, we show that the intersection of some dynamically related currents are well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.
Value-distribution of the Riemann zeta-function and related functions near the critical line

We study the value-distribution of the Riemann zeta-function and related functions on and near the critical line. Amongst others, we focus on the following: The critical line is a natural boundary of the Voronin-type universality property of the Riemann zeta-function. We study a modified concept of `universality' at the critical line: roughly speaking, we add a scaling factor to the vertical shifts that appear in Voronin's universality theorem. Levinson showed that almost all a-points of the Riemann zeta-function lie in a certain funnel-shaped region around the critical line. We rely on arguments of the theory of normal families and the notion of filling discs to detect a-points in this region which are very close to the critical line. According to a folklore conjecture (often attributed to Ramachandra) one expects that the values of the Riemann zeta-function on the critical line lie dense in the complex numbers. We show that there are certain curves which approach the critical line asymptotically such that the values of the zeta-function on these curves are dense in the complex numbers. The Lindel\"of hypothesis can be reformulated in terms of power moments to the right of the critical line. Tanaka showed recently that the expected asymptotic formulas for these power moments are true in a certain measure-theoretical sense. We provide a discrete and integrated version of Tanaka's result and extend it to a large class of Dirichlet series connected to the Riemann zeta-function.