Miracle-dz/UniFAR-FTUs huggingface dataset:
Aperiodic order and spherical diffraction, I: auto‐correlation of regular model sets

We study uniform and non‐uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as mathematical models of quasi‐crystals. We then define a notion of auto‐correlation for subsets of finite local complexitiy in arbitrary lcsc groups, which generalizes Hof's classical definition beyond the class of amenable groups, and provide a formula for the auto‐correlation of a regular model set. Along the way we show that the punctured hull of an arbitrary regular model set admits a unique invariant probability measure, even in the case where the punctured hull is non‐compact and the group is non‐amenable. In fact this measure is also the unique stationary measure with respect to any admissible probability measure.
Conformal invariance of lattice models

These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorphic functions and its applications to planar statistical physics (more precisely to the convergence of fermionic observables). Convergence to SLE is discussed briefly. Many open questions are included.
Simulation and Comparison of DVR and DSTATCOM Used For Voltage Sag Mitigation at Distribution Side

: Power Quality problem in a system leads to various disturbances such as voltage fluctuations, transients and waveform distortions that results in a mis-operation or a failure of end user equipment. There are different types of custom power devices like Distribution Static Compensator (D-STATCOM) and Dynamic Voltage Restorer (DVR) which can effectively use for mitigation of different type of power quality problems. This paper describes the technique of correcting the supply voltage sag distributed system and also describes performance comparison are presented between DVR and DSTATCOM to know how both the devices successfully been applied to power system for regulating system voltage effectively. DSTATCOM and DVR both of them based on VSI principle. A DVR is a series compensation device which injects a voltage in series with system and a DSTATCOM is a shunt compensation device which injects a current into the system to correct the power quality problems. This paper presents a power system operation with PI controller with abc to dq0 convertor approach. Total Harmonics Distortion (THD) is also calculated for the system with and without compensation. Results are presented to assess the performance of devices as a potential custom power solution. Improve dynamic voltage control and thus increase system load ability. This paper presents modeling and simulation of DVR & DSTATCOM in MATLAB/Simulink.
Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian

We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian [Formula: see text] in a Lipschitz bounded domain [Formula: see text] satisfying the exterior ball condition. The weight is a power of the distance to the boundary [Formula: see text] of [Formula: see text] that accounts for the singular boundary behavior of the solution for any [Formula: see text]. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension [Formula: see text], which is optimal for [Formula: see text].
Dead and Alive: Beliefs in Contradictory Conspiracy Theories

: Conspiracy theories can form a monological belief system: a self-sustaining worldview comprised of a network of mutually supportive beliefs. The present research shows that even endorsement of mutually incompatible conspiracy theories are positively correlated. In Study 1 ( n = 137), the more participants believed that Princess Diana faked her own death, the more they believed that she was murdered. In Study 2 ( n = 102), the more participants believed that Osama Bin Laden was already dead when U.S. special forces raided his compound in Pakistan, the more they believed he is still alive. Hierarchical regression models showed that mutually incompatible conspiracy theories are positively associated because both are associated with the view that the authorities are engaged in a cover-up (Study 2). The monological nature of conspiracy belief appears to be driven not by conspiracy theories directly supporting one another, but by broader beliefs supporting conspiracy theories in general.
Trust in Risk Sharing: A Double-Edged Sword

We analyze efficient risk-sharing arrangements when the value from deviating is determined endogenously by another risk sharing arrangement. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any coalition formed (joined) after deviations rely on a belief in future cooperation which we term “trust”. We treat the contracting conditions of original and deviation coalitions symmetrically and show that higher trust tightens incentive constraints since it facilitates the formation of deviating coalitions. As a consequence, although trust facilitates the initial formation of coalitions, the extent of risk sharing in successfully formed coalitions is declining in the extent of trust and efficient allocations might feature resource burning or utility burning: trust is indeed a double-edged sword.
On the structure of Brieskorn lattices, II

We give a simple proof of the uniqueness of extensions of good sections for formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K. Saito for the proof of convergence in the non-quasihomogeneous polynomial case. Our proof uses an exponential operator argument as in their paper, although we do not use polyvector fields nor smooth differential forms. We also present an apparently simpler algorithm for an inductive calculation of the coefficients of primitive forms in the Brieskorn-Pham polynomial case. In a previous paper on the structure of Brieskorn lattices, there were some points which were not yet very clear, and we give some explanations about these, e.g. on the existence and the uniqueness of primitive forms associated with good sections, where we present some rather interesting examples. In Appendix we prove the uniqueness up to a nonzero constant multiple of the higher residue pairings in some formal setting which is different from the one in the main theorem. This is questioned by D. Shklyarov.
THE ROLE OF DIGITALISATION IN THE PROCESS OF IMPROVING THE QUALITY OF URBAN PUBLIC SERVICES

There is a large body of research showcasing the enormous potential of digitalization in adressing several challanges public sector faces, such as bureacracy, transparency, efficiency, a better interaction with citizens, providing successfull examples and best practices. However, empirical research focusing on the user experience is not so well represented in the literature, despite the fact that one the key goals of e-services is to fit the needs and expectations of the citizens. In this paper we focus on digitalisation from the perspective of the beneficiaries, who from a total quality management approach should be the first to inform digitalization initiatives, but who in most cases are just passive receivers of the digitalization outcomes. We place our attention on urban mobility services offered by Sector 4 Bucharest Municipality because both before and during the pandemic they proved to be highly digital. Our findings reveal both the users ʼ, as well as the public services providers ʼ perspective, suggesting that although the perceived levels of digitalization and satisfaction with e-services are quite high, there is plenty of room for improving the quality of e-services by involving both citizens and employees in the design process and by boosting their level of digital skills.
Notes on Exploration in Linear MDPs

In this note we introduce LSVI-UCB [1] and provide its regret analysis. The note is also heavily inspired by that of Wen Sun [2]. For the purpose of clearly conveying the main ideas behind the analysis, we will be sketchy in several aspects: (1) we will omit the proof on the boundedness of the relevant parameters, especially when they appear in e.g., covering analysis in a poly-logarithmic manner, (2) we will not explicitly mention it when we need to split the failure probability over a constant number of estimation events of distinct nature. We will briefly mention it when we union bound over a variable number of events (e.g., T and H), but they will not appear in the bounds because we will use Õ(·) to suppress poly-logarithmic factors.
Analysis of quantum-mechanical states of the Mie-type ring shaped model via the Fisher's information entropy

In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is the strongest support of the modern quantum computation and information, which is basic for numerous technological developments. This study report the any $\ell-$state solution of the radial Schr\"{o}dinger equation with the Mie-type ring shaped diatomic molecular potential. Rotational-vibration of some few selected diatomic molecules are given. The probability distribution density of the system which gives the probability density for observing the electron in the state characterized by the quantum numbers $(n, l, m)$ in the Mie-type ring shaped diatomic molecular potential is obtained. Finally, we analyze this distribution via a complementary information measures of a probability distribution called as the Fisher's information entropy.
The Countermeasures of Training Practical Knowledge in Teaching for Normal College Students

: As an important stage of systematic teacher training, the practical knowledge of normal college students is not only an important basis to guide the practical activities of education and teaching, but also an objective embodiment of practical knowledge in the field of education. On the other hand, education is a career for training people, which determines the value orientation of practical knowledge for normal college students in the process of training. Therefore, this work first analyzed the problems existing in the process of training practical knowledge for normal college students, and then put forward some possible countermeasures for training practical knowledge in teaching. The research results in this work contribute to enhancing the practical knowledge for normal college students and thus to ultimately promote the sustainable professional development of teachers in the future.
Deep Beauty: A Universe of Processes and Some of Its Guises

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can then be converted into mathematical structure. With very little structural effort (i.e. in very abstract terms) and in a very short time span the categorical quantum mechanics (CQM) research program has reproduced a surprisingly large fragment of quantum theory. It also provides new insights both in quantum foundations and in quantum information, and has even resulted in automated reasoning software called `quantomatic' which exploits the deductive power of CQM. In this paper we complement the available material by not requiring prior knowledge of category theory, and by pointing at connections to previous and current developments in the foundations of physics. This research program is also in close synergy with developments elsewhere, for example in representation theory, quantum algebra, knot theory, topological quantum field theory and several other areas.
A Second Order Cone Programming Approach for Simulating Biphasic Materials

Strain limiting is a widely used approach for simulating biphasic materials such as woven textiles and biological tissue that exhibit a soft elastic regime followed by a hard deformation limit. However, existing methods are either based on slowly converging local iterations, or offer no guarantees on convergence. In this work, we propose a new approach to strain limiting based on second order cone programming (SOCP). Our work is based on the key insight that upper bounds on per‐triangle deformations lead to convex quadratic inequality constraints. Though nonlinear, these constraints can be reformulated as inclusion conditions on convex sets, leading to a second order cone programming problem—a convex optimization problem that a) is guaranteed to have a unique solution and b) allows us to leverage efficient conic programming solvers. We first cast strain limiting with anisotropic bounds on stretching as a quadratically constrained quadratic program (QCQP), then show how this QCQP can be mapped to a second order cone programming problem. We further propose a constraint reflection scheme and empirically show that it exhibits superior energy‐preservation properties compared to conventional end‐of‐step projection methods. Finally, we demonstrate our prototype implementation on a set of examples and illustrate how different deformation limits can be used to model a wide range of material behaviors.
Free and nearly free surfaces in $P^3$

We define the nearly free surfaces in $P^3$ and show that the Hilbert polynomial of the Milnor algebra of a free or nearly free surface in $P^3$ can be expressed in terms of the exponents. An analog of Saito's criterion of freeness in the case of nearly free divisors is proven and examples of irreducible free and nearly free surfaces are given.
Subspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$

We present two fast constructions of weak*-copies of l ∞ in H ∞ and show that such copies are necessarily weak*-complemented. Moreover, via a Paley-Wiener type of stability theorem for bases, a connection can be made in some cases between the two types of construction, via interpolating sequences (in fact these are at the basis of the second construction). Our approach has natural generalizations where H ∞ is replaced by an arbitrary dual space and l ∞ by l p (1 ≤ p ≤ ∞) relying on the notions of generalized interpolating sequence and bounded linear extension. An old (very simple but unpublished so far) construction of bases which are Besselian but not Hilbertian finds a natural place in this development.
Knowing Educational Psychology: A Tool to Smoothen the Teaching-Learning Process

When the idea of an efficient teacher comes in our mind, the first thing that we consider as the prominent issue is whether that person has proper knowledge of the subject that s/he is going to teach. The secondary concern surfaces whether that person is knowledgeable enough to present the subject matter. Now, one question that most of us never think about or simply ignore is: Are all these qualities enough to be a successful teacher? Who is going to answer this question? Who is going to judge whether a teacher is ‘perfect’ or not? Will the judge be another senior teacher or a prominent educationist in that field or the students who always closely observe the activities of the teacher? Some people may raise the objection saying how students can judge the teacher as they are not mature enough for having lack of knowledge and sufficient experiences of life beyond the classroom. To tackle such questions, one great source of help is to know theories and practices of educational psychology in depth as it fundamentally challenges the notion of considering the students as machines that run with different types of programs. It strongly asserts that the students are not machines, they are human beings with frequently changing characteristics, emotions, desires, moods, responses/reactions and so on. So, one of the objectives of this paper is to show how, by understanding the psychology of the students, a teacher can provide them proper guidance. Also, this paper aims at finding out different important issues/concerns by exploring and contextualizing various prominent psychological theories of education to create an overall positive as well as enabling educational environment both for the teacher and the learners. To attain this end, this paper uses insights from educational psychology in particular to keep the frame of discussion focused and manageable. Green University Review of Social Sciences Dec 2021; 7(1-2): 165-174
Spectral analysis of the Neumann-Poincar e operator and characterization of the gradient blow-up ∗

When perfectly conducting or insulating inclusions are closely located, stress which is the gradient of the solution to the conductivity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer poten
On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions

We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary condition depending on a pressure functional. In the stationary case we prove existence and uniqueness of a suitable weak solution to the system under a small data condition. The topic of the paper is driven by recent developments of vorticity based numerical methods for the Navier--Stokes equations.
An online generalized multiscale discontinuous Galerkin method (GMsDGM) for flows in heterogeneous media

Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.
Partial differential Chow forms and a type of partial differential Chow varieties

Abstract We first present an intersection theory of irreducible partial differential varieties with quasi-generic differential hypersurfaces. Then, we define partial differential Chow forms for irreducible partial differential varieties whose Kolchin polynomials are of the form And we establish for partial differential Chow forms most of the basic properties of their ordinary differential counterparts. Furthermore, we prove that a certain type of partial differential Chow varieties exist. Communicated by Jason Bell
Irreducible convex paving for decomposition of multidimensional martingale transport plans

Martingale transport plans on the line are known from Beiglbock & Juillet to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R^d, d larger than one. Our decomposition is a partition of R^d consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well-defined. We justify the relevance of our decomposition by proving the existence of a martingale transport plan filling these components. We also deduce from this decomposition a characterization of the structure of polar sets with respect to all martingale transport plans.
Entanglement and quantum state geometry of a spin system with all-range Ising-type interaction

The evolution of an N spin-1/2 system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the number of spins and the initial state. Also, the geometry of the manifold, which contains entangled states, is obtained. For this case we find the dependence of entanglement on the scalar curvature of the manifold and examine it for different numbers of spins in the system. Finally we show that the transverse magnetic field leads to a change in the manifold topology.
Gamma conjecture via mirror symmetry

The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the principal asymptotic class A_F equals the Gamma class G_F associated to Euler's $\Gamma$-function. We illustrate in the case of toric varieties, toric complete intersections and Grassmannians how this conjecture follows from mirror symmetry. We also prove that Gamma conjecture is compatible with taking hyperplane sections, and give a heuristic argument how the mirror oscillatory integral and the Gamma class for the projective space arise from the polynomial loop space.
Rational homotopy of complex projective varieties with normal isolated singularities

Abstract Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper, we prove, using mixed Hodge theory, that if the link of each singular point of X is ( n - 2 ) ${(n-2)}$ -connected, then X is a formal topological space. This result applies to a large class of examples, such as normal surface singularities, varieties with ordinary multiple points, hypersurfaces with isolated singularities and, more generally, complete intersections with isolated singularities. We obtain analogous results for contractions of subvarieties.
Oscillator versus prefundamental representations. II. Arbitrary higher ranks

We find the l-weights and the l-weight vectors for the highest l-weight q-oscillator representations of the positive Borel subalgebra of the quantum loop algebra Uq(L(sll+1)) for arbitrary values of l. Having this, we establish the explicit relationship between the q-oscillator and prefundamental representations. Our consideration allows us to conclude that the prefundamental representations can be obtained by tensoring q-oscillator representations.
Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert Spaces

Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by Eckstein and Bertsakas \cite{EP} in infinite dimensional Hilbert spaces. In this paper, by employing a kind of "partial" gap analysis, we prove the weak convergence of general preconditioned and relaxed ADMM in infinite dimensional Hilbert spaces, with preconditioning for solving all the involved implicit equations under mild conditions. We also give the corresponding ergodic convergence rates respecting to the "partial" gap function. Furthermore, the connections between certain preconditioned and relaxed ADMM and the corresponding Douglas-Rachford splitting methods are also discussed, following the idea of Gabay in \cite{DGBA}. Numerical tests also show the efficiency of the proposed overrelaxation variants of preconditioned ADMM.