Miracle-dz/UniFAR-FTUs huggingface dataset:
Hamilton-Jacobi Theorems for Nonholonomic Reducible Hamiltonian Systems on a Cotangent Bundle

Hamilton-Jacobi theorem reveals the deeply internal relationship between the generating function and the dynamical vector field of a Hamiltonian system. Because of the restriction given by constraints, in general, the dynamical vector field of nonholonomic Hamil- tonian system is not Hamiltonian, however, it can be described by the dynamical vector field of a distributional Hamiltonian system. In this paper, we give two types of Hamilton-Jacobi equation for a distributional Hamiltonian system, by the calculation in detail, and we give also an exactly restricted condition between the solution of the Type II of Hamilton-Jacobi equation, for the distributional Hamiltonian system, and the solution of the Type II of Hamilton-Jacobi equation, for the associated unconstrained Hamiltonian system. Moreover, we generalize the above results to nonholonomic reducible Hamiltonian system with symmetry, as well as with momentum map, and obtain two types of Hamilton-Jacobi equations for the nonholonomic re- duced distributional Hamiltonian systems. As an application, we give two examples to illustrate the theoretical results.
The Einstein constraint equations on compact manifolds with boundary

We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and prove existence of solutions in both the near-constant mean curvature (CMC) and far-from-CMC (for Yamabe positive metrics) cases. We also make partial progress in proving the results of previous ‘limit equation’ papers by Dahl, Gicquaud, Humbert and Sakovich.
Emotional Crisis Communication: The Effects of CEO’s Expression of Guilt and Anger on Organizational Reputation

ABSTRACT Organizational crises are emotionally-charged occurrences for both organizations and their stakeholders. There has been a growing body of research on the effects of emotions on organizational outcomes such as reputation, forgiveness, and negative word-of-mouth. The current study seeks to contribute to this growing body of research in emotional crisis communication by investigating the role of discrete emotions in a crisis, and the effects of such emotions on organizational reputation. Additionally, the current study seeks to investigate whether the effect of emotional expression depends on the crisis response strategy adopted. A between-subjects three (communicated emotion; anger vs. guilt vs. no emotion) × two (response strategy: rebuilding vs. denial) experiment was designed with 922 participants. The findings show that, in the context of a severe crisis, rebuilding strategies result in a more positive organizational reputation than denial strategies and that guilt was superior to anger regardless of response type. The implications of the study on organizational reputation and crisis management are discussed.
On the discrete Fuglede and Pompeiu problems

We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu property. Using this description and the revealed connection we prove that Fuglede's conjecture holds for $\mathbb{Z}_{p^n q^2}$, where $p$ and $q$ are different primes. In particular, we show that every spectral subset of $\mathbb{Z}_{p^n q^2}$ tiles the group. Further, using our combinatorial methods we give a simple proof for the statement that Fuglede's conjecture holds for $\mathbb{Z}_p^2$.
Explicating the Cognitive Process of a Physician’s Trust in Patients: A Moderated Mediation Model

Trust is considered a critical factor in the physician–patient relationship. However, little is known about the development and impact of physicians trusting their patients. A model that is premised on the integrated model of organizational trust was proposed in this article to reveal the cognitive processes involved in physicians’ trust, with perceived integrity and the ability of the patient as antecedents and the physicians’ communication efficacy as the outcome. A cross-sectional survey of 348 physicians in Zhejiang province, China, revealed that a physician’s trust in a patient mediated the relationship between the physicians’ perception of the integrity and ability of the patient, and the physician’s communication efficacy. The physicians’ educational backgrounds and work experience were also found to moderate an indirect effect: a lower level of education and longer work experience intensified the impact of the perceived integrity and ability of the patient on the physician’s trust, while shorter work experience made the association between the physician’s trust and communication efficacy more salient. This paper provided implications for both physician and patient sides.
Green Communication for More Package-Free Ecommerce Returns

The existing packed mail-based return mode in ecommerce has a considerable negative impact on the natural environment. In contrast, a package-free return mode accepts unpacked ecommerce returns using return points in-store and is a more eco-friendly service. On the basis of the push–pull–mooring (PPM) framework, this study aims to identify key factors in green communication that contribute to consumers switching from mail return services to package-free return services. A scenario-based online survey was conducted. Structural equation modeling was used to test the hypotheses. Push factors (consumer dissatisfaction) and a mooring factor (mail return habit) only manifested weak effects on switching intention. Regarding pull factors (service convenience and green value), in contrast to previous research, the effect of green value on switching intention was found to be much weaker than the effect of service convenience. Convenience was found to be the key factor in green communication. Our research adds value to green communication and the PPM framework. It updates existing knowledge concerning the role of consumer dissatisfaction, perceived green value, and perceived convenience of return service in green communication. This study also explains why the mooring factor of habit fails to predict switching intention.
Monotonicity of Zeros of Jacobi-Angelesco polynomials

We study the monotonic behaviour of the zeros of the multiple Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to the parameters $\alpha,\beta$ and $\gamma$. We prove that the zeros are monotonic functions of $\alpha$ and $\gamma$ and consider some special cases of how the zeros depend on $\beta$, especially in the presence of symmetry. As a consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre and Laguerre-Hermite multiple orthogonal polynomials too.
Beurling densities and frames of exponentials on the union of small balls

If x1, . , xm are finitely many points in R d, let Eǫ = ∪i=1 xi + Qǫ, where Qǫ = {x ∈ Rd, |xi| ≤ ǫ/2, i = 1, . , d} and let f denote the Fourier transform of f . Given a positive Borel measure μ on Rd, we provide a necessary and sufficient condition for the frame inequalities A ‖f‖2 ≤ ∫ Rd |f(ξ)| dμ(ξ) ≤ B ‖f‖2, f ∈ L(Eǫ), to hold for some A,B > 0 and for some ǫ > 0 sufficiently small. If m = 1, we show that the limits of the optimal lower and upper frame bounds as ǫ → 0 are equal, respectively, to the lower and upper Beurling density of μ. When m > 1, we extend this result by defining a matrix version of Beurling density. Given a (possibly dense) subgroup G of R, we then consider the problem of characterizing those measures μ for which the inequalities above hold whenever x1, . , xm are finitely many points in G (with ǫ depending on those points, but not A or B). We point out an interesting connection between this problem and the notion of well-distributed sequence when G = aZ for some a > 0. Finally, we show the existence of a discrete set Λ such that the measure μ = ∑ λ δλ satisfy the property above for the whole group R.
On ergodicity of mostly expanding semi-group actions

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our results improve the main result in [8], where the ergodicity for one dimensional fiber was proved. We will introduce Markov partition for finitely generated semi-group actions and then we establish ergodicity for a large class of finitely generated semi-groups of C^{1+alpha}-diffeomorphisms that admit a Markov partition. Moreover, we present some transitivity criteria for semi-group actions and provide a weaker form of dynamical irreducibility that suffices to ergodicity in our setting.
The Algebraic Structure of Quantity Calculus

Abstract The algebraic structure underlying the quantity calculus is defined axiomatically as an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them bound by algebraic restrictions. Subspaces, tensor product, and quotient spaces are considered, as well as homomorphisms to end with a classification theorem of these structures. The new structure provides an axiomatic foundation of quantity calculus which is centered on the concept of dimension, rather than on the concept of unit, which is regarded as secondary, and uses only integer exponents of the dimensions.
Shuffle group laws: applications in free probability

Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the Baker–Campbell–Hausdorff formula or the analytic expression of a Lie group law in exponential coordinates in the neighbourhood of the identity. Non‐commutative shuffle products happen to have similar properties with respect to pre‐Lie algebras. However, the situation is more complex since in the non‐commutative framework three exponential‐type maps and corresponding logarithms are naturally defined. This results in several new formal group laws together with new operations, for example, a new notion of adjoint action particularly well fitted to the new theory. These developments are largely motivated by various constructions in non‐commutative probability theory. The second part of the article is devoted to exploring and deepening this perspective. We illustrate our approach by revisiting universal products from a group‐theoretical viewpoint, including additive convolution in monotone, free and boolean probability, as well as the Bercovici–Pata bijection and subordination products.
On the necessity of bump conditions for the two-weighted maximal inequality

We study the necessity of bump conditions for the boundedness of the Hardy-Littlewood maximal operator $M$ from $L^p(v)$ into $L^p(w)$, where $1<p<\infty$. The conditions in question are obtained by replacing the average of $\sigma=v^{-\frac{1}{p-1}}$ in the Muckenhoupt $A_p$-condition by an average with respect to certain Banach function space, and are known to be sufficient for the two-weighted maximal inequality. We show that these conditions are in general not necessary for the boundedness of $M$ from $L^p(v)$ into $L^p(w)$.
WALL-CROSSING FORMULAS FOR FRAMED OBJECTS

We prove wall-crossing formulas for the motivic invariants of the moduli spaces of framed objects in the ind-constructible abelian categories. Developed techniques are applied in the case of the motivic Donaldson-Thomas invariants of quivers with potentials. Another application is a new proof of the formula for the motivic invariants of smooth models of quiver moduli spaces.
A note on the maximal out-degree of Galton-Watson trees

In this note we consider both the local maximal out-degree and the global maximal out-degree of Galton-Watson trees. In particular, we show that the tail of any local maximal out-degree and that of the offspring distribution are asymptotically of the same order. However for the global maximal out-degree, this is only true in the subcritical case.
Interturn Fault Detection in Induction Machines Based on High-Frequency Injection

An interturn short-circuit in the stator windings can lead to the breakdown of electrical machines. In the case of induction machines, several fault detection methods and faulted models have been developed in the recent decades. These models differ mainly in how the leakage inductances of the faulted winding are modeled. This work provides a generalized model for interturn short-circuit faults, using different assumptions for the leakage inductances. The model is validated with experimental results for an exhaustive set of fault parameters, and the influence of leakage inductances is analyzed. Moreover, the model is used to analyze the drawbacks of the negative-sequence fundamental current as a traditional fault signature. A high-frequency injection method for converter-fed machines is presented to overcome these limits. The proposed fault signature is the negative-sequence current at the injection frequency and it is evaluated experimentally at different operating conditions. The fault severity and its location are proved to be related to the proposed fault signature.
Gelfand-Kirillov dimension of cosemisimple Hopf algebras

In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D’Andrea-Pinzari-Rossi (2017).
Note on a double binomial sum relevant to the Hadamard maximal determinant problem

We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest because it can be used in proofs of lower bounds for the Hadamard maximal determinant problem. Our proof of the identity uses a two-variable variant of the method of telescoping sums.
Modelling Initiation Stage of Backward Erosion Piping through Analytical Models

Backward erosion piping, which is one of the leading causes of levee and dam failures, is more likely to occur when a flow is concentrated on a defect with an overlying low-permeability layer and a shallow erosion channel forming and progressing towards a seepage source. Two analytical models are presented to allow assessment of the seepage regime on the initiation stage of BEP. The variations between the two models are analysed, indicating that the effects of soil loosening have a major role in the assessment of BEP mechanisms. This paper also describes the reliability of using Xiao’s model in 3D analysis, which includes results and parametric analysis. Although the head in front of the tip of the erosion channel can be predicted by this accepted calculation model, which is essential for laboratory work on this topic, the model also has range and boundary limitations that need to be addressed for general prediction when BEP progresses with channel development.
On certain Möbius type solutions for the n-body problem in a positive space form

We study here the Mobius type solutions for the n-body problem in a two dimensional positive space form M^2_R. With methods of Mobius geometry and using the Iwasawa decomposition of the Mobius group of automorphisms Mob_2 (M^2_R), we state algebraic functional conditions for the existence of such type of solutions in M^2_R. We mention some examples of these type of solutions.
Sums of twisted circulants

The rate of convergence of simple random walk on the Heisenberg group over $Z/nZ$ with a standard generating set was determined by Bump et al [1,2]. We extend this result to random walks on the same groups with an arbitrary minimal symmetric generating set. We also determine the rate of convergence of simple random walk on higher-dimensional versions of the Heisenberg group with a standard generating set. We obtain our results via Fourier analysis, using an eigenvalue bound for sums of twisted circulant matrices. The key tool is a generalization of a version of the Heisenberg Uncertainty Principle due to Donoho-Stark [4].
Singular limits of K\"ahler-Ricci flow on Fano $G$-manifolds.

In this paper, we prove that any solution of K\"ahler-Ricci flow on a Fano compactification $M$ of semisimple complex Lie group, is of type II, if $M$ admits no K\"ahler-Einstein metrics. As an application, we found two Fano compactifications of $\mathrm{SO}_4(\mathbb{C})$ and one Fano compactification of $\mathrm{Sp}_4(\mathbb{C})$, on which the K\"ahler-Ricci flow will develop singularities of type II. To the authors' knowledge, these are the first examples of Ricci flow with singularities of type II on Fano manifolds in the literature.
Wrapped Floer cohomology and Lagrangian correspondences

We study Lagrangian correspondences between Liouville manifolds and construct functors between wrapped Fukaya categories. The study naturally brings up the question on comparing two versions of wrapped Fukaya categories of the product manifold, which we prove quasi-isomorphism on the level of wrapped Floer cohomology. To prove representability of these functors constructed from Lagrangian correspondences, we introduce the geometric compositions of Lagrangian correspondences under wrapping, as new classes of objects in the wrapped Fukaya category, which we prove to represent the functors by establishing a canonical isomorphism of quilted version of wrapped Floer cohomology under geometric composition.
Comparison of Physical Activity, Dual-Task Performance, and Cognitive Skills Between Problematic Video Game Players and Control Subjects

Introduction: This study aimed to compare the dual-task and cognitive skills of problematic video gamers and non-problematic video gamers based on the fact that cognitive skills (e.g., inhibition, decision-making, attentional control, time perception) and dual-task performance may be positively affected in individuals who play games. Methods: The study was conducted on 62 individuals. The study group (n=33) consisted of individuals who played games, and the control group (n=28) consisted of non-gamers. Their scores on exercise benefits and barriers perception, cognitive performance, cognitive skills, and dual-task performances were measured. The Montreal Cognitive Assessment (MoCA) scale was used to evaluate cognitive function, and the Trail Making Test (TMT) was used to determine attention, speed, and better motor performance. The Stroop test was used to evaluate executive functioning. Results: It was determined that the problematic game players group was faster at the Stroop 1 and Stroop 2 test times (respectively p=0.020, p=0.005). In the comparison of dual task-cognitive 10-meter walking) test times of both groups, it was seen that individuals in the problematic game players group were faster than the control subjects (p=0.044). Conclusion: It can be said that playing digital games improves the cognitive dual-task cost (DTC) and the executive functioning of individuals.
THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS

We revisit the problem of predicting the spin magnitude and direction of the black hole (BH) resulting from the merger of two BHs with arbitrary masses and spins inspiraling in quasi-circular orbits. We do this by analyzing a catalog of 619 recent numerical-relativity simulations collected from the literature and spanning a large variety of initial conditions. By combining information from the post-Newtonian approximation, the extreme mass-ratio limit, and perturbative calculations, we improve our previously proposed phenomenological formulae for the final remnant spin. In contrast with alternative suggestions in the literature, and in analogy with our previous expressions, the new formula is a simple algebraic function of the initial system parameters and is not restricted to binaries with spins aligned/anti-aligned with the orbital angular momentum but can be employed for fully generic binaries. The accuracy of the new expression is significantly improved, especially for almost extremal progenitor spins and for small mass ratios, yielding an rms error σ ≈ 0.002 for aligned/anti-aligned binaries and σ ≈ 0.006 for generic binaries. Our new formula is suitable for cosmological applications and can be employed robustly in the analysis of the gravitational waveforms from advanced interferometric detectors.
Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: I

This is the second of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. Using the notion of obstruction bundle data introduced in [FOOO8], we give a systematic way of constructing a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks which are compatible at the boundary and corners. More specifically, it defines a tree like K-system in the sense of [FOOO6, Definition 21.9]. The method given in this paper does not only simplify the description of the constructions in the earlier literature, but also is designed to provide a systematic utility tool for the construction of a system of Kuranishi structures in the future research. We also establish its uniqueness.
On sets defining few ordinary hyperplanes

Let P be a set of n points in real projective d-space, not all contained in a hyperplane, such that any d points span a hyperplane. An ordinary hyperplane of P is a hyperplane containing exactly d points of P. We show that if d > 4, the number of ordinary hyperplanes of P is at least 􀀀n􀀀1 d􀀀1 􀀀 Od(nb(d􀀀1)=2c) if n is suciently large depending on d. This bound is tight, and given d, we can calculate the exact minimum number for suciently large n. This is a consequence of a structure theorem for sets with few ordinary hyperplanes: For any d > 4 and K > 0, if n > CdK8 for some constant Cd > 0 depending on d, and P spans at most K 􀀀n􀀀1 d􀀀1 ordinary hyperplanes, then all but at most Od(K) points of P lie on a hyperplane, an elliptic normal curve, or a rational acnodal curve. We also nd the maximum number of (d+1)-point hyperplanes, solving a d-dimensional analogue of the orchard problem. Our proofs rely on Green and Tao's results on ordinary lines, our earlier work on the 3-dimensional case, as well as results from classical algebraic geometry.
Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d Super Yang-Mills

The instanton partition functions of $\mathcal{N}=1$ 5d super Yang-Mills are built using elements of the representation theory of quantum $\mathcal{W}_{1+\infty}$ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding-Iohara-Miki and quantum toroidal $\widehat{\mathfrak{gl}}(1)$ algebra. Exploiting the explicit action of the algebra on the partition function, we prove the regularity of the 5d qq-characters. These characters provide a solution to the Schwinger-Dyson equations, and they can also be interpreted as a quantum version of the Seiberg-Witten curve.