Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Erd\H{o}s-Ginzburg-Ziv invariant and zero-sum Ramsey number for intersecting families

Let $G$ be a finite abelian group, and let $m>0$ with $\exp(G)\mid m$. Let $s_{m}(G)$ be the generalized Erdős-Ginzburg-Ziv invariant which denotes the smallest positive integer $d$ such that any sequence of elements in $G$ of length $d$ contains a subsequence of length $m$ with sum zero in $G$. For any integer $r>0$, let $\mathcal{I}_m^{(r)}$ be the collection of all $r$-uniform intersecting families of size $m$. Let $R(\mathcal{I}_m^{(r)},G)$ be the smallest positive integer $d$ such that any $G$-coloring of the edges of the complete $r$-uniform hypergraph $K_{d}^{(r)}$ yields a zero-sum copy of some intersecting family in $\mathcal{I}_m^{(r)}$. Among other results, we mainly prove that $\Omega(s_{m}(G))-1\leq R (\mathcal{I}_{m}^{(r)}, \ G)\leq \Omega(s_{m}(G)),$ where $\Omega(s_{m}(G))$ denotes the least positive integer $n$ such that ${n-1 \choose r-1}\geq s_{m}(G)$, and we show that if $r\mid \Omega(s_{m}(G))-1$ then $R (\mathcal{I}_{m}^{(r)}, \ G)= \Omega(s_{m}(G))$.
Would You Like to Buy Food via Ecommerce App? The Mediating Role of Brand Image in Electronic Word of Mouth, Perceived Ease of Use, and Purchase Intention

The rapid development of online food delivery applications in Indonesia currently makes Shopee launch a new feature, Shopee Food. By joining the online food delivery application market in Indonesia, Shopee Food must be able to compete with other online food delivery applications. This study aims to analyzed the factors that influencing purchase intention in Shopee Food. Using Brand Image as the mediating factor for Perceived Ease of Us and Electronic Word-of-mouth, this study tries to explain customer intention to purchase food in shopeefood. This study used quantitate method with purposive sampling to draw the espondent, with total 345 respondents. The findings of this study found that word-of-mouth, perceived ease of use plays significant role on user purchase intention in Shopeefood, and brand image also significantly mediate the relationship of perceived ease of use and word of mouth toward intention to use.
Wilson Surfaces for Surface Knots: A Field Theoretic Route to Higher Knots

Holonomy invariants in strict higher gauge theory have been studied in depth aiming to applications to higher Chern–Simons theory. For a flat 2–connection, the holonomy of surface knots of arbitrary genus has been defined and its covariance properties under 1–gauge transformation and change of base data have been determined. Using quandle theory, a definition of trace over a crossed module such to yield surface knot invariants upon application to 2–holonomies has been given.
A support theorem for SLE curves

For all $\kappa > 0$, we show that the support of SLE$_\kappa$ curves is the closure in the sup-norm of the set of Loewner curves driven by nice (e.g. smooth) functions. It follows that the support is the closure of the set of simple curves starting at $0$.
Some properties of isoclinism in Lie superalgebras

Abstract Isoclinism of Lie superalgebras has been defined and studied currently. In this article, it is shown that for finite dimensional Lie superalgebras of same dimension, the notation of isoclinism and isomorphism are equivalent. Furthermore, we show that covers of finite dimensional Lie superalgebras are isomorphic using isoclinism concept.
Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case

In this work we consider a one-dimensional Brownian motion with constant drift moving among a Poissonian cloud of obstacles. Our main result proves convergence of the law of processes conditional on survival up to time $t$ as $t$ converges to infinity in the critical case where the drift coincides with the intensity of the Poisson process. The complements a previous result of T. Povel, who considered the same question in the case where the drift is strictly smaller than the intensity.
Lie-type derivations of finitary incidence algebras

Let $P$ be an arbitrary partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$. Under some natural assumption on $R$, we prove that each Lie-type derivation of $FI(P,R)$ is proper.
Validation of Flow Models as New Simulation Approach for Parcel Handling in Bulk Mode

Flow Models based on hyperbolic partial differential equations (conservation laws) are a well-established approach for the material flow simulation. Until now, they have been exclusively used for the simulation of cylindrical cargo. This paper investigates the application of flow models on cubical cargo as a new simulation approach for parcel logistics. Selected flow model parameters are adapted to cover this new situation. The simulation results of this macroscopic model are compared with the microscopic Discrete Element Method (DEM) where the cargo is approximated by superquadrics. An experimental setup especially designed for the validation of the considered flow model for cubical cargo bulk flow is presented. Results of the flow model are analyzed and validated against the results of experiment and DEM for the test setting.
A variational representation and Prekopa's theorem for Wiener functionals

In 1998, Boue and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals seems inevitable. In this paper, we extend the representation to unbounded functionals under a mild assumption on their integrability. As an immediate application of the extension, we prove an analogue of Prekopa's theorem for Wiener functionals, which is then applied to formulate the Brascamp-Lieb inequality in the framework of Wiener spaces.
Preperiodic points for quadratic polynomials over quadratic fields

To each quadratic number field $K$ and each quadratic polynomial $f$ with $K$-coefficients, one can associate a finite directed graph $G(f,K)$ whose vertices are the $K$-rational preperiodic points for $f$, and whose edges reflect the action of $f$ on these points. This paper has two main goals. (1) For an abstract directed graph $G$, classify the pairs $(K,f)$ such that the isomorphism class of $G$ is realized by $G(f,K)$. We succeed completely for many graphs $G$ by applying a variety of dynamical and Diophantine techniques. (2) Give a complete description of the set of isomorphism classes of graphs that can be realized by some $G(f,K)$. A conjecture of Morton and Silverman implies that this set is finite. Based on our theoretical considerations and a wealth of empirical evidence derived from an algorithm that is developed in this paper, we speculate on a complete list of isomorphism classes of graphs that arise from quadratic polynomials over quadratic fields.
Deformed Fourier models with formal parameters

The deformed Fourier matrices $H=F_M\otimes_QF_N$, with $Q\in\mathbb T^{MN}$, produce a matrix model $C(S_{MN}^+)\to M_{MN}(C(\mathbb T^{MN}))$. When $Q\in\mathbb T^{MN}$ is generic, the corresponding fiber can be investigated via algebraic techniques, and the main character law is asymptotically free Poisson. We present here an alternative point of view on these questions, using formal parameters instead of generic parameters, and analytic tools.
Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation

We present a regularized finite difference method for the logarithmic Schr\"odinger equation (LogSE) and establish its error bound. Due to the blow-up of the logarithmic nonlinearity, i.e. $\ln \rho\to -\infty$ when $\rho\rightarrow 0^+$ with $\rho=|u|^2$ being the density and $u$ being the complex-valued wave function or order parameter, there are significant difficulties in designing numerical methods and establishing their error bounds for the LogSE. In order to suppress the round-off error and to avoid blow-up, a regularized logarithmic Schr\"odinger equation (RLogSE) is proposed with a small regularization parameter $0<\varepsilon\ll 1$ and linear convergence is established between the solutions of RLogSE and LogSE in term of $\varepsilon$. Then a semi-implicit finite difference method is presented for discretizing the RLogSE and error estimates are established in terms of the mesh size $h$ and time step $\tau$ as well as the small regularization parameter $\varepsilon$. Finally numerical results are reported to confirm our error bounds.
Resolvent near zero energy on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach

Abstract We use a Lagrangian regularity perspective to discuss resolvent estimates near zero energy on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. In addition to the Lagrangian perspective we introduce and use a resolved pseudodifferential algebra to deal with zero energy degeneracies in a robust manner.
An upper bound on the asymptotic translation lengths on the curve graph and fibered faces

We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(\Sigma_n, \psi_n)$ of fibers and monodromies in the fibered cone, we show that the asymptotic translation length on the curve complex is bounded above by $1/\chi(\Sigma_n)^{1+1/r}$ as long as their projections to the fibered face converge to a point in the interior, where $r$ is the dimension of the $\psi_n$-invariant homology of $\Sigma_n$ (which is independent of $n$). As a corollary, if $b_1(M) = 2$, the asymptotic translation length on the curve complex of such a sequence of primitive elements behaves like $1/\chi(\Sigma_n)^{2}$. Furthermore, together with a work of E. Hironaka, our theorem can be used to determine the asymptotic behavior of the minimal translation lengths of handlebody mapping class groups and the set of mapping classes with homological dilatation one.
Oncology Simulation Model: A Comprehensive and Innovative Approach to Estimate and Project Prevalence and Survival in Oncology

Objective We demonstrate a new model framework as an innovative approach to more accurately estimate and project prevalence and survival outcomes in oncology. Methods We developed an oncology simulation model (OSM) framework that offers a customizable, dynamic simulation model to generate population-level, country-specific estimates of prevalence, incidence of patients progressing from earlier stages (progression-based incidence), and survival in oncology. The framework, a continuous dynamic Markov cohort model, was implemented in Microsoft Excel. The simulation runs continuously through a prespecified calendar time range. Time-varying incidence, treatment patterns, treatment rates, and treatment pathways are specified by year to account for guideline-directed changes in standard of care and real-world trends, as well as newly approved clinical treatments. Patient cohorts transition between defined health states, with transitions informed by progression-free survival and overall survival as reported in published literature. Results Model outputs include point prevalence and period prevalence, with options for highly granular prevalence predictions by disease stage, treatment pathway, or time of diagnosis. As a use case, we leveraged the OSM framework to estimate the prevalence of bladder cancer in the United States. Conclusion The OSM is a robust model that builds upon existing modeling practices to offer an innovative, transparent approach in estimating prevalence, progression-based incidence, and survival for oncologic conditions. The OSM combines and extends the capabilities of other common health-economic modeling approaches to provide a detailed and comprehensive modeling framework to estimate prevalence in oncology using simulation modeling and to assess the impacts of new treatments on prevalence over time.
A Continuous Time GARCH(p,q) Process with Delay

We investigate the properties of a continuous time GARCH process as the solution to a L\'evy driven stochastic functional integral equation. This process occurs as a weak limit of a sequence of discrete time GARCH processes as the time between observations converges to zero and the number of lags grows to infinity. The resulting limit generalizes the COGARCH process and can be interpreted as a COGARCH process with higher orders of lags. We give conditions for the existence, uniqueness and regularity of the solution to the integral equation, and derive a more conventional representation of the process in terms of a stochastic delayed differential equation. Path properties of the volatility process, including piecewise differentiability and positivity, are studied, as well as second order properties of the process, such as uniform L1 and L2 bounds, mean stationarity and asymptotic covariance stationarity.
Motion by mixed volume preserving curvature functions near spheres

In this paper we investigate the flow of hypersurfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact hypersurfaces without boundary that can be written as a graph over a sphere. The linearisation of the resulting fully nonlinear PDE is used to prove a short-time existence theorem for hypersurfaces that are sufficiently close to a sphere and, using centre manifold analysis, the stability of the sphere as a stationary solution to the flow is determined. We will find that for initial hypersurfaces sufficiently close to a sphere, the flow will exist for all time and the hypersurfaces will converge exponentially fast to a sphere. This result was shown for the case where the symmetric function is the mean curvature and the constraint is on the . nC 1/-dimensional enclosed volume by Escher and Simonett (1998).
Detecting effectivity of motives, their weights, connectivity, and dimension via Chow-weight (co)homology: a "mixed motivic decomposition of the diagonal"

We describe certain criteria for a motif $M$ to be $r$-effective, i.e., to belong to the $r$th Tate twist $Obj DM^{eff}_{gm,R}(r)=Obj DM^{eff}_{gm,R} \otimes L^{\otimes r}$ of effective Voevodsky motives (for $r\ge 1$; $R$ is the coefficient ring). In particular, $M$ is 1-effective if and only if a complex whose terms are certain Chow groups of zero-cycles is acyclic. The dual to this statement checks whether an effective motif $M$ belongs to the subcategory of $DM^{eff}_{gm,R}$ generated by motives of varieties of dimension $\le r$. These criteria are formulated in terms of the Chow-weight (co)homology of $M$. These (co)homology theories are introduced in the current paper and have several (other) remarkable properties: they yield a bound on the "weights" of $M$ (in the sense of the Chow weight structure defined by the first author) and detect the effectivity of "the lower weight pieces" of $M$. We also calculate the "connectivity" of $M$ (in the sense of Voevodsky's homotopy t-structure) and prove that the exponents of the higher motivic homology groups (of an "integral" motif) are bounded whenever these groups are torsion. These motivic properties of $M$ have important consequences for its cohomology. As a corollary, we prove that if Chow groups of an arbitrary variety $X$ vanish up to dimension $r-1$ then the highest Deligne weight factors of the (singular or etale) cohomology of $X$ with compact support are $r$-effective in the naturally defined sense. Our results yield a vast generalization of the so-called "decomposition of the diagonal" statements.
Invariant measures on multimode quantum Gaussian states

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability Spaces

We give a new condition on a metric measure space guaranteeing a $(1,p)$-Poincar\'e inequality for some $p$. This condition doesn't use a modulus of a curve family, is technically more flexible and allows for several applications. We also introduce an asymptotic version of our condition that guarantees rectifiability in terms of doubling metric measure spaces admitting Poincar\'e inequalities. Most importantly, we use the asymptotic condition to partially resolve a conjecture of Cheeger and Kleiner by showing that a space is a RNP-Lipschitz differentiability spaces if and only if it is rectifiable in terms of spaces admitting Poincar\'e inequalities and satisfies a natural technical condition. Quantitative connectivity is used to prove Poincar\'e inequalities under weaker assumptions than previously know. Firstly we partially solve a conjecture of Rajala by showing that $MCP(K,n)$-spaces defined by Ohta admit a $(1,p)$-Poincar\'e inequality for $p>n+1$. We generalize theorems of Brj\"orn and Dejarnette concerning weighted Orlicz-Poincar\'e inequalities. Finally certain non-homogenous and weighted versions of Poincar\'e inequalities are shown to self-improve to true Poincar\'e inequalities, which answers a question of Li and Bate. Finally Poincar\'e inequalities are constructed for certain metric measure spaces with $A_\infty$-weights.
Asymptotic Behaviour of Nonlinear Evolution Equations in Banach Spaces

We show how the approach of Yosida approximation of the derivative serves to obtain new results for evolution systems. Using this method we obtain multivalued time dependent perturbation results. Additionally, translation invariant subspaces $Y$ of the bounded and uniformly continuous functions are considered, to obtain criteria for the existence of solutions $u\in Y$ to the equation $$ u^{\prime}(t)\in A(t)u(t)+ \om u(t) + f(t), t\in \re, $$ or of solutions $u$ asymptotically close to $Y$ for the inhomogeneous differential equation \begin{eqnarray*} u^{\prime}(t)&\in& A(t)u(t) + \om u(t) + f(t), \ \ t > 0, u(0)&=&u_0, \end{eqnarray*} in general Banach spaces, where $A(t)$ denotes a possibly nonlinear time dependent dissipative operator. Particular examples for the space $Y$ are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior. Further, an application to functional differential equations is given.
Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties

We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in C^n by Lempert and by Larusson and Sigurdsson.
A note on $L^p$-norms of quasi-modes

In this note we show how improved $L^p$-estimates for certain types of quasi-modes are naturally equaivalent to improved operator norms of spectral projection operators associated to shrinking spectral intervals of the appropriate scale. Using this, one can see that recent estimates that were stated for eigenfunctions also hold for the appropriate types of quasi-modes.
Impact of Phase Noise on Secrecy Performance of Cell-Free Massive MIMO Networks with Multi-Antenna Users

This paper studied the effect of phase noise on secrecy performance of the cell-free massive MIMO network with multi-antenna user terminals, where a multi-antenna eavesdropper will actively contaminate the uplink training. Specifically, using discrete-time Wiener model and random matrix theory, tractable expression for the achievable secrecy rate is derived, which can provide precise evaluation of key factors including phase noise, multi-antenna and arbitrary system configuration. Analytical results illustrate that strong phase noise and high wiretapping power would lead to performance degradation while the network can acquire multiplexing gain by equipping multiple antennas. Also, it indicates that phase noise at the user terminals imposes more rigorous influence than that on access points (APs). Simulations are presented to corroborate the derived results.
Existence and stability of nonconstant positive steady states of morphogenesis models

In this paper, we study a one‐dimensional morphogenesis model considered by C. Stinner et al. (Math. Meth. Appl. Sci.2012;35: 445–465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady states through local bifurcation theories. Then we rigorously study the stability of these nonconstant solutions when the sensitivity functions are chosen to be linear and logarithmic, respectively. Finally, we present numerical solutions to illustrate the formation of stable inhomogeneous spatial patterns. Our numerical simulations show that this model can develop very complicated and interesting structures even over one‐dimensional finite domains. Copyright © 2014 John Wiley & Sons, Ltd.
Conformal metrics with prescribed gaussian and geodesic curvatures

We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by minimization of the Euler-Lagrange energy or via min-max methods. One of the main tools in our approach is a blow-up analysis of solutions, which in the present setting can have diverging volume. To our knowledge, this is the first time in which such an aspect is treated. Key ingredients in our arguments are: a blow-up analysis around a sequence of points different from local maxima; the use of holomorphic domain-variations; and Morse-index estimates.
A discrete data assimilation scheme for the solutions of the 2D Navier-Stokes equations and their statistics

Author(s): Foias, Ciprian; Mondaini, Cecilia F; Titi, Edriss S | Abstract: We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by systematic errors. Our algorithm is designed to work with a general class of observables, such as low Fourier modes and local spatial averages over finite volume elements. Under suitable conditions on the relaxation (nudging) parameter, the spatial mesh resolution and the time step between successive measurements, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to a term which depends on the size of the errors. A stationary statistical analysis of our discrete data assimilation algorithm is also provided.