Miracle-dz/UniFAR-FTUs huggingface dataset:
Cohomology jump loci of compact Kähler manifolds

We apply the method of Dimca-Papadima to study the cohomology jump loci in the representation variety and the moduli space of vector bundles with vanishing chern classes for a compact K\"ahler manifold. We introduce modules over differential graded Lie algebra to extend results of Dimca-Papadima to a general point in the representation variety or the moduli space. We show that locally the cohomology jump loci is isomorphic to the resonance variety via the exponential map. This paper generalizes a previous result of the author.
Around Poisson--Mehler summation formula

We study polynomials in $x$ and $y$ of degree $n+m:\allowbreak \{Q_{m,n}(x,y|t,q)\}_{n,m\geq 0}$ that appeared recently in the following identity: $\gamma_{m,n}(x,y|t,q) \allowbreak =\allowbreak \gamma_{0,0}(x,y|t,q) \allowbreak Q_{m,n}(x,y|t,q) $ where $\gamma_{m,n}(x,y|t,q) \allowbreak =\allowbreak \sum_{i\geq 0}\frac{t^{i}}{[i]_{q}}H_{i+n}(x|q) H_{m+i}(y|q)$, $\allowbreak $ $\{H_{n}(x|q)}_{n\geq -1}$ are the so-called $q-$% Hermite polynomials (qH). In particular we show that the spaces $span\{Q_{i,n-i}(x,y|t,q) :i=0,. ,n\}_{n\geq 0}$ are orthogonal with respect to a certain measure (two-dimensional $(t,q)-$Normal distribution) on the square $\{(x,y):|x|,|y|\leq 2/\sqrt{1-q}\} . $ We study structure of these polynomials expressing them with the help of the so-called Al-Salam--Chihara (ASC) polynomials and showing that they are rational functions of parameters $t$ and $q$. We use them in various infinite expansions that can be viewed as simple generalization of the Poisson-Mehler summation formula. Further we use them in the expansion of the reciprocal of the right hand side of the Poisson-Mehler formula.
Game Distinguishing Numbers of Cartesian Products of Graphs

The distinguishing number of a graph $H$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(H)$ is the least integer $d$ such that $H$ has a $d$-distinguishing coloring. A $d$-distinguishing coloring is a coloring $c:V(H)\rightarrow\{1,\dots,d\}$ invariant only under the trivial automorphism. In this paper, we continue the study of a game variant of this parameter, recently introduced. The distinguishing game is a game with two players, Gentle and Rascal, with antagonist goals. This game is played on a graph $H$ with a fixed set of $d\in\mathbb N^*$ colors. Alternately, the two players choose a vertex of $H$ and color it with one of the $d$ colors. The game ends when all the vertices have been colored. Then Gentle wins if the coloring is $d$-distinguishing and Rascal wins otherwise. This game defines two new invariants, which are the minimum numbers of colors needed to ensure that Gentle has a winning strategy, depending who starts the game. The invariant could eventually be infinite. In this paper, we focus on cartesian product, a graph operation well studied in the classical case. We give sufficient conditions on the order of two connected factors $H$ and $F$ relatively prime, which ensure that one of the game distinguishing numbers of the cartesian product $H\square F$ is finite. If $H$ is a so-called involutive graph, we give an upper bound of order $D^2(H)$ for one of the game distinguishing numbers of $H\square F$. Finally, using in part the previous result, we compute the exact value of these invariants for cartesian products of relatively prime cycles. It turns out that the value is either infinite or equal to $2$, depending on the parity of the product order.
DUALITY FOR COHOMOLOGY OF CURVES WITH COEFFICIENTS IN ABELIAN VARIETIES

In this paper, we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in Néron models of abelian varieties. This is a global function field version of the author’s previous work on local duality and Grothendieck’s duality conjecture. It generalizes the perfectness of the Cassels–Tate pairing in the finite base field case. The proof uses the local duality mentioned above, Artin–Milne’s global finite flat duality, the nondegeneracy of the height pairing and finiteness of crystalline cohomology. All these ingredients are organized under the formalism of the rational étale site developed earlier.
Priority Ranking and Consensus Formation: The Case of Ties

This paper investigates the problem of obtaining a compromise/consensus from a set of ordinal rankings of n objects supplied by m committee members. Earlier work by Cook and Seiford Cook, Wade D. , Lawrence M. Seiford. 1978. Priority ranking and consensus formation. Management Sci.24 16 1721-1732. dealt with the problem of consensus when attention was restricted to complete rankings only. That is, no ties were permitted. This paper examines the general problem which allows for tied preferences. A convex polyhedral representation is given of the feasible solution space, and a branch-and-bound procedure is developed for determining an optimal ranking. Computational results for various problem sizes are presented. Generalizations, and directions for further research are discussed.
Ultra-cold neutrons

Abstract Ultracold neutrons (UCN), neutrons with speeds less than 7 ms−1, have the surprising property that they are reflected at normal incidence by many solid materials and can be stored as a neutron gas in a ‘bottle’ for a time comparable with the neutron's spontaneous lifetime of 937 s. Their flight paths are bent because of gravity, they are brought to rest after vertical motion of only 2 m, and a magnetic field of 5 tesla, interacting with the neutron magnetic moment, is sufficient to reverse the direction of motion. This review contains an account of the way UCN interact with surfaces in which the interatomic spacing is much less than the neutron deBroglie wavelength, the construction of UCN sources, and some of the experiments which have already been carried out to study UCN interactions with materials, gravitation, magnetic and electric fields.
The conformal method and the conformal thin-sandwich method are the same

The conformal method developed in the 1970s and the more recent Lagrangian and Hamiltonian conformal thin-sandwich methods are techniques for finding solutions of the Einstein constraint equations. We show that they are manifestations of a single conformal method: there is a straightforward way to convert back and forth between the parameters for these methods so that the corresponding solutions of the Einstein constraint equations agree. The unifying idea is the need to clearly distinguish tangent and cotangent vectors to the space of conformal classes on a manifold, and we introduce a vocabulary for working with these objects without reference to a particular representative background metric. As a consequence of these conceptual advantages, we demonstrate how to strengthen previous near-CMC (constant mean curvature) existence and non-existence theorems for the original conformal method to include metrics with scalar curvatures that change sign.
Comparative study among analytical and numerical models for the performance evaluation of optical systems affected by polarization mode dispersion

In the present work the analytical models are applied to calculate the system performance for different fibre polarisation mode dispersion (PMD) conditions and for varying system parameters and the results obtained with them are compared to those obtained using the discrete random waveplate numerical model (DRW) model, assumed as a faithful description of the real fiber with all order PMD effects. Through this comparative analysis, never done before in literature to the authors knowledge, the accuracy of the analytical models in the approximation of high-order PMD effects is studied, and, among them, a precise analytical tool for the system impairments evaluation is found.
Mg II absorption by previously known galaxies at z≃0.5

We have obtained spectra at the Multiple Mirror Telescope of nine QSOs in order to search for Mg II λλ2796, 2803 absorption from intervening galaxies with previously determined redshifts between 0.2 and 0.7. We have detected two Mg II systems with the redshift of known galaxies, including one associated with a cluster of galaxies at z=0.362. From the lack of detectable Mg II absorption for a large number of other galaxies, we conclude that the galaxies that do absorb must have an effective cross section for absorption at least twice as large in radius as previously thought, in order to account for Mg II absorber statistics
Cycle-Complete Ramsey Numbers

The Ramsey number $r(C_{\ell },K_n)$ is the smallest natural number $N$ such that every red/blue edge colouring of a clique of order $N$ contains a red cycle of length $\ell $ or a blue clique of order $n$. In 1978, Erd̋s, Faudree, Rousseau, and Schelp conjectured that $r(C_{\ell },K_n) = (\ell -1)(n-1)+1$ for $\ell \geq n\geq 3$ provided $(\ell ,n) \neq (3,3)$. We prove that, for some absolute constant $C\ge 1$, we have $r(C_{\ell },K_n) = (\ell -1)(n-1)+1$ provided $\ell \geq C\frac{\log n}{\log \log n}$. Up to the value of $C$ this is tight since we also show that, for any $\varepsilon>0$ and $n> n_0(\varepsilon )$, we have $r(C_{\ell }, K_n) \gg (\ell -1)(n-1)+1$ for all $3 \leq \ell \leq (1-\varepsilon )\frac{\log n}{\log \log n}$. This proves the conjecture of Erd̋s, Faudree, Rousseau, and Schelp for large $\ell $, a stronger form of the conjecture due to Nikiforov, and answers (up to multiplicative constants) two further questions of Erd̋s, Faudree, Rousseau, and Schelp.
Uniqueness of photon spheres via positive mass rigidity

In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness. In this note we establish uniqueness of photon spheres by adapting the argument of Bunting and Masood-ul-Alam, which then allows certain assumptions to be relaxed. In particular, multiple photon spheres are allowed a priori. As a consequence of our result, we can rule out the existence of static configurations involving multiple "very compact" bodies and black holes.
Finite group actions on certain stably projectionless C*-algebras with the Rohlin property

We introduce the Rohlin property and approximate representability for finite group actions on stably projectionless C∗-algebras and study their basic properties. We give some examples of finite group actions on the RazakJacelon algebra W and show some classification results of these actions. This study is based on the work of Izumi, Robert’s classification theorem and Kirchberg’s central sequence C∗-algebras.
A short proof of Rudnev's point-plane incidence bound

In this note we give a shortened proof of a theorem of Rudnev, which bounds the number of incidences between points and planes over an arbitrary field. Rudnev's proof uses a map that goes via the four-dimensional Klein quadric to a three-dimensional space, where it applies a bound of Guth and Katz on intersection points of lines. We describe a simple geometric map that directly sends point-plane incidences to line-line intersections in space, allowing us to reprove Rudnev's theorem with fewer technicalities.
Unitary Invariants in Multivariable Operator Theory

This paper concerns unitary invariants for n-tuples T:=(Tl,.,Tn) of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger - Kato - Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of T in connection with several unitary invariants for n-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra Fn.
Supply chain coordination with information sharing in the presence of trust and trustworthiness

The strategic use of private information can cause efficiency losses in traditional principal–agent settings, which are found, for example, in supply chain interactions. One stream of research states that these efficiency losses cannot be overcome if all agents use their private information strategically. However, another stream of research highlights the importance of communication, trust, and trustworthiness in supply chain management. In many instances, supplier–buyer relationships are found to reflect a principal–agent context where the supplier acts as the principal and the buyer behaves as the agent. Typically, here it is assumed that the supplier has an a priori distribution assumption over the buyer's private information on cost positions or market conditions. However, little is said on how the principal obtains this distribution. Moreover, it is stressed that the assessment of the a priori distribution is not influenced by communication because of the strategic extent of information sharing. The underlying concept behind this study is that there are two types of buyers (agents). The first type always reports her private information truthfully while the second type does not. In this framework, the supplier (principal) adjusts his a priori distribution conditioned on the buyer's shared information and generates the menu of contracts with respect to the adjusted probabilities. The presented model highlights that the impact of communication on the supplier's, buyer's, and supply chain's performance level is ambiguous and mainly depends on the buyer's information-sharing behavior as well as the relative extent of trust and trustworthiness. This study gives valuable insights into which situations communication is likely to harm the overall supply chain performance, thereby increasing the awareness that the ever increasing claims for trust and information sharing in supply chain management have to be handled carefully.
On the distribution of the largest real eigenvalue for the real Ginibre ensemble

Let $\sqrt{N}+\lambda_{max}$ be the largest real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\rightarrow \infty$ distribution $P[\lambda_{max} 0$, \[ P[\lambda_{max}<t]=1-\frac{1}{4}\mbox{erfc}(t)+O\left(e^{-2t^2}\right). \] This is a rigorous confirmation of the corresponding result of Forrester and Nagao. We also prove that the left tail is exponential: for $t<0$, \[ P[\lambda_{max}<t]= e^{\frac{1}{2\sqrt{2\pi}}\zeta\left(\frac{3}{2}\right)t+O(1)}, \] where $\zeta$ is the Riemann zeta-function. Our results have implications for interacting particle systems. The edge scaling limit of the law of real eigenvalues for the real Ginibre ensemble is a rescaling of a fixed time distribution of annihilating Brownian motions (ABM's) with the step initial condition. Therefore, the tail behaviour of the distribution of $X_s^{(max)}$ - the position of the rightmost annihilating particle at fixed time $s>0$ - can be read off from the corresponding answers for $\lambda_{max}$ using $X_s^{(max)}\stackrel{D}{=} \sqrt{4s}\lambda_{max}$.
A bulk-surface reaction-diffusion system for cell polarization

We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in certain parameter regimes in which several reaction rates on the membrane as well as the diffusion coefficient within the cell are large. It turns out that in suitable scaling limits steady states converge to solutions of some obstacle type problems. For these limiting problems we prove the onset of polarization if the total mass of protein is sufficiently small. For some variants we can even characterize precisely the critical mass for which polarization occurs.
A Decentralized Event-Based Approach for Robust Model Predictive Control

In this paper, we propose an event-based sampling policy to implement a constraint-tightening, robust MPC method. The proposed policy enjoys a computationally tractable design and is applicable to perturbed, linear time-invariant systems with polytopic constraints. In particular, the triggering mechanism is suitable for plants with no centralized sensory node as the triggering mechanism can be evaluated locally at each individual sensor. From a geometrical viewpoint, the mechanism is a sequence of hyperrectangles surrounding the optimal state trajectory such that robust recursive feasibility and robust stability are guaranteed. The design of the triggering mechanism is cast as a constrained parametric-in-set optimization problem with the volume of the set as the objective function. Reparameterized in terms of the set vertices, we show that the problem admits a finite tractable convex program reformulation and a linear program relaxation. Several numerical examples are presented to demonstrate the effectiveness and limitations of the theoretical results.
Entropy and expansion

Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds. The inequality involves a constant characterizing the expansion properties of the system. Our results generalize to entropy inequalities used in recent work in invariant settings, including the edge-vertex inequality for factor-of-IID processes, Bowen's entropy inequalities, and Bollobas's entropy bounds in random regular graphs. The proof method yields inequalities for other measures of randomness, including covariance. As an application, we give upper bounds for independent sets in both finite and infinite graphs.
Twisted Blanchfield pairings and symmetric chain complexes

We define the twisted Blanchfield pairing of a symmetric triad of chain complexes over a group ring Z[G], together with a unitary representation of G over an Ore domain with involution. We prove that the pairing is sesquilinear, and we prove that it is hermitian and nonsingular under certain extra conditions. A twisted Blanchfield pairing is then associated to a 3-manifold together with a decomposition of its boundary into two pieces and a unitary representation of its fundamental group.
Integrated Higher-Order Sliding Mode Guidance and Autopilot for Dual Control Missiles

An integrated autopilot and guidance algorithm, robust to target maneuvers and missile’s model uncertainties, is developed using higher-order sliding mode control for interceptors steered by a combination of aerodynamic lift, sustainer thrust, and center-of-gravity divert thrusters. A smooth higher-order sliding mode guidance that is robust to target maneuvers generates flight-path trajectory angular rates and attitude rate commands. The attitude rate missilemaneuvers are aimed at producing desired aerodynamic lift and/or orienting the sustainer thrust. The lateral acceleration created by themissile attitudemaneuver is treated as a cooperative disturbance andaccounted for by the trajectory control. Robust to themissile’smodel uncertainties, higher-order (second-order) slidingmode autopilot is designed based on a nonlinear dynamic slidingmanifold. The proposed integrated autopilot and guidance algorithm also includes seeker/tracker bore-sight stabilization and estimation of target lateral acceleration. The algorithm is tested using computer simulations against a ballistic maneuvering target.
Conditions for permanence in well-known biological competition models

Reaction-diffusion systems are widely used to model the population densities of biological species competing for natural resources in their common habitat. It is often not too difficult to establish positive uniform upper bounds on solution components of such systems, but the task of establishing strictly positive uniform lower bounds (when they exist) can be quite troublesome. Two previously established criteria for the permanence (non-extinction and non-explosion) of solutions of general weakly-coupled competition-diffusion systems with diagonally convex reaction terms are used here as background to develop more easily verifiable and concrete conditions for permanence in various well-known competition diffusion models. These models include multi-component reaction-diffusion systems with (i) the by now classical Lotka-Volterra (logistic) reaction terms, (ii) higher order “logistic” interaction between the species, (iii) logistic-logarithmic reaction terms, (iv) Ayala-Gilpin-Ehrenfeld θ-interaction terms (which are used to model Drosophila competition), (v) logistic-exponential interaction between the species, (vi) Schoener-exploitation and (vii) modified Schoener-interference between the species. In (i) a known condition for permanence (for the ODE-system) is recovered, while in (ii)–(vii) new criteria for permanence are established.
Product Hardy Operators on Hardy Spaces

We study the product Hausdorff operator H (cid:2) on the product Hardy spaces, and prove that, for a nonnegative valued function (cid:2) , H (cid:2) is bounded on the product Hardy space H 1 ( R × R ) if and only if (cid:2) is a Lebesgue integrable function on ( 0 , ∞ ) × ( 0 , ∞ ). As an application, we know that the product Hardy operator H is not bounded on H 1 ( R × R ). On the other hand, we prove that (cid:3) H f (cid:3) H 1 ( R × R ) (cid:4) (cid:3) f (cid:3) H 1 ( R × R ) if f is an even function. Furthermore, using the H p ( R × R ) boundedness criterion of Fefferman, we prove that the k -th order Hardy operator is bounded on H p ( R × R ) whenever k > 1 /p − 1 .
Explicit asymptotics for certain single and double exponential sums

Abstract By combining classical techniques together with two novel asymptotic identities derived in recent work by Lenells and one of the authors, we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of Re{u} and Re{v} and for a variety of sets of summation, as well as particular cases of Mordell-Tornheim double sums.
Optimal control of singular Fourier multipliers by maximal operators

We control a broad class of singular (or “rough”) Fourier multipliers by geometrically-defined maximal operators via general weighted L(R) norm inequalities. The multipliers involved are related to those of Coifman– Rubio de Francia–Semmes, satisfying certain weak Marcinkiewicz-type conditions that permit highly oscillatory factors of the form ei|ξ| α for both α positive and negative. The maximal functions that arise are of some independent interest, involving fractional averages associated with tangential approach regions (related to those of Nagel and Stein), and more novel “improper fractional averages” associated with “escape” regions. Some applications are given to the theory of Lp − Lq multipliers, oscillatory integrals and dispersive PDE, along with natural extensions to higher dimensions. Dedicated to the memory of Adela Moyua, 1956–2013.