Miracle-dz/UniFAR-FTUs huggingface dataset:
Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity

We establish the monotonicity property for the mass of non-pluripolar products on compact Kahler manifolds, and we initiate the study of complex Monge-Ampere type equations with prescribed singularity type. Using the variational method of Berman-Boucksom-Guedj-Zeriahi we prove existence and uniqueness of solutions with small unbounded locus. We give applications to Kahler-Einstein metrics with prescribed singularity, and we show that the log-concavity property holds for non-pluripolar products with small unbounded locus.
Transience and Recurrence of Markov Processes
with Constrained Local Time

We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a broad class of Markov processes. In order to understand the distribution of the local time, we determine the distribution of a non-decreasing L\'evy process (the inverse local time) conditioned to remain above a given level which varies in time. We study a time-dependent region, in contrast to previous works in which a process is conditioned to remain in a fixed region (e.g. [21,27]), so we must study boundary crossing probabilities for a family of curves, and thus obtain uniform asymptotics for such a family. Main results include necessary and sufficient conditions for transience or recurrence of the conditioned Markov process. We will explicitly determine the distribution of the inverse local time for the conditioned process, and in the transient case, we explicitly determine the law of the conditioned Markov process. In the recurrent case, we characterise the "entropic repulsion envelope" via necessary and sufficient conditions.
Invariant Subspaces of Riesz Spectral Systems with Application to Fault Detection and Isolation

A large class of hyperbolic and parabolic partial differential equation (PDE) systems, such as reaction-diffusion processes, when expressed in the infinite-dimensional (Inf-D) framework can be represented as Riesz spectral (RS) systems. Compared to the finite dimensional (Fin-D) systems, the geometric theory of Inf-D systems for addressing certain fundamental control problems, such as disturbance decoupling and fault detection and isolation (FDI), is rather quite limited due to complexity and existence of various types of invariant subspaces notions. Interestingly enough, these invariant concepts are equivalent for Fin-D systems, although they are different in Inf-D representation. In this work, first equivalence of various types of invariant subspaces that are defined for RS systems are investigated. This enables one to define and specify the unobservability subspace for RS systems. Specifically, necessary and sufficient conditions are derived for equivalence of various types of conditioned invariant subspaces. Moreover, by using duality properties, various controlled invariant subspaces are developed. It is then shown that finite-rankness of the output operator enables one to derive algorithms for computing invariant subspaces that under certain conditions, and unlike methods in the literature, converge in a finite number of steps. A geometric FDI methodology for RS systems is then developed by invoking the introduced invariant subspaces. Finally, necessary and sufficient conditions for solvability of the FDI problem are provided and analyzed
On the number of comets around other single stars

It is shown how to obtain interesting limits on the number of comets in orbit around other single stars in clouds similar to the one present in our own solar system. The number of comets around white dwarf stars is constrained directly, and this in turn constrains the presence of comets around main-sequence stars. If a white dwarf possesses a cloud of comets similar to the Oort cloud, it will occassionally accrete a comet. The accretion of a comet may add enough heavy elements to the atmosphere of the white dwarf to produce a recognizable spectral signature; it is suggested that the calcium reported in the white dwarf G 74-7 is due to recent comet accretion. This signature will persist until sedimentation has removed the heavy elements from the atmosphere; the mean time between accretion events is comparable to the sedimentation time for cool DA stars, so this signature should be frequently observed if cometary systems are common. The possibility that cometary systems greater than or approximately equal to 3 times more massive than the Oort cloud are present around most white dwarf stars are excluded and how this limit can be improved is indicated. It is shown that a star keeps most of its comets during the vigorous mass loss phase prior to the appearance of the white dwarf star. Thus, the constraints obtained here may be applied to the main-sequence progenitors of the white dwarfs.
Counting common perpendicular arcs in negative curvature

Let $D^{-}$ and $D^{+}$ be properly immersed closed locally convex subsets of a Riemannian manifold with pinched negative sectional curvature. Using mixing properties of the geodesic flow, we give an asymptotic formula as $t\rightarrow +\infty$ for the number of common perpendiculars of length at most $t$ from $D^{-}$ to $D^{+}$ , counted with multiplicities, and we prove the equidistribution in the outer and inner unit normal bundles of $D^{-}$ and $D^{+}$ of the tangent vectors at the endpoints of the common perpendiculars. When the manifold is compact with exponential decay of correlations or arithmetic with finite volume, we give an error term for the asymptotic. As an application, we give an asymptotic formula for the number of connected components of the domain of discontinuity of Kleinian groups as their diameter goes to $0$ .
Transitivity of Automorphism Groups of Gizatullin Surfaces

We show that the automorphism group of a certain subclass of smooth Gizatullin surfaces with a distinguished and rigid extended divisor is generated by automorphisms of A1-fibrations. Moreover, such surfaces provide examples of smooth Gizatullin surfaces with a non-transitive action of the automorphism group. Thus, they represent counterexamples to Gizatullin's conjecture. For such surfaces we give explicit orbits of the natural action of the automorphism group in some special cases. Further, we present their automorphism groups as amalgamated products of two subgroups.
A note on lattices with many sublattices

For every natural number $n\geq 5$, we prove that the number of subuniverses of an $n$-element lattice is $2^n$, $13\cdot 2^{n-4}$, $23\cdot 2^{n-5}$, or less than $23\cdot 2^{n-5}$. By a subuniverse, we mean a sublattice or the emptyset. Also, we describe the $n$-element lattices with exactly $2^n$, $13\cdot 2^{n-4}$, or $23\cdot 2^{n-5}$ subuniverses.
Analysis of large unreliable stochastic networks

In this paper, a stochastic model of a large distributed system where users’ files are duplicated on unreliable data servers is investigated. Due to a server breakdown, a copy of a file can be lost, it can be retrieved if another copy of the same file is stored on other servers. In the case where no other copy of a given file is present in the network, it is definitively lost. In order to have multiple copies of a given file, it is assumed that each server can devote a fraction of its processing capacity to duplicate files on other servers to enhance the durability of the system. A simplified stochastic model of this network is analyzed. It is assumed that a copy of a given file is lost at some fixed rate and that the initial state is optimal: each file has the maximum number $d$ of copies located on the servers of the network. The capacity of duplication policy is used by the files with the lowest number of copies. Due to random losses, the state of the network is transient and all files will be eventually lost. As a consequence, a transient $d$-dimensional Markov process $(X(t))$ with a unique absorbing state describes the evolution this network. By taking a scaling parameter $N$ related to the number of nodes of the network, a scaling analysis of this process is developed. The asymptotic behavior of $(X(t))$ is analyzed on time scales of the type $t\mapsto N^{p}t$ for $0\leq p\leq d-1$. The paper derives asymptotic results on the decay of the network: Under a stability assumption, the main results state that the critical time scale for the decay of the system is given by $t\mapsto N^{d-1}t$. In particular, the duration of time after which a fixed fraction of files are lost is of the order of $N^{d-1}$. When the stability condition is not satisfied, that is, when it is initially overloaded, it is shown that the state of the network converges to an interesting local equilibrium which is investigated. As a consequence, it sheds some light on the role of the key parameters $\lambda$, the duplication rate and $d$, the maximal number of copies, in the design of these systems. The techniques used involve careful stochastic calculus for Poisson processes, technical estimates and the proof of a stochastic averaging principle.
On nonlinear scattering for quantum walks

We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QW such as Strichartz estimate. Such argument is standard in the study of nonlinear Schrodinger equations but it seems to be the first time to be applied to QW. We also numerically study the dynamics of QW and observe soliton like solutions.
Computing The Analytic Connectivity of A Uniform Hypergraph

The analytic connectivity, proposed as a substitute of the algebraic connectivity in the setting of hypergraphs, is an important quantity in spectral hypergraph theory. The definition of the analytic connectivity for a uniform hypergraph involves a series of optimization problems (POPs) associated with the Laplacian tensor of the hypergraph with nonnegativity constraints and a sphere constraint, which poses difficulties in computation. To reduce the involved computation, properties on the algebraic connectivity are further exploited, and several important structured uniform hypergraphs are shown to attain their analytic connectivities at vertices of the minimum degrees, hence admit a relatively less computation by solving a small number of POPs. To efficiently solve each involved POP, we propose a feasible trust region algorithm ({\tt FTR}) by exploiting their special structures. The global convergence of {\tt FTR} to the second-order necessary conditions points is established, and numerical results for both small and large size examples with comparison to other existing algorithms for POPs are reported to demonstrate the efficiency of our proposed algorithm.
The exact power law and Pascal pyramid

Let ω0, ω1, . , ωn be a full set of outcomes (letters, symbols) and let positive pi, i = 0, . , n, be their probabilities ( ∑n i=0 pi = 1). Let us treat ω0 as a stop symbol; it can occur in sequences of symbols (we call them words) only once, at the very end. The probability of a word is defined as the product of probabilities of its letters. We consider the list of all possible words sorted in the non-increasing order of their probabilities. Let p(r) be the probability of the rth word in this list. We prove that if at least one of ratios log pi/ log pj , i, j ∈ {1, . , n}, is irrational, then the limit limr→∞ p(r)/r 1/γ exists and differs from zero; here γ is the root of the equation ∑n i=1 p γ i = 1. Some weaker results were established earlier. We are first to write an explicit formula for this limit constant at the power function; it can be expressed (rather easily) in terms of the entropy of the distribution (p 1 , . . . , pn).
Vertex Models and Spin Chains in Formulas and Pictures

We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra ${\mathrm U}_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ are given. The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method. Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems.
Allelic variations in phenology genes of eastern U.S. soft winter and Korean winter wheat varieties and their associations with heading date

Wheat heading time is genetically controlled by phenology genes including vernalization (Vrn), photoperiod (Ppd) and earliness per se (Eps) genes. Characterization of the existing genetic variation in the phenology genes of wheat would provide breeding programs with valuable information necessary for the development of wheat varieties well-adapted to the local environment and early-maturing traits suitable for double-cropping system. One hundred forty-nine eastern U.S. soft winter (ESW) and 32 Korean winter (KW) wheat varieties were characterized using molecular markers for Vrn, Ppd, Eps and reduced-height (Rht) genes, and phenotyped for heading date (HD) in eastern U.S. region. The predominant alleles in ESW and KW varieties were the Ppd-A1b, Ppd-B1b and Ppd-D1a alleles at the Ppd-1 loci and the vrn-B1-Neuse and vrn-D3b alleles at the Vrn-B1 and Vrn-D3 loci. A single copy of the vrn-A1 allele was observed in 81.3% of KW varieties, but only in one ESW variety. The genetic variations for HD of ESW varieties were largely contributed by the Ppd-B1, Ppd-D1 and Vrn-D3 loci. The Rht-D1 locus largely contributed to the genetic variation for HD of KW varieties. A phenology gene pro�le at four major loci (Ppd-B1b/Ppd-D1a/vrn-A1(three or more copies)/vrn-D3b) was predominantly observed in 52.8% of ESW varieties, while 76.7% of KW varieties carried one of these two phenology gene pro�les: Ppd-B1b/Ppd-D1a/vrn-A1(one copy)/vrn-D3a or Ppd-B1b/Ppd-D1a/vrn-A1(one copy)/vrn-D3b. KW varieties headed on average 14 days earlier than ESW varieties in each crop year, largely due to the presence of a single copy of the vrn-A1 allele in the former.
High pressure study of structural and electronic properties of calcium chalcogenides

The structural and electronic properties of calcium chalcogenides CaX (X = S,Se,Te) under high pressure have been investigated using the full potential linearized augmented plane wave method within density functional theory. We used both the local density approximation and the generalized gradient approximation (GGA) that is based on exchange–correlation energy optimization for calculating the total energy. Moreover, the Engel–Vosko GGA formalism is applied so as to optimize the corresponding potential for band structure calculations. The equilibrium lattice constant for CaX compounds agrees well with the experimental results. The pressures at which these compounds undergo a structural phase transition from NaCl-type to CsCl-type were calculated. A numerical first-principles calculation of the elastic constants was used to calculate C11, C12 and C44. The energy band gaps at ambient conditions in the NaCl-type structure and the volume dependence of band gaps in the CsCl-type structure up to the band overlap metallization were investigated. Besides this, the nature of the chemical bond in these compounds was analysed in terms of electronic charge density.
Unsteadiness of an axisymmetric separating-reattaching flow : Numerical investigation

The separated flow over a cylinder elongated by another cylinder of a smaller diameter is investigated numerically at the high subsonic regime using zonal detached eddy simulation (ZDES) and compared with the experimental data of Depres, Reijasse, and Dussauge [AIAA J. 42, 2541 (2004)]. First, it is shown that this axisymmetric step flow has much in common with the two-dimensional facing step flows as regards the shear layer instability process. Second, the statistical and spectral properties of the pressure fluctuations are scrutinized. Close to the step, the surface pressure signature is characterized by low frequencies f.Lr∕U∞=O(0.08) (where Lr and U∞ denote, respectively, the mean reattachment length and free-stream velocity) and an upstream velocity of 0.26U∞ while in the second half-part of the recirculation higher frequencies fluctuations at f.Lr∕U∞≈0.6 and a downstream convection velocity 0.6U∞ are the dominant features. The current calculation shows that the separated bubble dynamics depends on v.
On the simulation of sound localization

Sound localization both in the horizontal and the median planes was simulated by the aid of a digital computer through two loudspeakers located in the traverse plane. The simulation was performed by the use of the measured head-related transfer function (HRTF) for two ears. Results of localization tests of three subjects with different sized pinnae show that:(1) When the subject's own HRTF was used in the simulation, natural sound localization in both planes can be performed with the same accuracy as real sound sources. (2) The differences between individual HRTFs affect the accuracy of localization in the simulation. In particular, in the median plane, an HRTF with a high angle-dependency seems to be more advantageous than one with a low angle-dependency.
ABC of ladder operators for rationally extended quantum harmonic oscillator systems

The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux–Crum–Krein–Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A±, B±, C±) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux–Crum–Krein–Adler transformations.
On the Units of Integral Group Rings

$U(ZG)|\epsilon(u)=1\}$ where $\epsilon:ZG\rightarrow Z$ is the augmentation map. In this paper we will study the following problems: Problem 1. How many eonjugate classes are there in $V(ZG)$ of subgroups of $V(ZG)$ isomorphic to $G$? Problem 2. Is there a torsion free normal subgroup $F$ of $V(ZG)$ such that $V(ZG)=F\cdot G$? Let $S. (resp. A.)$ denote the symmetric group (resp. alternating group) on $n$ symbols, and let $D$, denote the dihedral group of order $2n$ . Hughes and Pearson ([3]) raised Problem 1 with related problems and showed that there is only one conjugate class in $V(ZS_{3})$ of subgroups of $V(ZS_{3})$ isomorphic to $S_{3}$ . Polcino ([6]) showed that there are two conjugate classes in $V(ZD)$ of subgroups of $V(ZD_{4})$ isomorphic to $D_{4}$ . On the other hand, Dennis ([2]) solved affirmatively Problem 2 in the case where $G=S_{3}$ . Recently, Miyata ([5]) has solved Problem 2 in the case where $G=D_{n},$ $n$ odd. He has also solved Problem 1 with an additional hypothesis that the class group of $ZD_{n}$ is of odd order. Our main results are as follows: [I] Let $G$ be a finite metabelian group such that the exponent of $G/G$ ‘ is 1, 2, 3, 4 or 6, where $G^{\prime}$ is the commutator subgroup of G. Then there is a torsion free normal subgroup $F$ of $V(ZG)$ such that $V(ZG)=$
The theory of queues with a single server

1. The study of queues has been of interest to mathematicians and engineers for the past forty years, and a very extensive literature on the subject exists. The applications of the theory are many and varied, from Erlang's original work on telephone engineering, to present-day studies in the design of airports. The number of papers which deal with the theoretical side of the subject is, however, small, and it therefore seems desirable to attempt to develop a general theory which will cover the diverse practical requirements, so that the unity in the applications will become apparent. This paper gives such a development in the case where there is a single queue and a single server attending to it; the theory of multiple queues or many servers seems, except under simplifying assumptions which do not always correspond to reality, to be a problem of considerable difficulty. Previous work on the subject has mainly been confined to a special case where the customers arrive at random, as, for example, in a recent paper by Kendall(5);* the present theory makes no such assumption and allows the customers to join the queue in other ways, though the theory simplifies when the more restrictive assumption is made. The centre of interest in the present theory is the waiting times of the customers.
Accessibility of very low qa (VLQ) and ultra-low qa (ULQ) discharges in the SINP tokamak

Attempts to operate a tokamak at qa < 2 are normally found to terminate with a major disruption. In the SINP tokamak, however, it has been found possible to operate at qa < 1 with comparative ease. In this letter, an attempt is made to quantify the rate of current rise required to set up discharges having qa < 2 and qa < 1 by comparing the risetime with the resistive diffusion timescale. It has been observed that discharges with qa less than a particular value can be obtained if the time taken to cross the previous qa barrier is less than the resistive diffusion time. When the resistive diffusion time is less than the time taken to cross a particular qa barrier, it becomes extremely difficult to cross the next lower qa barrier
Spikes of the two-component elliptic system in $\bbr^4$ with Sobolev critical exponent

Consider the following elliptic system: \begin{equation*} \left\{\aligned&-\ve^2\Delta u_1+\lambda_1u_1=\mu_1u_1^3+\alpha_1u_1^{p-1}+\beta u_2^2u_1\quad&\text{in}\Omega,\\ &-\ve^2\Delta u_2+\lambda_2u_2=\mu_2u_2^3+\alpha_2u_2^{p-1}+\beta u_1^2u_2\quad&\text{in}\Omega,\\ &u_1,u_2>0\quad\text{in}\Omega,\quad u_1=u_2=0\quad\text{on}\partial\Omega,\endaligned\right. \end{equation*} where $\Omega\subset\bbr^4$ is a bounded domain, $\lambda_i,\mu_i,\alpha_i>0(i=1,2)$ and $\beta\not=0$ are constants, $\ve>0$ is a small parameter and $2 0$ small enough. The concentration behavior of the ground state solution as $\ve\to0^+$ is also studied. Furthermore, by combining the elliptic estimates and local energy estimates, we also obtain the location of the spikes as $\ve\to0^+$. To the best of our knowledge, this is the first attempt devoted to the spikes in the Bose-Einstein condensate in $\bbr^4$.
Local integrals of motion in many‐body localized systems

We review the current (as of Fall 2016) status of the studies on the emergent integrability in many‐body localized models. We start by explaining how the phenomenology of fully many‐body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motions, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many‐body mobility edge, and in dimensions larger than one.