Limit (Mathematics) Research Papers - Academia.edu (original) (raw)

2025, Metals

Size effects concern the anomalous scaling of relevant mechanical properties of materials and structures over a sufficiently wide dimensional range. In the last few years, thanks to technological advances, such effects have been experimentally detected also in the very high cycle fatigue (VHCF) tests. Research groups at Politecnico di Torino are very active in this field, observing size effects on fatigue strength, fatigue life and fatigue limit up to the VHCF regime for different metal alloys. In addition, different theoretical models have been put forward to explain these effects. In the present paper, two of them are introduced, respectively based on fractal geometry and statistical concepts. Furthermore, a comparison between the models and experimental results is provided. Both models are able to predict the decrement in the fatigue life and in the conventional fatigue limit.

2025

Traffic dependent speed limits have improved the security of highway traffic considerably. However, on highway sections controlled by variable speed limits large oscillations in speed can still be observed. On the basis of traffic data and a macroscopic traffic model, the influence of decentrally controlled speed limits on the states of highway traffic is analyzed. It is shown that local control of speed limits -which is typically applied -can lead to standing waves in speed. The anticipative control law proposed is able to prevent standing waves and can even damp out stop-and-go waves, such that a homogeneous traffic flow is gained.

2025, 2001 European Control Conference (ECC)

2025, Journal of Physics: Conference Series

Low frequency noise has been studied for two types of magnetic field sensors based on magnetic tunnel junctions (MTJ). The first structure, composed of a few large MTJs, is designed for low noise applications; the second one, composed of hundreds of small MTJs, is designed for general purposes. At low frequency, both structures exhibit 1/f noise, but with very different amplitudes. The sensors for general purposes show a much higher noise level compared to the low-noise sensors. However, the sensitivity of the low noise sensors is much smaller compared to the other ones. Thus, the limit of detection, defined as the ratio of noise and sensitivity, turns out to be roughly the same for both technologies. Using the advantages of each sensor could help to design a sensor with an improved limit of detection.

2025, Physical Review E

This work treats many-body aspects in an idealized class of reversible binding problems involving a static binding site with many difFusing point particles. In the noncompetitive limit, where no restriction exists on the number of simultaneously bound particles, the problem reduces to reversible aggregation. In the competitive limit, where only one particle may be simultaneously bound, it becomes a model for a pseudounimolecular reaction. The general formalism for both binding limits involves the exact microscopic hierarchy of diffusion equations for the N-body density functions. In the noncompetitive limit of independent particles, the hierarchy admits an analytical solution which may be viewed as a generalization of the Smoluchowski aggregation theory to the (idealized) reversible case. In the competitive limit, the hierarchy enables straightforward derivation of useful identities, determination of the ultimate equilibrium solution, and justification for several approximations. In particular, the utility of a density-expansion, short-time approximation is investigated. The approximation relies on the ability to solve the hierarchy numerically for a small number of particles. This direct-propagation algorithm is described in the numerical section.

2025, Physica A: Statistical Mechanics and its Applications

An accurate semi-analytic solution for reversible di usion-in uenced kinetics is presented in the pseudo-unimolecular target limit. It is shown to exhibit excellent agreement with Brownian simulations of the A + B C + D reaction.

2025, The Journal of Chemical Physics

A Brownian dynamics algorithm is developed for simulating many-body effects in one dimensional competitive reversible binding of otherwise noninteracting particles. It allows time steps hundreds of times larger than in conventional lattice random walks and enables us to simulate systems which are sufficiently large to approach the thermodynamic limit. The asymptotic long-time behavior is compared with mean-field predictions.

2025

We prove mean comparison results from a different perspective, where we introduce the concept of partial convolutions. For a parabolic initial data problem on the whole domain of dimension n we consider data functions which live on a subspace of lower dimension k and coefficient functions which live on the whole space or some subspace of dimension l. The pair of natural numbers (k, l) is called a strong partial convolution pair if for some coordinate transformations the coefficients functions of the equation and the initial data functions live in complementary linear spaces of dimension k and l respectively. Here the qualification ’strong’ indicates that this transformation exists without any further restriction concerning the intersection of the original linear subspaces involved, and that refined concepts are possible in this respect. For purely second order parabolic equations we show that (1, n) for any n ≥ 2 is a strong partial convolution pair. As a consequence new criteria fo...

2025, Acta Astronautica

Tethered satellite formations have recently gained increasing attention due to future mission proposals. Several different formations have been investigated for their dynamic properties and control schemes have been suggested. Formulating the equations of motion and investigation which geometries could form stable formations in space are cumbersome when done at a case to case basis, and a common framework providing a basic model of the dynamics of tethered satellite formations can therefore be advantageous. This paper suggests the use of graph theoretical quantities to describe a tethered satellite formation and proposes a method to deduce the equations of motion for the attitude dynamics of the formation in a compact form. The use of graph theory and Lagrange mechanics together allows a broad class of formations to be described using the same framework. A method is stated for finding stationary configurations and an upper limit of their number is determined. The method is shown to be valid for general tethered satellite formations that form a tree structure.

2025, Mathematical proceedings of the Cambridge Philosophical Society

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2025, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law ...

2025, Mathematical Proceedings of the Cambridge Philosophical Society

There are various notions of attractor in the literature, including measure (Milnor) attractors and statistical (Ilyashenko) attractors. In this paper we relate the notion of statistical attractor to that of the essential ω-limit set and prove some elementary results about these. In addition, we consider the convergence of time averages along trajectories. Ergodicity implies the convergence of time averages along almost all trajectories for all continuous observables. For non-ergodic systems, time averages may not exist even for almost all trajectories. However, averages of some observables may converge; we characterize conditions on observables that ensure convergence of time averages even in non-ergodic systems.

2025, Journal of the Mechanics and Physics of Solids

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2025, Statistics & Probability Letters

We study the existing models for right-censored competing risks data and with masked failure cause. By introducing a new random variable hidden behind the current models, we give a practical interpretation of the symmetry assumption made by almost all researchers in this field. We further point out that the drawback of the symmetry assumption is that it has a strong restriction on the underlying distribution function to be studied. Moreover, we correct an assumption in the current models.

2025, IEEE Transactions on Nuclear Science

A picosecond-range timing of charged particles and photons is a long-standing challenge for many high-energy physics, biophysics, medical and security applications. We present a design, technological pathway and challenges, and some properties important for realization of an ultrafast high-efficient room-temperature semiconductor scintillator based on selfassembled InAs quantum dots (QD) embedded in a GaAs matrix. Low QD density (<10 15 cm -3 ), fast (~5ps) electron capture, luminescence peak redshifted by 0.2-0.3 eV from GaAs absorption edge with fast decay time (0.5-1 ns) along with the efficient energy transfer in the GaAs matrix (4.2eV/pair) allows for fabrication of a semiconductor scintillator with the unsurpassed performance parameters. The major technological challenge is fabrication of a large volume (>1 cm 3 ) of epitaxial QD medium. This requires multiple film separation and bonding, likely using separate epitaxial films as waveguides for improved light coupling. Compared to traditional inorganic scintillators, the semiconductor-QD based scintillators could have about 5x higher light yield and 20x faster decay time, opening a way to gamma detectors with the energy resolution better than 1% and sustaining counting rates > 100 MHz. Picosecond-scale timing requires segmented low-capacitance photodiodes integrated with the scintillator. For photons, the proposed detector inherently provides the depth-of-interaction information.

2025, Probability Theory and Related Fields

We provide a probabilistic description of the stationary measures for the open KPZ on the spatial interval [0, 1] in terms of a Markov process Y , which is a Doob's h transform of the Brownian motion killed at an exponential rate. Our work builds on a recent formula of Corwin and Knizel which expresses the multipoint Laplace transform of the stationary solution of the open KPZ in terms of another Markov process T: the continuous dual Hahn process with Laplace variables taking on the role of time-points in the process. The core of our approach is to prove that the Laplace transforms of the finite dimensional distributions of Y and T are equal when the time parameters of one process become the Laplace variables of the other process and vice versa.

2025, Probability Theory and Related Fields

Motivated by recent results of Corwin and Knizel on stationary measures for the open KPZ equation on the spatial interval [0, 1], we study a pair of Markov processes with Laplace transforms that have dual representations, with the arguments of the Laplace transforms and the time parameters of the processes swapped. Combined with the results of Corwin and Knizel, our formula identifies the law of the stationary solutions for the open KPZ in terms of a Markov process which is a Doob's h transform of the Brownian motion killed at an exponential rate.

2025, ELEKTRIKA- Journal of Electrical Engineering

This paper proposes transmission line capacity enhancement with optimal location and sizing of UPFC on IEEE 14-bus network. This is necessary because of the increase in load growth with every passing day without an equivalent increase of line capacity which has brought many power systems closer to their stability limit. The dynamic and practical application of this proposed method is achieved by increasing linearly, the loading factor (λ) from 1.25 to 1.50 of the base case value of 1.0 and then, its effect is investigated. In each of the increment, the power flow result is obtained using Newton-Raphson method, while the optimal location and sizing of UPFC are done using Grey Wolf Optimization (GWO) technique. The voltage deviation before and after the installation of the FACTS device is also studied at each load variation. This approach will help the bulk dispatcher of power to plan ahead so as to meet and supply the ever-growing in the demand for adequate and reliable power system ...

2025

Variational-hemivariational inequalities refer to the inequality problems where both convex and nonconvex functions are involved. In this paper, we consider the numerical solution of a family of stationary variational-hemivariational inequalities by the finite element method. For a variational-hemivariational inequality of a general form, we prove convergence of numerical solutions. For some particular variational-hemivariational inequalities, we provide error estimates of numerical solutions, which are of optimal order for the linear finite element method under appropriate solution regularity assumptions. Numerical results are reported on solving a variational-hemivariational inequality modeling the contact between an elastic body and a foundation with the linear finite element, illustrating the theoretically predicted optimal first order convergence and providing their mechanical interpretations. Mathematics Subject Classification 65N30 · 65N15 · 74M10 · 74M15

2025, Comptes Rendus. Mathématique

Let D > 1 be a fixed integer. Given a smooth bounded, convex domain Ω ⊂ R D and H : R D → [0, ∞) a convex, even, and 1-homogeneous function of class C 3,α (R D \ {0}) for which the Hessian matrix D 2 (H p ) is positive definite in R D \ {0} for any p ∈ (1, ∞), we study the monotonicity of the principal frequency of the anisotropic p-Laplacian (constructed using the function H ) on Ω with respect to p ∈ (1, ∞). As an application, we find a new variational characterization for the principal frequency on domains Ω having a sufficiently small inradius. In the particular case where H is the Euclidean norm in R D , we recover some recent results obtained by the first two authors in .

2025, Revista Matemática Complutense

In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as p → ∞, of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.

2025, Nuclear Physics B

We develop a method to analyze the strong coupling limit of the Bethe ansatz equations supposed to give the spectrum of anomalous dimensions of the planar N = 4 gauge theory. This method is particularly adapted for the three rank-one sectors, su(2), su(1|1) and sl(2). We use the elliptic parametrization of the Bethe ansatz variables, which degenerates to a hyperbolic one in the strong coupling limit. We analyze the equations for the highest excited states in the su(2) and su(1|1) sectors and for the state corresponding to the twist-two operator in the sl(2) sector, both without and with the dressing kernel. In some cases we were able to give analytic expressions for the leading order magnon densities. Our method reproduces all existing analytical and numerical results for these states at the leading order.

2025

Within the !-limit set of a point,a uniform method is given for such problems as choosing for each point in its kernel a recurrent point that attacks it. In the light of recent counter-examples, the method appe- ars to be optimal. It is... more

2025, Journal of Symbolic Logic

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence ⟨Aλ ∣ λ a limit ordinal⟩ where for each λ. Aλ ⊆ λ2, there is a supertransitive inner model of Zermelo containing all ordinals in which for every λAλ = {a ∣ Φ(λ, a)}.

2025, Mathematical Proceedings of the Cambridge Philosophical Society

A point in Baire space is found for which the first derived ω-limit set is not Borel, whilst the second is empty. A second point is found for which the sequence of derived ω-limit sets does not stabilise until the first uncountable ordinal. The two points are recursive. This paper solves two problems left open in the author's paper [4] which will be cited as Delays. We begin by summarising the general background: further details and any unexplained notation will be found in that paper. For a short and informal motivation of this type of problem from the point of view of topological dynamics, the reader may wish to consult [1, introduction]. This paper, as did Delays, applies set-theoretic ideas to a problem of analysis, and therefore our notation will draw on that of two mathematical traditions. Thus we usually denote the set {0, 1, 2, . . .} of natural numbers by ω, though occasionally by N; this visual distinction allows us to write ω n for the ordinal power and N n for the set of n-tuples of natural numbers. N + is the set {1, 2, 3, . . .} of positive integers: in Definition 4•3 the difference between N and N + is important. Let X be a Polish space, and f : X -→ X a continuous map. We write x f y, or sometimes y f x, read x attacks y, if y is a cluster point of the set of successive images of x under f ; and we write ω f (x) for {y | x f y}, which is a closed set, being the intersection over all i of the closures of the sets {f n (x) | n i}. We define an operator Γ f on subsets of X by Using this operator and starting from a given point a ∈ X , we define a transfinite sequence of sets: as we take intersections at limit ordinals we shall have that for all ordinals α, β, α < β =⇒ A α (a, f ) ⊇ A β (a, f ).

2025, Bulletin of the London Mathematical Society

Examples are discussed of natural statements about irrational numbers that are equivalent, provably in ZFC, to strong set-theoretical hypotheses, and of apparently classical statements provable in ZFC of which the only known proofs use... more

2025

In this article we introduce the new classes of sequences of fuzzy numbers. We study some topological properties of these spaces and also we obtain some inclusion relations involving these classes of sequences of fuzzy numbers.

2025, IEEE Transactions on Reliability

This paper derives lower & upper reliability bounds for the 2-dimensional consecutive k-out-of-n:F system (Salvia Lasher, 1990) with independent but not necessarily ident i d y distributed components. A Weibull limit theorem is proved for... more

2025, The Journal of the Acoustical Society of America

Well-trained subjects identified with remarkable accuracy the temporal order of three contiguous pure tones of different frequencies, presented as a single sequence. For a given set of three frequencies covering a one-octave span, the minimum duration of each component tone necessary for absolute identification of a sequence was 2–7 msec on the average. A total frequency range narrower than 1/3–2/3 octave depressed the identifiability of temporal order, whereas increasing the frequency range beyond this limit had no appreciable effect. Simple harmonic relation between the three components was associated with higher identification performace than was a complex harmonic relation. In general, those temporal orders in which the frequency change was unidirectional were more easily identified than the others. Also, the highest and the lowest of the three tones in final position were recognized more often than any of the sequences and were, most probably, used by the observers as cues for ...

2025, International journal of applied mathematics, computational science and systems engineering

In this paper, we propose to study some nonlinear boundary problems for the dynamically modified operator by adding a viscosity term -𝛼𝛥𝑢 ′′ to the nonlinear vibrations of the plates. The field of application for vibrating plates is extensive. To meet user needs, we have considered the geometric shape, the density of the material constituting the plate, the plate thickness, and Poisson's ratio. Once the problems have been posed, our approach then consists of transforming them into nonlinear problems of the hyperbolic type. In this work, we study six boundary value problems and we prove for each problem an existence and uniqueness theorem. Finally, we demonstrate the existence of a solution to the stationary problem using a variant of Brouwer's fixed point theorem.

2025, Journal of Public Economics

Contributions to tax-preferred savings accounts are typically constrained by a contribution limit. These limits influence contributions not just in periods in which they bind, but in other periods as well. I develop a simple life-cycle model in which consumers exhibit "use-it-or-lose-it" contribution behaviour. This connects current contributions to future contribution limits, which leads to the result that an increase in contribution limits can decrease contributions. Empirical evidence provides support for the model -larger future contribution room is associated with smaller contributions.

2025, Journal of Futures Markets

In a futures market with a daily price-limit rule, trading occurs only at prices within limits determined by the previous day's settlement price. Price limits are set in dollars but can be expressed as return limits. When the daily return limit is triggered, the true equilibrium futures return (and price) is unobservable. In such a market, investors may suffer from information loss if the return "moves the limit." Assuming normally distributed futures returns with unknown means but known volatilities, we develop a Bayesian forecasting model in the presence of return limits and provide some numerical predictions. Our innovation is the derivation of the predictive density for futures returns in the presence of return limits.

2025, Physical Review Letters

The gravitational-wave (GW) sky may include nearby pointlike sources as well as stochastic backgrounds. We perform two directional searches for persistent GWs using data from the LIGO S5 science run: one optimized for pointlike sources and one for arbitrary extended sources. Finding no evidence to support the detection of GWs, we present 90% confidence level (C.L.) upper-limit maps of GW strain power with typical values between 2 À 20 Â 10 À50 strain 2 Hz À1 and 5 À 35 Â 10 À49 strain 2 Hz À1 sr À1 for pointlike and extended sources, respectively. The latter result is the first of its kind. We also set 90% C.L. limits on the narrow-band root-mean-square GW strain from interesting targets including Sco X-1, SN 1987A and the Galactic center as low as % 7 Â 10 À25 in the most sensitive frequency range near 160 Hz.

2025

Many-body Feshbach Hamiltonians in the two-body limit. NICO-LAI NYGAARD, University of Aarhus, JAMES E. WILLIAMS, PAUL S. JULI-ENNE, NIST -We discuss how the many-body theory of a gas with interactions controlled by a Feshbach resonance can be constructed in a manner, which incorporates the correct two-body physics. This entails the introduction of an energy dependent renormalized coupling constant for atom-molecule conversion that embodies the low energy scattering properties of the entrance channel potential. We demonstrate that with this model the binding energies of the dressed Feshbach molecules may be faithfully reproduced.

2025, IOS Press

Concern for descriptions of the ocean environment, especially with respect to wave, current and wind, in deep and shallow waters, and ice, as a basis for the determination of environmental loads for structural design. Attention shall be given to statistical description of these and other related phenomena relevant to the safe design and operation of ships and offshore structures. The committee is encouraged to cooperate with the corresponding ITTC committee.

2025, arXiv (Cornell University)

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain boundaries over time intervals. The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting. It implies that a weak solution indeed satisfies the balance law. In fact, it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.

2025, International Forum on Aeroelasticity and Structural Dynamics IFASD

During design and analysis phases of aircraft flutter boundaries are computed using analysis tools such as the p-k iterations or eigenvalue analysis. Also, for the purpose of certification flight flutter test (FFT) is conducted to predict the onset of flutter experimentally. However, from the practical perspective aeroelastic vibrations with finite amplitudes known as the Limit Cycle Oscillation (LCO) are more critical because they reveal the true nonlinear nature of the fluidstructure interaction. Previously, based on the concept of the Dynamic Eigen Decomposition (DED) and a frequency domain stability theorem, a new flutter prediction methodology was developed for applications to FFT with limited actuators and sensors. In this study, this technique is extended to include LCOs originating from a nonlinearity existing in a control surface freeplay. First, a linear flutter boundary is predicted using the DED method and data available at subcritical flight conditions. Next, a simple harmonic analysis of the control surface freeplay is carried out to extract important harmonic contents of the nonlinearity, and a new DED is formulated in two parameters, i.e., the variable dynamic pressure and the effective stiffness of the control surface hinge. Using the formulation, it is possible to predict LCO by extrapolating the dynamic eigenvalues obtained at the subcritical data points. The proposed methodology is demonstrated using computational simulations of a tapered wing with four flaps and a freeplay in one of the hinges. It is shown that the new approach yields accurate predictions of LCO without need for taking additional data, with only the data obtained during the FFT.

2025, New Journal of Physics

In this paper, we propose a quantum amplitude estimation method that uses a modified Grover operator and quadratically improves the estimation accuracy in the ideal case, as in the conventional one using the standard Grover operator. Under the depolarizing noise, the proposed method can outperform the conventional one in the sense that it can in principle achieve the ultimate estimation accuracy characterized by the quantum Fisher information in the limit of a large number of qubits, while the conventional one cannot achieve the same value of ultimate accuracy. In general this superiority requires a sophisticated adaptive measurement, but we numerically demonstrate that the proposed method can outperform the conventional one and approach to the ultimate accuracy, even with a simple non-adaptive measurement strategy.

2025, Physics Letters B

We have calculated MS Wilson coefficients and anomalous dimensions for the non-singlet part of the structure function F 2 in the large-N F limit. Our result agrees with exact two and three loop calculations and gives the leading N F... more

2025, Journal of Lightwave Technology

The noise power spectral density of a detector is essential for determining the frequency of operation and readout architecture that yields an optimal signal-to-noise ratio. In this work, we characterize a waveguide-integrated PbTe mid-infrared detector and report on its noise spectrum, highlighting the presence of a current-dependent 1/f term dominating at low frequency and/or high bias over the Johnson component typical of a photoconductor. This behaviour, together with the substantially flat frequency response in the range between 1 kHz to 1 MHz, guide towards a lock-in readout strategy, that allows one to operate in the region of minimum noise without penalties in the detection performance. Practical guidelines to optimize the readout resolution are provided and the limit of detection of a gas sensing system exploiting PbTe photoconductors is derived, as an example of how a careful co-design of sensors and electronics can dramatically improve the detection performance.

2025, 2016 Australasian Universities Power Engineering Conference (AUPEC)

Constraints to power transfer in the network may limit the load that can be supported by the transmission lines. To overcome these constraints various current uprating methods can be used. This paper discusses the developments in the use of Dynamic Line Thermal Rating (DLTR) techniques to obtain a higher rating of conductors, the general considerations for thermal uprate and High Temperature Low Sag (HTLS) conductor usage in uprating.

2025, AIP Conference Proceedings

In this paper, we present an efficient method to simulate multilayered anisotropic composite material with effective medium theory. Effective permittivity, permeability and orientation angle for a layered anisotropic composite medium are extracted with this equivalent model. We also derive analytical expressions for effective parameters and orientation angle with low frequency (LF) limit, which will be shown in detail. Numerical results are shown in comparing extracted effective parameters and orientation angle with analytical results from low frequency limit. Good agreements are achieved to demonstrate the accuracy of our efficient model.

2025, The Annals of Statistics

When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the observation locations. This paper explores conditions on the observation locations and the process model under which an asymptotic screening effect holds. A series of examples shows the difficulty in formulating a general result, especially for processes with different degrees of smoothness in different directions, which can naturally occur for spatial-temporal processes. These examples lead to a general conjecture and two special cases of this conjecture are proven. The key condition on the process is that its spectral density should change slowly at high frequencies. Models not satisfying this condition of slow high-frequency change should be used with caution.

2025, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications

2025, Colloquium Mathematicum

We consider the Cauchy problem for the focusing Hartree equation iu t + ∆u + (| • | -3 * |u| 2 )u = 0 in R 5 with the initial data in H 1 , and study the divergent property of infinite-variance and nonradial solutions. Letting Q be the ground state solution of then the corresponding solution u(t) either blows up in finite forward time, or exists globally for positive time and there exists a time sequence t n → +∞ such that ∇u(t n ) 2 → +∞. A similar result holds for negative time.

2025, International Journal of Game Theory

We analyze price leadership in a Stackelberg game with incomplete information and imperfect commitment. Sequential play is induced by an information system, represented by a spy, that reports the price of one firm to its rival before the latter chooses its own price. However, the Stackelberg leader may secretly revise its price with some probability. Therefore, the spy’s message is only an imperfect signal. This gives rise to a complex signaling problem where both sender and receiver of messages have private information and the sender has a chance to take another action with some probability. We find partially separating and pooling equilibria that satisfy equilibrium refinements such as the intuitive criterion and support collusive outcomes.

2025, Artificial Intelligence