We present a novel method of analysis and prove finite time asymptotically self‐similar blowup of the De Gregorio model [13, 14] for some smooth initial data on the real line with compact support. We also prove self‐similar blowup results for the generalized De Gregorio model [41] for the entire range of parameter on ℝ or for Hölder‐continuous initial data with compact support. Our strategy is to reformulate

We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on “Arithmetic Topology.” Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and engaged in shared discussions from their own perspectives as working mathematicians across various fields of study. Participants were explicitly asked to provide

These are lecture notes from the conference Arithmetic Topology at the Pacific Institute of Mathematical Sciences on applications of Morel’s \({\mathbb {A}}^1\)-degree to questions in enumerative geometry. Additionally, we give a new dynamic interpretation of the \({\mathbb {A}}^1\)-Milnor number inspired by the first-named author’s enrichment of dynamic intersection numbers.

Given \(d\in {\mathbb {N}}\), we prove that any polarized Enriques surface (over any field k of characteristic \(p \ne 2\) or with a smooth K3 cover) of degree greater than \(12d^2\) contains at most 12 rational curves of degree at most d. For \(d>2\), we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.

In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\)-type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\)-type binomial fractional difference sequence space \((1 \le

In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale–Kato–Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces \({\dot{B}}_{\infty ,\infty }^{0} \). Then we give a criterion on extension beyond T of our local solution. Our result may be also regarded

In this paper, we establish a sharp integral inequality for n-dimensional closed spacelike submanifolds with constant scalar curvature immersed with parallel normalized mean curvature vector field in the de Sitter space \(\mathbb S_p^{n+p}\) of index p, and we use it to characterize totally umbilical round spheres \(\mathbb S^n(r)\), with \(r>1\), of \(\mathbb S_1^{n+1}\hookrightarrow \mathbb S_p^{n+p}\)

In this article, we study hypersurfaces \(\Sigma \subset {\mathbb {R}}^{n+1}\) with constant weighted mean curvature, also known as \(\lambda \)-hypersurfaces. Recently, Wei-Peng proved a rigidity theorem for \(\lambda \)-hypersurfaces that generalizes Le–Sesum’s classification theorem for self-shrinkers. More specifically, they showed that a complete \(\lambda \)-hypersurface with polynomial volume

By studying a complex Monge–Ampère equation, we present an alternate proof to a recent result of Chu-Lee-Tam concerning the projectivity of a compact Kähler manifold Nn with Rick<0 for some integer k with 1

In this paper, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result states that the holomorphic sections produced by the theorem are in fact parallel, when the Chern connection associated with the singular metric is computed in the sense of currents, and the corresponding multiplier ideal sheaves

We find new characterizations for the points in the symmetrized polydisc𝔾n, a family of domains associated with the spectral interpolation, defined by 𝔾n:=∑1≤i≤nzi,∑1≤i

For positive p and real α let Aαp denote the weighted Bergman spaces of the unit ball 𝔹n introduced in [R. Zhao and K. Zhu, Theory of Bergman Spaces on the Unit Ball inℂn, Mémoires de la Société Mathématique de France, Vol. 115 (2008)]. It is well known that, at least in the case n=1, all functions in Aαp can be approximated in norm by their Taylor polynomials if and only if p>1. In this paper we

We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekovář and Scholl. This is achieved with the help of Morel’s work on weight t-structures and a detailed study of partial Frobenius. We prove in particular that the partial Frobenius extends to toroidal and minimal compactifications.

We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of $\overline {\mathcal {M}}_{g,n}$ is not pseudoeffective in some range, implying that $\overline {\mathcal {M}}_{12,6}$, $\overline {\mathcal {M}}_{12,7}$, $\overline {\mathcal {M}}_{13,4}$ and $\overline {\mathcal {M}}_{14,3}$ are uniruled. We provide upper bounds for the

We prove an equivalence between the Bryan-Steinberg theory of $\pi $-stable pairs on $Y = \mathcal {A}_{m-1} \times \mathbb {C}$ and the theory of quasimaps to $X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of both vertices are described explicitly via box counting. Then we apply the equivalence to study the implications

Let us denote by d(n) the number of divisors of n, by \({{\,\mathrm{li}\,}}(t)\) the logarithmic integral of t, by \(\beta _2\) the number \(\frac{\log 3/2}{\log 2}=0.584\ldots \) and by R(t) the function \(t\mapsto \frac{2\sqrt{t} +\sum _\rho t^\rho /\rho ^2}{\log ^2 t}\), where \(\rho \) runs over the non-trivial zeros of the Riemann \(\zeta \) function. In his PHD thesis about highly composite numbers

In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to Ramanujan’s parameters introduced in his Lost Notebook. Also, a handful of new identities involving these parameters will be established.

Scheduling of megaprojects is very challenging because of typical characteristics, such as expected long project durations, many activities with multiple modes, scarce resources, and investment decisions. Furthermore, each megaproject has additional specific characteristics to be considered. Since the number of nuclear dismantling projects is expected to increase considerably worldwide in the coming

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with a purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These K3 surfaces can be realized as the minimal resolution of the double cover of $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along a specific $(4,\,4)$ curve. We show that, up to a

The purpose of this article is to study the relationship between numerical invariants of certain subspace arrangements coming from reflection groups and numerical invariants arising in the representation theory of Cherednik algebras. For instance, we observe that knowledge of the equivariant graded Betti numbers (in the sense of commutative algebra) of any irreducible representation in category |${\mathscr{O}}$|

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles in the plane [ 42]. We also propose certain natural open questions and conjectures, whose confirmation would provide new insights on configuration spaces of trees

The capsule network (CapsNet) is a promising model in computer vision. It has achieved excellent results on MNIST, but it is still slightly insufficient in real images. Deepening capsule architectures is an effective way to improve performance, but the computational cost hinders their development. To overcome parameter growth and build an efficient architecture, this paper proposes a tensor capsule

Let Dm be an elliptic curve over ℚ of the form y2 = x3 − m2x + m2, where m is an integer. In this paper we prove that the two points P−1 = (−m, m) and P0 = (0, m) on Dm can be extended to a basis for Dm(ℚ) under certain conditions described explicitly.

In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop

While the international lockdown for the COVID-19 pandemic has greatly influenced the global economy, we are still confronted with the dilemma about the economy recession when the stock market hits record highs repeatedly. As we know, since portfolio selection is often affected by many non-probabilistic factors, it is of not easiness to obtain the precise probability distributions of the return rates

An accelerated life test of a product or material consists of the observation of its failure time when it is subjected to conditions that stress the usual ones. The purpose is to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. A widely used method to provoke an early failure in a mechanism is to modify the temperature at which

Due to the unbalance between Asian and Western countries in terms of higher education development and pressure from global competition, universities in several East Asian countries have striven to become world-class universities (WCUs) by actively assessing themselves using various global ranking systems and subsequently investing in key performance indicators. Numerous scholars have suggested that

This article concerns various lifting properties of formal triangular matrix rings. The first aim is to study idempotent lifting ideals of formal triangular matrix rings. In connection with the idempotent lifting property, we also describe strong lifting, enabling and fully lifting ideals of formal triangular matrix rings. Moreover, we give a description for an ideal of a triangular matrix ring to

We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k. We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k+ and

Radioembolization (RE) is a treatment for patients with liver cancer, one of the leading cause of cancer-related deaths worldwide. RE consists of the transcatheter intraarterial infusion of radioactive microspheres, which are injected at the hepatic artery level and are transported in the bloodstream, aiming to target tumors and spare healthy liver parenchyma. In paving the way towards a computer platform

In this work, our goal is to present and discuss similarity techniques for ordered observations between time series and non-time dependent data. The purpose of the study was to measure whether ordered observations of data sets are displayed at or close to, the same time points for the case of time series and with the same or similar frequencies for the case of non-time dependent data sets. A simultaneous

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that

The Legendre polynomials \(P_n(x)\) are defined by $$\begin{aligned} P_n(x)=\sum _{k=0}^n\left( {\begin{array}{c}n+k\\ k\end{array}}\right) \left( {\begin{array}{c}n\\ k\end{array}}\right) \left( \frac{x-1}{2}\right) ^k\quad (n=0,1,2,\ldots ). \end{aligned}$$ In this paper, we prove two congruences concerning Legendre polynomials. For any prime \(p>3\), by using the symbolic summation package Sigma

In this paper, we give a mirror construction and we obtain a mirror Fourier transform \(\mathcal {F}_{\lambda }\) associated with this mirror construction. Subsequently, we consider the noncommutative Volterra equation \(S_{\theta }V_{[-1,0]}=e^{\mathbf {i}\theta }V_{[-1,0]}S_{\theta }\) using this mirror Fourier transform \(\mathcal {F}_{\lambda }\), where \(V_{[-1,0]}\) is the Volterra operator on

We consider a planar system \(z'=f(t,z)\) under non-resonance or double resonance conditions and obtain the existence of \(2\uppi \)-periodic solutions by combining a rotation number approach together with Poincaré-Bohl theorem. Firstly, we allow that the angular velocity of solutions of \(z'=f(t,z)\) is controlled by the angular velocity of solutions of two positively homogeneous system \(z'=L_i(t

The “N-Body Problem” refers to the study of the dynamics of a system of N point masses, moving under their mutual gravitational attraction. For such a system, it is classical that there are conserved quantities of center of mass, linear momentum, angular momentum and energy. The level sets \({\mathfrak {M}}(c,h)\) of these conserved quantities are parameterized by the angular momentum c and the energy

In this paper, we investigate the Kaczmarz–Tanabe method for exact and inexact linear systems. The Kaczmarz–Tanabe method is derived from the Kaczmarz method, but is more stable than that. We analyze the convergence and the convergence rate of the Kaczmarz–Tanabe method based on the singular value decomposition theory, and discover two important factors, i.e., the second maximum singular value of Q

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation

A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous finite element methods simplifies formulations and reduces programming complexity. The purpose of this paper is to introduce a new WG method without stabilizers on polytopal mesh that has convergence rates one order higher

Abstract:This paper presents a combinatorial approximation of the monoidal topological complexity of a simplicial complex that controls reserved robot motions in . We introduce an upper bound of using the -iterated barycentric subdivision of modulo the diagonal and consider the refinement of the approximation. We show that can be described as for sufficiently large . As an example, we consider a simplicial

Abstract:We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that, for any nondiscrete metrizable space , the function space is not countable dense homogeneous. This answers a question posed recently by R. Hernández-Gutiérrez

Abstract:We compute the knot Floer filtration induced by a cable of the meridian of a knot in the manifold obtained by large integer surgery along the knot. We give a formula in terms of the original knot Floer complex of the knot in the three-sphere. As an application, we show that a knot concordance invariant of Hom can equivalently be defined in terms of filtered maps on the Heegaard Floer homology

Abstract:In this paper we investigate the 0-concordance classes of 2-knots in , an equivalence relation that is related to understanding smooth structures on 4-manifolds. Using Rochlin's invariant, and invariants arising from Heegaard-Floer homology, we will prove that there are infinitely many 0-concordance classes of 2-knots.

Abstract:The goal of this short paper is to show that the hyperbolic metric is uniquely determined by the induced metric on the strictly convex smooth boundary for dimension .

Abstract:In this paper, we extend the work by the first author and Q. Chen [Duke Math. J. 162 (2013), pp. 1149-1169] to classify -dimensional () complete -flat gradient steady Ricci solitons. More precisely, we prove that any -dimensional complete noncompact gradient steady Ricci soliton with vanishing D-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends

Abstract:We clarify the relation between an affine function and a Busemann function in a geodesically complete Finsler manifold. As an application, we give the characterization of a Minkowski space by means of the dimension of the vector space consisting of all affine functions on a Finsler manifold.

Abstract:Delay in feedback is inevitable in a multi-agent system due to time lags in information processing for self-organization. The well-known Cucker-Smale model incorporated with this information processing delay has been recently studied, and it was shown (at least for a two-agent system) that as long as the delay is below a threshold value, the system exhibits the flocking behavior where the

Abstract:This paper is concerned with the pulsating traveling waves of a periodic lattice dynamical system with monostable nonlinearity. We first establish the exponential upper and lower bounds of the pulsating wave profiles at minus infinity. Then we prove the uniqueness result and derive the asymptotic behavior of all non-critical monostable pulsating traveling waves. This might be the first time

Abstract:We prove that given a non-wandering point of a Sobolev- homeomorphism we can create closed trajectories by making arbitrarily small perturbations. As an application, in the planar case, we obtain that generically the closed trajectories are dense in the non-wandering set.

Abstract:We show that local weak solutions to parabolic systems of -Laplace type are Hölder continuous in time with values in a spatial Lebesgue space and Hölder continuous on almost every time line. We provide an elementary and self-contained proof building on the local higher integrability result of Kinnunen and Lewis.

Abstract:Let () be a ball. We consider the Dirichlet Laplacian associated with and prove that its eigenvalue counting function has an asymptotics as .

Abstract:We consider the equation , , , where periodically depends on and is of bistable type. Classical results showed that for a large class of initial functions, the solutions converge to a periodic traveling wave if it connects two linearly stable time-periodic states. Under some conditions on the initial functions, we prove this convergence result by a new approach which allows the time-periodic

Abstract:In this paper we establish a lower bound for the distance induced by the Kähler-Einstein metric on pseudoconvex domains with positive hyperconvexity index (e.g. positive Diederich-Fornæss index). A key step is proving an analog of the Hopf lemma for Riemannian manifolds with Ricci curvature bounded from below.

Abstract:One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space and for any Banach space of continuous real-valued functions on which embeds densely in there exists a residual set of functions in that Banach space for which the maximising measure is unique. We extend this result by showing that this residual set is additionally prevalent

Abstract:In this work, we introduce a variant form of uniform convexity in partially ordered Banach spaces. This uniform convexity property is more adequate than norm uniform convexity when studying the fixed point problem for monotone nonexpansive mappings.

Abstract:We show that for any Banach space and any compact topological group such that the norm of is -invariant, the set of norm attaining -invariant functionals on is dense in the set of all -invariant functionals on , where a mapping is called -invariant if for every and every , . In contrast, we show also that the analog of Bollobás result does not hold in general. A version of Bollobás and James'

Abstract:We continue the study of the equisingularity of determinantal singularities for essentially isolated singularities (EIDS). These singularities are generic except at isolated points.

Abstract:Let be a random complex polynomial whose roots are sampled i.i.d. from a radial distribution in the complex plane. A natural question is how the distribution of roots evolves under repeated (say times) differentiation of the polynomial. We conjecture a mean-field expansion for the evolution of : The evolution of corresponds to the evolution of random Taylor polynomials We discuss some numerical

Abstract:We prove that a Banach space of continuous functions has a renorming that is uniformly rotund in every direction (URED) if and only if the compact space supports a strictly positive measure.