We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$ . As a main step, we derive a labelling set for the irreducible $2$ -Brauer characters of the finite symplectic groups $\operatorname {Sp}_{2n}(q)$ (with odd q), together with the action of automorphisms. As a further important ingredient, we prove a Jordan decomposition for

For a character χ of a finite group G, the number χ c ( 1 ) = [ G : ker χ ] χ ( 1 ) is called the codegree of χ. Let N be a normal subgroup of G and set Irr ( G | N ) = Irr ( G ) − Irr ( G / N ) . Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of | N | , p q divides none of the codegrees of elements of Irr ( G | N ) , then Fit ( N ) ≠ { 1 } and N is either

We investigate the solution space to certain A-hypergeometric 𝒟-modules, which were defined and studied by Gelfand, Kapranov, and Zelevinsky. We show that the solution space can be identified with certain relative cohomology group of the toric variety determined by A, which generalizes the results of Huang, Lian, Yau and Zhu. As a corollary, we also prove the existence of rank one points for complete

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold (M2n+1,J,𝜃) into a compact Riemannian manifold (Nm,gij). We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold N is non-positive. Moreover, without the curvature assumption on the target

We prove that for any type F4 unitary affine VOA V𝔣4l, sufficiently many intertwining operators satisfy polynomial energy bounds. This finishes the Wassermann type analysis of intertwining operators for all WZW-models.

We mainly study the random sampling and reconstruction in multiply generated shift-invariant subspaces Vp,q(Φ) of mixed Lebesgue spaces Lp,q(R×Rd). Under suitable conditions for the generators Φ, we can prove that if the sampling sizes are large enough for both variables, the sampling stability holds with high probability for all functions in Vp,q(Φ) whose energy is concentrated on a compact subset

Multi-order fractional differential equations have been studied due to their applications in modeling, and solved using various mathematical methods. We present explicit analytical solutions for several families of Langevin differential equations with general fractional orders, both homogeneous and inhomogeneous cases. The results can be written, in general and special cases, by means of a recently

In this paper, based on the iteration framework (Tian et al., 2019) and relaxed two-step splitting (RTSS) iteration method (Xie and Ma, 2018), we present two relaxed iteration methods for solving the PageRank problem, which are the relaxed generalized inner-outer (RGIO) and relaxed generalized two-step splitting (RGTSS) iteration methods, respectively. Next, their overall convergence properties are

In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection πλ,μ:V𝔸(λ)∨⊗𝔸V𝔸(μ)∨↠V𝔸(λ+μ)∨ sending the tensor product of the highest weight vectors to the highest weight vector in terms of convolution products. When the quiver Hecke algebra is symmetric and the base field

Deep neural networks have successfully been trained in various application areas with stochastic gradient descent. However, there exists no rigorous mathematical explanation why this works so well. The training of neural networks with stochastic gradient descent has four different discretization parameters: (i) the network architecture; (ii) the amount of training data; (iii) the number of gradient

In earlier work we defined a computational saddle transition problem which arises in the dynamics of certain hyperbolic toral automorphisms, and proved, using the shadowing lemma, that in an appropriate model of computation this problem is in Oracle NP, up to a highly restricted oracle. In this note we show similar methods can be extended to a far larger class of dynamical systems, a class which is

An AF algebra 𝔄 is said to be an AFℓ algebra if the Murray–von Neumann order of its projections is a lattice. Many, if not most, of the interesting classes of AF algebras existing in the literature are AFℓ algebras. We construct an algorithm which, on input a finite presentation (by generators and relations) of the Elliott semigroup of an AFℓ algebra 𝔄, generates a Bratteli diagram of 𝔄. We generalize

Let p∈(1,∞), ρ∈(2,∞) and W be a matrix Ap weight. In this paper, we introduce a version of variation 𝒱ρ(𝒯n,∗) for matrix Calderón–Zygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the Lp(W)-boundedness of 𝒱ρ(𝒯n,∗) with norm ∥𝒱ρ(𝒯n,∗)∥Lp(W)→Lp(W)≤C[W]Ap1+1p−1−1p by first proving a sparse domination of the variation of the scalar Calderón–Zygmund operator

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compatible filter and 𝒜/ Θ (F). Moreover, a representation

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω:=Ω0\Ω¯1⊂𝕉N, N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric

Let 𝒭 be a commutative ring with unity, 𝒜, 𝒝 be 𝒭-algebras, 𝒨 be (𝒜, 𝒝)-bimodule and 𝒩 be (𝒝, 𝒜)-bimodule. The 𝒭-algebra 𝒢 = 𝒢(𝒜, 𝒨, 𝒩, 𝒝) is a generalized matrix algebra defined by the Morita context (𝒜, 𝒝, 𝒨, 𝒩, ξ𝒨𝒩, Ω𝒩𝒨). In this article, we study Jordan σ-derivations on generalized matrix algebras.

This short note is concerned with Nicholson’s blowflies equation with Dirichlet boundary. For the challenging non-monotone case, we show the exponential convergence rate by the energy method, where the key observation is that the energy integrations for the perturbations on the inner boundary will be disappeared automatically, even the solutions at the boundary are non-zero.

This paper considers a modified Leslie–Gower delayed reaction–diffusion predator–prey model with prey harvesting of Michaelis–Menten type and subject to homogeneous Neumann boundary condition. The global asymptotic stability of the positive constant steady state of the model is analyzed further and an existing global stability result is improved.

In this paper, we deal with the existence and multiplicity of solutions of Kirchhoff-type problem (0.1)−a+b∫RN|∇u|2dx△u+u=f(x,u),inRN,u∈H1(RN),where N≥3. Under more relaxed assumptions on f, we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrival solutions by using the genus properties in critical point theory.

In the present paper, we consider the following discrete Schrödinger equations In the present paper, we consider the following discrete Schrödinger equations m(∑k∈Z(|Δuk−1|2+Vk|uk|2))(−Δ2uk−1+Vkuk)−ωuk=fk(uk)k∈Z,where m is a continuous function and V={Vk} is a positive potential, ω∈R, Δuk−1=uk−uk−1 and Δ2=Δ(Δ) is the one dimensional discrete Laplacian operator. Under some suitable assumptions on fk

In this paper, a three-species food web stochastic model with generalist predator is proposed and studied. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distribution implies that all species can coexist

This paper presents a pseudopotential lattice Boltzmann model for multicomponent flows involving large viscosity ratios. Firstly, a rigorous Chapman-Enskog analysis is conducted to show that previous models cannot recover the correct governing equation with a single-relaxation-time scheme when the viscosity ratio is not unity. Then, based on this analysis, we established a modified model to obtain

A long standing problem, which has its roots in low-dimensional homotopy theory, is to classify all finite groups G for which the integral group ring ℤG has stably free cancellation (SFC). We extend results of R. G. Swan by giving a condition for SFC and use this to show that ℤG has SFC provided at most one copy of the quaternions ℍ occurs in the Wedderburn decomposition of the real group ring ℝG.

The Hamming graph H(n,q) is the graph whose vertices are the words of length n over the alphabet {0,1,…,q−1}, where two vertices are adjacent if they differ in exactly one coordinate. The adjacency matrix of H(n,q) has n+1 distinct eigenvalues n(q−1)−q⋅i with corresponding eigenspaces Ui(n,q) for 0≤i≤n. In this work we study functions belonging to a direct sum Ui(n,q)⊕Ui+1(n,q)⊕⋯⊕Uj(n,q) for 0≤i≤j≤n

We develop a theory of Frobenius functors for symmetric tensor categories (STC) 𝒞 over a field 𝒌 of characteristic p, and give its applications to classification of such categories. Namely, we define a twisted-linear symmetric monoidal functor F:𝒞→𝒞⊠Verp, where Verp is the Verlinde category (the semisimplification of Rep𝐤(ℤ/p)); a similar construction of the underlying additive functor appeared

In this paper, we study hybrid subconvexity bounds for class group 𝐿-functions associated to quadratic extensions K/Q (real or imaginary). Our proof relies on relating the class group 𝐿-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bound for Eisenstein series E⁢(z,1/2+i⁢t)≪εy1/2⁢(|t|+1)1/3+ε, y≫1, extending

Load is the main external disturbance of a parallel robot manipulator. This disturbance will cause dynamic coupling among different degrees of freedom and make heaps of model-based control methods difficult to apply. In order to compensate this disturbance, it is crucial to obtain an accurate dynamic model of load. However, in practice, the load is always uncertain and its dynamic parameters are arduous

In the process of rapid urbanization, urban heat island (UHI) effect has been showing more and more significant impacts on human well-being. Therefore, a more detailed understanding of the impact of three-dimensional (3D) building morphology on UHI effect across a continuum of spatial scales will be necessary to guide and improve the human settlement.This study selected 31 provincial capital cities

A robust adaptive fuzzy nonlinear controller based on dynamic surface and integral sliding mode control strategy (ADSISMC) is proposed to realize trajectory tracking for a class of quadrotor UAVs. In this study, the composite factors including parametric uncertainties and external disturbances are added to controller design, which make it more realistic. The quadrotor model is divided into two subsystems

The Belt and Road (BR) Initiative (BRI) is usually examined in geopolitics perspectives, while the studies ignored the consistency of the BRI with the world economy and China’s historical international business. This study developed a maritime big data system to analyze global interactions upon the global maritime network generated from the system. The BR is coupled with Chinese overseas construction

In the evaluation of teaching quality, aiming at the shortcomings of slow convergence of BP neural network and easy to fall into local optimum, an online teaching quality evaluation model based on analytic hierarchy process (AHP) and particle swarm optimization BP neural network (PSO-BP) is proposed. Firstly, an online teaching quality evaluation system was established by using the analytic hierarchy

We fix z0 ∈ ℂ and a field 𝔽 with ℂ ⊂ 𝔽 ⊂ 𝓜z0 := the field of germs of meromorphic functions at z0. We fix f1, …, fr ∈ 𝓜z0 and we consider the 𝔽-algebras S := 𝔽[f1, …, fr] and S¯:=F[f1±1,…,fr±1]. We present the general properties of the semigroup rings

In this paper, we present necessary and sufficient conditions of boundedness of L-index in joint variables for vector-valued functions analytic in the unit ball B2={z∈C2:|z|=|z1|2+|z2|2<1}, where L = (l1, l2): 𝔹2 → R+2 is a positive continuous vector-valued function.

As COVID-19 restrictions continue to upend plans for data collection, scientists stuck at home are finding innovative ways to adapt their research questions. Here’s what they’re doing.

A second lockdown saps scientific creativity, says John Tregoning, but vaccine news and US election result offer hope at the end of a challenging year.

The first known African plant to use reptiles as its primary pollinator, how to adapt when your fieldwork is cancelled and neutrinos reveal the Sun’s inner workings.

AstraZeneca plans a new trial to confirm a striking improvement in efficacy. Plus, Japan’s ‘cluster busting’ COVID strategy might have hit its limits and how to build an unofficial board of mentors.

Abstract Let X be a set and f : X → X be a map. We denote by 𝒫(f) the topology defined on X whose closed sets are the subsets A of X with f (A) ⊆ A. A topology on X is said to be a primal topology, if it is a 𝒫(f) for some map f. Our aim here is to characterize when the product of an arbitrary family of topological spaces is a primal space.

Abstract Let R be a commutative ring and Xi.c (R) denotes the set of all integrally closed maximal subrings of R. It is shown that if R is a non-field G-domain, then there exists S ∈ Xi.c (R) with (S : R) = 0. If K is an algebraically closed field which is not absolutely algebraic, then we prove that the polynomial ring K[X] has an integrally closed maximal subring with zero conductor too; a characterization

Let 𝐺 be a nonabelian group. We say that 𝐺 has an abelian partition if there exists a partition of 𝐺 into commuting subsets A1,A2,…,An of 𝐺 such that |Ai|⩾2 for each i=1,2,…,n. This paper investigates problems relating to groups with abelian partitions. Among other results, we show that every finite group is isomorphic to a subgroup of a group with an abelian partition and also isomorphic to a

We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.

Let 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1H)G for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

Let 𝑛 be an integer greater than or equal to 3, and let (R,Δ) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group U2⁢n+1⁡(R,Δ) normalised by a relative elementary subgroup EU2⁢n+1⁡((R,Δ),(I,Ω)), then there is an odd form ideal (J,Σ) such that

We classify the locally compact second-countable (l.c.s.c.) groups 𝐴 that are abelian and topologically characteristically simple. All such groups 𝐴 occur as the monolith of some soluble l.c.s.c. group 𝐺 of derived length at most 3; with known exceptions (specifically, when 𝐴 is Qn or its dual for some n∈N), we can take 𝐺 to be compactly generated. This amounts to a classification of the possible

Let 𝐴 be a finite group acting by automorphisms on the finite group 𝐺. We introduce the commuting graph Γ⁢(G,A) of this action and study some questions related to the structure of 𝐺 under certain graph theoretical conditions on Γ⁢(G,A).

Abstract:Let be a CM elliptic curve defined over . We establish an asymptotic formula for the number of primes for which the reduction modulo of is cyclic over short intervals. This extends previous work of Akbary, Cojocaru, M. R. Murty, V. K. Murty, and Serre. Also, in light of the work of Freiberg, Kim, Kurlberg, Liu, and Wu, we estimate the average exponent of and the second moment of the number

Abstract:We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product decomposition for a noncommutative Cartan subalgebra is unique. We relate the property of being a noncommutative Cartan subalgebra to aperiodic inclusions and effectivity

Abstract:Let be a quadratic, monic polynomial with coefficients in , where is a localization of a number ring . In this paper, we first prove that if is non-square and non-isotrivial, then there exists an absolute, effective constant with the following property: for all primes such that the reduced polynomial is non-square and non-isotrivial, the squarefree Zsigmondy set of is bounded by . Using this

Abstract:Let be an interval and let , be arbitrary elements of and , respectively, with . The paper contains the proof of the estimate and it is shown that cannot be replaced by a smaller universal constant. The argument rests on the existence of a special function enjoying appropriate size and concavity requirements.

Abstract:Let be a finite group, and a prime number; a character of is called -constant if it takes a constant value on all the elements of whose order is divisible by . This is a generalization of the very important concept of characters of -defect zero. In this paper, we characterize the finite -solvable groups having a faithful irreducible character that is -constant and not of -defect zero, and

Abstract:Let be an integer greater than three and be an odd prime. In this paper we prove that at least one of the following groups: , , , or is a Galois group of for infinitely many integers . This is achieved by making use of a slight modification of a group theory result of Khare, Larsen, and Savin, and previous results of the author on the images of the Galois representations attached to cuspidal

Abstract:Let be a split connected reductive algebraic group, let be the corresponding affine Hecke algebra, and let be the corresponding asymptotic Hecke algebra in the sense of Lusztig. When , and the parameter is specialized to a prime power, Braverman and Kazhdan showed recently that for generic values of , has codimension two as a subalgebra of , and described a basis for the quotient in spectral

Abstract:We show that the stable homotopy groups of the -equivariant sphere spectrum and the -motivic sphere spectrum are isomorphic in a range. This result supersedes previous work of Dugger and the third author.

Abstract:We show that there are only finitely many triples of integers such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an -unit that is also a positive integer. The proof is based on a result of Corvaja and Zannier and thus is ultimately a consequence of the Schmidt subspace theorem.

In this paper, we mainly investigate the conjugation of the sylowizer that was introduced by Gaschütz (Math Z 122(4):319–320, 1971) and study the p-supersolvability of finite groups by analyzing the intersection between \(O^{p}(G)\) and sylowizers of p-subgroups. As a continuation of research (Lei and Li in Arch Math (Basel) 114:367–376, 2020), we also give some characterizations on p-nilpotent groups

We consider a semidirect product G = K ⋉ V where K is a connected compact Lie group acting by automorphisms on a finite-dimensional real vector space V equipped with an inner product <, >. By Ĝ we denote the unitary dual of G and by 𝔤‡/G we denote the space of admissible coadjoint orbits, where 𝔤 is the Lie algebra of G. It was indicated by Lipsman that the correspondence between Ĝ and 𝔤‡/G is bijective

Given a sequence of independent standard Gaussian variables (Zn), the classical Pisier algebra P is the class of all continuous functions f on the unit circle T such that for each t ∈ 𝕋, the random Fourier series \( {\sum}_{n\in \mathrm{\mathbb{Z}}}{Z}_n\hat{f}(n)\times \exp \left(2\pi \mathrm{i} nt\right) \) converges in L2 and the corresponding sums constitute a Gaussian process that admits a continuous

The notion of essential amenability of Banach algebras has been defined and investigated. We introduce this concept for Fr´echet algebras. Then numerous well-known results concerning the essential amenability of Banach algebras are generalized for Fréchet algebras. Moreover, related results for the Segal–Fréchet algebras are also provided. As the main result, it is proved that if (𝒜,pℯ) is an amenable

For any p ∈ (0, ∞], ω > 0, β ∈ (0, 2ω), and any measurable set B ⊂ Id ≔ [0, d], μB ≤ β, we deduce a sharp Remez-type inequality$$ {\left\Vert {x}_{\pm}\right\Vert}_{\infty}\le \frac{{\left\Vert {\left(\varphi +c\right)}_{\pm}\right\Vert}_{\infty }}{{\left\Vert \varphi +c\right\Vert}_{L_p\left({I}_{2\upomega}\backslash {B}_y^c\right)}}{\left\Vert x\right\Vert}_{L_p\left({I}_d\backslash B\right)} $$

For any partition 𝜎 of the set ℙ of all primes, it is proved that if every complete Hall set of type 𝜎 for a finite 3'-group G is reducible into a certain subgroup H of G, then H is 𝜎-subnormal in G.