We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.

Binary images are prevalent in digital systems and have a wide range of applications including texts, fingerprint recognition, handwritten signatures, stellar astronomy, barcodes, and vehicle license plates. The recorded binary images are often degraded by blur and additive noise due to environmental effects and imperfections in the imaging system. In this paper, we study the problem of recovering

In this paper, we propose a shift-dependent uncertainty measure related to extropy. Dynamic versions of the proposed measure are also considered along with their various properties. Nonparametric estimators for the new measures are also obtained. The methods are illustrated using simulated and real data sets.

In this paper, we propose a novel numerical technique to a 2D multi-term time and space fractional Bloch-Torrey equations defined on an irregular convex domains. First, we consider the problem with space integral Laplacian operator. We present the semi-discrete and fully-discrete schemes by using the L1 formula on a temporal graded mesh and an unstructured-mesh Galerkin finite element method (FEM)

We prove a weighted Sobolev trace embedding in the upper half‐space and give its best constant. This embedding can be employed to study a number of critical boundary problems. In this direction, we obtain existence and nonexistence results for a class of semilinear elliptic equations with nonlinear boundary conditions involving critical growth. These equations are closely related to the study of self‐similar

An effective lower bound on the entropy of some explicit quadratic plane Cremona transformations is given. The motivation is that such transformations (Hénon maps, or Feistel ciphers) are used in symmetric key cryptography. Moreover, a hyperbolic plane Cremona transformation g is rigid, in the sense of [5], and under further explicit conditions some power of g is tight.

This paper considers the following fundamental problem about intersections in projective space: When is the intersection of a (varying) curve with a (fixed) hypersurface a general set of points on the hypersurface?

Recent progress in optical fibers is impressive, while nonlinear Schrödinger-type models are seen in fiber optics and other fields (such as ferromagnetism, plasma physics, Bose–Einstein condensation and oceanography). Hereby, our symbolic computation on a three-coupled variable-coefficient nonlinear Schrödinger system is performed, for the picosecond-pulse attenuation/amplification in a multicomponent

In this paper, we study the solution theory in the Sobolev space for the nonlinear differential equation: Dtny(t)=f(t,y),n≥1 with given initial values Dtky(0)=dk,k=0,1,…,n−1,n≥1. By assuming that function f(t,y)∈Lp(0,b) and tβf(t,y) is continuous with respect to y where p>1 and 0≤β<1, we prove that this problem admits a solution in space Wpn(0,b) and the solution is absolutely stable in the L∞-norm

The present study deals with a thermal analysis of porous fins subjected to internal heat generation, convection, and radiation energy transfer considering an actual system of analysis under the moving condition of the fin. The main aspiration to carryout this analysis is to establish a correct approach to derive the governing equation for energy transfer in porous fins. The physical explanation was

Let vi be vectors in Rd and {εi} be independent Rademacher random variables. Then the Littlewood–Offord problem entails finding the best upper bound for supx∈RdP(∑εivi=x). Generalizing the uniform bounds of Littlewood–Offord, Erdős and Kleitman, a recent result of Dzindzalieta and Juškevičius provides a non-uniform bound that is optimal in its dependence on ‖x‖2. In this short note, we provide a simple

This study first investigates robust iterative learning control (ILC) issue for a class of two-dimensional linear discrete singular Fornasini–Marchesini systems (2-D LDSFM) under iteration-varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2-D LDSFM is derived. A simple P-type ILC law is proposed such that the ILC tracking

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them

The productivity of researchers and the impact of the work they do are a preoccupation of universities, research funding agencies, and sometimes even researchers themselves. The h-index (h) is the most popular of different metrics to measure these activities. This research deals with presenting a practical approach to model the h-index based on the total number of citations (NC) and the duration from

We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.

In natural ecosystems, the efficiency of energy transfer from resources to consumers determines the biomass structure of food webs. As a general rule, about 10% of the energy produced in one trophic level makes it up to the next1–3. Recent theory suggests this energy transfer could be further constrained if rising temperatures increase metabolic growth costs4, although experimental confirmation in

A Correction to this paper has been published: https://doi.org/10.1038/s41586-021-03379-5.

Electro-acoustics researcher David Monacchi preserves the soundscapes of endangered forests to convey the risks they face.

Just 1% of scientists capture more than one-fifth of all citations globally — and the inequality is growing.

Trapped in a holding pattern, and nostalgic for lab lunches and field trips, researchers share their hopes for a lockdown-free future.

Tempted to try your hand at a new technique? These tools will help you on your way.

Explore whether the coronavirus can spread from frozen wildlife, remember the father of the Anthropocene and get to know the microbial ecosystem on our skin.

AbstractWe introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of examples. Among other properties, we prove the characteristic leaf correspondence

We construct some braided quantum groups over the circle group. These are analogous to the free orthogonal quantum groups. They generalise the braided quantum SU(2) groups for a complex deformation parameter. We describe their irreducible representations and fusion rules and study when they are monoidally equivalent. A key tool here is to describe the bosonisation of our braided compact quantum groups

Let d and n be positive integers and let K be a totally real number field of discriminant d and degree n. We construct a theta series \(\theta _{K} \in {\mathcal {M}}_{d,n}\), where \({\mathcal {M}}_{d,n}\) is a space of modular forms defined in terms of n and d. Moreover, if d is square free and n is at most 4 then \(\theta _{K}\) is a complete invariant for K. We also investigate whether or not the

Kida’s formula in classical Iwasawa theory relates the Iwasawa \(\lambda \)-invariants of p-extensions of number fields. Analogue of this formula was subsequently established for the Iwasawa \(\lambda \)-invariants of Selmer groups under an appropriate \(\mu =0\) assumption. In this paper, we give a conceptual (but conjectural) explanation that such a formula should also hold when \(\mu \ne 0\). The

Let V(T) denote the number of sign changes in \(\psi (x) - x\) for \(x\in [1, T]\). We show that \(\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi + 1.867\cdot 10^{-30}\), where \(\gamma _{1} = 14.13\ldots \) denotes the ordinate of the lowest-lying non-trivial zero of the Riemann zeta-function. This improves on a long-standing result by Kaczorowski.

We provide a new and very short proof of the fact that a spherical functor between certain triangulated categories induces an auto‐equivalence.

Inspired by work of Lipshitz–Sarkar, we show that the module structure on link Floer homology detects split links. Using results of Ni, Alishahi–Lipshitz, and Lipshitz–Sarkar, we establish an analogous detection result for sutured Floer homology.

Montel’s fundamental normality test (published in 1912) provides a strong sufficient condition for normality: a family \(\mathscr {F}\) of functions meromorphic in a region \(\varOmega \) is normal there if there exist three distinct values a, b, c in the extended complex plane \({\mathbb {C}}_\infty \) such that each f in \(\mathscr {F}\) omits in \(\varOmega \) each of these values. In 1954 Montel

We study the maximum modulus set, \({{\mathcal {M}}}(p)\), of a polynomial p. We are interested in constructing p so that \({{\mathcal {M}}}(p)\) has certain exceptional features. Jassim and London gave a cubic polynomial p such that \({{\mathcal {M}}}(p)\) has one discontinuity, and Tyler found a quintic polynomial \({\tilde{p}}\) such that \({{\mathcal {M}}}({\tilde{p}})\) has one singleton component

We study the directed polymer model for general graphs (beyond \({\mathbb {Z}}^d\)) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an \(L^2\) region, and of very strong disorder, in terms of properties of the graph and of the random walk. We study in some detail (biased) random walk on various trees including the Galton–Watson trees

We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching two different plane waves \(A_j\mathrm {e}^{\mathrm {i}\phi _j}\mathrm {e}^{-2\mathrm {i}B_jx}\), \(j=1,2\) as \(x\rightarrow \pm \infty \). Using Riemann–Hilbert techniques and Deift–Zhou steepest descent arguments, we study the long-time asymptotics of the solution. We detect that each of

In this paper we are concerned with a long-standing conjecture of Huneke and Wiegand. We introduce a new class of ideals and prove that each ideal from such class satisfies the conclusion of the conjecture in question. We also study the relation between the class of Burch ideals and that of the ideals we define, and construct several examples that corroborate our results.

The purpose of this research is to introduce a Jungck–S iterative method with –convexity and hence unify different comparable iterative schemes existing in the literature. A Jungck–S orbit is constructed, and escape radius is derived with our scheme. A new escape radius is also obtained for generating the fractals. Julia and Mandelbrot set are visualized with the help of proposed algorithms based on

This paper is about a novel representation based on lossless encoding for medical images. It relies on directional codes for efficient storage and transmission. Image compression is a recent research, where removal or elimination of redundant information is carried out in an image. In this paper, for medical image compression, an edge- and texture-based entropy coding is presented. The proposed work

The purpose of this paper is to present an example of an Ordinary Differential Equation \(x'=F(x)\) in the infinite-dimensional Hilbert space \(\ell ^2\) with F being of class \(\mathcal {C}^1\) in the Fréchet sense, such that the origin is an asymptotically stable equilibrium point but the spectrum of the linearized operator DF(0) intersects the half-plane \(\mathfrak {R}(z)>0\). The possible existence

In this paper, we investigate the asymptotic dynamics of a time-periodic parasitic–mutualistic model of mistletoes and birds in heterogeneous environment with the especial concerns over the spreading–vanishing scenarios, in which the Stefan class free boundary is introduced as the spreading frontier. By defining the ecological reproduction number and generalizing it as the spatial-temporal risk index

In this paper, we prove the existence of a random exponential attractor (a positively invariant, compact, random set with finite fractal dimension that attracts any trajectory exponentially) for the 3D non-autonomous damped Navier–Stokes equation with additive noise, which implies that the asymptotic behavior of solutions for the equation can be described by finite independent parameters. The key and

We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order \(n-1\) with \(n\ge 3\) and \(d\ge 2\). If \(\varepsilon \ll 1\) is the size of the initial datum, we prove that the lifespan \(T_\varepsilon \) of solutions is \(O(\varepsilon ^{-A(n-2)^-})\) where \(A\equiv A(d,n)= 1+\frac{3}{d-1}\) when n is even and \(A= 1+\frac{3}{d-1}+\max (\frac{4-d}{d-1}

For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure of this control set is proved.

We study the discrete dynamics of standard (or left) polynomials $f(x)$ over division rings D. We define their fixed points to be the points $\lambda \in D$ for which $f^{\circ n}(\lambda )=\lambda $ for any $n \in \mathbb {N}$, where $f^{\circ n}(x)$ is defined recursively by $f^{\circ n}(x)=f(f^{\circ (n-1)}(x))$ and $f^{\circ 1}(x)=f(x)$. Periodic points are similarly defined. We prove that $\lambda

We consider a nonlinear parametric Neumann problem driven by the anisotropic (p, q)-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result

Elicitors, such as salicylic acid (SA), stand as the effective agents that are applied to plant cell suspension cultures for the fabrication of biomaterials. At this project, we have studied the elicitor effects on the increase in phenols, PAL activities, POX, and CAT enzymes that exist in the cell culture of Salvia leriifolia. Upon the addition of SA to the cell culture, an increase has been detected

This study highlights, for the first time, the effect of Algerian nettle (Urtica dioïca L.) water extract against some phytopathogens bacteria. Results showed that water extract exhibited high level of total phenol content (261.7 ± 5.1 mg g−1 GAE) and a remarkable antioxidant activity (IC50 = 20.0 ± 0.6 µg mL−1) comparable to Trolox as reference (IC50 = 16.5 ± 0.5 µg mL−1). Moreover, results showed

In this paper, we consider the generalized porous medium equation. For small initial data u0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global

Presently, a green Internet of Things (IoT) based energy aware network plays a significant part in the sensing technology. The development of IoT has a major impact on several application areas such as healthcare, smart city, transportation, etc. The exponential rise in the sensor nodes might result in enhanced energy dissipation. So, the minimization of environmental impact in green media networks

Following (Shevtsova, 2013) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen’s, Rozovskii’s, and Wang–Ahmad’s inequalities and their structural improvements obtained in our previous works. The above inequalities involve algebraic truncated third-order moments and the classical

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized

Central and East European (CEE) countries are attractive among emerging markets due to a combination of factors such as economic growth and market potential. Although the CEE countries as a whole have a very high degree of connectivity, each country has different market opportunities and external environment, so agricultural enterprises wanting to enter the CEE market must take into account the diverse

Diversification in a portfolio is an important tool for the systematic risk management that is inherent to different asset classes. The composition of a portfolio with domestic and international assets is seen as one of the main alternatives for building a diversified portfolio, as this approach tends to reduce portfolio return exposure depending on country factors. However, in scenarios where industry

A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate

Kernel partial least squares regression (KPLS) is a non-linear method for predicting one or more dependent variables from a set of predictors, which transforms the original datasets into a feature space where it is possible to generate a linear model and extract orthogonal factors also called components. A difficulty in implementing KPLS regression is determining the number of components and the kernel

For spaces of analytic functions defined on an open set in \({\mathbb {C}}^n\) that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces for which this result holds true consist of the Hardy space \(H^p({\mathbb {D}}^n) \, (0< p < \infty )\), the Drury–Arveson space \({\mathcal {H}}^2_n\), and

In the present paper, we investigate an eddy current problem in a three-dimensional domain containing a moving non-magnetic workpiece. A time discretization scheme based on the backward Euler method is proposed to approximate the original problem. The convergence of the scheme is proved using the Reynolds transport theorem and the corresponding error estimates are derived under appropriate assumptions

An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives was obtained in Yang and Srivastava (Commun Nonlinear Sci Numer Simul 29(1–3):499–504, 2015). In this paper, we obtain the numerical solution of damped forced oscillator problems by employing the operational matrix of integration of Bernoulli orthonormal

We suggest a sufficient setting on any linear space of sequences $\mathcal{V}$ such that the class $\mathbb{B}^{s}_{\mathcal{V}}$ of all bounded linear mappings between two arbitrary Banach spaces with the sequence of s-numbers in $\mathcal{V}$ constructs a map ideal. We define a new sequence space $(\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }$ for definite functional υ by the domain of $(r_{1},r_{2})$

In this paper, we consider and investigate a convex minimization problem of the sum of two convex functions in a Hilbert space. The forward-backward splitting algorithm is one of the popular optimization methods for approximating a minimizer of the function; however, the stepsize of this algorithm depends on the Lipschitz constant of the gradient of the function, which is not an easy work to find in

Let μ be a positive finite Borel measure on the unit circle. The associated Dirichlet space D(μ) consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against the Poisson integral of μ. We give a sufficient condition on a Borel subset E of the unit circle which ensures that E is a uniqueness set for D(μ). We also give somes examples of positive Borel