In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function P:ℤ≥0→ℤ, then there exists an integer N>0 such that if (X,ℱ) is a canonical or nef model of a foliation of general type with Hilbert polynomial χ⁢(X,𝒪X⁢(m⁢Kℱ))=P⁢(m) for all m∈ℤ≥0, then |m⁢Kℱ| defines a birational map for all m≥N.

In this paper we discuss coefficient problems for functions in the class 𝒞0⁢(k). This family is a subset of 𝒞, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate

In 2018, Das et al. [Characterization of rough weighted statistical statistical limit set, Math. Slovaca 68(4) (2018), 881–896] (or, Ghosal et al. [Effects on rough 𝓘-lacunary statistical convergence to induce the weighted sequence, Filomat 32(10) (2018), 3557–3568]) established the result: The diameter of rough weighted statistical limit set (or, rough weighted 𝓘-lacunary limit set) of a sequence

Let x = {xn}n=1∞ be a sequence of positive numbers, and 𝓙x be the collection of all subsets A ⊆ ℕ such that ∑k∈Axk < +∞. The aim of this article is to study how large the summable subsequence could be. We define the upper density of summable subsequences of x as the supremum of the upper asymptotic densities over 𝓙x, SUD in brief, and we denote it by D*(x). Similarly, the lower density of summable

In this present investigation, we will concern with the family of normalized analytic error function which is defined by

Let G be a p-group, and let χ be an irreducible character of G. The codegree of χ is given by |G:ker(χ)|/χ(1). Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree

Let ℜ be a ring with center Z⁢(ℜ). In this paper, we study the higher-order commutators with power central values on rings and algebras involving generalized derivations. Motivated by [A. Alahmadi, S. Ali, A. N. Khan and M. Salahuddin Khan, A characterization of generalized derivations on prime rings, Comm. Algebra 44 2016, 8, 3201–3210], we characterize generalized derivations and related maps that

In this paper, we consider a natural extension in the context of d-orthogonality for asymptotic analysis of orthogonal polynomials. We introduce, for several d-orthogonal polynomials, asymptotic expansions in terms of d-Hermite ones. From these expansions, several limits between d-orthogonal polynomials are obtained.

A hybrid second derivative three-step method of order 7 is proposed for solving first order stiff differential equations. The complementary and main methods are generated from a single continuous scheme through interpolation and collocation procedures. The continuous scheme makes it easy to interpolate at off-grid and grid points. The consistency, stability, and convergence properties of the block

This paper is concerned with the maximum likelihood estimators of the Beta-Pareto distribution introduced in Akinsete et al. (2008), which comes from the mixing of two probability distributions, Beta and Pareto. Since these estimators cannot be obtained explicitly, we use nonlinear optimization methods that numerically provide these estimators. The methods we investigate are the method of Newton-Raphson

There exist pentadiagonal matrices which are diagonally similar to symmetric matrices. In this work we describe explicitly the diagonal matrix that gives this transformation for certain pentadiagonal matrices. We also consider particular classes of pentadiagonal matrices and obtain recursive formulas for the characteristic polynomial and explicit formulas for their eigenvalues.

Hydrocarbon reservoirs’ formation damage is one of the essential issues in petroleum industries that is caused by drilling and production operations and completion procedures. Ineffective implementation of drilling fluid during the drilling operations led to large volumes of filtrated mud penetrating into the reservoir formation. Therefore, pore throats and spaces would be filled, and hydrocarbon mobilization

In this work the complete version of Stirling’s formula, which is composed of the standard terms and an infinite asymptotic series, is used to obtain exact values of the logarithm of the gamma function over all branches of the complex plane. Exact values can only be obtained by regularization. Two methods are introduced: Borel summation and Mellin–Barnes (MB) regularization. The Borel-summed remainder

The rapid growth in the amount of data in the digital world leads to the need for data compression, and so forth, reducing the number of bits needed to represent a text file, an image, audio, or video content. Compressing data saves storage capacity and speeds up data transmission. In this paper, we focus on the text compression and provide a comparison of algorithms (in particular, entropy-based arithmetic

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard

We design a mechanism of the players’ sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal

Let G be a simple graph of order n. The Estrada index and Laplacian Estrada index of G are defined by E E ( G ) = ∑ i = 1 n e λ i ( A ( G ) ) and L E E ( G ) = ∑ i = 1 n e λ i ( L ( G ) ) , where { λ i ( A ( G ) ) } i = 1 n and { λ i ( L ( G ) ) } i = 1 n are the eigenvalues of its adjacency and Laplacian matrices, respectively. In this paper, we establish almost sure upper bounds and lower bounds

In this paper, we define and study the concept of the factorizable semihypergroup, i.e., a semihypergroup that can be written as a hyperproduct of two proper sub-semihypergroups. We consider some classes of semihypergroups such as regular semihypergroups, hypergroups, regular hypergroups, and polygroups and investigate their factorization property.

A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response

In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally

In this paper, we consider the linear fractional differential equation By obtaining the Green’s function we derive the Lyapunov-type inequality for such a boundary value problem. Furthermore, we use the contraction mapping theorem to study the existence of a unique solution for the corresponding nonlinear problem.

In this paper, we prove weighted norm inequalities for vector-valued multilinear singular integrals with nonsmooth kernels and commutators on generalized weighted Morrey space.

A number of families of q-extensions of analytic functions in the open unit disk $\mathbb{U}$ have been defined by means of basic (or q-)calculus and considered from many distinctive prospectives and viewpoints. In this paper, we generalize and study certain subclasses of analytic functions involving higher-order q-derivative operators. We settle characteristic equations for these presumably new classes

We first introduce the weighted averaged projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces and then we establish some inequalities for the weighted averaged projection sequence. Using the inequalities, we prove the asymptotic regularity and the $\unicode[STIX]{x1D6E5}$ -convergence of the weighted averaged projection sequence. Furthermore, we prove the strong convergence of the sequence

Many phenomena in geometry and analysis can be explained via the theory of $D$ -modules, but this theory explains close to nothing in the non-archimedean case, by the absence of integration by parts. Hence there is a need to look for alternatives. A central example of a notion based on the theory of $D$ -modules is the notion of holonomic distributions. We study two recent alternatives of this notion

This paper completes the construction of $p$ -adic $L$ -functions for unitary groups. More precisely, in Harris, Li and Skinner [‘ $p$ -adic $L$ -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure’, Doc. Math.Extra Vol. (2006), 393–464 (electronic)], three of the authors proposed an approach to constructing such $p$ -adic $L$ -functions (Part I). Building on more recent

This paper focuses on the bargaining behavior of supply chain members and studies the stability of the bargaining system. There are two forms of bargaining in the process of negotiation. One is separate bargaining, and the other is that the automobile manufacturers form an alliance and bargain with the supplier collectively. We explore the influence of bargaining power and adjustment speed on the stability

Trajectory planning is the foundation of locomotion control for quadruped robots. This paper proposes a bionic foot-end trajectory which can adapt to many kinds of terrains and gaits based on the idea of trajectory planning combining Cartesian space with joint space. Trajectory points are picked for inverse kinematics solution, and then quintic polynomials are used to plan joint space trajectories

Industrial ecology is an advanced form and ideal model of modern industrial development, in which the industrial ecosystem is the core. Based on the PSR model, this paper builds a comprehensive evaluation index system for urban industrial ecosystem development and selects 14 prefecture-level cities in Liaoning Province of the traditional industrial area in Northeastern China as cases to calculate the

Hear the biggest stories from the world of science | 02 July 2020

Chemokines and their receptors mediate cell migration, which influences multiple fundamental biological processes and disease conditions, such as inflammation and cancer1. Although ample efforts have been invested into the structural investigation of the chemokine receptors and receptor–chemokine recognition2–4, less is known about endogenous chemokine-induced receptor activation and G protein coupling

Emissions of sulfur hexafluoride soared over the 40 years to 2018, despite some countries’ efforts to curb its use.

Conservation scientist Claudine Loisel is spellbound by the stained-glass splendours that survived a devastating fire at Paris’s famous cathedral.

A recent fire at a natural history museum in Minas Gerais is forcing some researchers to relive the pain of losing priceless specimens and artefacts.

Time to prepare for another mission.

Gravitational-wave detector goes quantum to overcome the limits of the Heisenberg uncertainty principle. Plus: why it’s so hard to know when we will reach herd immunity to COVID-19, and how flying snakes glide through the air.

Indirect imaging of potential-energy landscapes in materials.

When waves propagate through a weak disordered potential with correlation length larger than the wavelength, they form channels (branches) of enhanced intensity that keep dividing as the waves propagate1. This fundamental wave phenomenon is known as branched flow. It was first observed for electrons1,2,3,4,5,6 and for microwave cavities7,8, and it is generally expected for waves with vastly different

Mutations in proteolipid protein 1 (PLP1) result in failure of myelination and neurological dysfunction in the X-linked leukodystrophy Pelizaeus-Merzbacher disease (PMD)1,2. Most PLP1 mutations, including point mutations and supernumerary copy variants, lead to severe and fatal disease. PLP1-null patients and mice, however, can display comparatively mild phenotypes, suggesting that PLP1-suppression

The latest science news, in brief.

Fibroblast, epithelial and endothelial cells aid organ-specific defence.

Endogenous proteins tracked across the blood-brain barrier.

The European Union must improve how it collects forest data, which are essential to its ambitions in biodiversity and climate change.

Effects of vacuum fluctuations in a gravitational-wave detector.

Dental enamel is a principal component of teeth1, and has evolved to bear large chewing forces, resist mechanical fatigue and withstand wear over decades2. Functional impairment and loss of dental enamel, caused by developmental defects or tooth decay (caries), affect health and quality of life, with associated costs to society3. Although the past decade has seen progress in our understanding of enamel

Forests provide a series of ecosystem services that are crucial to our society. In the European Union (EU), forests account for approximately 38% of the total land surface1. These forests are important carbon sinks, and their conservation efforts are vital for the EU’s vision of achieving climate neutrality by 20502. However, the increasing demand for forest services and products, driven by the bioeconomy

The interiors of giant planets remain poorly understood. Even for the planets in the Solar System, difficulties in observation lead to large uncertainties in the properties of planetary cores. Exoplanets that have undergone rare evolutionary processes provide a route to understanding planetary interiors. Planets found in and near the typically barren hot-Neptune ‘desert’1,2 (a region in mass–radius

The mammalian immune system implements a remarkably effective set of mechanisms for fighting pathogens1. Its main components are haematopoietic immune cells, including myeloid cells that control innate immunity, and lymphoid cells that constitute adaptive immunity2. However, immune functions are not unique to haematopoietic cells, and many other cell types display basic mechanisms of pathogen defence3

Oral antiretroviral agents provide life-saving treatments for millions of people living with HIV, and can prevent new infections via pre-exposure prophylaxis1,2,3,4,5. However, some people living with HIV who are heavily treatment-experienced have limited or no treatment options, owing to multidrug resistance6. In addition, suboptimal adherence to oral daily regimens can negatively affect the outcome

Valence electrons contribute a small fraction of the total electron density of materials, but they determine their essential chemical, electronic and optical properties. Strong laser fields can probe electrons in valence orbitals1,2,3 and their dynamics4,5,6 in the gas phase. Previous laser studies of solids have associated high-harmonic emission7,8,9,10,11,12 with the spatial arrangement of atoms

Plant hormones coordinate responses to environmental cues with developmental programs1, and are fundamental for stress resilience and agronomic yield2. The core signalling pathways underlying the effects of phytohormones have been elucidated by genetic screens and hypothesis-driven approaches, and extended by interactome studies of select pathways3. However, fundamental questions remain about how information

Mammalian cells reorganize their proteomes in response to nutrient stress through translational suppression and degradative mechanisms using the proteasome and autophagy systems1,2. Ribosomes are central targets of this response, as they are responsible for translation and subject to lysosomal turnover during nutrient stress3,4,5. The abundance of ribosomal (r)-proteins (around 6% of the proteome;

The vascular interface of the brain, known as the blood–brain barrier (BBB), is understood to maintain brain function in part via its low transcellular permeability1,2,3. Yet, recent studies have demonstrated that brain ageing is sensitive to circulatory proteins4,5. Thus, it is unclear whether permeability to individually injected exogenous tracers—as is standard in BBB studies—fully represents blood-to-brain

The mechanistic target of rapamycin complex 1 (mTORC1) is a key metabolic hub that controls the cellular response to environmental cues by exerting its kinase activity on multiple substrates1,2,3. However, whether mTORC1 responds to diverse stimuli by differentially phosphorylating specific substrates is poorly understood. Here we show that transcription factor EB (TFEB), a master regulator of lysosomal

The cortex organizes sensory information to enable discrimination and generalization1,2,3,4. As systematic representations of chemical odour space have not yet been described in the olfactory cortex, it remains unclear how odour relationships are encoded to place chemically distinct but similar odours, such as lemon and orange, into perceptual categories, such as citrus5,6,7. Here, by combining chemoinformatics

The measurement of minuscule forces and displacements with ever greater precision is inhibited by the Heisenberg uncertainty principle, which imposes a limit to the precision with which the position of an object can be measured continuously, known as the standard quantum limit1,2,3,4. When light is used as the probe, the standard quantum limit arises from the balance between the uncertainties of the

Ribosomes accurately decode mRNA by proofreading each aminoacyl-tRNA that is delivered by the elongation factor EF-Tu1. To understand the molecular mechanism of this proofreading step it is necessary to visualize GTP-catalysed elongation, which has remained a challenge2,3,4. Here we use time-resolved cryogenic electron microscopy to reveal 33 ribosomal states after the delivery of aminoacyl-tRNA by

Nuclear processes, such as V(D)J recombination, are orchestrated by the three-dimensional organization of chromosomes at multiple levels, including compartments1 and topologically associated domains (TADs)2,3 consisting of chromatin loops4. TADs are formed by chromatin-loop extrusion5,6,7, which depends on the loop-extrusion function of the ring-shaped cohesin complex8,9,10,11,12. Conversely, the cohesin-release

Scientists carrying out routine monitoring in China have found that pigs are widely infected with a virus with the potential to trigger a pandemic. Plus, cosmic rays could explain why DNA is right-handed, and quantum computers work better when no one’s around.

In this paper we derive local L2 error estimates for penalized least-squares approximation on the d-dimensional unit sphere Sd⊆Rd+1, given noisy, scattered, local data representing an underlying function from a Sobolev space of order s>d∕2 defined on a non-empty connected open set Ω⊆Sd with Lipschitz-continuous boundary. The quadratic regularization functional has two terms, one measuring the squared