AbstractWe propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.

Given a crossed module of groupoids N→G, we construct (1) a natural homomorphism from the product groupoid ℤ×(N⋊G)⇉N to the crossed product groupoid N⋊G⇉N and (2) a transgression map from the singular cohomology H∗(G•,ℤ) of the nerve of the groupoid G to the singular cohomology H∗−1(N⋊G)•,ℤ of the nerve of the crossed product groupoid N⋊G. The latter turns out to be identical to the transgression map

Recently in Charalambopoulos et al. (2020), we presented a methodology aiming at reconstructing bounded total variation (⁠|$TV$|⁠) conductivities via a technique simulating the so-called half-quadratic minimization approach, encountered in Aubert & Kornprobst (2002, Mathematical Problems in Image Processing. New York, NY: Springer). The method belongs to a duality framework, in which the auxiliary

AbstractThis paper considers the stationary problem of density-suppressed motility models proposed in Fu et al. (2012) and Liu et al. (2011) in one dimension with Neumman boundary conditions. The models consist of parabolic equations with cross-diffusion and degeneracy. We employ the global bifurcation theory and Helly compactness theorem to explore the conditions under which non-constant stationary

In this note we consider 1D problems within the context of a new class of elastic bodies. Under suitable conditions on the constitutive equations we prove instability and nonexistence of solutions similar to those in place for the linearized theory. The last section is devoted to describing the spatial behavior of the solutions.

The concern in this paper is the problem of finding—or, at least, approximating—functions, defined within and on the boundary of a tangential polygon, functions whose Laplacian is |$-1$| and which satisfy a homogeneous Robin boundary condition on the boundary. The parameter in the Robin condition is denoted by |$\beta $|⁠. The integral of the solution over the interior, denoted by |$Q$|⁠, is, in the

In this work, we propose mathematical formulations that detail the effect of the dielectric strength of dielectric material on the spatial distribution of electric field in an infinite space with a conducting plate. Using the dielectric strength of air as the maximum limit for the magnitude of electric field intensity and the equivalence of stored charge between two different zones, we determine the

We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces relative to weak generalized controlled deformation retracts. On ordinary coarse cohomology, our secondary cup product agrees with a secondary product defined by Roe. For coarsifications of topological coarse (co-)homology theories, our secondary cup and

AbstractReactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular importance for the simulation and control of secondary settling tanks (SSTs) in water resource recovery facilities (WRRFs), formerly known as wastewater treatment

AbstractA common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature

The general three-component nonlinear Schrödinger (gtc-NLS) equations are completely integrable and contain the self-focusing, defocusing and mixed cases, which are applied in many physical fields. In this paper, we would like to use the Fokas method to explore the initial-boundary value (IBV) problem for the gtc-NLS equations with a |$4\times 4$| matrix Lax pair on a finite interval based on the inverse

Let \((r_n)_{n=1}^\infty \) be a non-decreasing sequence of radii in \((0, \infty )\), and let \((\theta _n)_{n=1}^\infty \) be a sequence of independent random arguments uniformly distributed in \([0, 2\pi )\). In this paper, we establish a new sufficient condition on the sequence \((r_n)_{n=1}^\infty \) under which \((r_ne^{i\theta _n})_{n=1}^\infty \) is almost surely a zero set for Fock spaces

We consider the discontinuous piecewise differential equations of the form(dx1dtdx2dt)={a0(t)+a1(t)x1+....+an(t)x1n,if0⩽t⩽π,b0(t)+b1(t)x2+....+bm(t)x2m,ifπ⩽t⩽2π, where a0(t),a1(t),...,an(t) and b0(t),b1(t),...,bm(t) are 2π-periodic functions in the variable t, and we study the number of limit cycles of such equations on the cylinder. In this way we give exact bounds for the maximum number of limit

In this paper we determine extensions of higher degree between indecomposable modules over gentle algebras. In particular, our results show how such extensions either eventually vanish or become periodic. We give a geometric interpretation of vanishing and periodicity of higher extensions in terms of the surface underlying the gentle algebra. For gentle algebras arising from triangulations of surfaces

Analogs of Waring–Hilbert problem on Cantor sets are explored. The focus of this paper is on the Cantor ternary set C. It is shown that, for each m≥3, every real number in the unit interval [0,1] is the sum x1m+x2m+⋯+xnm with each xj in C and some n≤6m. Furthermore, every real number x in the interval [0,8] can be written as x=x13+x23+⋯+x83, the sum of eight cubic powers with each xj in C. Another

We discuss several results in electrostatics: Onsager’s inequality, an extension of Earnshaw’s theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible, we try to provide a brief historical context and references.

This is an elementary introduction to the representation theory of finite semigroups. We illustrate the Clifford–Munn correspondence between the representations of a semigroup and the representations of its maximal subgroups. The emphasis throughout is on naturally occurring examples.

The networks of this – primarily (but not exclusively) expository – compendium are strongly connected, finite directed graphs X, where each oriented edge (x,y) is equipped with a positive weight (conductance) a(x,y). We are not assuming symmetry of this function, and in general we do not require that along with (x,y), also (y,x) is an edge. The weights give rise to a difference operator, the normalised

We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator T that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous symmetric functions in which this operator is triangular. This allows us to compute the eigenvalues of T, which turn out to be nonnegative integers.

We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$, improving the previously known error term for the counting function as $T\to +\infty $. We also resolve some natural variants of the problem concerning points with prime coordinates and points that are visible from the origin.

This paper first proposes a statistic for measuring the correlation between two random variables. Because the data are usually polluted by noise and the feature of the data is usually task-relevant, this paper proposes to perform a transformation on the data before measuring their correlation. In addition, since the kernel method is a commonly used data transformation method in the field of machine

We describe a computationally efficient approach to resolving equations of the form \(C_1x^2 + C_2 = y^n\) in coprime integers, for fixed values of \(C_1\), \(C_2\) subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm–Liouville operator defined in terms of right and left fractional Riemann–Liouville

We extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states \(\rho ^{\otimes n}\) against convex combinations of quantum states \(\sigma ^{\otimes n}\) can be written as a regularized quantum relative entropy formula. We prove that

For a graph $\Gamma$, let $K(H_{\Gamma },\,1)$ denote the Eilenberg–Mac Lane space associated with the right-angled Artin (RAA) group $H_{\Gamma }$ defined by $\Gamma$. We use the relationship between the combinatorics of $\Gamma$ and the topological complexity of $K(H_{\Gamma },\,1)$ to explain, and generalize to the higher TC realm, Dranishnikov's observation that the topological complexity of a

This paper studies the Eulerian–Lagrangian and Eulerian–Eulerian approaches for the simulation of interaction between free surface flow and particles. The dynamics of the fluid as well as the transport of the particles in the Eulerian description is solved using the lattice Boltzmann method. To minimize artificial diffusion in particle transport the lattice Boltzmann method with direction-dependent

A certain type of queueing system that is quite common in manufacturing systems occurs when the time between the arrivals of items approximately follows an exponential distribution with rate λ, the services are mechanized and their times may be considered approximately constant (b). In Kendall notation, such a queueing system is well known as an M∕D∕1 queue; despite being one of the simplest queueing

Spatial generalized linear mixed models are commonly employed for modeling discrete spatial responses that are acquired on a continuous area. A standard assumption in these models is that the latent variables are normally distributed, however skewed residuals appear in some spatial generalized linear mixed models. In this study, we consider a closed skew Gaussian random field for the spatial latent

A new concept of a quantum-like mixture model is introduced. It describes the mixture distribution with the assumption that a point is generated by each Gaussian at the same time. The quantum-like mixture Gaussian improves the classification accuracy in machine learning by indicating that the uncertain points should not be assigned to any class. It increases the accuracy of the mixture Gaussian model

This paper presents a computationally efficient and robust evolutionary algorithm to find the better permutation of weighting phase factors in minimizing envelope fluctuations of orthogonal frequency division multiplexing signals. The proposed optimization method is called the seasons algorithm, in which its main inspiration is the growth and survival of trees in nature. This algorithm formulates fluctuation

Having control over your data is a right and a duty that every citizen has in our digital society. It is often that users skip entire policies of applications or websites to save time and energy without realizing the potential sticky points in these policies. Due to obscure language and verbose explanations majority of users of hypermedia do not bother to read them. Further, sometimes digital media

The notion of \(n\times m\)-valued Łukasiewicz algebras with negation (or \(NS_{n \times m}\)-algebras) was introduced by C. Sanza in Notes on \(n\times m\)-valued Łukasiewicz algebras with negation, Logic J. of the IGPL 12, 6 (2004), 499–507. These algebras constitute a non-trivial generalization of n-valued Łukasiewicz–Moisil algebras and they are a particular case of matrix Łukasiewicz algebras

This study deals with the classical and Bayesian estimation of reliability in a multicomponent stress–strength model by assuming that both stress and strength variables follow exponentiated Pareto distribution. First, the maximum likelihood method is used to estimate reliability. The asymptotic confidence interval is constructed. We also propose two bootstrap confidence intervals. Next, the Bayesian

The Pentagon Problem of Erdős problem asks to find an n-vertex triangle-free graph that is maximizing the number of 5-cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladký, Král’, Norin, and Razborov. Recently, Palmer suggested a more general problem of maximizing the number of 5-cycles in Kk+1-free graphs. Using flag algebras, we show that every Kk+1-free

To analyze multimodal three-dimensional medical images, interpolation is required for resampling which—unavoidably—introduces an interpolation error. In this work we describe the interpolation method used for imaging and neuroimaging and we characterize the Gibbs effect occurring when using such methods. In the experimental section we consider three segmented three-dimensional images resampled with

In this paper, we give necessary and sufficient conditions in terms of \(\mathcal {F}_{\nu }(f)\), the Bessel transform of f, to ensure that f belongs either to one of the generalized Lipschitz classes \(H_{\alpha }^m\) and \(h_{\alpha }^m\) for \(\alpha >0\).

The effectiveness of the national/regional healthcare system is one of the keys to prevent the spread of COVID-19. In the face of this unknown pandemic, where the healthcare system should continue to be promoted and improved are crucial decision issues. In the past, most studies have used the subjective opinions of experts for analysis and decision-making processes when investigating complicated decision-making

In this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication network system have been discussed in this paper to identify the critical components

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections

Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithmetic operations of fuzzy sets. The interval range is an important characterization of a fuzzy set. The interval range is also useful for analyses and applications

Three-term conjugate gradient methods have attracted much attention for large-scale unconstrained problems in recent years, since they have attractive practical factors such as simple computation, low memory requirement, better descent property and strong global convergence property. In this paper, a hybrid three-term conjugate gradient algorithm is proposed and it owns a sufficient descent property

Synchronous homopolar motors (SHMs) have been attracting the attention of researchers for many decades. They are used in a variety of equipment such as aircraft and train generators, welding inverters, and as traction motors. Various mathematical models of SHMs have been proposed to deal with their complicated magnetic circuit. However, mathematical techniques for optimizing SHMs have not yet been

Teaching the fundamentals of computer programming in a first course (CS1) is a complex activity for the professor and is also a challenge for them. Nowadays, there are several teaching strategies for dealing with a CS1 at the university, one of which is the use of analogies to support the abstraction process that a student needs to carry for the appropriation of fundamental concepts. This article presents

In this paper, we show the application of the meshless numerical method called “Generalized Finite Diference Method” (GFDM) for solving a model for tumor growth with nutrient density, extracellular matrix and matrix degrading enzymes, [recently proposed by Li and Hu]. We derive the discretization of the parabolic–hyperbolic–parabolic–elliptic system by means of the explicit formulae of the GFDM. We

This work presents a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) worldwide. The model presents the infection dynamics and emphasizes the role of the immune system: both the humoral response as well as the adaptive immune response. We built a mathematical model of delay differential equations describing a simplified view of the mechanism between

In this paper, we study the extended Hamilton–Jacobi Theory in the context of dynamical systems with symmetries. Given an action of a Lie group G on a manifold M and a G-invariant vector field X on M, we construct complete solutions of the Hamilton–Jacobi equation (HJE) related to X (and a given fibration on M). We do that along each open subset U⊆M, such that πU has a manifold structure and πU:U→πU

This paper is mainly concerned with the exact controllability for a class of impulsive ψ-Caputo fractional evolution equations with nonlocal conditions. First, by generalized Laplace transforms, a mild solution for considered problems is introduced. Next, by the Mönch fixed point theorem, the exact controllability result for the considered systems is obtained under some suitable assumptions. Finally

In the present work, different algorithms for contact detection in multibody systems based on smooth contact modelling approaches are presented. Beginning with the simplest ones, some difficult interactions are subsequently introduced. In addition, a brief overview on the different kinds of contact/impact modelling is provided and an underlining of the advantages and the drawbacks of each of them is

In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type $(\Xi (\Delta,r) )_{\psi }$ under definite function ψ. We introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on $(\Xi

The structure of faults beneath Salt Lake City, Utah, shows how the ground could liquefy during a shaking.

‘Superscattering’ material is used to construct a mini-doorway that is invisible in the microwave portion of the spectrum.

Aerial images boast a level of detail that could help the rover navigate to features of scientific interest.

As the world recovers, students still need help to get back on track, say Ruth Gotian and Christine Pfund.

Scientists praise the budget boost slated for the National Science Foundation, but worry the legislation could dampen international collaborations.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues to evolve around the world, generating new variants that are of concern based on their potential for altered transmissibility, pathogenicity, and coverage by vaccines and therapeutics1–5. Here we report that 20 human sera, drawn 2 or 4 weeks after two doses of BNT162b2, neutralize engineered SARS-CoV-2 with a USA-WA1/2020 genetic

Food bags, drink bottles and similar items account for the biggest share of plastic waste near the shore.

Cases of dengue fever plummeted in a trial of modified virus-resistant mosquitoes. Plus, four urgent questions about long COVID and clues to the mysterious origins of fast radio bursts.

Consider a generalized bidimensional continuous-time risk model with heavy-tailed claims and Brownian perturbations, in which the claim sizes from each line of business are dependent according to the dependence structure first proposed by [12] and later generalized by [21], while the claim-number processes from different lines of business are almost arbitrarily dependent. Under the assumption that

Consider the classical problem of rational simultaneous approximation to a point in \({\mathbb {R}}^{n}\). The optimal lower bound on the gap between the induced ordinary and uniform approximation exponents has been established by Marnat and Moshchevitin in 2018. Recently Nguyen, Poels and Roy provided information on the best approximating rational vectors to the points where the gap is close to this