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The Virasoro algebra, defined by the basis elements { L n , c ˆ } n ∈ Z with commutation relations [ L m , L n ] = (m − n) L m + n + δ m + n , 0 ⋅ (C m c ˆ) and [ L m , c ˆ ] = 0 , is an infinite-dimensional Lie algebra with many applications in various areas of Mathematics and Theoretical Physics. Here the symbol δ i , j denotes the Kronecker delta and C m = (m (m 2 − 1)) / 12. This algebra admits a natural Z -grading. Over an infinite field of characteristic different from 2 and 3, we describe the graded identities of the Virasoro algebra for this grading. It turns out that all these Z -graded identities are consequences of a collection of polynomials of degree 2, 3 and 4 and that they do not admit a finite basis. [ABSTRACT FROM AUTHOR]

This paper deals with the study of the existence and multiplicity of solutions for the class of nonlocal problems that have arised in recent developments in the mathematical physics of string theory and cosmology given by (P) { − Δ e − c Δ u + u = λ P (x) (u + f (x , u)) , in R N lim | x | → ∞ ⁡ u (x) = 0 , u ∈ H c , ∞ (R N) , where N ≥ 3 , c > 0 , λ > 0 , P : R N → R is a positive continuous function, f : R N × R → R is C 1 -function, e − c Δ is defined via a power series and H c , ∞ (R N) is a Hilbert space as introduced in [11]. The main tools used here are: the Minimax Theorems and a bifurcation result via variational methods due to Rabinowitz. [ABSTRACT FROM AUTHOR]

This paper focuses on the vector fields on the quasi-periodically forced circle flow { φ ˙ = ϱ + f (φ , θ) , θ ˙ = ω : = (1 , α). The system given above is the model in [14] , where Krikorian-Wang-You-Zhou prove that the system above is C ∞ rotations reducible by assuming that f is analytic in (φ , θ) ∈ T × T 2 , T = R / Z , the basic frequency ω is not super-Liouvillean and ρ f : = ρ (ϱ + f (φ , θ)) is Diophantine with respect to ω (ρ f is fibered rotation number of above system). As the application of the reducible result, some fundamental phenomena in mathematical physics such as the linearizable ones and those displaying mode-locking are locally dense for C ∞ -topology are also given in [14]. We, in this work, improve the result in [14] by weakening the regularity of f to be ultra-differentiable in θ ∈ T 2 , f is still analytic in φ ∈ T and ω , ρ f satisfy the same hypotheses in [14]. With the hypotheses above, we also prove that the flow above is C ∞ rotations reducible, thus the phenomena in mathematical physics given in [14] will also hold in our setting. Our proof, same as the one in [14] , is based on a modified KAM (Kolmogorov–Arnold–Moser) theorem but with the problem from analytic topology to ultra-differentiable topology. [ABSTRACT FROM AUTHOR]

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding eigenfunctions is one of the basic tasks in mathematical and computational physics. With the help of tensor neural network, the high dimensional integrations included in the loss functions of the machine learning process can be computed with high accuracy. The high accuracy of high dimensional integrations can improve the accuracy of the machine learning method for computing multi-eigenpairs of high dimensional eigenvalue problems. Here, we introduce the tensor neural network and design the machine learning method for computing multi-eigenpairs of the high dimensional eigenvalue problems. The proposed numerical method is validated with plenty of numerical examples. [ABSTRACT FROM AUTHOR]

We present a method to compute polynomial conservation laws for systems of partial differential equations (PDE s). The method only relies on linear algebraic computations and is complete, in the sense it can find a basis for all polynomial fluxes that yield conservation laws, up to a specified order of derivatives and degree. We compare our method to state-of-the-art algorithms based on the direct approach on a few PDE systems drawn from mathematical physics. [ABSTRACT FROM AUTHOR]

The interplay between set-theoretic solutions of the Yang–Baxter equation of Mathematical Physics, skew braces, regular subgroups, and Hopf–Galois structures has spawned a considerable body of literature in recent years. In a recent paper, Alan Koch generalised a construction of Lindsay N. Childs, showing how one can obtain bi-skew braces (G , ⋅ , ∘) from an endomorphism of a group (G , ⋅) whose image is abelian. In this paper, we characterise the endomorphisms of a group (G , ⋅) for which Koch's construction, and a variation on it, yield (bi-)skew braces. We show how the set-theoretic solutions of the Yang–Baxter equation derived by Koch's construction carry over to our more general situation, and discuss the related Hopf–Galois structures. [ABSTRACT FROM AUTHOR]

• Presentation of fine tuned assignments for HPC and parallel programming courses. • All assignments tested on students in three interconnected courses. • Covering vectorization, caches, multicore CPUs, GPUs, and multi-node problems. • Introducing 5 widely used technologies (TBB, OpenMP, CUDA, OpenMPI, and Spark). Programming courses usually focus on software-engineering problems like software decomposition and code maintenance. While computer-science lessons emphasize algorithm complexity, technological problems are usually neglected although they may significantly affect the performance in terms of wall time. As the technological problems are best explained by hands-on experience, we present a set of homework assignments focused on a range of technologies from instruction-level parallelism to GPU programming to cluster computing. These assignments are a product of a decade of development and testing on live subjects – the students of three performance-related software courses at the Faculty of Mathematics and Physics of the Charles University in Prague. [ABSTRACT FROM AUTHOR]

Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas of mathematics and physics and have attracted much attention over the last thirty years. In this paper we investigate whether conditions such as being a Lie algebra, cyclic, simple, semisimple, solvable, supersolvable or nilpotent in such an algebra are preserved by lattice isomorphisms. [ABSTRACT FROM AUTHOR]

We are concerned with one-dimensional scalar surface growth model arising from the physical process of molecular epitaxy. The mathematical theory of the surface growth model is known to share a number of striking similarities with the Navier-Stokes equations, including the results regarding existence and uniqueness of solutions. In this paper, we shall investigate an important subject in mathematical physics: the energy conservation for weak solutions of the surface growth model. As an analogue of the Navier-Stokes equations, we find some sufficient integral conditions that guarantee the validity of energy equality. As far as we know, this is the first result in this aspect. [ABSTRACT FROM AUTHOR]

• A review on solving nonlinear hyperbolic systems of PDEs containing Dirac δ measures. • A review on α -product applications to some nonlinear models arising in mathematical physics. • Under certain conditions, δ waves in the Klein-Gordon equation behave like classical solitons in the sine-Gordon equation. The present paper studies the interaction of Dirac δ -waves in models ruled by the nonlinear Klein-Gordon equation u t t − c 2 u x x = ϕ (u) , where c > 0 is a real number and ϕ is an entire function taking real values on the real axis. Such study is made using a product of distributions that both extends the meaning of ϕ (u) for certain distributions u and allows the definition of a solution concept consistent with the classical solution concept. From such study, it emerges that in several nonlinear Klein-Gordon equations Dirac δ -waves behave like classical solitons in the sine-Gordon equation. As particular cases, this work examines the phi-four equation and the sine-Gordon equation. [ABSTRACT FROM AUTHOR]

In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical physics and in the field of shape analysis and template registration. Depending on the order of the metric, we will prove both local and global well-posedness results for these equations. As a result of our analysis we will also obtain new commutator estimates for elliptic pseudo-differential operators. [ABSTRACT FROM AUTHOR]

Three-dimensional structural dynamics of a submerged fluid-filled circular cylindrical shell subjected to an external shock wave is addressed for the scenario of different internal and external fluids. A semi-analytical model based on the use of the classical apparatus of mathematical physics is employed, and the focus of the study is on understanding how the peak values of the compressive and tensile stress evolve when the acoustic properties of the internal fluid change. It is demonstrated that the peak tensile stress can be very sensitive to such changes, while the respective response of the peak compressive stress is quasi-linear. It is also shown that for the present system, it is not always possible to rely on the parametric studies based on the use of simplified, computationally cheaper two-dimensional models even when conservatives estimates of the peak stress are sought because the peak stress values predicted by such models can be both higher and lower than the values predicted by the more realistic, fully three-dimensional models. The dominance of the transverse stress over the longitudinal one is established for all scenarios considered. The spatial and temporal locations of the stress peaks are analyzed as well, and the practical implications of the respective findings are highlighted. [ABSTRACT FROM AUTHOR]

We recall the definition of the O -operators on bimodules over associative algebras (also called generalized Rota-Baxter operators), and we introduce the notions of compatible O -operators and of O N -structures. We show that an O N -structure gives rise to a hierarchy of O -operators and that a solution of the strong Maurer-Cartan equation on the associative twilled algebra associated to an O -operator gives rise to a pair of O N -structures which are naturally in duality. We introduce the notions of PN-, ΩN- and P Ω -structures on associative algebras and study their relations. [ABSTRACT FROM AUTHOR]

Abstract Under investigation in this work is the general coupled nonlinear Schrödinger (gCNLS) equation, which can be reduced to several integrable equations. By using Darboux-dressing transformation, the new localized wave solutions of the equation are constructed. These solutions exhibit breather waves and rogue waves on a multi-soliton background. Moreover, the dynamics of these solutions is analyzed with some graphics. Our results can be of much importance in enriching and predicting rogue wave phenomena arising in nonlinear wave fields. Highlights • We investigate the new breather wave and rogue wave solutions of the general coupled nonlinear Schrödinger (gCNLS) equation • By using Darboux transformation, the new localized wave solutions of the equation are constructed. These solutions exhibit breather waves and rogue waves on a soliton background. • Our results can be of much importance in enriching and predicting rogue wave phenomena arising in nonlinear wave fields. • This method is also suitable for other nonlinear differential equations in the field of mathematical physics. [ABSTRACT FROM AUTHOR]

Abstract A hierarchy of reduced-order models of wave propagation in a periodic elastic layer is used to study the periodicity-induced stop-band effects. At each approximation level, the eigenfrequency problem for a unit symmetric periodicity cell with appropriate boundary conditions is shown to be equivalent to the problem of identification of frequencies separating pass- and stop-bands. Factorization of eigenfrequency equations and of equations defining positions of pass- and stop-bands for individual Floquet modes is demonstrated. The difference between accuracy levels of reduced order models for homogeneous and periodic layers is highlighted and explained. [ABSTRACT FROM AUTHOR]

Abstract Uniform acoustic waveguides in initially quiescent inhomogeneous media are governed by Bergmann's wave equation. The transverse modes are independent of the ambient gradient, but there is a void of papers on the cut-on conditions of the higher order axial modes. This paper presents a sufficient cut-on condition and discusses its application to hard-walled ducts in which the mean temperature varies linearly and exponentially along the duct axis. [ABSTRACT FROM AUTHOR]

Abstract The point spread function (PSF) based deconvolution algorithms may fall short due to the inconformity between the actual beam pattern of acoustic sources and the theoretical PSF. CLEAN-SC, originally developed for delay and sum beamforming with planar microphone arrays, can circumvent the inconformity. This paper devotes to adapting CLEAN-SC to spherical harmonics beamforming (SHB). The core of adapting CLEAN-SC to SHB is to express the output of SHB in the spatial domain as a specific form of matrix operation completely. We solve the issue and establish CLEAN-SC with spherical microphone arrays. Its performance is analyzed and compared with PSF based CLEAN. CLEAN-SC with spherical microphone arrays can improve spatial resolution and suppress sidelobes more effectively, as well as quantify the sound pressure contribution accurately. Moreover, it has better convergence, higher computational efficiency, and stronger robustness to interference such as background noise and frequency response mismatch of microphone and measurement channel. This study provides an alternative approach for acoustic source identification in three-dimensional space. Highlights CLEAN-SC is adapted to SHB with spherical microphone arrays. It can identify the acoustic sources accurately. It has obvious advantages over SHB in resolution and dynamic range. It has faster computation, better convergence, and stronger robustness than CLEAN. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on analysis of a friction-induced mechanical oscillator with cubic nonlinearity and an applied dynamical model of dry friction. The studied model is based on the classical LuGre approach to friction force modelling. Lyapunov exponents spectrum of the frictional oscillator is calculated by means of a recently implemented method of their estimation for non-smooth systems. Results of the numerical research, observations of the nature of the oscillator's response and interaction of the applied dynamic friction model with the oscillator are reported. Highlights • The dynamics of stick-slip oscillator with cubic nonlinearity is demonstrated. • Modified LuGre friction model is applied. • The stability of the system is proven by conditional Lyapunov exponents. • The correlation (synchrony) between oscillator response and dynamics of friction force is confirmed. [ABSTRACT FROM AUTHOR]

Abstract An analytical vibration response in the time domain for an axially translating and laterally vibrating string with mixed boundary conditions is considered in this paper. The domain of the string is a constant, dependent upon the general initial conditions. The translating tensioned strings possess different types of mixed boundary conditions, such as fixed_dashpot, fixed_spring-dashpot, fixed_mass-spring-dashpot. An analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycle of boundary reflection for strings is provided, which is dependent upon the string length. Each cycle is divided into three time intervals according to the travelling speed and direction of the string. Applying D'Alembert's principle and the reflection properties, expressions for the reflected waves under three different non-classical boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals by using a reflected wave superposition method. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark- β method solution. The energy expressions for a travelling string with a fixed_dashpot boundary condition is obtained and the time domain curves for the total energy and the change of energy at the boundaries are given. [ABSTRACT FROM AUTHOR]

Abstract We find a dual version of a previous double-bosonisation theorem whereby each finite-dimensional braided-Hopf algebra B in the category of comodules of a coquasitriangular Hopf algebra A has an associated coquasitriangular Hopf algebra Image 1. As an application we find new generators for c q [ S L 2 ] reduced at q a primitive odd root of unity with the remarkable property that their monomials are essentially a dual basis to the standard PBW basis of the reduced Drinfeld–Jimbo quantum enveloping algebra u q (s l 2). Our methods apply in principle for general c q [ G ] as we demonstrate for c q [ S L 3 ] at certain odd roots of unity. [ABSTRACT FROM AUTHOR]

Abstract We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form H = H V − i C ⁎ C , where H V = H 0 + V is self-adjoint and C is a bounded operator. We study the wave operators associated to H and H 0. We prove that they are asymptotically complete if and only if H does not have spectral singularities on the real axis. For Schrödinger operators, the spectral singularities correspond to real resonances. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider an initial-boundary value problem of the p-Laplacian parabolic equation { u t (x , t) = div (| ∇ u (x , t) | p − 2 ∇ u (x , t)) + f (u (x , t)) , (x , t) ∈ Ω × (0 , + ∞) , u (x , t) = 0 , (x , t) ∈ ∂ Ω × [ 0 , + ∞) , u (x , 0) = u 0 ≥ 0 , x ∈ Ω ‾ , where p ≥ 2 and Ω is a bounded domain of R N (N ≥ 1) with smooth boundary ∂Ω. The main contribution of this work is to introduce a new condition (C p) α ∫ 0 u f (s) d s ≤ u f (u) + β u p + γ , u > 0 for some α , β , γ > 0 with 0 < β ≤ (α − p) λ 1 , p p , where λ 1 , p is the first eigenvalue of p-Laplacian Δ p , and we use the concavity method to obtain the blow-up solutions to the above equations. In fact, it will be seen that the condition (C p) improves the conditions ever known so far. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with a time periodic competition–diffusion system { u t = u x x + u (r 1 (t) − a 1 (t) u − b 1 (t) v) , t > 0 , x ∈ R , v t = d v x x + v (r 2 (t) − a 2 (t) u − b 2 (t) v) , t > 0 , x ∈ R , where u (t , x) and v (t , x) denote the densities of two competing species, d > 0 is some constant, r i (t) , a i (t) and b i (t) are T -periodic continuous functions. Under suitable conditions, it has been confirmed by Bao and Wang (2013) [2] that this system admits periodic traveling fronts connecting two stable semi-trivial T -periodic solutions (p (t) , 0) and (0 , q (t)) associated to the corresponding kinetic system. In the present work, we first investigate the asymptotic behavior of periodic bistable traveling fronts with non-zero speeds at infinity by a dynamical approach combined with the two-sided Laplace transform method. With these asymptotic properties, we then obtain some key estimates. As a result, by applying the super- and subsolutions techniques as well as the comparison principle, we establish the existence and various qualitative properties of the so-called entire solutions defined for all time and the whole space, which provides some new spreading ways other than periodic traveling waves for two strongly competing species interacting in a heterogeneous environment. [ABSTRACT FROM AUTHOR]

Abstract The goal of this paper is to develop the Equivariant Degree based method for studying relative periodic solutions in the setiings with lack of smoothness and/or genericity. In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting Γ × S 1 -spatial symmetries. The existence of branches of relative periodic solutions together with their symmetric classification is established using the equivariant twisted Γ × S 1 -degree with one free parameter. As a case study, we consider a delay differential model of coupled identical passively mode-locked semiconductor lasers with the dihedral symmetry group Γ = D 8 ; and, a system of hysterestic electro-mechanical oscillators coupled in the same symmetric fashion. [ABSTRACT FROM AUTHOR]

Abstract The used methods in our papers [1–13] named new modified and extended auxiliary equation methods. The calculations of our article were correct. All solutions satisfied the partial differential equations in our papers. Highlights • The hydrodynamic mathematical methods. • We present nonlinear Schrodinger equation. • Solitary wave to the generalized nonlinear higher order of dynamical equation. • Fractional generalized reaction duffing equations. [ABSTRACT FROM AUTHOR]

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it allows the user to approximate the value of the integral without explicit knowledge of an expression for the boundary surface. Instead, a tesselation of the node set is utilized to inform the algorithm of the domain geometry. Further, the method applies to node sets featuring spatially varying density, facilitating its use in Applied Mathematics, Mathematical Physics and myriad other application areas, where the locations of the nodes might be fixed by experiment or previous simulation. By using the RBF-FD-like approach, the proposed algorithm computes quadrature weights for N arbitrarily scattered nodes in only O (N log ⁡ N) operations with tunable orders of accuracy. • A fast and accurate method for quadrature over 3D volumes with smooth boundaries. • High orders of accuracy are achieved on node sets featuring no particular uniformity. • Can be distributed to any number of available processors. • Knowledge of an expression for the boundary surface is unnecessary. [ABSTRACT FROM AUTHOR]

We show that solution to the Hermite–Padé type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev–Petviashvili) system and of its adjoint linear problem. Our result explains the appearance of various ingredients of the integrable systems theory in application to multiple orthogonal polynomials, numerical algorithms, random matrices, and in other branches of mathematical physics and applied mathematics where the Hermite–Padé approximation problem is relevant. We present also the geometric algorithm, based on the notion of Desargues maps, of construction of solutions of the problem in the projective space over the field of rational functions. As a byproduct we obtain the corresponding generalization of the Wynn recurrence. We isolate the boundary data of the Hirota system which provide solutions to Hermite–Padé problem showing that the corresponding reduction lowers dimensionality of the system. In particular, we obtain certain equations which, in addition to the known ones given by Paszkowski, can be considered as direct analogs of the Frobenius identities. We study the place of the reduced system within the integrability theory, which results in finding multidimensional (in the sense of number of variables) extension of the discrete-time Toda chain equations. [ABSTRACT FROM AUTHOR]

In this note we investigate the form of a class of idempotents, called generalized bi-circular idempotents on spaces of continuously differentiable functions defined on the interval [ 0 , 1 ] and with values in the complex numbers. [ABSTRACT FROM AUTHOR]

We investigate an M / M / 1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments. For the approximating process we determine the steady-state distribution, the transient distribution and a first-passage-time density. [ABSTRACT FROM AUTHOR]

We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a delicate interplay between integral, rational, and mod p cohomology, as well as cohomology with U ( 1 ) coefficients and differential forms. Along the way we develop computational techniques in differential cohomology, including a Künneth decomposition, that should also be useful in their own right, and point to applications to higher geometry and mathematical physics. [ABSTRACT FROM AUTHOR]

We give a classification of all exact structures on a given idempotent complete additive category. Using this, we investigate the structure of an exact category with finitely many indecomposables. We show that the relation of the Grothendieck group of such a category is generated by AR conflations. Moreover, we obtain an explicit classification of (1) Gorenstein-projective-finite Iwanaga–Gorenstein algebras, (2) Cohen–Macaulay-finite orders, and more generally, (3) cotilting modules U with U ⊥ of finite type. In the appendix, we develop the AR theory of exact categories over a noetherian complete local ring, and relate the existence of AR conflations to the AR duality and dualizing varieties. [ABSTRACT FROM AUTHOR]

Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Camassa–Holm equation, which is a model for shallow water waves. We first establish the existence of solitary wave solutions for the equation without delay. And then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system, especially the geometric singular perturbation theory and invariant manifold theory. According to the relationship between solitary wave and homoclinic orbit, the Camassa–Holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution. It is proved that the equation with disturbance also possesses homoclinic orbit, and there exists solitary wave solution of the delayed Camassa–Holm equation. [ABSTRACT FROM AUTHOR]

In our previous work, motivated by the study of tropical polynomials, a definition for prime congruences was given for an arbitrary commutative semiring. It was shown that for additively idempotent semirings this class exhibits some analogous properties to prime ideals in ring theory. The current paper focuses on the resulting notion of Krull dimension, which is defined as the length of the longest chain of prime congruences. Our main result states that for any additively idempotent semiring A , the semiring of polynomials dim ⁡ A [ x 1 , … , x n ] and the semiring of Laurent polynomials A [ x 1 ± 1 , … , x n ± 1 ] , we have dim ⁡ A [ x 1 ± 1 , … , x n ± 1 ] = dim ⁡ A [ x 1 , … , x n ] = dim ⁡ A + n . [ABSTRACT FROM AUTHOR]

We consider a noncommutative standard model with a minimal coupling scalar field and a dynamical deformation between the canonical momenta of its scale factor and scalar field, and a chameleon model with a non-minimally coupling scalar field. We indicate that there is a correspondence between these two models, more specific, actually between the noncommutative parameter and the chameleon coupling strength, and also between the matter density of the chameleon model and the noncommutative geometry. In addition, the analogy constrains the type of the matter field in the chameleon model to be nearly a cosmic string-like during the inflation. Thus, the scenario enables the evolution of the universe being described by one single scalar field. That is, the effects of the chameleon and the inflaton can be described by one single scalar field which plays the role of inflaton in the very early universe and then, acts as a chameleon field. Moreover, the proposed correspondence procedure not only sets some constraints on the noncommutative parameter and the chameleon coupling constant, but also nearly specifies functions of the scalar field and its potential. [ABSTRACT FROM AUTHOR]

We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the renormalons is provided by exploiting an analytic solution of the generic one-loop renormalization group equations in multi-field theories. Methods to evaluate the regions in coupling space where the theory is resummable are described. The generalization is then illustrated in a toy model with two coupled scalar fields, representing the simplest extension of the one-field analysis presented in the seminal works of the subject. Furthermore, possible links to realistic theories are briefly discussed. [ABSTRACT FROM AUTHOR]

Let Y be a complex algebraic variety, G ↷ Y an action of an algebraic group on Y , U ⊆ Y ( C ) a complex submanifold, Γ < G ( C ) a discrete, Zariski dense subgroup of G ( C ) which preserves U , and π : U → X ( C ) an analytic covering map of the complex algebraic variety X expressing X ( C ) as Γ \ U . We note that the theory of elimination of imaginaries in differentially closed fields produces a generalized Schwarzian derivative χ ˜ : Y → Z (where Z is some algebraic variety) expressing the quotient of Y by the action of the constant points of G . Under the additional hypothesis that the restriction of π to some set containing a fundamental domain is definable in an o-minimal expansion of the real field, we show as a consequence of the Peterzil–Starchenko o-minimal GAGA theorem that the prima facie differentially analytic relation χ : = χ ˜ ∘ π − 1 is a well-defined, differential constructible function. The function χ nearly inverts π in the sense that for any differential field K of meromorphic functions, if a , b ∈ X ( K ) then χ ( a ) = χ ( b ) if and only if after suitable restriction there is some γ ∈ G ( C ) with π ( γ ⋅ π − 1 ( a ) ) = b . [ABSTRACT FROM AUTHOR]

We consider the conjectures from [10] about Landau–Ginzburg Hodge numbers associated to tamely compactifiable Landau–Ginzburg models. We test these conjectures in case of dimension two, verifying some and giving a counterexample to the other. [ABSTRACT FROM AUTHOR]

In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are related to quantum state tomography (Caves et al., 2004), quantum cryptography (Fuchs and Sasaki, 2003) [ 1 ], and foundational studies (Fuchs, 2002) [ 2 ]. However, constructing SIC-POVMs is notoriously hard. Although some SIC-POVMs have been constructed numerically, there does not exist an infinite class of them. In this paper, we propose two constructions of approximately SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. We employ difference sets to present the first construction and the dimension of the approximately SIC-POVMs is q + 1 , where q is a prime power. Notably, the dimension of this framework is new. The second construction is based on partial geometric difference sets and works whenever the dimension of the framework is a prime power. [ABSTRACT FROM AUTHOR]

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation. [ABSTRACT FROM AUTHOR]

If the physical properties of a structural component are sufficiently random then the statistical distribution of the natural frequencies and mode shapes tends to a universal distribution associated with the Gaussian Orthogonal Ensemble (GOE) of random matrices. Previous work has exploited this result to yield expressions for the relative variance of the energy of the response of a random system to harmonic excitation. The derivation of these expressions employed random point process theory, and in the theoretical development it was assumed that the modal generalised forces were uncorrelated. Although this assumption is often valid, there are cases in which correlations between the generalised forces can significantly affect the response variance, and in the present work the existing theory is extended to include correlations of this type. The extended theory is applicable to both single frequency responses and to band average responses, and the developed closed form expressions are validated by comparison with direct simulations for a random plate structure. [ABSTRACT FROM AUTHOR]

Three-dimensional structural dynamics of a circular cylindrical shell submerged in fluid and subjected to two consecutive spherical shock waves is addressed using a semi-analytical model based on the classical apparatus of mathematical physics. It is established that for certain values of the delay between the first and second incident wavefronts, the highest stress observed in the system significantly (by up to 50%) exceeds the peak stress observed for the single-front loading of the same intensity. Although this result is quantitatively the same as the one reported for the simplified two-dimensional model of the system, it is demonstrated that there exist very substantial differences between the evolution of the peak stress predicted by the two models when the three-dimensionality of the incident shock waves is pronounced. It is thus established that the presented three-dimensional model is a far more reliable pre-design analysis tool for such loadings than its two-dimensional counterpart. [ABSTRACT FROM AUTHOR]

For suitable initial and boundary data, we construct infinitely many weak solutions to the nematic liquid crystal flows in dimension three. These solutions are in the axisymmetric class with bounded energy and “backward bubbling” at a large time. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem of a fluid–particle interaction model in R 3 , namely, compressible Navier–Stokes equations coupled with Smoluchowski equation. When the initial data ( ρ 0 , u 0 , η 0 ) is of small energy around steady state ( ρ ⋆ , 0 , η ⋆ ) , the global well-posedness and large-time behavior of classical solutions are investigated. Vacuum is allowed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss several results regarding existence, non-existence and asymptotic properties of solutions to u ⁗ + q u ″ + f ( u ) = 0 , under various hypotheses on the parameter q and on the potential F ( t ) = ∫ 0 t f ( s ) d s , generally assumed to be bounded from below. We prove a non-existence result in the case q ≤ 0 and an existence result of periodic solution for: 1) almost every suitably small (depending on F ), positive values of q ; 2) all suitably large (depending on F ) values of q . Finally, we describe some conditions on F which ensure that some (or all) solutions u q to the equation satisfy ‖ u q ‖ ∞ → 0 , as q ↓ 0 . [ABSTRACT FROM AUTHOR]

We study the regularization of an oriented 1-foliation F on M ∖ Σ where M is a smooth manifold and Σ ⊂ M is a closed subset, which can be interpreted as the discontinuity locus of F . In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus Σ as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions. [ABSTRACT FROM AUTHOR]

In this paper we consider the Fornberg–Whitham (FW) equation and we give sufficient conditions on the initial data to lead to wave-breaking. [ABSTRACT FROM AUTHOR]

The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples. [ABSTRACT FROM AUTHOR]