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The integration of information technology and manufacturing technology (IOITMT) is a strategic idea proposed by China. As the smallest unit of integration, manufacturing enterprises can be seen as the root of IOITMT. However, the current situation of IOITMT in China shows that intelligent manufacturing still has a long way to go and that the implementation effect of IOITMT requires urgent improvement. The dynamic evolution of IOITMT is accompanied by the integration and coevolution of internal technologies and also affects the performance of enterprises. Taking technical efficiency as a measure of IOITMT, the purpose of the current study is to develop an internal dynamic evolutionary mechanism framework for IOITMT of a single cycle in manufacturing enterprises. The framework is based on the theory of self-organization and convergence and uses convergence theory to discuss the evolution mode of technical efficiency in the three stages of IOITMT under the guidance of order parameters. This paper finds that the technical efficiency of IOITMT is influenced by the ratio of convergence parameters r1/r2, and adjusting the convergence intensity can effectively improve the performance of enterprises. Hence, this paper provides important theoretical guidance for the advancement of IOITMT of Chinese manufacturing enterprises.

In the study of the constant in Ahlfors' second fundamental theorem involving a set E_{q} of q points, branch values of covering surfaces outside E_{q} bring a lot of troubles. To avoid this situation, for a given surface S, it is useful to construct a new surface So such that L(So) =H(S), and all branch values of So are contained in E_{q}. The goal of this paper is to prove the existence of such So, which generalizes Lemma 9.1 and Theorem 10.1 in Zhang G.Y.: The precise bound for the area-length ratio in Ahifors' theory of covering surfaces. Invent math 191:197-253(2013), This paper is a preparation for the further research on Ahlfors' theorey of covering surfaces

Cathodic protection is defined as a method for slowing down or complete elimination of corrosion processes on underground or underwater, insulated or uninsulated metal structures. Protection by cathodic protection system is achieved by polarizing protected object to more negative value, with respect to its equilibrium potential. Design of the cathodic protection system implies determination of the electric potential and current density on the electrode surfaces after installation of the cathodic protection system. Most efficient way for determination of the electric potential and current density in the cathodic protection system is by applying numerical techniques. When modeling cathodic protection systems by numerical techniques, electrochemical reactions that occur on electrode surfaces are taken into account by polarization characteristics. Because of nature of the electrochemical reactions, polarization characteristics are nonlinear and under certain conditions can be time – varying (dynamic nonlinear polarization characteristics). This paper deals with numerical modeling of the cathodic protection system with dynamic nonlinear polarization characteristics. Numerical model presented in this paper is divided in the two parts. First part, which is based on the direct boundary element method, is used for the calculation of the distribution of electric potential and current density on the electrode surfaces in the spatial domain. Second part of the model is based on the finite difference time domain method and is used for the calculation of the electric potential and current density change over time. The use of presented numerical model is demonstrated on two simple geometrically examples.

Our paper begins with a revision of the spectral theory for commutative Banach algebras, which enables us to prove the $$L^p_{\omega }$$ -conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the literature. In particular, we do not resort to any structural theorems for locally compact groups at this stage. Subsequently, we discuss nilpotent, locally compact groups. The climax of the paper is the proof of the $$L^p_{\omega }$$ -conjecture for these groups.

Insolvency risk measures play important role in the theory and practice of risk management. In this paper, we provide a numerical procedure to compute vectors of their exact values and prove for them new upper and/or lower bounds which are shown to be attainable. More precisely, we investigate a general insolvency risk measure for a regime-switching Sparre Andersen model in which the distributions of claims and/or wait times are driven by a Markov chain. The measure is defined as an arbitrary increasing function of the conditional expected harm of the deficit at ruin, given the initial state of the Markov chain. A vector-valued operator L, generated by the regime-switching process, is introduced and investigated. We show a close connection between the iterations of L and the risk measure in a finite horizon. The approach assumed in the paper enables to treat in a unified way several discrete and continuous time risk models as well as a variety of important vector-valued insolvency risk measures.

International audience; In this paper, we consider a semi-linear fourth order parabolic equation in a bounded smooth domain Ω with homogeneous Dirichlet and Neumann boundary conditions. The main result of this paper is the null controllability and the exact controllability to the trajectories at any time T > 0 for the associated control system with a control function acting at the interior.; Dans ce papier, on considère uneéquation parabolique semi-linéaire de quatrième ordre dans un domaine borné régulier Ω avec des conditions aux limites de type Dirichlet et Neumann homogènes. Le résultat principal de ce papier concerne la contrôlabilitéà zéro et la contrôlabilité exacte pour tout T > 0 du système de contrôle associé avec un contrôle agissantà l'interieur.

This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.

This paper deals with properties of the ultraproducts for various structures. We introduce and study the concept of the ergodic action of a group with respect to a normal state on an abelian von Neumann algebra. In particular, we provide an example showing that the ultraproduct of ergodic states, generally speaking, is not ergodic. The ultraproduct of the Radon measures on a compact convex subset of a locally convex space is also investigated in the paper. As is well-known, the study of the extreme points in the state set for a $$C^{*}-$$ algebra is a very interesting problem in itself. Considering the ultraproducts of $$C^{*}$$ -algebras and the states on these algebras, we get quite nontrivial results.

In the paper, the elementary net closure problem is considered. An elementary net (net without a diagonal) σ = (σij)i ≠ j of additive subgroups σij of field k is called “closed” if elementary net group E(σ) does not contain new elementary transvections. Elementary net σ = (σij) is called “supplemented” if table (with a diagonal) σ = (σij), 1 ≤ i, j ≤ n, is a (full) net for some additive subgroups σii of field k. The supplemented elementary nets are closed. The necessary and sufficient condition for the supplementarity of elementary net σ = (σij) is the implementation of inclusions σijσjiσij ⊆ σij (for any i ≠ j). The question (Kourovka Notebook, Problem 19.63) is investigated of whether it true that, for closure of elementary net σ = (σij) it suffices to implement inclusions $$\sigma _{{ij}}^{2}{{\sigma }_{{ji}}}$$ ⊆ σji for any i ≠ j (here, ($$\sigma _{{ij}}^{2}$$ denotes the additive subgroup of field k generated by the squares from σij). The elementary nets for which the latter inclusions are satisfied are called “weakly supplemented elementary nets.” The concepts of supplemented and weakly supplemented elementary nets coincide for fields of odd characteristic. Thus, the aforementioned question of the sufficiency of weak supplementarity for the closure of an elementary net is relevant for the fields of characteristics 0 and 2. In this paper, examples of weakly supplemented but not supplemented elementary nets are constructed for the fields of characteristics 0 and 2. An example of a closed elementary net that is not weakly supplemented is constructed.

The present paper is a continuation of our research that was devoted to the theory of the boundary behavior of mappings in the Sobolev classes (mappings with generalized derivatives) on Riemann surfaces. Here we develop the theory of the boundary behavior of the mappings in the class of FLD (mappings with finite length distortion) first introduced for the Euclidean spaces in the article of Martio-Ryazanov-Srebro-Yakubov at 2004 and then included in the known book of these authors at 2009 on the modern mapping theory. As was shown in the recent papers of Kovtonyuk-Petkov-Ryazanov at 2017, such mappings, generally speaking, are not mappings in the Sobolev classes, because their first partial derivatives can be not locally integrable. At the same time, this class is a natural generalization of the well-known significant classes of isometries and quasiisometries. We prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extensions to the boundary of the mappings with finite length distortion between domains on Riemann surfaces by Caratheodory prime ends. The criterion for the continuous extension of the inverse mapping to the boundary is turned out to be the very simple condition on the integrability of the dilatations in the first power. The criteria for the continuous extension of the direct mappings to the boundary have a much more refined nature. One of such criteria is the existence of a majorant for the dilatation in the class of functions with finite mean oscillation, i.e., having a finite mean deviation from its mean value over infinitesimal disks centered at boundary points. As consequences, the corresponding criteria for a homeomorphic extension of mappings with finite length distortion to the closures of domains by Caratheodory prime ends are obtained.

This paper deals with normal submanifolds immersed in a Riemannian manifold $${\overline{M}}$$ . We generalized some recent results of surfaces in space forms obtained by Hernandez-Lamoneda and Ruiz-Hernandez (Bull Braz Marh Soc (NS) 49:447–462, 2018) to arbitrary submanifolds. More precisely, given a submanifold M in $${\overline{M}}$$ , we study the submanifolds formed by orthogonal geodesics to M, and call it a ruled normal submanifold to M. In the first part of this paper, we analyze these submanifolds and establish some geometric properties of them. Furthermore, we extend some properties about the lines of curvature and using the ideas of [3] also give an extension of the classical Theorem of Bonnet to hypersurfaces of $${\overline{M}}$$ .

In this paper we consider a link $$B_{n,\rho }$$Bn,ρ between Baskakov type operators $$B_{n,\infty }$$Bn,∞ and genuine Baskakov–Durrmeyer type operators $$ B_{n,1}$$Bn,1 depending on a positive real parameter $$\rho $$ρ. The topic of the present paper is the pointwise limit relation $$\left( B_{n,\rho }f\right) \left( x\right) \rightarrow \left( B_{n,\infty }f\right) \left( x\right) $$Bn,ρfx→Bn,∞fx as $$\rho \rightarrow \infty $$ρ→∞ for $$x\ge 0.$$x≥0. As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions f of polynomial growth.

The paper describes the results of a functional-geometric study of the necessary and sufficient conditions for the existence of a differential realization in the terms of the tensor product of real Hilbert spaces. There are considered continuous infinite-dimensional dynamical system in the class of controlled bilinear nonstationary ordinary differential equations of the second order (including quasi-linear hyperbolic models) in a separable Hilbert space. Therefore the topological and metric conditions for the continuity of the RayleighRitz operator with the calculation of the fundamental group of its image are analytically substantiated. The results of paper give incentives for generalizations in the qualitative theory of nonlinear structural identification of higher order multi-linear differential models.

This paper gives an explicit formula of the asymptotic expansion of the Kobayashi–Royden metric on the punctured sphere ℂ ⁢ ℙ 1 ∖ { 0 , 1 , ∞ } {\mathbb{CP}^{1}\setminus\{0,1,\infty\}} in terms of the exponential Bell polynomials. We prove a local quantitative version of the Little Picard’s Theorem as an application of the asymptotic expansion. Furthermore, the approach in the paper leads to the interesting consequence that the coefficients in the asymptotic expansion are rational numbers. Furthermore, the explicit formula of the metric and the conclusion regarding the coefficients apply to more general cases of ℂ ⁢ ℙ 1 ∖ { a 1 , … , a n } {\mathbb{CP}^{1}\setminus\{a_{1},\ldots,a_{n}\}} , n ≥ 3 {n\geq 3} , as well, and the metric on ℂ ⁢ ℙ 1 ∖ { 0 , 1 3 , - 1 6 ± 3 6 ⁢ i } {\mathbb{CP}^{1}\setminus\{0,\frac{1}{3},-\frac{1}{6}\pm\frac{\sqrt{3}}{6}i\}} will be given as a concrete example of our results.

This paper is devoted to some counting functions of level one and level three in the case of quotient space generated by some strictly hyperbolic Fuchsian group and the upper half-plane. Each of the functions is represented as a sum of some explicit part plus the error term. The explicit part is indexed over singularities of the corresponding Selberg zeta function. In particular, the obtained error term is not larger than O ( x 3/4) . The method applied in this paper follows traditional approach for achieving the error terms in the case of locally symmetric spaces of real rank one. In order to establish an analogy with the classical case, we consider the counting functions divided by x and x3, respectively.

This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013). The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time. The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system. These observations are obtained by taking the direct approach of numerical experimentation.

In this paper we generalize the result (obtained by the author earlier in the paper titled “Products and coproducts in the category $${{\mathcal {S}}}(B)$$ of Segal topological algebras”) about the existence of the coproduct of objects of the category $${\mathcal S}(B)$$ from finite collection of objects of $${{\mathcal {S}}}(B)$$ to any collection of objects of $${{\mathcal {S}}}(B)$$ .

In order to accurately divide the traffic control subarea and improve the regional coordination control effect, this paper studies the key technologies of traffic control subarea division from the influence of the discrete characteristics of the fleet on the coordinated control. Correlation analysis method and regression analysis method are used to construct the correlation model of adjacent intersections. The principle and process of transportation subarea division are designed by using analytic hierarchy process, and a new traffic subarea division model is proposed. Taking Gulou Street in Miyun District of Beijing as an example, combined with the green wave coordination optimization method, the new model was applied and simulated in SimTraffic. The simulation results show that the average delay of the intersection is reduced by 21.4%, the total number of stops is reduced by 9.62%, and the travel time is shortened by 8.75%. The new intersection degree model and the coordinated control scheme obtained by the traffic subarea division model make the highest traffic efficiency. That is, to verify the scientific research method of this paper, the research results are reliable and the practical application value is high.

This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.

This paper continues a series of studies dealing with noninvasive preoperative methods for localizing eloquent areas of the human brain. The inverse problem of magnetoencephalography (MEG) is illposed and difficult for both analytical and numerical solutions. An analytical formula is derived for the solution of the forward problem that computes the magnetic field on the surface of the head from the known location and orientation of a current dipole in the low-frequency approximation in the spherical model. In addition, the paper considers the question of stability of solutions of the inverse problem of MEG to the effect of noise. The solution is unstable to the effect of noise on its angular component, but the deviation from the true solution is much less than the noise variance.

The F-index F(G) of a graph G is obtained by the sum of cubes of the degrees of all the vertices in G. It is defined in the same paper of 1972 where the first and second Zagreb indices are introduced to study the structure-dependency of total π-electron energy. Recently, Furtula and Gutman [J. Math. Chem. 53 (2015), no. 4, 1184–1190] reinvestigated F-index and proved its various properties. A connected graph with order n and size m, such that m = n + 2, is called a tricyclic graph. In this paper, we characterize the extremal graphs and prove the ordering among the different subfamilies of graphs with respect to F-index in $\begin{array}{} \displaystyle {\it\Omega}^{\alpha}_n \end{array}$, where $\begin{array}{} \displaystyle {\it\Omega}^{\alpha}_n \end{array}$ is a complete class of tricyclic graphs with three, four, six and seven cycles, such that each graph has α ≥ 1 pendant vertices and n ≥ 16 + α order. Mainly, we prove the bounds (lower and upper) of F(G), i.e $$\begin{array}{} \displaystyle 8n+12\alpha +76\leq F(G)\leq 8(n-1)-7\alpha + (\alpha+6)^3 ~\mbox{for each}~ G\in {\it\Omega}^{\alpha}_n. \end{array}$$

The theory of mixed multiplicities of filtrations by $m$-primary ideals in a ring is introduced in a recent paper by Cutkosky, Sarkar and Srinivasan. In this paper, we consider the positivity of mixed multiplicities of filtrations. We show that the mixed multiplicities of filtrations must be nonnegative real numbers and give examples to show that they could be zero or even irrational. When $R$ is analytically irreducible, and $\mathcal I(1),\ldots,\mathcal I(r)$ are filtrations of $R$ by $m_R$-primary ideals, we show that all of the mixed multiplicities $e_R(\mathcal I(1)^{[d_1]},\ldots,\mathcal I(r)^{[d_r]};R)$ are positive if and only if the ordinary multiplicities $e_R(\mathcal I(i);R)$ for $1\le i\le r$ are positive. We extend this to modules and prove a simple characterization of when the mixed multiplicities are positive or zero on a finitely generated module., 15 pages

In this paper, we use stochastic integration in the framework of signed measures, together with the technique of time changes. Let Q be a bounded non-null signed measure on $$(\varOmega ,{\mathcal {F}}, {{P}}),$$ such that $$\left| Q\right| $$ and P are equivalent. In the first part of the paper, we generalize the results of stochastic calculus in Beghdadi-Sakrani (Seminaire de probabilites XXXVI, Springer, 2003) to Q-local martingales and we give some examples. In the second part, we prove that the class of Q-semimartingales is invariant under time changes. We establish the famous formulas of time-changed local martingales as well as the representation of a Q-local martingale as a time-changed Brownian motion.

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers and several integer sequences related to them have been studied. In the present paper, new sets of Bell–Sheffer polynomials are introduced. Connections with Bell numbers are shown.

Elastic waves cause energy loss during the transmission of coal measures. These losses include propagation loss, dielectric absorption loss, scattering loss, and frequency migration loss. The absorption loss is mainly caused by the inelastic absorption. The scattering loss is caused by the uneven heat absorption in the formation. The frequency shift loss is caused by the piezoelectric effect of coal-bearing formations and the intermodulation of different frequency signals. After considering the influence factors of the coal seam structure, this paper presents a model of low-frequency elastic waves loss coefficient. The paper proposed the loss coefficient of the elastic wave in the coal measure strata by considering two main attenuation mechanisms: intrinsic absorption and scattering. This paper theoretically studied the effects of the model parameters such as density, porosity, particle size, and wave frequency on the loss of wave energy using COMSOL simulation. Besides, the comparison of MATLAB simulation results shows that the simulation results produced by the model proposed in this paper are similar to the models embedded in COMSOL. This work can be applied to coal, oil, and gas exploration and is also helpful to study the mechanisms of wave attention on the low-frequency band.

The aim of this paper is twofold. First, we introduce a new method for evaluating the multiplicity of a given discrete series representation in the space of level 1 automorphic forms of a split classical group $G$ over $\mathbf {Z}$ , and provide numerical applications in absolute rank $\leq 8$ . Second, we prove a classification result for the level one cuspidal algebraic automorphic representations of $\mathrm{GL}_{n}$ over $\mathbf {Q}$ ( $n$ arbitrary) whose motivic weight is $\leq 24$ . In both cases, a key ingredient is a classical method based on the Weil explicit formula, which allows to disprove the existence of certain level one algebraic cusp forms on $\mathrm{GL}_{n}$ , and that we push further on in this paper. We use these vanishing results to obtain an arguably “effortless” computation of the elliptic part of the geometric side of the trace formula of $G$ , for an appropriate test function. Thoses results have consequences for the computation of the dimension of the spaces of (possibly vector-valued) Siegel modular cuspforms for $\mathrm{Sp}_{2g}(\mathbf {Z})$ : we recover all the previously known cases without relying on any, and go further, by a unified and “effortless” method.

In this paper, we introduce the associated geodesic-Einstein flow for a relative ample line bundle L over the total space $$\mathcal {X}$$ of a holomorphic fibration and obtain a few properties of that flow. In particular, we prove that the pair $$(\mathcal {X}, L)$$ is nonlinear semistable if the associated Donaldson type functional is bounded from below and the geodesic-Einstein flow has long-time existence property. We also define the associated S-classes and C-classes for $$(\mathcal {X}, L)$$ and obtain two inequalities between them when L admits a geodesic-Einstein metric. Finally, in the appendix of this paper, we prove that a relative ample line bundle is geodesic-Einstein if and only if an associated infinite rank bundle is Hermitian–Einstein.

This paper analyses the periodic signals in the time series to recognize human activity by using a mobile accelerometer. Each point in the timeline corresponds to a segment of historical time series. This segments form a phase trajectory in phase space of human activity. The principal components of segments of the phase trajectory are treated as feature descriptions at the point in the timeline. The paper introduces a new distance function between the points in new feature space. To reval changes of types of the human activity the paper proposes an algorithm. This algorithm clusters points of the timeline by using a pairwise distances matrix. The algorithm was tested on synthetic and real data. This real data were obtained from a mobile accelerometer.

In 1940, M. G. Krein obtained necessary and sufficient conditions for the extension of a continuous function f defined in an interval (-a, a), a > 0, to a positive definite function on the whole number axis R. In addition, Krein showed that the function 1 - |x|, |x| < a, can be extended to a positive definite one on R if and only if 0 < a ≤ 2, and this function has a unique extension only in the case a = 2. The present paper deals with the problem of uniqueness of the extension of the function 1 - |x|, |x| ≤ a, a G (0,1), for a class of positive definite functions on R whose support is contained in the closed interval [-1,1] (the class T). It is proved that if a ∈ [1/2,1] and Re ϕ(x) = 1 - |x|, |x| ≤ a, for some ϕ ∈ T, then ϕ(x) = (1 - |x|) +, x G R. In addition, for any a G (0,1/2), there exists a function ϕ ∈ T such that ϕ(x) = 1 - |x|, |x| ≤ a, but ϕ(x) ≠ (1 - |x|)+. Also the paper deals with extremal problems for positive definite functions and nonnegative trigonometric polynomials indirectly related to the extension problem under consideration.

This paper studies the asymptotic behavior of the exact constants of the Nikolskii inequalities for the space $$\Pi _n^d$$ of spherical polynomials of degree at most n on the unit sphere $$\mathbb{S}{^d} \subset {^{d + 1}}$$ as n → ∞. It is shown that for 0 < p < ∞, $$\mathop {\lim }\limits_{x \to \infty } \sup \left\{ {\frac{{{{\left\| P \right\|}_{{L^\infty }({\mathbb{S}^d})}}}}{{{n^{\tfrac{d}{p}}}{{\left\| P \right\|}_{{L^p}({\mathbb{S}^d})}}}}:P \in \Pi _n^d} \right\} = \sup \left\{ {\frac{{{{\left\| f \right\|}_{{L^\infty }({\mathbb{R}^d})}}}}{{{{\left\| f \right\|}_{{L^p}({\mathbb{R}^d})}}}}:f \in \varepsilon _p^d} \right\},$$ where $$\varepsilon _p^d$$ denotes the space of all entire functions of spherical exponential type at most 1 whose restrictions to ℝd belong to the space Lp(ℝd), and it is agreed that 0/0 = 0. It is also proved that for 0 < p < q < ∞, $$\liminf _{n \rightarrow \infty} \sup \left\{\frac{\|P\|_{L^{q}\left(\mathbb{S}^{d}\right)}}{n^{d(1 / p-1 / q)}\|P\|_{L^{p}\left(\mathbb{S}^{d}\right)}}: P \in \Pi_{n}^{d}\right\} \geq \sup \left\{\frac{\|f\|_{L^{q}\left(\mathbb{R}^{d}\right)}}{\|f\|_{L^{p}\left(\mathbb{R}^{d}\right)}}: f \in \mathcal{E}_{p}^{d}\right\}.$$ These results extend the recent results of Levin and Lubinsky for trigonometric polynomials on the unit circle. The paper also determines the exact value of the Nikolskii constant for nonnegative functions with p = 1 and q = ∞: $$\lim _{n \rightarrow \infty} \sup _{0 \leq P \in \Pi_{n}^{d}} \frac{\|P\|_{L^{\infty}\left(\mathbb{S}^{d}\right)}}{\|P\|_{L^{1}\left(\mathbb{S}^{d}\right)}}=\sup _{0 \leq f \in \mathcal{E}_{1}^{d}} \frac{\|f\|_{L^{\infty}\left(\mathbb{R}^{d}\right)}}{\|f\|_{L^{1} \mathbb{R}^{d}}}=\frac{1}{4^{d} \pi^{d / 2} \Gamma(d / 2+1)}.$$

A graph Γ is called a bi-circulant if it admits a cyclic group as a group of automorphisms acting semiregularly on the vertices of Γ with two orbits. The characterization of tetravalent edgetransitive bi-circulants was given in several recent papers. In this paper, a classification is given of connected tetravalent vertex-transitive bi-circulants of order twice an odd integer.

The main motive of the paper is to look on rectifying and osculating curves on a smooth surface. In this paper we find the normal and geodesic curvature for a rectifying curve on a smooth surface and we also prove that geodesic curvature is invariant under the isometry of surfaces such that rectifying curves remain. We find a sufficient condition for which an osculating curve on a smooth surface remains invariant under isometry of surfaces and also we prove that the component of the position vector of an osculating curve α(s) on a smooth surface along any tangent vector to the surface at α(s) is invariant under such isometry.

In this paper, we establish the following Stein–Weiss inequality with the fractional Poisson kernel. Then we prove that there exist extremals for the Stein–Weiss inequality (⋆), and that the extremals must be radially decreasing about the origin. We also provide the regularity and asymptotic estimates of positive solutions to the integral systems which are the Euler–Lagrange equations of the extremals to the Stein–Weiss inequality (⋆) with the fractional Poisson kernel. Our result is inspired by the work of Hang, Wang and Yan, where the Hardy–Littlewood–Sobolev type inequality was first established when γ=2 and α=β=0. The proof of the Stein–Weiss inequality (⋆) with the fractional Poisson kernel in this paper uses recent work on the Hardy–Littlewood–Sobolev inequality with the fractional Poisson kernel by Chen, Lu and Tao, and the present paper is a further study in this direction.

The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by Cabrer et al., give access to a viable method for studying admissible rules within relevance logic, specifically for extensions of the deductive system R-mingle.This paper builds on the work already done on the theory of natural dualities for Sugihara algebras. Its purpose is to provide an integrated suite of multisorted duality theorems of a uniform type, encompassing finitely generated quasivarieties and varieties of both Sugihara algebras and Sugihara monoids, and embracing both the odd and the even cases. The overarching theoretical framework of multisorted duality theory developed here leads on to amenable representations of free algebras. More widely, it provides a springboard to further applications.

This paper classifies Poisson structures with the reduced simple normal crossing divisor on a product of Fano varieties of Picard number 1. The characterization of even-dimensional projective spaces from the viewpoint of Poisson structures is given by Lima and Pereira. In this paper, we generalize the characterization of projective spaces to any dimension.

This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.

This paper is a condensation of my arXiv monograph entitled Schwartz “The phase transition in 5 point energy minimization”, 2016. arXiv:1610.03303, which contains a complete proof that there is a constant such that the triangular bi-pyramid is the minimizer, amongst all 5 point configurations on the sphere, with respect to the power law potential $$R_s(r)=\mathrm{sign}(s)/r^s$$, if and only if . In this paper we explain the main ideas and give proofs for some of the key lemmas.

It has been stated that Industry 4.0’s goal is, among others, the sustainable success in a market characterized by exigent and informed consumers demanding personalized products and services, where the level of manufacturing complexity increases with level of product customization. Even though different manufacturing complexity measures have been developed, there seems to be a lack of a comprehensive metric that address both the mass customization variety-induced complexity, and the complexity derived from the adoption of the Industry 4.0 paradigm. The main original contribution of this paper is the development of an entropy-based (entropic) formulation to address this last issue. Its validity and usefulness is put to the test via a discrete-event simulation study of a mass customization production system operating within an Industry 4.0 context. Our findings show that the entropic formulation acts as a fairly good trend indicator of the system’s performance parameter increase/decrease, but not as an estimator of the final values. A discussion of the managerial implications of the obtained results is offered at the end of the paper.

This is a follow-up of the paper J. Fernandez-Bonder, A. Ritorto and A. Salort, H-convergence result for nonlocal elliptic-type problems via Tartar’s method, SIAM J. Math. Anal., 49 (2017), pp. 2387–2408, where the classical concept of H-convergence was extended to fractional $$p$$ -Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that the weak- $$*$$ convergence of the coefficients is an equivalent condition for H-convergence of the sequence of nonlocal operators. This result takes advantage of nonlocality and is in stark contrast to the local $$p$$ -Laplacian case.

It is well known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution. In this paper we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in $\mathsf{PSPACE}$. Within the same complexity bound we can decide whether the solution set is empty, finite, or infinite. In the second part of the paper we apply the results for twisted equations to obtain in $\mathsf{PSPACE}$ an EDT0L description of the solution set of equations with rational constraints for finitely generated virtually free groups in standard normal forms with respect to a natural set of generators. If the rational constraints are given by a homomorphism into a fixed (or "small enough") finite monoid, then our algorithms can be implemented in $\mathsf{NSPACE}(n^2\log n)$, that is, in quasi-quadratic nondeterministic space. Our results generalize the work by Lohrey and S\'enizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to both complexity and expressive power. Neither paper gave any concrete complexity bound and the results in these papers are stated for subsets of solutions only, whereas our results concern all solutions., Comment: 72 pages, 14 figures. Small edits to the exposition in Section 15. An extended abstract of a preliminary version of this paper was presented at ICALP 2017

Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are universal hypergraphic automata. The input symbol semigroup of such automaton is an algebra of mappings which is considered as a derivative algebraic system for such automaton. Semigroup properties of the derivative algebraic system are interconnected with properties of the automaton. Thus, we can obtain a lot of information about a universal hypergraphic automaton studying its input symbol semigroups. In this paper, we found an abstract characterization of universal hypergraphic automata and an abstract characterization of input symbol semigroups of such automata. The results of the paper present effective tools for further analysis of the interrelation of algebraic and elementary properties of universal hypergraphic automata and their input symbol semigroups.

T. Ikeda and H. Katsurada have developed the theory of the Gross-Keating invariant of a quadratic form in their recent papers [IK1] and [IK2]. In particular, they prove that the local factor of the Fourier coefficients of the Siegel-Eisenstein series is completely determined by the Gross-Keating invariant with extra datum, called the extended GK datum, in [IK2]. On the other hand, such local factor is a special case of the local densities for a pair of two quadratic forms. Thus we propose a general question if the local density can be determined by certain series of the Gross-Keating invariants and the extended GK datums. In this paper, we prove that the answer to this question is affirmative, for the local density of a single quadratic form defined over an unramified finite extension of $\mathbb{Z}_2$. In the appendix, T. Ikeda and H. Katsurada compute the local density formula of a single binary quadratic form defined over any finite extension of $\mathbb{Z}_2$., 32 pages

In this paper, we study questions related to the theory of stochastic processes on Lie nilpotent groups. In particular, we consider the stochastic process on the Heisenberg group H3(ℝ) whose trajectories satisfy the horizontal conditions in the stochastic sense relative to the standard contact structure on H3 (ℝ). It is shown that this process is a homogeneous Markov process relative to the Heisenberg group operation. There was found a representation in the form of a Wiener integral for a one-parameter linear semigroup of operators for which the Heisenberg sublaplacian generated by basis vector fields of the corresponding Lie algebra L(H3) is producing. The main method of solving the problem in this paper is using the path integrals technique, which indicates the common direction of further development of the results.

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation, $${\rm{i}}u_t-u_{xx}+{\rm{i}}(|u|^4u)_x=0, \;\; x\in\mathbb{T}.$$ The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established. The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem. We mention that in the present paper the mean value of u does not need to be zero, but small enough, which is different from the assumption (1.7) in Geng-Wu [J. Math. Phys., 53, 102702 (2012)].

In [10], Pickrell fully characterizes the unitarily invariant probability measures on infinite Hermitian matrices. An alternative proof of this classification is given by Olshanski and Vershik in [9], and in [3] Borodin and Olshanski deduce from this proof that under any of these invariant measures, the extreme eigenvalues of the minors, divided by the dimension, converge almost surely. In this paper, we prove that one also has a weak convergence for the eigenvectors, in a sense that is made precise. After mapping Hermitian to unitary matrices via the Cayley transform, our result extends a convergence proven in our paper with Maples and Nikeghbali [6], for which a coupling of the circular unitary ensemble of all dimensions is considered.

A conjecture of Kotschick predicts that a compact Kähler manifold X fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao [10], we use our approach to prove Kotschick’s conjecture for smooth projective three-folds.

In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G. For a special case of two irreducible components with G$=\mathbb Z_2$, we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G-SFT applications, including a new connection to involutions of cellular automata., The paper has been augmented considerably and the second version is now 81 pages long. This version has been accepted for publication in Transactions of the American Mathematical Society

A graph G(V, E) is claw-free if no vertex has three pairwise non-adjacent neighbours. The maximum weight stable set (MWSS) problem in a claw-free graph is a natural generalization of the matching problem and has been shown to be polynomially solvable by Minty and Sbihi in 1980. In a remarkable paper, Faenza, Oriolo and Stauffer have shown that, in a two-step procedure, a claw-free graph can be first turned into a quasi-line graph by removing strips containing all the irregular nodes and then decomposed into {claw, net}-free strips and strips with stability number at most three. Through this decomposition, the MWSS problem can be solved in $$\mathcal{O}(|V|(|V| \log |V| + |E|))$$ time. In this paper, we describe a direct decomposition of a claw-free graph into {claw, net}-free strips and strips with stability number at most three which can be performed in $$\mathcal{O}(|V|^2)$$ time. In two companion papers we showed that the MWSS problem can be solved in $$\mathcal{O}(|E| \log |V|)$$ time in claw-free graphs with $$\alpha (G) \le 3$$ and in $$\mathcal{O}(|V| \sqrt{|E|})$$ time in {claw, net}-free graphs with $$\alpha (G) \ge 4$$ . These results prove that the MWSS problem in a claw-free graph can be solved in $$\mathcal{O}(|V|^2 \log |V|)$$ time, the same complexity of the best and long standing algorithm for the MWSS problem in line graphs.

This paper is based mainly on Titchmarsh’s theorem (Introduction to the theory of Fourier integrals. Clarendon Press, Oxford, 1937, Theorem 84) in the one-dimensional case. Abilov et al. (Comput Math Math Phys 48:2146, 2008) proved two useful estimates for the Fourier transform in the space of square integral multivariable functions on certain classes of functions characterized by the generalized continuity modulus, and these estimates are proved by Abilovs for only two variables, using a translation operator. The purpose of this paper is to study these estimates for Quaternion Fourier transforms, also the functions satisfy Lipschitz conditions of certain orders. Thus we study the Quaternion Fourier transforms of Lipschitz function in the functions space $$L^r({\mathbb {R}}^{2},{\mathcal {H}})$$, where $${\mathcal {H}}$$ a quaternion algebra which will be specified in due course.