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In this paper, all graphs are assumed to be finite. For s ≥ 1 and a graph Γ, if for every pair of isomorphic connected induced subgraphs on at most s vertices there exists an automorphism of Γ mapping the first to the second, then we say that Γ is s -connected-set-homogeneous, and if every isomorphism between two isomorphic connected induced subgraphs on at most s vertices can be extended to an automorphism of Γ, then we say that Γ is s -connected-homogeneous. For n ≥ 1 , a graph Γ is said to be locally 2 K n if the subgraph [ Γ (u) ] induced on the set of vertices of Γ adjacent to a given vertex u is isomorphic to 2 K n. Note that 2-connected-set-homogeneous but not 2-connected-homogeneous graphs are just the half-arc-transitive graphs which are a quite active topic in algebraic graph theory. Motivated by this, we posed the problem of characterizing or classifying 3-connected-set-homogeneous graphs of girth 3 which are not 3-connected-homogeneous in Zhou (2021) [54]. Until now, there have been only two known families of 3-connected-set-homogeneous graphs of girth 3 which are not 3-connected-homogeneous, and these graphs are locally 2 K n with n = 2 or 4. In this paper, we complete the classification of finite 3-connected-set-homogeneous graphs which are locally 2 K n with n ≥ 2 , and all such graphs are line graphs of some specific 2-arc-transitive graphs. Furthermore, we give a good description of finite 3-connected-set-homogeneous but not 3-connected-homogeneous graphs which are locally 2 K n and have solvable automorphism groups. This is then used to construct some new 3-connected-set-homogeneous but not 3-connected-homogeneous graphs as well as some new 2-arc-transitive graphs. [ABSTRACT FROM AUTHOR]

In this paper, we give an alternative construction of a certain class of deformed double current algebras. These algebras are deformations of |$ U(\textrm {End}(\Bbbk ^r)[x,y]) $| and they were initially defined and studied by N. Guay in his papers. Here, we construct them as algebras of endomorphisms in Deligne category. We do this by taking an ultraproduct of spherical subalgebras of the extended Cherednik algebras of finite rank. [ABSTRACT FROM AUTHOR]

The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis. The main contribution of this paper is in introducing the general fractional integrals and derivatives of the functions on a finite interval. As in the case of the Riemann–Liouville fractional integrals and derivatives on a finite interval, we define both the left- and the right-sided operators and investigate their interconnections. The main results presented in the paper are the 1st and the 2nd fundamental theorems of Fractional Calculus formulated for the general fractional integrals and derivatives of the functions on a finite interval as well as the formulas for integration by parts that involve the general fractional integrals and derivatives. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of finite energy traveling waves for the Gross-Pitaevskii equation. This problem has deserved a lot of attention in the literature, but the existence of solutions in the whole subsonic range was a standing open problem till the work of Mariş in 2013. However, such result is valid only in dimension 3 and higher. In this paper we first prove the existence of finite energy traveling waves for almost every value of the speed in the subsonic range. Our argument works identically well in dimensions 2 and 3. With this result in hand, a compactness argument could fill the range of admissible speeds. We are able to do so in dimension 3, recovering the aforementioned result by Mariş. The planar case turns out to be more intricate and the compactness argument works only under an additional assumption on the vortex set of the approximating solutions. [ABSTRACT FROM AUTHOR]

This paper initially presents bounds for the joint tail and the conditional tails of the backward and forward recurrence times. Using these bounds, we deliver an improvement to the lower bound for the renewal function given by Brown [Inequalities for distributions with increasing failure rate. In: Gelfand AE, editors. Contributions to the theory and applications of statistics, a volume in honour of Herbert Solomon. Orlando, FL: Academic; 1987. p. 3–17] for IFR inter-arrival times. Finally, this paper proposes a renewal type equation for the expected number of renewals in (t , t + h ] and, under certain conditions, improves Lorden's [On excess over the boundary. Ann Math Stat. 1970;41(2):520–527] well-known general upper bound for the expected number of renewals in (t , t + h ]. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann–Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the Δ 2 , which will be useful to obtain the convexity results. We examine the correlation between the positivity of ( w 0 RL Δ α f) (t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2 , 3) , H k , ϵ and M k , ϵ . The decrease of these sets allows us to obtain the relationship between the negative lower bound of ( w 0 RL Δ α f) (t) and convexity of the function on a finite time set N w 0 P : = { w 0 , w 0 + 1 , w 0 + 2 , ... , P } for some P ∈ N w 0 : = { w 0 , w 0 + 1 , w 0 + 2 , ... } . The numerical part of the paper is dedicated to examinin the validity of the sets H k , ϵ and M k , ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem. [ABSTRACT FROM AUTHOR]

The finite frequency domain H ∞ consensus control problem of neutral multi-agent systems with the input delay is investigated in this paper for the first time. According to the linear transformation, the problem of H ∞ consensus is converted into a set of H ∞ stability problems. Through the Lyapunov theory, combined with the time-delay interval decomposition method, a less conservative controller design method for the state feedback controller is presented. And the obtained controller can ensure closed-loop multi-agent systems to fulfil the consensus. Utilizing the generalised Kalman-Yakubovich-Popov (GKYP) lemma, the sufficient condition is derived for multi-agent systems achieving the H ∞ performance in the finite frequency domain (FFD). Then, via the orthogonal spatial information of the input matrix, the conservativeness of obtained design approach is further declined. Moreover, the design method with less conservativeness is proposed for the dynamic output feedback controller. Finally, a numerical case and a multi-pendulum system controlled by the multi-motor system are presented in this paper to demonstrate the availability and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

The current article gives a new approach that is efficient for the design of a low-order H∞ controller over a finite time interval. The system under consideration is a linear discrete time system affected by norm bounded disturbances. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, reducing the number of variables in Linear Matrix Inequalities (LMIs). Thus, reduced order H∞ controller parameters are given to guarantee a finite time H∞ bound (FTB-H∞) for a closed-loop system. The method of the finite time stability, that is proven in this paper by the Lyapunov theory, can be applied to a wide range of process models. Numerical examples demonstrating the effectiveness of the results developed are presented at the end of this paper. [ABSTRACT FROM AUTHOR]

Let U q − be the negative part of the quantum enveloping algebra, and σ the algebra automorphism on U q − induced from a diagram automorphism. Let U _ q − be the quantum algebra obtained from σ , and B ˜ (resp. B _ ˜) the canonical signed basis of U q − (resp. U _ q −). Assume that U q − is simply-laced of finite or affine type. In our previous papers [10] , [11] , we have proved by an elementary method, that there exists a natural bijection B ˜ σ ≃ B _ ˜ in the case where σ is admissible. In this paper, we show that such a bijection exists even if σ is not admissible, possibly except some small rank cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose clustering algorithms based on finite mixture and infinite mixture models of exponential approximation to the Multinomial Generalized Dirichlet (EMGD), Multinomial Beta-Liouville (EMBL) and Multinomial Shifted- Scaled Dirichlet (EMSSD) with Bayesian inference. The finite mixtures have already shown superior performance in real data sets clustering using the Expectation--Maximization approach. The proposed approaches in this paper are based on a Monte Carlo simulation technique namely Gibbs sampling algorithm including an additional Metropolis--Hastings step, and we utilize exponential family conjugate prior information to construct their posterior relying on Bayesian theory. Furthermore, we also present the infinite models based on Dirichlet processes, which results in clustering algorithms that do not require the specification of the number of mixture components to be given in advance and selects it in a principled manner. The performance of our Bayesian approaches was evaluated in some challenging real-world applications concerning text sentiment analysis, fake news detection, and human face gender recognition. [ABSTRACT FROM AUTHOR]

German is a V2 language, i.e., a declarative clause has the finite verb in the position immediately after the first constituent. Traditionally, this order is derived by raising the verb to C and putting a single constituent into the so-called pre-field. Arguably, there are three options to fill the first position: (i) topicalization (A'-movement), (ii) formal movement, which raises the highest constituent in the ongoing derivation (A-movement), or (iii) merging a constituent which is only legitimate there (base-generation). Theoretically, any major constituent can occupy the pre-field. However, it has been observed that certain expressions cannot appear there. In its narrower focus, the paper argues that there are more pre-field-phobic expressions than standardly assumed, and that these expressions, although at first glance heterogeneous, fall into two classes. One can be defined structurally and is considered in the second part of this paper; the other class can be captured in terms of meaning and comprises a specific type of expressive adverbial (discussed in the first and main part). The paper's message in a broader sense is that syntax restricts the occurrence of expressive expressions. It is shown that the sentence-initial position in German does not allow material which is exclusively use-conditional in the sense of expressive meaning. [ABSTRACT FROM AUTHOR]

Möbius transforms of capacities or games were considered as a tool for extensions of capacities to particular aggregation functions in several papers. This is, for example, the case of the Lovász extension coinciding with the Choquet integral, or the Owen extension that is also known as multilinear extension. In this paper, a much deeper study of the links between the Möbius transforms of real-valued functions defined on finite bounded posets and aggregation functions is performed. We introduce a Möbius product of any two real-valued functions defined on an arbitrary finite bounded poset, and then, fixing the poset (2 N , ⊆) , N = { 1 , ... , n } , we propose and discuss a construction method for n -ary aggregation functions based on the Möbius product of any capacity on N and a real-valued function g x , x ∈ [ 0 , 1 ] n , defined on 2 N and determined by some appropriate n -ary aggregation function. We provide some necessary and some sufficient conditions for the introduced construction to yield an aggregation function for any capacity. For the binary case, a complete characterization of conditions under which our approach results in an aggregation function for each capacity m is given. [ABSTRACT FROM AUTHOR]

Dynamical decoupling is a key method to mitigate errors in a quantum mechanical system, and we studied it in a series of papers dealing, in particular, with the problems arising from unbounded Hamiltonians. The standard bangbang model of dynamical decoupling, which we also used in those papers, requires decoupling operations with infinite amplitude, which is, strictly speaking, unrealistic from a physical point of view. In this paper, we look at decoupling operations of finite amplitude, discuss under what assumptions dynamical decoupling works with such finite amplitude operations, and show how the bangbang description arises as a limit, hence justifying it as a reasonable approximation. [ABSTRACT FROM AUTHOR]

This paper refines the classical notion of a stochastic D-bifurcation to the respective family of n-point motions for homogeneous Markovian stochastic semiflows, such as stochastic Brownian flows of homeomorphisms, and their generalizations. This notion essentially detects at which level the support of the invariant measure of the k-point bifurcation has more than one connected component. Stochastic Brownian flows and their invariant measures were shown by Kunita (1990) to be rigid, in the sense of being uniquely determined by the 1-and 2-point motions. Hence, only stochastic n-point bifurcation of level n = 1 or n = 2 can occur. For general homogeneous stochastic Markov semiflows this turns out to be false. This paper constructs minimal examples of where this rigidity is false in general on finite space and studies the complexity of the resulting n-point bifurcations. [ABSTRACT FROM AUTHOR]

With an increase in tracking time, the operating cost of the controller will increase accordingly. Considering the biological applications of Boolean control networks (BCNs), it is necessary to study the control problem of BCNs over finite time. In this paper, we study the output tracking problem of a BCN with disturbance inputs in a given finite time. First, the logical form of BCNs is transformed into an algebraic form using the semi-tensor product (STP) method. Then, the robust output tracking problems of a reference output trajectory and the outputs of a reference system over finite time are transformed into the robust reachability problem of the BCNs. Based on the truth matrix technique, two necessary and sufficient conditions are provided for the trackability of the reference outputs over finite time. Moreover, two algorithms are proposed to design the controllers in the case of the traceable outputs. It should be pointed out that the truth matrix method we used here has some unique features, including its simple computation and concise expression. Finally, two illustrative examples are presented to demonstrate the results in this paper. [ABSTRACT FROM AUTHOR]

Let G be a finite simple graph with Laplacian polynomial ψ G , λ = ∑ k = 0 n − 1 n − k c k λ k . In an earlier paper, the coefficients c n − 4 and c n − 5 for forests with respect to some degree-based graph invariants were computed. The aim of this paper is to continue this work by giving an exact formula for the coefficient c n − 6 . [ABSTRACT FROM AUTHOR]

Graphs considered in this paper are simple finite undirected graph without loops or multiple edges. A simple graph where each vertex has degree 3 is called a cubic graph. A cubic graph, that is, 1-connected or cubic bridge graph is traceable if it contains a Hamiltonian path. Otherwise, we called it non-traceable. In this paper, we introduce a new family of cubic graphs called Non-Traceable Cubic Bridge Graph (NTCBG) that satisfies the conjecture of Zoeram and Yaqubi (2017). In addition, we define two important connected components of NTCBG those are the central fragment that gives assurance for a graph to be non-traceable and its branch. Some properties of a NTCBG such as chromatic number and clique number are also provided. [ABSTRACT FROM AUTHOR]

We study critical GI/G/1 queues under finite second-moment assumptions. We show that the busy-period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy-period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further use this to demonstrate a Balancing Reduces Asymptotic Variance of Outputs (BRAVO) phenomenon for the work-output process (namely the busy time). This yields new insight on the BRAVO effect. A second contribution of the paper is in settling previous conjectured results about GI/G/1 and GI/G/s BRAVO. Previously, infinite buffer BRAVO was generally only settled under fourth-moment assumptions together with an assumption about the tail of the busy period. In the current paper, we strengthen the previous results by reducing to assumptions to existence of 2 + ϵ moments. [ABSTRACT FROM AUTHOR]

For the Stokes system in the half space, Kang [Math. Ann. 331 (2005), pp. 87-109] showed that a solution generated by a compactly supported, Hölder continuous boundary flux may have unbounded normal derivatives near the boundary. In this paper we first prove explicit global pointwise estimates of the above solution, showing in particular that it has finite global energy and its derivatives blow up everywhere on the boundary away from the flux. We then use the above solution as a profile to construct solutions of the Navier-Stokes equations which also have finite global energy and unbounded normal derivatives due to the flux. Our main tool is the pointwise estimates of the Green tensor of the Stokes system proved by us in an earlier paper. We also examine the Stokes flows generated by dipole bumps' boundary flux, and identify the regions where the normal derivatives of the solutions tend to positive or negative infinity near the boundary. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the morality's role in one of the most important promises professed by transhumanism, the promise of human immortality. This purpose will be carried out through the interpretation of the short tale: The Immortal by Jorge Luis Borges. This in order to unveil the close relationship that exists between the moral dimension of man - the question of what should I do - and the recognition of his finitude, of his becoming, as a being that forms his own narrative in the world. [ABSTRACT FROM AUTHOR]

This paper will deal with differentiability properties of the class of Hellinger–Kantorovich distances HK Λ , Σ (Λ , Σ > 0) which was recently introduced on the space M (R d) of finite nonnegative Radon measures. The derivatives of t ↦ HK Λ , Σ (μ t , ν t) 2 , for absolutely continuous curves (μ t) t , (ν t) t in (M (R d) , HK Λ , Σ) , will be computed L 1 -a.e.. The characterization of absolutely continuous curves in (M (R d) , HK Λ , Σ) will be refined. [ABSTRACT FROM AUTHOR]

Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories. [ABSTRACT FROM AUTHOR]

In this paper, we study lattice gauge theory on Z 4 with finite Abelian structure group. When the inverse coupling strength is sufficiently large, we use ideas from disagreement percolation to give an upper bound on the decay of correlations of local functions. We then use this upper bound to compute the leading-order term for both the expected value of the spin at a given plaquette as well as for the two-point correlation function. Moreover, we give an upper bound on the dependency of the size of the box on which the model is defined. The results in this paper extend and refine results by Chatterjee and Borgs. [ABSTRACT FROM AUTHOR]

This paper employs and develops the exact wave-based vibration analysis approach to investigate the propagation properties of a designed finite lightweight locally resonant (LR) beam with two-degree-of-freedom (2-DOF) force-moment-type resonators attached periodically inside. By deriving the propagation, reflection, and transmission matrices of the structural discontinuities, the vibration of the LR beam can be described as structural waves. By assembling wave relations into the beam, the approach shows high efficiency because the forced vibration problem of the lightweight LR structure is turned to be the solution to a related set of matrix equations. The accuracy of the developed approach is validated with two examples carried out using the finite element method. In addition, the influence of the main parameters of the LR beam is studied and we found that the increase in the mass of the resonator and the stiffness of the spring are more sensitive in broadening the width and increasing the center frequency of the band gap of the designed lightweight LR beam. The proposed structure and analysis approach in this paper may provide an exact and efficient means for the design and analysis of structures in which damping and lightweight properties are required, such as space-arm and the framework of antennas in the field of aerospace. [ABSTRACT FROM AUTHOR]

In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. For illustration of our methods a constructive proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert manifolds do not exist for nonzero Euler class, in particular elliptic 3-manifolds. Each type of elliptic 3-manifold is then considered and the possible group actions that fit the given construction. This is shown to be all but a few cases that have been considered elsewhere. Finally, a presentation for the quotient space under such an action is constructed and a specific example is generated. [ABSTRACT FROM AUTHOR]

The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). [ABSTRACT FROM AUTHOR]

In this paper we continue our investigations of 4-dimensional complexes in [A. Cavicchioli, F. Hegenbarth, F. Spaggiari, Four-dimensional complexes with fundamental class, Mediterr. J. Math. 17 (2020), 175]. We study a class of finite oriented 4-complexes which we call FC 4 {\mathrm{FC}_{4}} -complexes, defined as follows. An FC 4 {\mathrm{FC}_{4}} -complex is a 4-dimensional finite oriented CW-complex X with a single 4-cell such that H 4 ⁢ (X , ℤ) ≅ ℤ {H_{4}(X,\mathbb{Z})\cong\mathbb{Z}} with a fundamental class [ X ] ∈ H 4 ⁢ (X , ℤ) {[X]\in H_{4}(X,\mathbb{Z})}. By well-known results of Wall, any Poincaré complex is of this type. We are interested in two questions. First, for which 3-complexes K does an element [ φ ] ∈ π 3 ⁢ (K) {[\varphi]\in\pi_{3}(K)} exist such that K ∪ φ D 4 {K\cup_{\varphi}D^{4}} is a Poincaré complex? Second, if there exists one, how many others can be constructed from K? The latter question was addressed studied in the above cited previous paper of the authors. In the present paper we deal with the first problem, and give necessary and sufficient conditions on K and [ φ ] ∈ π 3 ⁢ (K) {[\varphi]\in\pi_{3}(K)} to satisfy Poincaré duality with ℤ {\mathbb{Z}} - and Λ-coefficients. Here Λ denotes the integral group ring of π 1 ⁢ (K) {\pi_{1}(K)}. Before, we give a classification of all FC 4 {\mathrm{FC}_{4}} -complexes based on the finite 3-complex K, and make some remarks concerning ℤ {\mathbb{Z}} - and Λ-Poincaré duality. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlocal nonlinear Schrödinger equation (NNLSE), which is an important extension of the nonlinear Schrödinger equation (NLSE). Since the nonlinearity of NNLSE involves a convolution, numerical approximation of its solution is very expensive. To achieve an efficient numerical method for solving the NNLSE, according to the property of convolution, we firstly present a partial differential equation (PDE) method to transfer the NNLSE from an integro-differential equation to an equivalent or approximate system of PDEs, and the numerical solution of the NNLSE can then be obtained by solving these PDEs. Based on the recently developed finite integration method (FIM), we derive an improved method (IFIM) in this paper. The novelty of this IFIM is that the quadrature method is only used once instead of multiple times for multi-layer integral, so it consumes less running time and provides higher accuracy. In addition, we adapt a second-order operator-splitting method (OS2) at each time-step to ensure a convergent solution for long-time integration. Several numerical experiments are given to verify the efficiency and accuracy of the proposed IFIM for solving the NNLSE. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of multiple agents circumnavigating group targets within finite time. Unlike most existing works in which agents can circumnavigate with a regular-shaped trajectory in the mission area, the problem of agents with an irregular-shaped trajectory in the area with obstacles is addressed in the paper. The agents can only obtain the bearing information of the targets. First, a scheme for establishing the group targets as an extended convex hull is presented. And the boundary of the extended convex hull is taken as the scheduled irregular-shaped trajectory. Then, a finite-time estimator is presented to localise the positions of the targets and their geometric centre. Afterward, a finite-time control protocol is proposed to drive agents along the irregular-shaped trajectory within finite time. Subsequently, an obstacle avoidance method is provided for agents to avoid obstacles on the path to the expected trajectory. Finally, simulation results validate the effectiveness of the theoretical results in this paper. [ABSTRACT FROM AUTHOR]

Let G (V , X) be a finite and simple graph of order n and size m. The complement of G, denoted by G ¯ , is the graph obtained by removing the lines of G and adding the lines that are not in G. A graph is self-complementary if and only if it is isomorphic to its complement. In this paper, we define δ -complement and δ ′ -complement of a graph as follows. For any two points u and v of G with deg u = deg v remove the lines between u and v in G and add the lines between u and v which are not in G. The graph thus obtained is called δ -complement of G. For any two points u and v of G with deg u ≠ deg v remove the lines between u and v in G and add the lines between u and v that are not in G. The graph thus obtained is called δ ′ -complement of G. The graph G is δ (δ ′) -self-complementary if G ≅ G δ (G ≅ G δ ′) . The graph G is δ (δ ′) -co-self-complementary if G δ ≅ G ¯ (G δ ′ ≅ G ¯) . This paper presents different properties of δ and δ ′ -complement of a given graph. [ABSTRACT FROM AUTHOR]

In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the series, we present duality theorems for combinations of stars and combs: dominating stars and dominated combs. As dominating stars exist if and only if dominated combs do, the structures complementary to them coincide. Like for arbitrary stars and combs, our duality theorems for dominated combs (and dominating stars) are phrased in terms of normal trees or tree‐decompositions. The complementary structures we provide for dominated combs unify those for stars and combs and allow us to derive our duality theorems for stars and combs from those for dominated combs. This is surprising given that our complementary structures for stars and combs are quite different: Those for stars are locally finite whereas those for combs are rayless. [ABSTRACT FROM AUTHOR]

This paper addresses the log-optimal portfolio, which is the portfolio with finite expected log-utility that maximizes the expected logarithm utility from terminal wealth, for an arbitrary general semimartingale model. The most advanced literature on this topic elaborates existence and characterization of this portfolio under the no-free-lunch-with-vanishing-risk (NFLVR for short) assumption, while there are many financial models violating NFLVR and admitting the log-optimal portfolio. In this paper, we provide a complete and explicit characterization of the log-optimal portfolio and its associated optimal deflator, give necessary and sufficient conditions for their existence, and elaborate their duality no matter what the market model. Furthermore, our characterization gives an explicit and direct relationship between log-optimal and num'eraire portfolios without changing the probability or the num'eraire. [ABSTRACT FROM AUTHOR]

Aiming at the precision loss problem of most low-complexity Root-MUSIC algorithms at present, a low-complexity Root-MUSIC algorithm with precision compensation ability is studied and proposed. The algorithm reconstructs the autocorrelation matrix with Toeplitz shape according to the first row of the approximate data observation matrix obtained by finite snapshots, so that the reconstructed autocorrelation matrix has Hermitian property. After decomposing the reconstructed autocorrelation matrix, the noise subspace is obtained, the noise subspace is flipped and split, a new root-finding polynomial is reconstructed, and then the DOA estimated value is obtained by the root-finding method. The algorithm proposed in this paper using Toeplitz matrix reconstruction and root polynomial reduction effectively improves the DOA estimation accuracy of the improved Root-MUSIC algorithm. And the time complexity of the improved algorithm is no higher than that of previous algorithms. Under different incident sources and sampling snapshots, the algorithm proposed in this paper also shows stronger robustness and stability. [ABSTRACT FROM AUTHOR]

In this paper, we establish some stochastic comparison results for two finite mixture models where the corresponding random variables follow one of the parental families of distributions, namely, proportional odds, proportional hazards, and proportional reversed hazards. The results of this paper are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out. [ABSTRACT FROM AUTHOR]

This paper is concerned with global solvability of a fully parabolic system of Keller–Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic positive motility function under a certain smallness assumption at infinity, which however permits the motility function to be arbitrarily large within a finite region. Then uniform-in-time boundedness of classical solutions is established whenever the motility function has strictly positive lower and upper bounds in any dimension N ≥ 1 , or decays at a certain slow rate at infinity for N ≥ 2. Our results remove the crucial non-increasing requirement on the motility function in some recent work [10,13,16] and hence allow for both chemo-attractive and chemo-repulsive effect, or their co-existence in applications. The key ingredient of our proof lies in an important improvement of the comparison method developed in [10,16,18]. [ABSTRACT FROM AUTHOR]

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V , and G is not metacyclic. Then G always has a regular orbit on V except for a few "small" cases. We completely classify these cases in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove that for any bounded set of finite perimeter \Omega \subset \mathbb {R}^n, we can choose smooth sets E_k \Subset \Omega such that E_k \rightarrow \Omega in L^1 and \begin{align*} \limsup _{i \rightarrow \infty } P(E_i) \le P(\Omega)+C_1(n) \mathscr {H}^{n-1}(\partial \Omega \cap \Omega ^1). \end{align*} In the above \Omega ^1 is the measure-theoretic interior of \Omega, P(\cdot) denotes the perimeter functional on sets, and C_1(n) is a dimensional constant. Conversely, we prove that for any sets E_k \Subset \Omega satisfying E_k \rightarrow \Omega in L^1, there exists a dimensional constant C_2(n) such that the following inequality holds: \begin{align*} \liminf _{k \rightarrow \infty } P(E_k) \ge P(\Omega)+ C_2(n) \mathscr {H}^{n-1}(\partial \Omega \cap \Omega ^1). \end{align*} In particular, these results imply that for a bounded set \Omega of finite perimeter, \begin{align*} \mathscr {H}^{n-1}(\partial \Omega \cap \Omega ^1)=0 \end{align*} holds if and only if there exists a sequence of smooth sets E_k such that E_k \Subset \Omega, E_k \rightarrow \Omega in L^1 and P(E_k) \rightarrow P(\Omega). [ABSTRACT FROM AUTHOR]

The paper studies a bounded symmetric operator A ε in L 2 (R d) with (A ε u) (x) = ε − d − 2 ∫ R d a ((x − y) / ε) μ (x / ε , y / ε) (u (x) − u (y)) d y ; here ε is a small positive parameter. It is assumed that a (x) is a non-negative L 1 (R d) function such that a (− x) = a (x) and the moments M k = ∫ R d | x | k a (x) d x , k = 1 , 2 , 3 , are finite. It is also assumed that μ (x , y) is Z d -periodic both in x and y function such that μ (x , y) = μ (y , x) and 0 < μ − ⩽ μ (x , y) ⩽ μ + < ∞. Our goal is to study the limit behaviour of the resolvent (A ε + I) − 1 , as ε → 0. We show that, as ε → 0 , the operator (A ε + I) − 1 converges in the operator norm in L 2 (R d) to the resolvent (A 0 + I) − 1 of the effective operator A 0 being a second order elliptic differential operator with constant coefficients of the form A 0 = − div g 0 ∇. We then obtain sharp in order estimates of the rate of convergence. [ABSTRACT FROM AUTHOR]

In this paper, the averaging principle is studied for a class of multi-scale stochastic partial differential equations driven by α -stable process, where α ∈ (1 , 2). Using the technique of Poisson equation, we prove that the orders of strong and weak convergence are 1 − 1 / α and 1 − r for any r ∈ (0 , 1) respectively. The main contributions extend Wiener noise considered by Bréhier in [6] to α -stable process, and the finite dimensional case considered by Sun et al. in [36] to the infinite dimensional case. [ABSTRACT FROM AUTHOR]

Consider the blow-up Y of a weighted projective plane at a point in the open orbit over a field of characteristic 0. We assume that there exists a curve C on Y such that C 2 < 0 and C. E = 1 , where E is the exceptional curve. In this paper we give a (very simple) necessary and sufficient condition for finite generation of the Cox ring of Y (Theorem 1.2). It is an affirmative answer to a conjecture due to He and Kurano-Nishida. [ABSTRACT FROM AUTHOR]

We in this paper improve a method for establishing the finite time blow‐up solutions on the parabolic or pseudoparabolic equations. And we apply it to restudy the finite time blow‐up and upper bound for the blow‐up time on the initial boundary value problem of ut−Δut−Δu=|u|p−1u$$ {u}_t-\Delta {u}_t-\Delta u&amp;#x0003D;{\left&amp;#x0007C;u\right&amp;#x0007C;}&amp;#x0005E;{p-1}u $$. Specifically, we prove that I(u0)<0$$ I\left({u}_0\right)&lt;0 $$ is a sufficient condition of the existence of finite time blow‐up solutions and 2(p−1)−1‖u0‖H012(p−1)‖∇u0‖22−2(p+1)J(u0)$$ \frac{2{\left(p-1\right)}&amp;#x0005E;{-1}{\left\Vert {u}_0\right\Vert}_{H_0&amp;#x0005E;1}&amp;#x0005E;2}{\left(p-1\right){\left\Vert \nabla {u}_0\right\Vert}_2&amp;#x0005E;2-2\left(p&amp;#x0002B;1\right)J\left({u}_0\right)} $$ is a new upper bound for the blow‐up time, which generalizes the results of previous studies in the variational sense. Moreover, we estimate the upper blow‐up rate of these solutions, too. [ABSTRACT FROM AUTHOR]

In this paper, we prove that any mean curvature flow translator Σ 2 ⊂ R 3 with finite total curvature and one end must be a plane. We also prove that if the translator Σ has multiple ends, they are asymptotic to a plane Π containing the direction of translation and can be written as graphs over Π . Finally, we determine that the ends of Σ are strongly asymptotic to Π and obtain quantitative estimates for their asymptotic behavior. [ABSTRACT FROM AUTHOR]

In this paper we complement and generalize some constructions of fuzzy implications based on two arbitrary copulas, obtaining new fuzzy implications. By means of (restricted) aggregation functions acting on [ 0 , 1 ] S , where S is a fixed finite or infinite set, and related S -systems of fuzzy implications and transforming functions, we introduce and discuss a rather general method for constructing fuzzy implications. Several examples illustrating our results are also included. [ABSTRACT FROM AUTHOR]

In this paper, the finite thrust nonplanar transfer and cooperative rendezvous are investigated. The indirect method is adopted in the optimization process. The energy-optimal to fuel-optimal continuation is performed by using the homotopy method. An initial guess generator (IGG) is designed based on a simplified dynamical model to overcome the difficulty in providing the initial guess. Some reasonable simplifications on the dynamical model are applied based on the near-circular near-coplanar transfer. The initial guess can be obtained by analytically solving a system of linear equations. Therefore, the IGG has high computational efficiency. Moreover, the terminal time and state are estimated by IGG to deal with the cooperative rendezvous problem. Numerical examples are presented and the validity of the "IGG-Homotopy" combined algorithm is verified. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce the concept of conformable matrix sine and cosine functions, which help us to seek explicit formula of solutions to a conformable type linear oscillating system by using the variation of constants method. Secondly, we establish some sufficient conditions to guarantee the finite time stability results and give sufficient and necessary conditions to examine that a linear conformable system is relatively controllable. Further, we apply fixed point theorem to prove relatively controllable result for a semilinear conformable system. Finally, examples are presented to illustrate the validity of the main theorems. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following Choquard‐type equation: −Δλu=∫ℝN|y|λβ|u(y)|p|x−y|λαdy|x|λβ|u(x)|p−2u(x)inℝN,$$ -{\Delta}_{\lambda }u={\int}_{{\mathbb{R}}^N}\frac{{\left|y\right|}_{\lambda}^{\beta }{\left|u(y)\right|}^p}{{\left|x-y\right|}_{\lambda}^{\alpha }} dy{\left|x\right|}_{\lambda}^{\beta }{\left|u(x)\right|}^{p-2}u(x)\kern6.05pt \mathrm{in}\kern6.05pt {\mathbb{R}}^N, $$where N,p>2$$ N,p>2 $$, 0<α

In this paper, a new finite element for 2D non-prismatic (curved and tapered) elastic beams with narrow rectangular cross-section is proposed. The element is geometrically exact, hence capable of handling large displacements and finite rotations, and allows for cross-section arbitrary warping through the inclusion of additional degrees of freedom (DOFs). These additional DOFs make it possible to capture the non-standard shear stress distributions that are developed in tapered members. All expressions required to implement the proposed finite element are derived and written in a simple vector/matrix form. To assess the accuracy and demonstrate the capabilities of the proposed element, several numerical examples are presented. For comparison purposes, results obtained with refined meshes of standard 2D finite elements are also shown. It is concluded that the proposed element leads to very accurate results with a small computational cost. [ABSTRACT FROM AUTHOR]