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We prove a strictification theorem for cartesian closed bicategories. First, we adapt Power's proof of coherence for bicategories with finite bilimits to show that every bicategory with bicategorical cartesian closed structure is biequivalent to a 2-category with 2-categorical cartesian closed structure. Then we show how to extend this result to a Mac Lane-style "all pasting diagrams commute" coherence theorem: precisely, we show that in the free cartesian closed bicategory on a graph, there is at most one 2-cell between any parallel pair of 1-cells. The argument we employ is reminiscent of that used by Čubrić, Dybjer, and Scott to show normalisation for the simply-typed lambda calculus (Čubrić et al., 1998). The main results first appeared in a conference paper (Fiore and Saville, 2020) but for reasons of space many details are omitted there; here we provide the full development. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the converse of Baer's theorem for two-nilpotent variety of class row (n,m) is carried out. Baer proved that finiteness of G/Zn(G) implies that γn+1(G) is finite. Hekster proved the converse of the Baer's theorem with the assumption that G can be finitely generated. The Baer's theorem can be considered as a result of a classical theorem by Schur denoting that finiteness of G/Z(G) leads to the finiteness of G ′. The converse of the Baer's theorem has been proved conditionally by Taghavi et al. (2019), as well. In the Main Theorem, we prove that, if γm,n(G) ∩ Zn,m(G) = 1 and γm,n+i(G) is finite for some n, i,m ≥ 0. Then G/Zn,m(G) is finite in which γm,n(G) and Zn,m(G) denote verbal and marginal subgroups with respect to two-nilpotent variety of class row (n,m). Thus the generalization of the converse of Baer's theorem for two-nilpotent variety of groups valids by considering i = 0. In this article some other results are attained by the converse of the Baer's theorem. It is also concluded that when n = m = 1. Similar results are obtained for variety of the soluble groups. In addition, the converse of the Schur's theorem which proved by Halasi and Podoski is concluded in this paper, for two-nilpotent variety. We have also obtained some similar results of Chakaneh et al. (2019) for (n,m)-isoclinic family of groups and (1,m)-stem groups. [ABSTRACT FROM AUTHOR]

The paper presents a detailed description of an algorithm of Estonian syllabification. The paper has a dual goal: justify the algorithm with references to phonology, and make it robust enough for using on real-life texts. The algorithm is presented as a commented set of finite state transducer expressions. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic Plateau problem in ℍ 2 × ℝ. We construct the first examples of non-fillable finite curves with no thin tail in S ∞ 1 × ℝ. [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 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]

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]

It is well known that one-dimensional integral equations of the convolution type considered on a finite interval cannot generally be solved by quadratures in contrast to similar equations considered on the entire line or on the half-line. For this reason, when studying their spectrum, some asymptotic method must be used. The paper considers a convolution-type integral operator with a logarithmic kernel defined on a finite interval. Using the Fourier transform, the problem is successively reduced to a conjugation problem and to a singular integral equation on the half-line in which the integral operator is not a contraction. It is shown that the leading part of the integral equation thus obtained can be inverted explicitly. The cases of even and odd eigenfunctions are considered, in each of which the asymptotics of the eigenvalues and eigenfunctions of the original operator is found. [ABSTRACT FROM AUTHOR]

In this paper, we prove a conjecture stated by the first two authors establishing the closure of the numerical range of a certain class of n + 1-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal (n + 1) × (n + 1) matrices. Furthermore, when n + 1 is odd, we show that the size of such matrices simplifies to n 2 + 1. [ABSTRACT FROM AUTHOR]

Many industrial facilities involve splitting production systems of different complexities and arrangements. The accurate and efficient evaluation of the associated performance measures is, therefore, of great importance. This challenging task can be accomplished by applying mathematical models of production system engineering at different intricacies. This paper presents the development and application of the analytical approach to splitting production systems modelling. The same problem is also addressed using the finite state method as a semi-analytical model. Several theoretical examples were considered to validate the finite state method that proved to be quite efficient and accurate. Finally, the developed modelling approach was applied in the case of a wood-processing facility. The obtained results were validated successfully against the acquired factory-floor data. [ABSTRACT FROM AUTHOR]

This paper proposes a high-speed deterministic digital technique to calibrate the errors due to capacitance mismatch and finite op-amp gain. Unlike other calibration techniques, this technique requires neither forcing the inputs of the intermediate stages being calibrated to exact voltages, nor reducing the gains of each stage to avoid saturation of output digital codes. A 1.5 bits/stage, 10 stages, 9 bits pipeline ADC with the three most significant stages calibrated is demonstrated in this paper. For a 10% mismatch in capacitances in the 3 MSB stages of the pipelined ADC, the calibration technique improved SNDR by more than 20 dB and SFDR by around 27 dB. The technique can also be slightly modified to calibrate algorithmic ADCs. For a 7% mismatch in capacitances of the algorithmic ADC, the proposed calibration technique improved SNDR by 18 dB and SFDR by around 28 dB. [ABSTRACT FROM AUTHOR]

Emil Post's tag system problem posed the question of whether or not a tag system {N = 3, P(0) = 00, P(1) = 1101} has a configuration, simulation of which will never halt or end up in a loop. Over the subsequent decades, there were several attempts to find an answer to this question, including a recent study, during which the first 284 initial configurations were checked. This paper presents a family of configurations of this type in the form of strings AnBCm that evolve to An+1BCm+1 after a finite number of steps. The proof of this behavior for all non-negative n and m is described later in this paper as a finite verification procedure, which is computationally bounded by 20 000 iterations of tag. [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]

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]

It is well recognized that there emerged a trend of inward‐looking trade policies even before the COVID pandemic crippled the world. These were reflected in both BREXIT and US‐China trade conflicts. As countries become inward‐oriented, usually local prices start rising. With this backdrop, this paper explores how rising local prices are likely to affect employment in the short and long runs when we accommodate for the finite change in a general equilibrium structure whereby sectors not only contract but might also close down altogether due to the capital reallocation effect following a price incentive. [ABSTRACT FROM AUTHOR]

The buffer allocation problem in production lines is an NP-hard combinatorial optimisation problem. This paper proposes a new hybrid optimisation approach (using simulation) relying on genetic algorithm (GA) and finite perturbation analysis (FPA). Unlike the infinitesimal perturbation analysis, which deals with small (infinitesimal variation) perturbations for estimating gradients of the performance measure, FPA deals with larger (finite) or more lasting perturbations. It is an extension specifically dedicated to discrete decision variables and applicable to most discrete-event dynamic systems. The proposed method allows a global search using GA, with refinement in specific solution-space regions using FPA. The main objective is to maximise the average production rate of a production line with unreliable machines, by allocating the total buffer capacity in locations between machines. Extensive numerical experiments show that: (1) the proposed hybrid GA-FPA method clearly outperforms the state-of-the-art methods from the literature; (2) combining FPA and GA is beneficial when compared to employing GA or FPA independently. [ABSTRACT FROM AUTHOR]

In this paper we give a complete list of non-isometric bidimensional S¹-invariant Kähler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a classical and long-staying problem addressed among others in [7] and [31]. [ABSTRACT FROM AUTHOR]

In this paper the authors introduce an analogue of the nilpotent cone, N, for a classical Lie superalgebra, g, that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra, g = g0 ⊕ g1 with Lie G0 = g0, it is shown that there are finitely many G0-orbits on N. Later the authors prove that the Duflo-Serganova commuting variety, X, is contained in N for any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper. [ABSTRACT FROM AUTHOR]

The goal of this paper is to contribute to the classification of the phase portraits of planar quadratic differential systems according to their structural stability. Artés et al. (Mem Am Math Soc 134:639, 1998) proved that there exist 44 structurally stable topologically distinct phase portraits in the Poincaré disc modulo limit cycles in this family, and Artés et al. (Structurally unstable quadratic vector fields of codimension one, Springer, Berlin, 2018) showed the existence of at least 204 (at most 211) structurally unstable topologically distinct phase portraits of codimension-one quadratic systems, modulo limit cycles. In this work we begin the classification of planar quadratic systems of codimension two in the structural stability. Combining the sets of codimension-one quadratic vector fields one to each other, we obtain ten new sets. Here we consider set AA obtained by the coalescence of two finite singular points, yielding either a triple saddle, or a triple node, or a cusp point, or two saddle-nodes. We obtain all the possible topological phase portraits of set AA and prove their realization. We got 34 new topologically distinct phase portraits in the Poincaré disc modulo limit cycles. Moreover, in this paper we correct a mistake made by the authors in the book of Artés et al. (Structurally unstable quadratic vector fields of codimension one, Springer, Berlin, 2018) and we reduce to 203 the number of topologically distinct phase portrait of codimension one modulo limit cycles. [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]

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 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]

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]

This paper considers the problems of finite determinacy and approximation of flat analytic maps from germs of real (resp. complex) analytic spaces to \mathbb {R}^m (resp. \mathbb {C}^m). It is shown that the flatness of analytic maps from germs of real (resp. complex) analytic spaces whose local rings are Cohen-Macaulay is finitely determined. Further, it is shown that flat maps from complete intersection (resp. Cohen-Macaulay) analytic germs can be approximated arbitrarily well by polynomial (resp. Nash) maps in such a way that the Hilbert-Samuel function of the special fibre is preserved. It is also proved that in the complex case the preservation of the Hilbert-Samuel function implies the preservation of Whitney's tangent cone. [ABSTRACT FROM AUTHOR]

This paper is a sequel to Wang and Du [15], on the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the spreading front is represented by the free boundaries in the model. In [15], it was shown that the model is well-posed, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy; however, the spreading speed was not determined. In this paper, we completely determine the spreading speed of the model when spreading happens. We find a threshold condition for the diffusion kernels J1 and J2 such that the asymptotic spreading speed is finite precisely when this condition is satisfied. Moreover, this speed is determined by a unique semi-wave solution which exists exactly when this threshold condition holds. When this condition is not satisfied, and spreading is successful, we prove that the asymptotic spreading speed is infinite, namely accelerated spreading happens. [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]

In recent days, a combination of finite mixture model (FMM) and hidden Markov model (HMM) is becoming popular for partitioning heterogeneous temporal data into homogeneous groups (clusters) with homogeneous time points (regimes). The regression mixtures commonly considered in this approach can also accommodate for covariates present in data. The classical fixed covariate approach, however, may not always serve as a reasonable assumption as it is incapable of accounting for the contribution of covariates in cluster formation. This paper introduces a novel approach for detecting clusters and regimes in time series data in the presence of random covariates. The computational challenges related to the proposed model has been discussed, and several simulation studies are performed. An application to United States COVID-19 data yields meaningful clusters and regimes. [ABSTRACT FROM AUTHOR]

In the search for the critical point of strongly interacting matter, one of the key tools is to look at event-by-event fluctuations of different event observables expecting their non-monotonic behavior. It is crucial for the experiments to eliminate an influence of the trivial volume fluctuations on the physics observables of interest. This may be done by an application of the accurate centrality selection and by means of special measures using different estimators of initial conditions. It is also feasible to apply some theoretical approaches in estimation of all the possible sources of unwanted fluctuations. In this paper, we present results obtained in the developed Monte-Carlo model of particle production with particle emitting sources being interacting quark–gluon strings of finite length in rapidity space. Implemented strings dynamics in rapidity causes non-uniform string density over it and brings fluctuations to the system event-wise. The model also takes into account, event-by-event, the string fusion phenomenon caused by string overlap in the transverse plane. It is this process of fusion that modifies string fragmentation characteristics and changes the mean values of multiplicities and transverse momenta of produced particles. Using this model and Monte-Carlo event generator PYTHIA, the calculations were done for the strongly intensive quantities , and . [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]

In their recent paper (2019 arXiv:1904.03424), the first author, Kiriki and Soma introduced a concept of pointwise emergence to measure the complexity of irregular orbits. They constructed a residual subset of the full shift with high pointwise emergence. In this paper we consider the set of points with high pointwise emergence for topologically mixing subshifts of finite type. We show that this set has full topological entropy, full Hausdorff dimension, and full topological pressure for any Hölder continuous potential. Furthermore, we show that this set belongs to a certain class of sets with large intersection property. This is a natural generalization of Färm and Persson (2011 Nonlinearity 24 1291â€"1309) to pointwise emergence and CarathĂ©odory dimension. [ABSTRACT FROM AUTHOR]

The present paper generalizes the results of our paper "On the finite presentability of the group F/[M, N]" to an arbitrary family of normal subgroups {Ni | i ∈ I} in a free group F. We obtain conditions for finite presentability of the quotient group F/ ∏ [Ni, Nj]. In both papers, the proof of the main result is based on the properties of verbal wreath products introduced by Alfred Lvovich Shmelkin. [ABSTRACT FROM AUTHOR]

Given an infinite family of extended real-valued functions f i , i ∈ I , and a family H of nonempty finite subsets of I, the H -partial robust sum of f i , i ∈ I , is the supremum, for J ∈ H , of the finite sums ∑ j ∈ J f j . These infinite sums arise in a natural way in location problems as well as in functional approximation problems, and include as particular cases the well-known sup function and the so-called robust sum function, corresponding to the set H of all nonempty finite subsets of I, whose unconstrained minimization was analyzed in previous papers of three of the authors (https://doi.org/10.1007/s11228-019-00515-2 and https://doi.org/10.1007/s00245-019-09596-9). In this paper, we provide ordinary and stable zero duality gap and strong duality theorems for the minimization of a given H -partial robust sum under constraints, as well as closedness and convex criteria for the formulas on the subdifferential of the sup-function. [ABSTRACT FROM AUTHOR]

In this paper, we consider roots of multivariate polynomials over a finite grid. When given information on the leading monomial with respect to a fixed monomial ordering, the footprint bound [Footprints or generalized Bezout's theorem, IEEE Trans. Inform. Theory46(2) (2000) 635–641, On (or in) Dick Blahut's 'footprint', Codes , Curves Signals (1998) 3–9] provides us with an upper bound on the number of roots, and this bound is sharp in that it can always be attained by trivial polynomials being a constant times a product of an appropriate combination of terms consisting of a variable minus a constant. In contrast to the one variable case, there are multivariate polynomials attaining the footprint bound being not of the above form. This even includes irreducible polynomials. The purpose of the paper is to determine a large class of polynomials for which only the mentioned trivial polynomials can attain the bound, implying that to search for other polynomials with the maximal number of roots one must look outside this class. [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]

The spiral shape is ubiquitous in everyday life, and the spiral is also present in electrochemical impedance spectroscopy. By analyzing the diffusion of two ions in the opposite direction in the finite layer, the relative diffusion impedance equation can be obtained and used to simulate a series of different shapes of the Nyquist plots, including spiral shapes. In this paper, the variation law of the spiral Nyquist plot under different conditions is analyzed, and the application of the relative diffusion impedance equation in the area of thin-film solar cells and hydrogen permeation is discussed. [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]

An nθ graph is an n‐valent graph with two vertices. From symmetry considerations, it has vertex–edge transitivity 1 1. Here, they are considered extended with divalent vertices added to the edges to explore the simplest piecewise‐linear tangled embeddings with straight, non‐intersecting edges (sticks). The simplest tangles found are those with 3n sticks, transitivity 2 2, and with 2⌊(n − 1)/2⌋ ambient‐anisotopic tangles. The simplest finite and 1‐, 2‐ and 3‐periodic decussate structures (links and tangles) are described. These include finite cubic and icosahedral and 1‐ and 3‐periodic links, all with minimal transitivity. The paper also presents the simplest tangles of extended tetrahedra and their linkages to form periodic polycatenanes. A vertex‐ and edge‐transitive embedding of a tangled srs net with tangled and polycatenated θ graphs and vertex‐transitive tangled diamond (dia) nets are described. [ABSTRACT FROM AUTHOR]

In this paper, the control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF performance. A numerical tractable method for designing a controller is obtained through matrixing, thus giving conveniently the expression of controller with linear matrix inequality as tool kit. [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]

Rate-Splitting Multiple Access (RSMA) is an emerging flexible and powerful multiple access for downlink multi-antenna networks. In this paper, we introduce the concept of RSMA into short-packet downlink communications. We design optimal linear precoders that maximize the sum rate with Finite Blocklength (FBL) constraints. The relations between the sum rate and blocklength of RSMA are investigated for a wide range of network loads and user deployments. Numerical results demonstrate that RSMA can achieve the same transmission rate as Non-Orthogonal Multiple Access (NOMA) and Space Division Multiple Access (SDMA) with smaller blocklengths (and therefore lower latency), especially in overloaded multi-antenna networks. Hence, we conclude that RSMA is a promising multiple access for low-latency communications. [ABSTRACT FROM AUTHOR]

This paper revisits one of the least understood elements of Derrida's corpus: his sustained critique of Lacan's conception of the letter operative in the unconscious. Showing where and how this critique has been misconstrued, the paper demonstrates that the ultimate significance of Derrida's intervention lies in how it brings forward the uncritical conception of heterogeneity found in Lacan. In this way, Derrida's engagement with Lacan, from 'Positions' all the way up to the late seminars on The Beast and the Sovereign, sheds crucial light on how the core 'ultra-transcendental' structures of deconstruction are to be understood. Above all, it allows us to see how the ultra-transcendental logic of différance entails the thinking of finitude Derrida came to call la vie la mort, life death. [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]

In this paper we consider the question of when the set of Hecke eigenvalues of a cusp form on GL_n(\mathbb {A}_F) is contained in the set of Hecke eigenvalues of a cusp form on GL_m(\mathbb {A}_F) for n \leq m. This question is closely related to a question about finite dimensional representations of an abstract group, which also we consider in this work. [ABSTRACT FROM AUTHOR]

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In this paper, a 4-pole quasi-elliptic planar bandpass filter at Q-band on the liquid crystal polymer (LCP) is presented. The conventional design and development process of millimetre wave filters required to consider the surface roughness effects from the design stage for accurate development of filter at high frequency. Finite surface roughness of rolled copper and its impact on electrical performance are studied. Polishing is one of the methods to improve the conductor surface roughness. An improvement of 50% in surface roughness is reported for the rolled copper on the LCP, resulting in better than 1 dB insertion loss of the bandpass filter. Commensurate simulation and measurement results are presented. [ABSTRACT FROM AUTHOR]