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Given two functions ƒ,g : {0,1}n → {0,1}, a mapping ψ : {0,1}n → {0,1}n is said to be a mapping from f to g if it is a bijection and ƒ(z) = g(ψ(z)) for every z ∈ {0,1}n. In this paper we study Lipschitz mappings between Boolean functions. Our first result gives a construction of a C-Lipschitz mapping from the Majority function to the Dictator function for some universal constant C. On the other hand, there is no n/2-Lipschitz mapping in the other direction, namely from the Dictator function to the Majority function. This answers an open problem posed by Daniel Varga in the paper of Benjamini, Cohen and Shinkar (FOCS 2014 [1]). We also show a mapping from Dictator to XOR that is 3-local, 2-Lipschitz, and its inverse is O(log(n))-Lipschitz, where by L-local mapping we mean that each output bit of the mapping depends on at most L input bits. Next, we consider the problem of finding functions such that any mapping between them must have large average stretch, where the average stretch of a mapping φ is defined as (φ) = Ex,i[ (φ(x),φ(x+ei)]. We show that any mapping φ from XOR to Majority > must satisfy avgStretch (φ) ≥ c √n for some absolute constant c > 0. In some sense, this gives a ‘function analogue’ to the question of Benjamini, Cohen and Shinkar (FOCS 2014 [1]), who asked whether there exists a set A ⊆ {0,1}n of density 0.5 such that any bijection from {0,1}n−1 to A has large average stretch. Finally, we show that for a random balanced function ƒ: {0,1}n → {0,1}n, with high probability there is a mapping φ from Dictator to ƒ such that both φ and φ−1 have constant average stretch. In particular, this implies that one cannot obtain lower bounds on average stretch by taking uniformly random functions. [ABSTRACT FROM AUTHOR]

SUMMARY: Autonomous multi-agent systems show promise in countless applications, but can be hindered in environments where inter-agent communication is limited. In such cases, this paper considers a scenario where agents communicate intermittently through a cloud server. We derive a graph transformation mapping the kernel of a graph's Laplacian to a desired configuration vector while retaining graph topology characteristics. The transformation facilitates derivation of a self-triggered controller driving agents to prescribed configurations while regulating instances of inter-agent communication. Experimental validation of the theoretical results shows the self-triggered approach drives agents to a desired configuration using fewer control updates than traditional periodic implementations. [ABSTRACT FROM AUTHOR]

In this paper we prove uniqueness theorems for mappings $F\in W_{\text{loc}}^{1,n}(\mathbb{B}^{n};\mathbb{R}^{n})$ of finite distortion $1\leq K(x)=\Vert \mathit{DF}(x)\Vert ^{n}/J_{F}(x)$ satisfying some integrability conditions. These types of theorems fundamentally state that if a mapping defined in $\mathbb{B}^{n}$ has the same boundary limit $a$ on a ‘relatively large’ set $E\subset \unicode[STIX]{x2202}\mathbb{B}^{n}$ , then the mapping is constant. Here the size of the set $E$ is measured in terms of its $p$ -capacity or equivalently its Hausdorff dimension. [ABSTRACT FROM AUTHOR]

The Krasnosel’skiĭ–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-$O$ rate to little-$o$ without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the convergence rate of summable sequences. Then we apply the result to give new results on convergence rates for the proximal point algorithm and the Douglas–Rachford method. [ABSTRACT FROM PUBLISHER]

This paper analyses the pseudo almost periodicity of the impulsive neoclassical growth model. We investigate the existence, uniqueness and exponential stability of the pseudo almost periodic solution. Moreover, an example is given to illustrate the significance of the main findings. [ABSTRACT FROM AUTHOR]

In the context of topological mapping, the automatic segmentation of an environment into meaningful and distinct locations is still regarded as an open problem. This paper presents an algorithm to extract places online from image sequences based on the algebraic connectivity of graphs or Fiedler value, which provides an insight into how well connected several consecutive observations are. The main contribution of the proposed method is that it is a theoretically supported alternative to tuning thresholds on similarities, which is a difficult task and environment dependent. It can accommodate any type of feature detector and matching procedure, as it only requires non-negative similarities as input, and is therefore able to deal with descriptors of variable length, to which statistical techniques are difficult to apply. The method has been validated in an office environment using exclusively visual information. Two different types of features, a bag-of-words model built from scale invariant feature transform (SIFT) keypoints, and a more complex fingerprint based on vertical lines, color histograms, and a few Star keypoints, are employed to demonstrate that the method can be applied to both fixed and variable length descriptors with similar results. [ABSTRACT FROM AUTHOR]

Dorff et al. ['Convolutions of harmonic convex mappings', Complex Var. Elliptic Equ. 57 (5) (2012), 489–503] formulated a question concerning the convolution of two right half-plane mappings, where the normalisation of the functions was considered incorrectly. In this paper, we reformulate the problem correctly and provide a solution to it in a more general form. We also obtain two new theorems which correct and improve related results. [ABSTRACT FROM AUTHOR]

This paper proposes a new two-stage estimation and inference procedure for a class of partially identified models. The procedure can be considered an extension of classical minimum distance estimation procedures to accommodate inequality constraints and partial identification. It involves no tuning parameter, is nonconservative, and is conceptually and computationally simple. The class of models includes models of interest to applied researchers, including the static entry game, a voting game with communication, and a discrete mixture model. Besides, a technical contribution is an implicit correspondence lemma which generalizes the implicit function theorem to multivalued implicit maps. [ABSTRACT FROM AUTHOR]

This paper presents a framework for the interactions between the processes of mapping and rerepresentation within analogy making. Analogical reasoning systems for use in design tasks require representations that are open to being reinterpreted. The framework, interpretation-driven mapping, casts the process of constructing an analogical relationship as requiring iterative, parallel interactions between mapping and interpreting. This paper argues that this interpretation-driven approach focuses research on a fundamental problem in analogy making: how do the representations that make new mappings possible emerge during the mapping process? The framework is useful for both describing existing analogy-making models and designing future ones. The paper presents a computational model informed by the framework Idiom, which learns ways to reinterpret the representations of objects as it maps between them. The results of an implementation in the domain of visual analogy are presented to demonstrate its feasibility. Analogies constructed by the system are presented as examples. The interpretation-driven mapping framework is then used to compare representational change in Idiom to that in three previously published systems. [ABSTRACT FROM PUBLISHER]

Let $V$ be a hypersurface with an isolated singularity at the origin defined by the holomorphic function $f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)$. The Yau algebra, $L(V)$ , is the Lie algebra of derivations of the moduli algebra of $V$. It is a finite-dimensional solvable algebra and its dimension $\unicode[STIX]{x1D706}(V)$ is the Yau number. Fewnomial singularities are those which can be defined by an $n$ -nomial in $n$ indeterminates. Yau and Zuo [‘A sharp upper estimate conjecture for the Yau number of weighted homogeneous isolated hypersurface singularity’, Pure Appl. Math. Q.12(1) (2016), 165–181] conjectured a bound for the Yau number and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper, we verify this conjecture for weighted homogeneous fewnomial surface singularities. [ABSTRACT FROM AUTHOR]

SUMMARY: This paper presents an overview of the most recent vision-based multi-rotor micro unmanned aerial vehicles (MUAVs) intended for autonomous navigation using a stereoscopic camera. Drone operation is difficult because pilots need the expertise to fly the drones. Pilots have a limited field of view, and unfortunate situations, such as loss of line of sight or collision with objects such as wires and branches, can happen. Autonomous navigation is an even more difficult challenge than remote control navigation because the drones must make decisions on their own in real time and simultaneously build maps of their surroundings if none is available. Moreover, MUAVs are limited in terms of useful payload capability and energy consumption. Therefore, a drone must be equipped with small sensors, and it must carry low weight. In addition, a drone requires a sufficiently powerful onboard computer so that it can understand its surroundings and navigate accordingly to achieve its goal safely. A stereoscopic camera is considered a suitable sensor because of its three-dimensional (3D) capabilities. Hence, a drone can perform vision-based navigation through object recognition and self-localise inside a map if one is available; otherwise, its autonomous navigation creates a simultaneous localisation and mapping problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the bounded approximation property for the weighted space $\mathcal{HV}$(U) of holomorphic mappings defined on a balanced open subset U of a Banach space E and its predual $\mathcal{GV}$(U), where $\mathcal{V}$ is a countable family of weights. After obtaining an $\mathcal{S}$-absolute decomposition for the space $\mathcal{GV}$(U), we show that E has the bounded approximation property if and only if $\mathcal{GV}$(U) has. In case $\mathcal{V}$ consists of a single weight v, an analogous characterization for the metric approximation property for a Banach space E has been obtained in terms of the metric approximation property for the space $\mathcal{G}_v$(U). [ABSTRACT FROM PUBLISHER]

In dense urban areas, conventional Global Navigation Satellite Systems (GNSS) positioning can exhibit errors of tens of metres due to the obstruction and reflection of the signals by the surrounding buildings. By using Three-Dimensional (3D) mapping of the buildings, the accuracy can be significantly improved. This paper demonstrates the first integration of GNSS shadow matching with 3D-mapping-aided GNSS ranging. The integration is performed in the position domain, whereby separate ranging and shadow matching position solutions are computed, then combined using direction-dependent weighting. Two weighting strategies are compared, one based on the computation of ranging-based and shadow matching position error covariance matrices, and a deterministic approach based on the street azimuth. Using experimental data collected from a u-blox GNSS receiver, it is shown that both integrated position solutions are significantly more accurate than either shadow matching or 3D-mapping-aided ranging on their own. The overall Root Mean Square (RMS) horizontal accuracy obtained using covariance-based weighting was 6·1 m, a factor of four improvement on the 25·9 m obtained using conventional GNSS positioning. Results are also presented using smartphone data, where shadow matching is integrated with conventional GNSS positioning. [ABSTRACT FROM AUTHOR]

The continuity problem, i.e., the question whether effective maps between effectively given topological spaces are effectively continuous, is reconsidered. In earlier work, it was shown that this is always the case, if the effective map also has a witness for non-inclusion. The extra condition does not have an obvious topological interpretation. As is shown in the present paper, it appears naturally where in the classical proof that sequentially continuous maps are continuous, the Axiom of Choice is used. The question is therefore whether the witness condition appears in the general continuity theorem only for this reason, i.e., whether effective operators are effectively sequentially continuous. For two large classes of spaces covering all important applications, it is shown that this is indeed the case. The general question, however, remains open. Spaces in this investigation are in general not required to be Hausdorff. They only need to satisfy the weaker T0 separation condition. [ABSTRACT FROM AUTHOR]

The Birkhoff orthogonality has been recently intensively studied in connection with the geometry of Banach spaces and operator theory. The main aim of this paper is to characterize the Birkhoff orthogonality in ${\mathcal{L}}(X;Y)$ under the assumption that ${\mathcal{K}}(X;Y)$ is an $M$-ideal in ${\mathcal{L}}(X;Y)$. Moreover, we survey the known results, as well as giving some new and more general ones. Furthermore, we characterize an approximate Birkhoff orthogonality in ${\mathcal{K}}(X;Y)$. [ABSTRACT FROM AUTHOR]

The family ${\mathcal{F}}_{\unicode[STIX]{x1D706}}$ of orientation-preserving harmonic functions $f=h+\overline{g}$ in the unit disc $\mathbb{D}$ (normalised in the standard way) satisfying $$\begin{eqnarray}h^{\prime }(z)+g^{\prime }(z)=\frac{1}{(1+\unicode[STIX]{x1D706}z)(1+\overline{\unicode[STIX]{x1D706}}z)},\quad z\in \mathbb{D},\end{eqnarray}$$ for some $\unicode[STIX]{x1D706}\in \unicode[STIX]{x2202}\mathbb{D}$, along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in ${\mathcal{F}}_{\unicode[STIX]{x1D706}}$ are convex. [ABSTRACT FROM AUTHOR]

In this paper, for the convolution and convex combination of harmonic mappings, the radii of univalence, full convexity and starlikeness of order $\unicode[STIX]{x1D6FC}$ are explored. All results are sharp. By way of application, the univalent radius and the Bloch constant of the convolution of two bounded harmonic mappings are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the concept of meet F-continuous posets is introduced. The main results are: (1) A poset P is meet F-continuous iff its normal completion is a meet continuous lattice iff a certain system χ(P) which is, in the case of complete lattices, the lattice of all Scott closed sets is a complete Heyting algebra; (2) A poset P is precontinuous iff P is meet F-continuous and quasiprecontinuous; (3) The category of meet continuous lattices with complete homomorphisms is a full reflective subcategory of the category of meet F-continuous posets with cut-stable maps. [ABSTRACT FROM AUTHOR]

In this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively. [ABSTRACT FROM PUBLISHER]

Metric regularity theory lies at the very heart of variational analysis, a relatively new discipline whose appearance was, to a large extent, determined by the needs of modern optimization theory in which such phenomena as nondifferentiability and set-valued mappings naturally appear. The roots of the theory go back to such fundamental results of the classical analysis as the implicit function theorem, Sard theorem and some others. This paper offers a survey of the state of the art of some principal parts of the theory along with a variety of its applications in analysis and optimization. [ABSTRACT FROM PUBLISHER]

For the Andes Cordillera, where observed mass-balance records are sparse, long-term glacier velocity measurements potentially represent a useful tool for assessing glacier health. Utilising manual and automatic feature-tracking techniques applied to Corona, Landsat and ASTER satellite imagery, this paper presents surface velocity fluctuations for Glaciar Universidad between 1967 and 1969, and 1985 and 2015, the longest such time series available for the Andes Cordillera, outside Patagonia. This time series reveals an increase in the surface velocities of the main glacier trunk between 1967 and 1987 (~90%) followed by a deceleration between 1987 and 2015 (~80%), with ice velocities observed between 2014 and 2015 possibly representing a 48 a low. In response to the surface velocity fluctuations, the glacier front advanced between 1985 and 1992 (cumulative change of 137 ± 14 m), and again to a lesser magnitude during the 1996–98 and 2004–08 periods. Although having exhibited possible surge behaviour during the 1940s, the synchrony of the glacier changes presented for Glaciar Universidad with those reported for nearby glaciers, suggests that this glacier is responding to climatic trends. If the above scenario is true, the results indicate a general pattern of increasingly negative glacier mass-balance conditions since the late 1980s. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals. [ABSTRACT FROM PUBLISHER]

Clunie and Sheil-Small ['Harmonic univalent functions', Ann. Acad. Sci. Fenn. Ser. A. I. Math. 9 (1984), 3-25] gave a simple and useful univalence criterion for harmonic functions, usually called the shear construction. However, the application of this theorem is limited to planar harmonic mappings that are convex in the horizontal direction. In this paper, a natural generalisation of the shear construction is given. More precisely, our results are obtained under the hypothesis that the image of a harmonic function is a union of two sets that are convex in the horizontal direction. [ABSTRACT FROM AUTHOR]

In this paper we prove the following result: let $m,n\geq 1$ be distinct integers, let $R$ be an $mn(m+n)|m-n|$-torsion free semiprime ring and let $D:R\rightarrow R$ be an $(m,n)$-Jordan derivation, that is an additive mapping satisfying the relation $(m+n)D(x^{2})=2mD(x)x+2nxD(x)$ for $x\in R$. Then $D$ is a derivation which maps $R$ into its centre. [ABSTRACT FROM PUBLISHER]

In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results. [ABSTRACT FROM PUBLISHER]

This paper investigates a 6-degree-of-freedom foldable parallel mechanism for the ship-based stabilized platform, which is driven by closed chain linkages. The velocity and acceleration mappings between the moving platform and inputs of the closed chain linkages are deduced in the form of the first- and second-order influence coefficient matrices. The continuous stiffness matrix is deduced; furthermore, the translation and rotational stiffness along any direction are also deduced. With directional stiffness, the singularity of the mechanism is analyzed, and the explanation of the singularity is given from the viewpoint of stiffness. The directions the platform cannot move or lose its constraints are got from directional stiffness. [ABSTRACT FROM PUBLISHER]

Localization and mapping in indoor environments, such as airports and hospitals, are key tasks for almost every robotic platform. Some researchers suggest the use of Range-Only (RO) sensors based on WiFi (Wireless Fidelity) technology with SLAM (Simultaneous Localization And Mapping) techniques to solve both problems. The current state of the art in RO SLAM is mainly focused on the filtering approach, while the study of smoothing approaches with RO sensors is quite incomplete. This paper presents a comparison between filtering algorithms, such as EKF and FastSLAM, and a smoothing algorithm, the SAM (Smoothing And Mapping). Experimental results are obtained in indoor environments using WiFi sensors. The results demonstrate the feasibility of the smoothing approach using WiFi sensors in an indoor environment. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to study geometric properties of non-degenerate smooth projective varieties of small degree from a birational point of view. First, using the positivity property of double point divisors and the adjunction mappings, we classify smooth projective varieties in $\mathbb{P}$r of degree d ⩽ r + 2, and consequently, we show that such varieties are simply connected and rationally connected except in a few cases. This is a generalisation of P. Ionescu's work. We also show the finite generation of Cox rings of smooth projective varieties in $\mathbb{P}$r of degree d ⩽ r with counterexamples for d = r + 1, r + 2. On the other hand, we prove that a non-uniruled smooth projective variety in $\mathbb{P}$r of dimension n and degree d ⩽ n(r − n) + 2 is Calabi–Yau, and give an example that shows this bound is also sharp. [ABSTRACT FROM AUTHOR]

The inverse dynamics model of a novel (3-UPU)+(3-UPS+S) serial–parallel manipulator (S-PM) formed by a 3-UPU PM and a 3-UPS+S PM connected in serial is studied in this paper. First, the inverse position, velocity, and acceleration of this S-PM are studied systematically. Second, the velocity mapping relations between each component and the terminal platform of (3-UPU)+(3-UPS+S) S-PM are derived. Third, the dynamics model of the whole (3-UPU)+(3-UPS+S) S-PM is established by means of the principle of virtual work. The process for establishing the dynamics model of this S-PM is fit for other S-PMs. [ABSTRACT FROM PUBLISHER]

In this paper we introduce and motivate the concept of orientation data, as it appears in the framework for motivic Donaldson–Thomas theory built by Kontsevich and Soibelman. By concentrating on a single simple example we explain the role of orientation data in defining the integration map, a central component of the wall crossing formula. [ABSTRACT FROM PUBLISHER]

While the back-and-forth method has been often attributed to Cantor, it turns out that in the original proof of the characterisation of countable linear dense orders, the mapping is constructed in a single direction. Cameron has called this method Forth and has shown that it can fail to build an automorphism for some homogeneous structures. We give in this paper a characterisation of those homogeneous structures for which Forth always builds an automorphism. This generalises results by Cameron and McLeish. [ABSTRACT FROM PUBLISHER]

In this paper we introduce stable systems of inclusions, which feature chosen arrows A ↪ B to capture the notion that A is a subobject of B, and proposes them as an alternative context to stable systems of monics to discuss partiality. A category C equipped with such a system $\mathscr{I}$, called an i-category, is shown to give rise to an associated category ∂(C,$\mathscr{I}$) of partial maps, which is a split restriction category whose restriction monics are inclusions. This association is the object part of a 2-equivalence between such inclusively split restriction categories and i-categories. $\mathscr{I}$ determines a stable system of monics $\mathscr{I}$+ on C, and, conversely, a stable system of monics $\mathscr{M}$ on C yields an i-category (C[$\mathscr{M}$],$\mathscr{M}$+), giving a 2-adjunction between i-categories and m-categories. The category of partial maps Par(C,$\mathscr{M}$) is isomorphic to the full subcategory of ∂(C[$\mathscr{M}$],$\mathscr{M}$+) comprising the objects of C, and ∂(C,$\mathscr{I}$) ≅ Par(C,$\mathscr{I}$+). [ABSTRACT FROM AUTHOR]

Continuous lattices were characterised by Martín Escardó as precisely those objects that are Kan-injective with respect to a certain class of morphisms. In this paper we study Kan-injectivity in general categories enriched in posets. As an example, ω-CPO's are precisely the posets that are Kan-injective with respect to the embeddings ω ↪ ω + 1 and 0 ↪ 1.For every class $\mathcal{H}$ of morphisms, we study the subcategory of all objects that are Kan-injective with respect to $\mathcal{H}$ and all morphisms preserving Kan extensions. For categories such as Top0 and Pos, we prove that whenever $\mathcal{H}$ is a set of morphisms, the above subcategory is monadic, and the monad it creates is a Kock–Zöberlein monad. However, this does not generalise to proper classes, and we present a class of continuous mappings in Top0 for which Kan-injectivity does not yield a monadic category. [ABSTRACT FROM AUTHOR]

In this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of $\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps. [ABSTRACT FROM AUTHOR]

Suppose that $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E$ and $E'$ denote real Banach spaces with dimension at least 2 and that $D\subset E$ and $D'\subset E'$ are domains. Let $\varphi :[0,\infty )\to [0,\infty )$ be a homeomorphism with $\varphi (t)\geq t$. We say that a homeomorphism $f: D\to D'$ is $\varphi $-FQC if for every subdomain $D_1 \subset D$, we have $\varphi ^{-1} (k_D(x,y))\leq k_{D'} (f(x),f(y))\leq \varphi (k_D(x,y))$ holds for all $x,y\in D_1$. In this paper, we establish, in terms of the $j_D$ metric, a necessary and sufficient condition for a homeomorphism $f: E \to E'$ to be FQC. Moreover, we give, in terms of the $j_D$ metric, a sufficient condition for a homeomorphism $f: D\to D'$ to be FQC. On the other hand, we show that this condition is not necessary. [ABSTRACT FROM PUBLISHER]

As a benefit of modularization of complex systems, original equipment manufacturers (OEMs) can choose suppliers in a less constricted way when faced with new or evolving requirements. However, new suppliers usually add uncertainties to the system development. Because suppliers are tightly integrated into the design process in modular design and therefore greatly influence the outcome of the OEM's products, the uncertainty along with requirements satisfaction of the suppliers and their modules should be controlled starting from potential supplier identification. In addition, to better satisfy new requirements, the potential supplier identification should be combined with architecture generation to enable the new technology integration. In this paper, we propose the Architecture & Supplier Identification Tool, which generates all possible architectures and corresponding suppliers based on new requirements through matrix mapping and propagation. Using the Architecture & Supplier Identification Tool, the overall uncertainty and requirements satisfaction of generated architectures can be estimated and controlled. The proposed method aims at providing decision support for early design of complex systems, thereby helping OEMs have an integrated view of suppliers and system architectures in requirements satisfaction and overall uncertainty. [ABSTRACT FROM PUBLISHER]

Jardine (2016) claims that tonal phonology is more formally complex than the phonology of other segmental features, in that only tonal phonology goes beyond the class of weakly deterministic maps. He then goes on to argue that this formal distinction is superior to any available treatment in Optimality Theory. This reply points out that Jardine's formal distinction conflates attested and unattested tonal patterns, which can be distinguished in Optimality Theory, given a substantively defined constraint set. [ABSTRACT FROM PUBLISHER]

In this paper we study the algebraic structure of ω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case. [ABSTRACT FROM AUTHOR]

We prove a generalmulti-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers D. Our results rely on a classical bijection with mobiles (objects exhibiting a tree structure), combined with refined analytic tools to deal with the systems of equations on infinite variables that arise. We also discuss possible extensions to maps of higher genus and to weighted maps. [ABSTRACT FROM AUTHOR]

We study linear mappings which preserve vectors at a specific angle. We introduce the concept of $(\unicode[STIX]{x1D700},c)$ -angle preserving mappings and define $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ as the 'smallest' number $\unicode[STIX]{x1D700}$ for which $T$ is an $(\unicode[STIX]{x1D700},c)$ -angle preserving mapping. We derive an exact formula for $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ in terms of the norm $\Vert T\Vert$ and the minimum modulus $[T]$ of $T$. Finally, we characterise approximately angle preserving mappings. [ABSTRACT FROM AUTHOR]

Precise Point Positioning/Inertial Navigation System (PPP/INS) integrated navigation based on PPP and low-accuracy INS is often used to provide position and attitude information for vehicle-mounted or airborne mobile mapping systems. With proper processing, the position accuracy of PPP/INS is comparable to that of Differential Global Navigation Satellite System (DGNSS)/INS, but the accuracy of the attitude, especially the yaw angle, cannot be guaranteed. However, the yaw angle is crucial for mobile mapping systems. To compensate for the insufficiency of PPP/INS, we have designed a Multi-Antenna GNSS (MAGNSS)/INS integrated navigation system. First, the attitude determination method using MAGNSS is presented in detail. Then, the MAGNSS attitude is combined with the PPP position and velocity as measurements for integration with the INS. Thus, PPP/INS integrated navigation was improved to MAGNSS/INS integrated navigation. Finally, a three-hour car-borne test was conducted to evaluate the performance of the proposed method. The results indicate that the attitude determined from MAGNSS is accurate and stable over time. Compared to PPP/INS, MAGNSS/INS integrated navigation can improve the attitude accuracy significantly because of the inclusion of MAGNSS attitude. [ABSTRACT FROM AUTHOR]

At the ANZIAM conference in Hobart in February 2018, there were several talks on the solution of Laplace problems in multiply connected domains by means of conformal mapping. It appears to be not widely known that such problems can also be solved by the elementary method of series expansions with coefficients determined by least-squares fitting on the boundary. (These are not convergent series; the coefficients depend on the degree of the approximation.) Here we give a tutorial introduction to this method, which converges at an exponential rate if the boundary data are sufficiently well-behaved. The mathematical foundations go back to Runge in 1885 and Walsh in 1929. One of our examples involves an approximate Cantor set with up to 2048 components. [ABSTRACT FROM AUTHOR]

Let R be a graded ring. We introduce the concepts of Ding gr-injective and Ding gr-projective R-modules, which are the graded analogues of Ding injective and Ding projective modules. Several characterizations and properties of Ding gr-injective and Ding gr-projective modules are obtained. In addition, we investigate the relationships among Gorenstein gr-flat, Ding gr-injective and Ding gr-projective modules. [ABSTRACT FROM AUTHOR]

We use elementary skein theory to prove a version of a result of Stylianakis (Stylianakis, The normal closure of a power of a half-twist has infinite index in the mapping class group of a punctured sphere, arXiv:1511.02912) who showed that under mild restrictions on m and n, the normal closure of the mth power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures. [ABSTRACT FROM AUTHOR]

Let A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups. [ABSTRACT FROM AUTHOR]

Varieties of the form $G\times S_{\!\text{reg}}$, where $G$ is a complex semisimple group and $S_{\!\text{reg}}$ is a regular Slodowy slice in the Lie algebra of $G$, arise naturally in hyperkähler geometry, theoretical physics and the theory of abstract integrable systems. Crooks and Rayan [‘Abstract integrable systems on hyperkähler manifolds arising from Slodowy slices’, Math. Res. Let., to appear] use a Hamiltonian $G$-action to endow $G\times S_{\!\text{reg}}$ with a canonical abstract integrable system. To understand examples of abstract integrable systems arising from Hamiltonian $G$-actions, we consider a holomorphic symplectic variety $X$ carrying an abstract integrable system induced by a Hamiltonian $G$-action. Under certain hypotheses, we show that there must exist a $G$-equivariant variety isomorphism $X\cong G\times S_{\!\text{reg}}$. [ABSTRACT FROM AUTHOR]

Let ${\mathcal{A}}$ be a unital torsion-free algebra over a unital commutative ring ${\mathcal{R}}$. To characterise Lie $n$-higher derivations on ${\mathcal{A}}$, we give an identity which enables us to transfer problems related to Lie $n$-higher derivations into the same problems concerning Lie $n$-derivations. We prove that: (1) if every Lie $n$-derivation on ${\mathcal{A}}$ is standard, then so is every Lie $n$-higher derivation on ${\mathcal{A}}$; (2) if every linear mapping Lie $n$-derivable at several points is a Lie $n$-derivation, then so is every sequence $\{d_{m}\}$ of linear mappings Lie $n$-higher derivable at these points; (3) if every linear mapping Lie $n$-derivable at several points is a sum of a derivation and a linear mapping vanishing on all $(n-1)$th commutators of these points, then every sequence $\{d_{m}\}$ of linear mappings Lie $n$-higher derivable at these points is a sum of a higher derivation and a sequence of linear mappings vanishing on all $(n-1)$th commutators of these points. We also give several applications of these results. [ABSTRACT FROM AUTHOR]

The principle ( ) of Sierpinski is the assertion that there is a family of functions $\left\{ {{\varphi _n}:{\omega _1} \to {\omega _1}|n \in \omega } \right\}$ such that for every $I \in {[{\omega _1}]^{{\omega _1}}}$ there is n ε ω such that ${\varphi _n}[I] = {\omega _1}$. We prove that this principle holds if there is a nonmeager set of size ω1 answering question of Arnold W. Miller. Combining our result with a theorem of Miller it then follows that ( ) is equivalent to $non\left( {\cal M} \right) = {\omega _1}$. Miller also proved that the principle of Sierpinki is equivalent to the existence of a weak version of a Luzin set, we will construct a model where all of these sets are meager yet $non\left( {\cal M} \right) = {\omega _1}$. [ABSTRACT FROM AUTHOR]

We present a family of continuous piecewise linear maps of the unit interval into itself that are all chaotic in the sense of Li and Yorke [‘Period three implies chaos’, Amer. Math. Monthly82 (1975), 985–992] and for which almost every point (in the sense of Lebesgue) in the unit interval is an eventually periodic point of period $p,p\geq 3$, for a member of the family. [ABSTRACT FROM PUBLISHER]

We propose a relational computing paradigm based on Eilenberg machines, an effective version of Eilenberg's X-machines suitable for general non-deterministic computation. An Eilenberg machine generalizes a finite-state automaton, seen as its control component, with a computation component over a data domain specified as a relational algebra, its actions being interpreted as binary relations over the data domain. We show various strategies for the sequential simulation of our relational machines, using variants of the reactive engine. In a particular case of finite machines, we show that bottom-up search yields an efficient complete simulator.Relational machines may be composed in a modular fashion, since atomic actions of one machine can be mapped to the characteristic relation of other relational machines acting as its parameters.The control components of machines can be compiled from regular expressions. Several such translations have been proposed in the literature, which we briefly survey. [ABSTRACT FROM AUTHOR]