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In this paper, a very low spur 5.9-GHz integer-N frequency synthesizer designed for a Cellular Vehicle-to-Everything (C-V2X) receiver is presented. The PLL is referenced to a 10-MHz crystal oscillator and the design is implemented in a 65-nm CMOS process. The output of the synthesizer has differential quadrature topology and provides the local oscillator signal to a downconverter mixer of C-V2X receiver. Post-layout simulations show that the reference spurs are better than −88 dBc through loop sampling technique which was implemented in a 11.8-GHz VCO design for the first time to the best of our knowledge. The best spur level without the loop sampling technique applied is limited to −55 dBc. Using the loop sampling technique provides a spur reduction of 33 dB which is a significant improvement at this frequency. Based on post-layout simulations, the design has a phase noise of −97/−99/−114 dBc for 10 kHz/100 kHz/1 MHz frequency offsets, respectively, which presents competitive numbers with the designs in the literature. The design has 1.2-V nominal supply voltage for the analog and digital blocks. The total power dissipation of the synthesizer core is 6 mW from a 1.2-V supply while the output buffers driving a 100-fF load consumes 18 mW. [ABSTRACT FROM AUTHOR]

Catastrophe theory (CT) emerged out of problems in pure mathematics. The insights and language of differential topology, from which CT sprang, are foreign to most economists. The purpose of this paper is to explain how to use Abstract CT in economic modelling. To this end, we spell out a step‐by‐step procedure that can be understood without a knowledge of differential topology. The corollary advantage of our systematic procedure is that it brings into sharp focus the limited relevance of CT for economic modelling. The paper is developed in four stages. The first stage provides a gentle introduction to the key mathematical concepts for readers new to CT. The second stage consists of a brief description of the structure of economic modelling. In the third stage, a procedure about how to use CT in economic modelling is spelled out. The last stage summarises the main ideas of CT and points out the snags that a modeller will inevitably encounter when applying CT to economics. [ABSTRACT FROM AUTHOR]

In 1979, Hartley and Kawauchi proved that the Conway polynomial of a strongly negative amphichiral knot factors as f (z)f (-z). In this paper, we normalize the factor f (z) to define the half-Conway polynomial. First, we prove that the half-Conway polynomial satisfies an equivariant skein relation, giving the first feasible computational method, which we use to compute the half-Conway polynomial for knots with 12 or fewer crossings. This skein relation also leads to a diagrammatic interpretation of the degree-one coefficient, from which we obtain a lower bound on the equivariant unknotting number. Second, we completely characterize polynomials arising as half-Conway polynomials of knots in S3, answering a problem of Hartley-Kawauchi. As a special case, we construct the first examples of non-slice strongly negative amphichiral knots with determinant one, answering a question of Manolescu. The double branched covers of these knots provide potentially non-trivial torsion elements in the homology cobordism group. [ABSTRACT FROM AUTHOR]

This paper presents an implementation of a 14-bit 2.5 MS/s differential Successive-Approximation-Register (SAR) analog-to-digital converter (ADC) to be used for sensing multiple analog input signals. A differential binary-weighted with split capacitance charge-redistribution capacitive digital-to-analog converter (CDAC) utilizing the conventional switching technique is designed, without using any calibration mechanism for fast power-on operation. The CDAC capacitor unit has been optimized for improved linearity without calibration technique. The SAR ADC has a differential input range 3.6 Vpp, with a SNDR of 80.45 dB, ENOB of 13.07, SFDR of 87.16 dB and dissipates an average power of 0.8 mW, while operating at 2.5 V/1 V for analog/digital power supply. The INL and DNL is +0.22/−0.34 LSB and +0.42/−0.3 LSB, respectively. A prototype ADC has been fabricated in a conventional CMOS 65 nm technology process. [ABSTRACT FROM AUTHOR]

The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is a very well behaved analogue of a differential structure in the context of stratified topological spaces, satisfying good properties such as the existence of resolutions of singularities and handlebody decompositions. In this paper we prove Ayala, Francis and Tanaka's conjecture that any Whitney stratified space admits a canonical conically smooth structure. We thus establish a connection between the theory of conically smooth spaces and the classical examples of stratified spaces from differential topology. [ABSTRACT FROM AUTHOR]

This paper presents a reconfigurable cross-connected (CC) wireless power transceiver (TRX) operating at 6.78 MHz and implemented for bidirectional device-to-device (D2D) charging with high efficiency and small system volume. We propose, for the first time, a CC topology applied to a differential class-D power amplifier for significant switching loss reduction. Two delay-locked loops (DLLs) for each power NMOS transistor form the reconfigurable controller, realizing the adaptive deadtime control in the transmitter (TX) mode and the off-delay compensation in the receiver (RX) mode, leading to high power conversion efficiency and safe operation. To realize the inductive load for the TX mode in the whole coupling range at the resonant frequency, we use an on-chip tunable capacitor. Furthermore, we also study the power link efficiency in the D2D direct charging system and verify that the near-maximum power link efficiency can be inherently achieved in this scenario. The proposed wireless power TRX, fabricated in a 0.35- $\mu \text{m}$ CMOS process with 5-V devices, measured a peak D2D total efficiency of 77.2% when the output power is 0.7 W. The maximum charging power is 2.74 W with a total efficiency of 62.7% and the maximum transmission distance is 24 mm, both measured. [ABSTRACT FROM AUTHOR]

This paper establishes several results for coalgebraic structure in 8-categories, specifically with connections to the spectral noncommutative geometry of cobordism theories. We prove that the categories of comodules and modules over a bialgebra always admit suitably structured monoidal structures in which the tensor product is taken in the ambient category (as opposed to a relative (co)tensor product over the underlying algebra or coalgebra of the bialgebra). We give two examples of higher coalgebraic structure: first, following Hess we show that for a map of En-ring spectra: A B, the associated 8-category of descent data is equivalent to the 8-category of comodules over BA B, the so-called descent coring; secondly, we show that Thom spectra are canonically equipped with a highly structured comodule structure which is equivalent to the 8-categorical Thom diagonal of Ando, Blumberg, Gepner, Hopkins and Rezk (which we describe explicitly) and that this highly structured diagonal decomposes the Thom isomorphism for an oriented Thom spectrum in the expected way indicating that Thom spectra are good examples of spectral noncommutative torsors. [ABSTRACT FROM AUTHOR]

This paper presents a two-step single-slope (TS-SS) analog-to-digital converter (ADC) for CMOS image sensors (CIS). The proposed TS-SS ADC divides the pixel signal into small and large signal regions using a precomparator. When quantizing large pixel signals, the TS-SS ADC enters accelerated mode, which leverages the differential topology of the ramp generator to speed up quantization. The accelerated mode reduces the row cycle, resulting in a 31.3% reduction at 320 MHz clock from 27.3 to 18.75 µs. The designed 12-bit TS-SS ADC was designed in a 110 nm 1P4M CMOS technology, and its linearity was verified by process corner post-simulation and Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

This paper analyzes the relation between commodity spot, forward prices, and convenience yield under incomplete markets. Since production is a necessary process for commodity markets, we include firms that use inputs and produce outputs in our model. Thus, we show a financial pricing model of spot and forward commodity in an explicit fashion with production under incomplete markets. One of the most important results of this paper is the difference between commodity spot and forward equilibrium price can be explained by the discounted shadow price of storage constraint minus the discounted marginal storage cost and it can be interpreted as the net convenience yield in the existing literature. Here the discounted factor is affected by the incompleteness of the markets. We prove the generic existence of the equilibrium and thus the obtained spot forward price relation is the equilibrium price formula. We also derive the firm's optimal production plan and trading strategy. [ABSTRACT FROM AUTHOR]

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: "simple" models, "Hodge-coupled" models, and "order-coupled" (Dirac) models. Our framework is based on topology and discrete differential geometry, as well as gradient systems and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models. [ABSTRACT FROM AUTHOR]

Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The goal of this paper is to bring some new perspective on this topic. We explain how to prove the holonomic approximation theorem for first-order jets using convex integration. More precisely, we first prove that this theorem can easily be reduced to proving flexibility of some specific relation. Then we prove this relation is open and ample, hence its flexibility follows from off-the-shelf convex integration. [ABSTRACT FROM AUTHOR]

This paper presents a novel analog front-end for EMG sensor signal processing powered by 1 V. Such a low supply voltage requires specific design steps enabled using the 28 nm fully depleted silicon on insulator (FDSOI) technology from STMicroelectronics. An active ground circuit is implemented to keep the input common-mode voltage close to the analog ground and to minimize external interference. The amplifier circuit comprises an input instrumentation amplifier (INA) and a programmable-gain amplifier (PGA). Both are implemented in a fully differential topology. The actual performance of the circuit is analyzed using the corner and Monte Carlo analyses that comprise fifth-hundred samples for the global and local process variations. The proposed circuit achieves a high common-mode rejection ratio (CMRR) of 105.5 dB and a high input impedance of 11 G Ω with a chip area of 0.09 mm 2 . [ABSTRACT FROM AUTHOR]

In this paper, we prove that the Morse index of the critical Möbius band in the 4-dimensional Euclidean ball B 4 equals 5. It is conjectured that this is the only embedded non-orientable free boundary minimal surface of index 5 in B 4 . One of the ingredients in the proof is a comparison theorem between the spectral index of the Steklov problem and the energy index. The latter also enables us to give another proof of the well-known result that the index of the critical catenoid in B 3 equals 4. [ABSTRACT FROM AUTHOR]

In this paper we compare parameter estimation by Grassmann manifold optimization and sequential candidate set algorithm in a structured principal fitted component (PFC) model. The structured PFC model extends the form of the covariance matrix of a random error to relieve the limits that occur due to too simple form of the matrix. However, unlike other PFC models, structured PFC model does not have a closed form for parameter estimation in dimension reduction which signals the need of numerical computation. The numerical computation can be done through Grassmann manifold optimization and sequential candidate set algorithm. We conducted numerical studies to compare the two methods by computing the results of sequential dimension testing and trace correlation values where we can compare the performance in determining dimension and estimating the basis. We could conclude that Grassmann manifold optimization outperforms sequential candidate set algorithm in dimension determination, while sequential candidate set algorithm is better in basis estimation when conducting dimension reduction. We also applied the methods in real data which derived the same result. [ABSTRACT FROM AUTHOR]

This paper studies a class of superlinear damped vibration equations with nonlocal boundary conditions on time scales by using the calculus of variations. We consider the Cerami condition, while the nonlinear term does not satisfy Ambrosetti-Rabinowitz condition such that the critical point theory could be applied. Then we establish the variational structure in an appropriate Sobolev's space, obtain the existence of infinitely many large energy solutions. Finally, two examples are given to prove our results. [ABSTRACT FROM AUTHOR]

In this paper we focus on the integrable Teichmüller spaces Tp (p > 0) which are subspaces of the symmetric subspace of the universal Teichmüller space. We prove that every element of Tp for 0

1- diffeomorphism. [ABSTRACT FROM AUTHOR]

In this paper we study the Banach manifold made up of simple C m + μ -domains in the Euclidean space R n . This manifold is merely a topological or a C 0 Banach manifold not possessing a differentiable structure. It has now been recognized by some researchers that in this manifold some points are differentiable in the sense that it is still possible to introduce the concepts of tangent vectors and the tangent space at such a point. However, a careful study shows that definitions of these concepts are not as simple as it might look at first sight. In fact, to establish a useful calculus theory on this manifold certain technical difficulties must be overcome. In this paper we use standard language of differential topology to make a systematic investigation to this manifold and build it into a quasi-differentiable Banach manifold. Consequent, it is possible to consider differential equations in this Banach manifold. As an application we also discuss how to reduce some important free boundary problems into differential equations in such a manifold or some of its vector bundles. [ABSTRACT FROM AUTHOR]

Due to its simplicity, efficiency, and dependability, the multipulse rectifier is widely used in electrical systems. In the presented work, an optimum design of an 18-pulse rectifier is achieved by comparing the most used configurations on the market. The 18-phase shifting autotransformer (18-PSAT) rectifier is a cheaper alternative to conventional rectifiers to reduce system harmonics. After a thorough study of the market needs and available use, this paper discusses four different structures that provide harmonic levels according to IEEE 519 limitations. An innovative 18-PSAT is shown, studied, simulated, produced, and tested with low power loss rates. The Delta differential configuration primarily emphasises lowering the loss power rating for improved power quality. With its simple structure, easy assembly, and direct connection to diodes, the proposed Delta differential configuration provides higher power quality and can cancel harmonics. To determine which 18-PSAT rectifier unit has the best weight, size, and power quality, a comparison of the selected topologies is made. A comprehensive comparison of each topology has simulation results showing current, voltage, and total harmonic distortion (THD) using MATLAB Simulink. The simulation results show that the total harmonic distortion is under 2.9 % when adopting the suggested Delta differential configuration topology. Compared to other designs, the suggested 18-pulse layout reduces overall cost and footprint by a large margin. It is also demonstrated that the DC load power is about 85 % of the recommended rectifier rating. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced a new class of open and closed functions called Igds-closed and Igds-open functions in ideal topological spaces and also investigated some of its characterizations and properties with the existing sets. [ABSTRACT FROM AUTHOR]

The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the set of all connected components of level sets including singular points. Reeb graphs are fundamental and important in the algebraic and differential topological theory of Morse functions and their generalizations. In this paper, as a related fundamental and important study, for given graphs, we construct certain smooth functions inducing the graphs as the Reeb graphs. Such works have been demonstrated by Masumoto, Michalak, Saeki, Sharko etc. and also by the author since 2000s. We present new smooth functions on suitable 3-dimensional closed orientable manifolds through explicit constructive methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider the feasibility of linear interference alignment (IA) for multiple-input-multiple-output (MIMO) channels with constant coefficients for any number of users, antennas, and streams per user, and propose a polynomial-time test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. In particular, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians), and the solution set (channels, decoders, and precoders satisfying the IA polynomial equations), not only as algebraic sets, but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zero-measure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the bounded-error probabilistic polynomial complexity class. [ABSTRACT FROM AUTHOR]

While different RF functionalities, such as an amplifier or a mixer, have been designed using the graphene FET (GFET) devices, the balun circuit has not been explored. In this paper, two innovative active balun architectures are presented taking advantage of the GFET’s unique symmetrical and ambipolar behavior, respectively. The symmetry-based active balun circuit is realized using an advanced SiC-based GFET RF technology. After circuit design and optimization using a large signal GFET compact model, the circuit has been fabricated and characterized. Measurement results confirm its excellent functionality. Circuit simulation shows that the second architecture exploring the GFETs ambipolar behavior gives equivalent results compared with the first architecture. Both topologies avoid asymmetric impedance matching and result in the accurate amplitude and phase balance of the balun. [ABSTRACT FROM AUTHOR]

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo-Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo-Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light-like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light-like homogeneous geodesic. [ABSTRACT FROM AUTHOR]

This paper studies stationary Markov perfect equilibria in multidimensional models of dynamic bargaining, in which the alternative chosen in one period determines the status quo for the next. We generalize a sufficient condition for existence of equilibrium due to Anesi and Seidmann, 2015. We then use this existence result to show that if a weak gradient restriction holds at an alternative, then when players are sufficiently patient, there is a continuum of equilibria with absorbing sets arbitrarily close to that alternative. A sufficient condition for our gradient restriction is that the gradients of all players' utilities are linearly independent at that alternative. When the dimensionality of the set of alternatives is high, this linear independence condition holds at almost all alternatives, and equilibrium absorbing sets are dense in the set of alternatives. This implies that constructive techniques, which are common in the literature, fail to identify many plausible outcomes in dynamic bargaining games. [ABSTRACT FROM AUTHOR]

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multi-layer graph, where the common vertex set represents the entities and the edges on different layers capture the similarities of the entities in term of the different modalities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. To this end, we propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse relationships between entities. As an illustrative application of our framework, we use our algorithm in clustering methods and test its performance on several synthetic and real world datasets where it is shown to be superior to baseline schemes and competitive to state-of-the-art techniques. Our generic framework further extends to numerous analysis and learning problems that involve different types of information on graphs. [ABSTRACT FROM PUBLISHER]

The subject of this paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the spacetime and the vector bundle that are usually independently assumed to hold are now derived from a minimal set of assumptions based on the recent progress in differential geometry and topology. [ABSTRACT FROM AUTHOR]

In this paper we study the periodic shadowing property and show that expansive dynamical systems that have the pseudo-orbit tracing property (POTP) also have the periodic shadowing. In addition, the convers is proved for chain transitive systems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose an alternative formulation of income tax that is based on simultaneous utility maximization of both the taxpayer and the government. This method is different from both the fixed income tax method which applies a fixed rate irrespective of the income level, and the graduated income tax formulation which is based on incremental tax rates. Welfare properties of the simultaneous utility maximization income tax formulation such as Pareto optimality, majority voting, social optimality, and unproductive taxation are studied. It is proven that the utility based taxation satisfies all welfare properties. [ABSTRACT FROM AUTHOR]

We prove a $${C^\infty}$$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $${C^\infty}$$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral invariants in embedded contact homology. A key new ingredient of this paper is an analysis of an area-preserving map near its fixed point, which is based on some classical results in Hamiltonian dynamics: existence of KAM invariant circles for elliptic fixed points, and convergence of the Birkhoff normal form for hyperbolic fixed points. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors showed that metrics which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique foliation by stable spheres with constant mean curvature. In this paper we extend that result to all asymptotically hyperbolic metrics for which the trace of the mass term is positive. We do this by combining the Kazdan-Warner obstructions with a theorem due to De Lellis and Müller. [ABSTRACT FROM AUTHOR]

This paper provides certain computations with transfer associated with projective bundles of \mathrm {Spin} vector bundles. One aspect is to revise the proof of the main result of [Trans. Amer. Math. Soc.349 (1997), pp. 4385-4399] which says that all fourfold products of the Ray classes are zero in symplectic cobordism. [ABSTRACT FROM AUTHOR]

Given a differential Batalin--Vilkovisky algebra , the associated odd differential graded Lie algebra is always smooth formal. The quantum differential graded Lie algebra is not always smooth formal, but when it is — for example, when a version of the Lemma holds — there is a weak Frobenius manifold structure on the homology of that is important in applications and relevant to quantum correlation functions. In this paper, we prove that is smooth formal if and only if the spectral sequence associated to the filtration on the complex degenerates at . A priori, this degeneration means that a collection of first-order obstructions vanish and we prove that it follows that all obstructions vanish. For those differential BV algebras that arise from the Hochschild complex of a Calabi–Yau category, the degeneration of this spectral sequence is an expression of the noncommutative Hodge to deRham degeneration, conjectured by Kontsevich and Soibelman and proved to hold in certain cases by Kaledin. The results in this paper imply that the noncommutative Hodge to de Rham degeneration conjecture is equivalent to the existence of a versal solution to the quantum master equation. At the end of the paper, some physical considerations are mentioned. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to propose a new notion on prominent areas of a city defined by two types of comprehensive prominence for identifying urban spatial structure. Not only geometric attributes and topological attributes but also thematic attributes of irregular areas (e.g. districts of a city) are used to define these indices. In the paper, first the topological prominence related to geometric attributes such as size, location, and shape of areas is constructed by spatial weight matrix. Second, for finding comprehensive prominences, the principle axis factor model is adopted, and the first factor score is defined as the comprehensive prominence 1. Then, the proportion of thematic attributes of each area occupied in across the city is used to define the comprehensive prominence 2. Finally, we use these comprehensive prominences to extract some important regions in Matsudo City of Chiba Prefecture in Japan. The areas composing those regions show a high topological prominence, have a large population, have many offices, and are located around the train station. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the case of submersions. It is observed that any smooth mapping can be C0-approximated by a possibly "unfair" cofrontal or a frontal. However, global "fair" cofrontals are very restrictive to exist. Then we give a method to construction "fair" cofrontals with fiber-dimension one and a target-local diffeomorphism classification of such cofrontals, under some finiteness condition. [ABSTRACT FROM AUTHOR]

Location of the static VAR compensator (SVC) and other types of shunt compensation devices is important for the enhancement of the voltage stability for practical power systems. With the theory of the normal forms of diffeomorphism, this paper proposes a new method to solve this problem. The proposed method makes use of the nonlinear participation factors, in which the nonlinearity of power systems can be taken into consideration. As a result, the most suitable location where the SVC should be used in power system can be determined, even for the cases in which the system is characterized with strong nonlinearity. In order to show the effectiveness of the proposed method, the New England 39-bus power system with SVC is used as an example. Calculation results show that with the SVC located at the place where the proposed method determined, the voltage stability is considerably enhanced. The steady-state voltage stability index and the time domain simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Consider oriented surfaces immersed in R[sup3]. Associated to them, here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature Κ, given by the product of the principal curvatures κ[sub1], κ[sub2] is positive. The leaves of the foliations are the lines of harmonic mean curvature, also called characteristic or diagonal lines, along which the normal curvature of the immersion is given by Κ/H, where H = (κ[sub1] + κ[sub2])/2 is the arithmetic mean curvature. That is, Κ/H= ((1/κ[sub1] + 1/κ[sub2]/2)[sup-1] is the harmonic mean of the principal curvatures κ[sub1], κ[sub2] of the immersion. The singularities of the foliations are the umbilic points and parabolic curves, where κ[sub1] = κ[sub2] and Κ = 0, respectively. Here are determined the structurally stable patterns of harmonic mean curvature lines near the umbilic points, parabolic curves and harmonic mean curvature cycles, the periodic leaves of the foliations. The genericity of these patterns is established. This provides the three essential local ingredients to establish sufficient conditions, likely to be also necessary, for Harmonic Mean Curvature Structural Stability of immersed surfaces. This study, outlined towards the end of the paper, is a natural analog and complement for that carried out previously by the authors for the Arithmetic Mean Curvature and the Asymptotic Structural Stability of immersed surfaces. [13, 14, 17], and also extended recently to the case of the Geometric Mean Curvature Configuration [15]. [ABSTRACT FROM AUTHOR]

In this paper, by using the variational method and the critical point theorem because of Brezis and Nirenberg, we investigate the existence of solutions to a class of second-order impulsive Hamiltonian system. [ABSTRACT FROM AUTHOR]

Using results on the topology of moduli space of polygons (Jaggi, Ph.D. Thesis, University of Bern, ; Kapovich and Millson, J. Differ. Geom. 42:133-164, ), it can be shown that for a planar robot arm with n segments there are some values of the base-length, z ( i.e., length of line joining the base of the arm with its end-effector), at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected components, while at other values it has one connected component. We first review some of these known results relating the value of z with the connectivity of the constrained configuration space. Then the main design problem addressed in this paper is the construction of pairs of continuous inverse kinematics for arbitrary robot arms, with the property that the two inverse kinematics agree ( i.e. return the same configuration) when the constrained configuration space has a single connected component, but they give distinct configurations (one in each connected component) when the configuration space of the constrained arm has two components. This design is made possible by a fundamental theoretical contribution in this paper-a classification of configuration spaces of robot arms such that the type of path that the system (robot arm) takes through certain critical values of the forward kinematics function is completely determined by the class to which the configuration space of the arm belongs. This classification result makes the aforesaid design problem tractable, making it sufficient to design a pair of inverse kinematics for each class of configuration spaces (three of them in total). The motivation for this work comes from a more extensive problem of motion planning for the end effector of a robot arm, in which the ability to continuously sample one configuration from each connected component of the constrained configuration spaces of the arm enables us to dramatically reduce the dimensionality of the space in which the planning has to be performed, without sacrificing algorithmic completeness. We start the paper with the general motivation, but address only the problem of sampling such configurations when there is no obstacle in the environment-a problem that in itself is non-trivial. We demonstrate the simplicity and the low complexity of the presented algorithm through a Javascript + HTML5 based implementation available at . [ABSTRACT FROM AUTHOR]

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

Let M be a 2n-dimensional closed unitary manifold with a Tn−1-action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary Tn−1-manifold M is just determined by the equivariant Chern numbers c ω T n − 1 [M], where ω = (i1, i2,..., i6) are the multi-indexes for all i1, i2,..., i6 ∈ ℕ. Then we show that if M does not bound equivariantly, then the number of fixed points is greater than or equal to ⌈n/6⌉ + 1, where ⌈n/6⌉ denotes the minimum integer no less than n/6. [ABSTRACT FROM AUTHOR]

In this paper, we consider a simple superlinear Duffing equation x'' + 2x³ + p (t) = 0 (0.1) with impulses, where p(t + 1) = p(t) is an integrable function in ℝ. In order to apply Moser's twist theorem, we need to ensure that the corresponding Poincaré map of (0.1) is quite close to a standard twist map but it is not usually achieved due to the existence of impulses. Two types of impulsive functions which overcome this problem with different effects in the Poincaré map are provided here. In both cases, there are large invariant curves diffeomorphism to circles surrounding the origin and going to the infinity, which confine the solutions in its interior and therefore lead to the boundedness of all solutions. Furthermore, it turns out that the solutions starting at t = 0 on the invariant curves are quasiperiodic. [ABSTRACT FROM AUTHOR]

This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny–Study distance on this space. [ABSTRACT FROM PUBLISHER]

This paper studies questions related to the local behavior of almost everywhere differentiable maps with the N, N, ACP, and ACP properties whose quasiconformality characteristic satisfies certain growth conditions. It is shown that, if a map of this type grows in a neighborhood of an isolated boundary point no faster than a function of the radius of a ball, then this point is either a removable singular point or a pole of this map. [ABSTRACT FROM AUTHOR]

Recent breakthroughs in machine learning shift the paradigm of wireless communication towards intelligence radios. One of their core operations is automatic modulation recognition (AMR). Existing research focuses on coherent modulation schemes such as QAM and FSK. The AMR of (noncoherent) space–time modulation remains an uncharted area despite its deployment in modern multiple-input-multiple-output (MIMO) systems. The scheme using a so-called Grassmann constellation enables rate enhancement. In this paper, we propose an AMR approach for Grassmann constellation based on data clustering, which differs from traditional AMR based on classification using a modulation database. The approach allows algorithms for clustering on the Grassmann manifold (or the Grassmannian), such as Grassmann K-means and depth-first search, to be applied to AMR. We further develop an analytical framework for studying and designing these algorithms in the context of AMR. First, the expectation-maximization algorithm for Grassmann constellation detection is proved to be equivalent to clustering (K-means) on the Grassmannian for a high SNR. Thereby, a well-known machine-learning result that was originally established only for the Euclidean space is rediscovered for the Grassmannian. Next, we tackle the challenge on theoretical analysis of data clustering by introducing probabilistic metrics for measuring the inter-cluster separability and intra-cluster connectivity of received space–time symbols and deriving them using tools from differential geometry. The results provide useful insights into the effects of various parameters ranging from the signal-to-noise ratio to constellation size, facilitating algorithmic design. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of sublinear or superlinear p(x)‐Laplacian equations in RN. Some new criteria to guarantee that the existence of multiple solutions for the considered problem is established by using the Morse theory and minimax methods. [ABSTRACT FROM AUTHOR]

This article presents novel methodologies and practical design considerations for a $D$ -band transmit/receive (T/R) front-end module (FEM) in 22-nm fully depleted silicon-on-insulator (FD-SOI/FDX) CMOS technology for beyond-5G wireless communication. An ABCD-matrix-based synthesis methodology is proposed to co-design the T/R switch (SW) topology, including the power amplifier (PA) output and the low noise amplifier (LNA) input matching networks, to minimize the losses in both Tx and Rx modes. Based on this synthesis, an asymmetric T/R SW topology is realized with intrinsic electrostatic discharge (ESD) protection. Both the stacked-field-effect transistor (FET) PA and LNA adopt differential topologies with transformer-based matching networks to eliminate unwanted effects from common-mode parasitics. Passive gain-boosting techniques are used for both PA and LNA to enhance different TRx specifications. A reusable unit-cell layout strategy is applied for transistor arrays to accelerate the multiple-stage PA implementation and maintain uniform performance and minimal parasitics. At 140 GHz, the Tx achieves a power gain $G_{p}$ of 33.6/35.7 dB, a saturated output power $P_{\mathrm{ sat}}$ of 12.5/14.7 dBm, a peak power-added efficiency (PAE) of 10.8/11.3%, and an output 1-dB compression point (OP1dB) of 9.4/11.2 dBm with nominal/boosted supplies. An average output power (${P_{out}}_{avg}$)/PAE of 4.9 dBm/2% is obtained for a 4-GHz bandwidth 64-QAM single-carrier signal at an error-vector magnitude (EVM) of −24.8 dB. Moreover, its Tx-mode reliability has been assessed. At 140 GHz, the Rx achieves a 20-dB $G_{p}$ , a −24-dBm input 1-dB compression point (IP1dB), and a 9.2-dB noise figure (NF) with only 20-mW power consumption from a 0.8-V supply. This compact FEM has a PA/LNA core area of 0.024/0.032 mm2, respectively. [ABSTRACT FROM AUTHOR]

Letfbe a diffeomorphism of a closedmanifoldM, and letbe a closedf-invariant set. In this paper, by applying the reasoning developed in Wen et al. [J. Differ. Equ. 246 (2009), pp. 340–357] based on Liao, we study chain transitive sets in view of shadowing theory, and it is proved thatis chain transitive and-stably shadowing if and only ifis hyperbolic basic set. As a corollary, for a chain componentoff, it is proved thatis-stably shadowing if and only ifis a hyperbolic homoclinic class. [ABSTRACT FROM AUTHOR]