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We introduce graded E ∞ -rings and graded modules over them, and study their properties. We construct projective schemes associated to connective N -graded E ∞ -rings in spectral algebraic geometry. Under some finiteness conditions, we show that the ∞ -category of almost perfect quasi-coherent sheaves over a spectral projective scheme Proj (A) associated to a connective N -graded E ∞ -ring A can be described in terms of Z -graded A-modules. [ABSTRACT FROM AUTHOR]

In this paper I present an alternative reading and interpretation of the cuneiform tablet BM 76829. I suggest that the obverse of the tablet contains a simple astrological scheme linking the sign of the zodiac in which a child is born to the maximum length of life, and that the reverse contains a copy of a scheme relating parts of the body to the signs of the zodiac. [ABSTRACT FROM AUTHOR]

In this paper, we study the Nyström type subsampling for large-scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nyström type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of the multi-penalty least-square regularization scheme under the general source condition in vector-valued function setting, therefore the results can also be applied to multi-task learning problems. We achieve the optimal minimax convergence rates of the multi-penalty regularization using the concept of effective dimension for the appropriate subsampling size. We discuss an aggregation approach based on the linear function strategy to combine various Nyström approximants. Finally, we demonstrate the performance of the multi-penalty regularization based on Nyström type subsampling on the Caltech-101 dataset for multi-class image classification and NSL-KDD benchmark dataset for intrusion detection problem. [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate the flutter control scheme of super long-span bridges with various aspect ratios (e.g. width to height (B/H)) using passive aerodynamic countermeasures. Through a series of wind tunnel testing and theoretical analysis, three types of passive aerodynamic countermeasures, i.e. vertical central stabilizer (VCS), wind barrier and inspection rail, were investigated for five typical aspect ratios of a closed-box girder bridge. The results show that both the aspect ratio and flutter critical wind speed generally increase with the decrease of the ratio of torsional and vertical frequencies of the bridge. In the case of an aspect ratio of 8.9, a downward VCS (DVCS) has a much better flutter performance than that of an upward VCS (UVCS) because aerodynamic damping of Part A and Part D could produce a higher heaving degree of freedom (DOF) participation level. Furthermore, the position variation of wind barriers is superior to their shape variation for the bridge with an aspect ratio of 8.3, and the flutter performance of the girder with a combination of the wind barrier (WB3P3) and UDVCS with 0.3 h/H DVCS appears to be better than that without countermeasures. In addition, the installation of an inspection rail near the bottom point of an inclined-web (IR3) has the best flutter control effect among four positions of inspection rails. [ABSTRACT FROM AUTHOR]

This paper is devoted to study measure solutions μ t h to perturbed nonlinear structured population models where t denotes time and h controls the size of perturbation. We address differentiability of the map h ↦ μ t h. After showing that this type of results cannot be expected in the space of bounded Radon measures M (R +) equipped with the flat metric, we move to the slightly bigger spaces Z = M (R +) ‾ (C 1 + α) ⁎ . We prove that when α > 1 2 , the map h ↦ μ t h is differentiable in Z. The proof exploits approximation scheme of a nonlinear problem from previous studies and is based on the iteration of an implicit integral equations obtained from study of the linear equation. The result shows that space Z is a promising setting for optimal control of phenomena governed by such type of models. [ABSTRACT FROM AUTHOR]

• A kernel separation method is proposed to compute the singular integral accurately. • Four singular integrals with different ordered kernel are computed directly with the help of the kernel separation method. • A patch subdivision scheme is developed based on the relation between the product of wave velocity, time and the distance. In the implementation of time-domain boundary element method for elasto-dynamic problems, there are two types of singularities: the wave front singularity arising when the product of wave velocity and time is equal to the distance between the source point and the field point, and the spatial singularity arising when the source point coincides with the field point. In this paper, the singularity of the first type in the integrand is eliminated by an analytical integration over time, Cauchy principal value and Hadamard finite part integral. Four types of singularities with different orders appear in the integrand after analytical time integration. In order to accurately calculate the integral, in which the integrand is piecewise continuous, the integral domain is subdivided into several patches based on the relation between the product of wave velocity and time and the distance. In singular patches, the integrands are separated into a regular part and a singular part. The regular part can be computed by traditional numerical integration method such as Gaussian integration, while the singular part can be analytically integrated. Using the proposed method, the spatial singular integrals can be calculated directly. Numerical examples using various kinds of elements are presented to verify the proposed method. [ABSTRACT FROM AUTHOR]

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then postulate a second type of concept and a second type of reflective abstraction that accounts for its construction, the abstraction of commonality (AOC). [ABSTRACT FROM AUTHOR]

In this work, we develop an optimization approach to optimize the distribution of porous material layer inside cavity. The optimization seeks to improve the absorbing effects of the porous material, decreasing the noise level at regions of interest or increasing the sound energy dissipated by the porous material. To achieve the preset optimization aim, two different objective functions are accordingly defined. The acoustic absorption characteristics of porous materials are numerically described using the Delany–Bazley–Miki empirical model and modeled by the admittance boundary conditions in the boundary element analysis. Based on the solid isotropic material with penalization method, an admittance interpolation scheme is established between the element admittance and artificial element density. This transforms the discrete optimization into a continuous optimization problem, which can be solved by a gradient solver with the sensitivity information. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method and the fast multipole method to calculate the sensitivities of the objective function with respect to a large number of design variables. Finally, we validate the proposed optimization approach through a cabin example. [ABSTRACT FROM AUTHOR]

The problem of representing logical implications and proofs by mathematical objects is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation problems. Examples of mathematical considerations are given. Arguments supporting such an advance and its applications in mathematical research guidance and publication standards are given. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust control for non-cooperative rendezvous is investigated based on implicit Lyapunov function (ILF) method. The dynamical model of relative motion between two spacecrafts is established in the body coordinate system of the chaser spacecraft without using the target-orbital information. In view of unknown inertia parameters and external disturbances, an ILF control-observer scheme is introduced, where the ideal controller is first designed and then estimated by the observer. The closed-loop system is proved to be finite-time stable, and the controller and observer gains are, respectively, obtained by solving linear matrix inequalities and parameterised nonlinear matrix inequalities. To reduce the computational burden, analytical solutions to these matrix inequalities are provided. The effectiveness of the theoretical results is demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a real-time, dynamic three-dimensional (3D) shape reconstruction scheme based on the Fourier-transform profilometry (FTP) method is achieved with a short-wave infrared (SWIR) indium gallium arsenide (InGaAs) camera for monitoring applications in low illumination environments. A SWIR 3D shape reconstruction system is built for generating and acquiring the SWIR two-dimensional (2D) fringe pattern of the target. The depth information of the target is reconstructed by employing an improved FTP method, which has the advantages of high reconstruction accuracy and speed. The maximum error in depth for static 3D shape reconstruction is 1.15 mm for a plastic model with a maximum depth of 36 mm. Meanwhile, a real-time 3D shape reconstruction with a frame rate of 25 Hz can be realized by this system, which has great application prospects in real-time dynamic 3D shape reconstruction, such as low illumination monitoring. In addition, for real-time dynamic 3D shape reconstruction, without considering the edge areas, the maximum error in depth among all frames is 1.42 mm for a hemisphere with a depth of 35 mm, and the maximum error of the average of all frames in depth is 0.52 mm. [ABSTRACT FROM AUTHOR]

The main problem of that article is effectiveness / ineffectiveness of an axiological system of the sustainable development as the base of a program of activities taken in individual and social-political scale. The problem was presented from the view of Alain Badiou's ethics, which is a trial of overcoming weaknesses of the contemporary ethics of the mainstream, especially very low effectiveness of the ethics in the sphere of social practice. For developing the title problem there was applied the critique of contemporary ethics as the ethics of consensus, conducted by Badiou. Established research prospect has a limited application. It allows exclusively and only for drawing a conclusions in the matter of possible usability of the ethics of sustainable development in the activities leading to the change of dominant stereotypes of thinking and standards of conduct nowadays. From the point of view of Badiou's ethics this is the first, but necessary step on the way to answer a following question - does the ethic of sustainable development have actual causative power and is it effective in initiating and performing social changes? [ABSTRACT FROM AUTHOR]

Singularity category is an important invariant for rings of infinite global dimension and for singular varieties. It is quite an active subject widely studied by a number of authors. Let (X,OX) be a Gorenstein scheme satisfying (ELF) condition below. We will show that the sin- gularity category Dsg(X) is triangle equivalent to the stable category MCM(X) of maximal Cohen-Macaulay sheaves over X. [ABSTRACT FROM AUTHOR]

In the present paper, a multi-step reconstruction procedure is proposed for high order finite volume schemes on unstructured grids using compact stencil. The procedure is a recursive algorithm that can eventually provide sufficient relations for high order reconstruction in a multi-step procedure. Two key elements of this procedure are the partial inversion technique and the continuation technique. The partial inversion can be used not only to obtain lower order reconstruction based on existing reconstruction relations, but also to regularize the existing reconstruction relations to provide new relations for higher order reconstructions. The continuation technique is to extend the regularized relations on the face-neighboring cells to current cell as additional reconstruction relations. This multi-step procedure is operationally compact since in each step only the relations defined on a compact stencil are used. In the present paper, the third and fourth order finite volume schemes based on two-step quadratic and three-step cubic reconstructions are studied. [ABSTRACT FROM AUTHOR]

We prove the existence of nonnegative weak solutions to a class of second- and fourth-order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility function posed on the whole space ℝ d {{{\mathbb{R}}^{d}}} , for arbitrary d ≥ 1 {d\geq 1}. Exploiting a very formal gradient flow structure, the cornerstone of our proof is a modified version of the classical minimizing movement scheme for gradient flows. The mobility function is required to satisfy – at each time point separately – the conditions by which one can define a modified Wasserstein distance on the space of probability densities with finite second moment. The explicit dependency on the time variable is assumed to be at least of Lipschitz regularity. We also sketch possible extensions of our result to the case of bounded spatial domains and more general mobility functions. [ABSTRACT FROM AUTHOR]

Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes how faculty mentors leveraged challenges in the mentoring program's early stages based on their reflections and initial mentee outcomes to create a more effective mentoring program. Recommendations based on research and practice are provided for other university programs interested in mentoring future mathematics teachers. [ABSTRACT FROM AUTHOR]

The union of near-field communication (NFC) and mobile devices has led to significant changes in payment systems over recent years. Currently, NFC-based services are the leading form of mobile payment method. In particular, many companies that use electronic payment services are adopting NFC systems to replace credit cards. Additionally, the safety of communication has been enhanced by using standard techniques to activate NFC services. The properties of mobile NFC payments provide a business model for the Internet of Things (IoT) environment. However, electronic payment methods based on NFC are still vulnerable to various security threats. One example is the case of credit card data hacking under the KS X 6928 standard. In particular, the security level of the NFC payment method in passive mode is limited by the storage, power consumption, and computational capacity of the low-cost tags. Recently, chaotic encryption based on Chebyshev polynomials has been used to address certain security issues. Our proposed scheme is based on the Chebyshev chaotic map, unlike traditional encryption protocols that apply complex cryptography algorithms. Considering the tag limitations, the hash, XOR, and bitwise operations in the proposed scheme provide high-level security for payment environments. We propose a security-enhanced transaction scheme based on Chebyshev polynomials for mobile payment services in an IoT device environment considering the signature record-type definition and KS X 6928 standard. [ABSTRACT FROM AUTHOR]

We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high rank or full rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as pre-conditioners. This yields an automated method to construct preconditioners for locally translation-invariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the nonlocal component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods. [ABSTRACT FROM AUTHOR]

Abstract We introduce a novel method to construct conforming meshes for an evolving branched curve immersed in a given background mesh in 2D and 3D. The proposed method is built on the successive node snapping (SNS) scheme proposed by Wan and Shen (2016) and Wan et al. (2019) which is able to generate a conforming mesh for a simple evolving curve in 2D and 3D. The essence of the SNS scheme is to snap chosen nodes to the curve, and to simultaneously relax the nodes within the neighborhood of the curve. Following the curve, each portion of the curve's vicinity is adjusted to obtain a mesh conforming to the entire curve. The core of the generalization of the SNS scheme for a branched curve is to assign each branch a matching node , from which we start to adjust the mesh for the branch via a procedure similar to that for a simple curve. The approach to determine the matching node is based on minimizing mesh distortion. The proposed approach inherits the main advantage of the SNS scheme, including unaltered nodal connectivities, small adjustment of nodes, no a priori conformity requirements on the background mesh, and permitting obtuse-angled triangular or tetrahedral background mesh as well as acute-angled ones. As all the operations on the mesh are local, the proposed method is especially suitable for evolving branched curve problems in which the curve updates a little bit at each time/ load step. Numerical examples in 2D and 3D are provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with the input-to-state stabilization problem for a class of delayed differential systems. Both time-delay in state and bounded exogenous disturbances are taken into account in the model. An event-triggered strategy, which depends simultaneously on the latest sampled state and a non-negative threshold, is proposed to reduce the transmission frequency of the feedback control signals with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to evaluate the dynamical performance of the controlled systems with considering the effects from both exogenous disturbances and event-triggered scheme. The estimations of the upper bounds for the system state and the measurement error are employed to analyze and further exclude the Zeno behavior for the proposed event-triggered scheme. The controller gain and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this work a high order scheme is proposed for solving the heat conduction problems. In this scheme, the governing equation of heat conduction is firstly written into a system of first-order partial differential equations which are integrated over the control volumes around each node point and a finite time step. The resulting time integrals are approximated by numerical quadrature with an undetermined weighting parameter. The error analysis allows us to determine the parameter and the ratio of the time step to the square of grid spacing by making the error of the scheme as small as possible. Both theoretical and numerical results show that the proposed high order scheme can achieve at least sixth order accuracy at the expense of the same computing cost as the traditional finite volume method. And the high order scheme demonstrates a better performance than the high order compact finite difference method and the Runge–Kutta discontinuous Galerkin method. [ABSTRACT FROM AUTHOR]

Abstract In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using Von-Neumann stability analysis. We have proved the method is unconditionally stable when 0 < λ q < min (1 μ 0 , 2 γ) and 0 < γ ≤ 1, and demonstrated the method is also stable numerically in the case 1 μ 0 < λ q ≤ 2 γ and log 3 2 ≤ γ ≤ 1. The accuracy and convergence of the scheme was also investigated and found to be of order O (Δ t 1 + γ) in time and O (Δx 2) in space. To confirm the accuracy and stability of the proposed method we provide three examples with one including a linear reaction term. [ABSTRACT FROM AUTHOR]

Abstract This paper aims to deliver another approach of solving hyperbolic system of equation into the field of computational electromagnetics, known as the residual distribution (RD) or fluctuation splitting method. The RD scheme fills the interstice between finite-element method (FEM) and finite-volume method (FVM), where its idea of calculating flux residual imitates the FVM, but the numerical solutions within a discretized triangular mesh is interpolated with similitudes to the FEM. It was originally designed as a remedy to capture shock problem in Euler system under compact stencil, but its extension to linear-preserving scheme which is the main cause of this work, capable of giving second-order-accurate results and is congenial to the FEM framework. The RD scheme is always vertex-centered therefore has all the conserved variables E and H located at the same nodal point. This topology evades having both vertex-centered and cell-centered coordination in one single mesh, and permits time-discretization other than the staggered time marching scheme, such as the common backward-time discretization which is unconditionally stable. Another contribution of this work is to suggest that row-mass-lumping of the consistent mass-matrix would not mar too much the second-order-accuracy of LDA-RD scheme, which is an upwind scheme where the mass-matrix an impediment for time-updating during the last decade. A prior reconstruction of the upwind mass-matrix is done before lumping up the mass-matrix so that the time-marching nodal update is consistent with the distribution of mass-matrix. The current work covers 3 basic exercises of electromagnetics, they are 2D radiation problem, 2D scattering problem and 3D waveguide propagation. For the 2D scattering and 3D waveguide problems, the perfect electric conductor (PEC) boundary condition is successfully applied using RD construction. [ABSTRACT FROM AUTHOR]

Abstract The paper provides a spectral collocation numerical scheme for the approximation of the solutions of stochastic fractional differential equations. The discretization of the operator leads to a system of nonlinear algebraic equations, whose coefficient matrix can be computed by an automatic procedure, consisting of linear steps. A selection of numerical experiments confirming the effectiveness of the approach is given, with respect to various sets of function bases and of collocation points. [ABSTRACT FROM AUTHOR]

Abstract The Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is presented. This analysis is carried out on the example of a model linear advection equation. The results of Fourier analysis are presented as graphs of the dependence of the dispersion and dissipative characteristics of the bicompact schemes on the dimensionless wave number and the Courant number. The dispersion and dissipative properties of bicompact schemes are compared with those of other widely used difference schemes for hyperbolic equations. It is shown that bicompact schemes have one of the best spectral resolutions among the difference schemes being compared. [ABSTRACT FROM AUTHOR]

Among the bivariate subdivision schemes available, spline-based schemes, such as Catmull-Clark and Loop, are the most commonly used ones. These schemes have known continuity and can be evaluated at arbitrary parameter values. In this work, we develop a C 1 spline-based scheme based on cubic half-box splines. Although the individual surface patches are triangular, the associated control net is three-valent and thus consists in general of mostly hexagons. In addition to introducing stencils that can be applied in extraordinary regions of the mesh, we also consider boundaries. Moreover, we show that the scheme exhibits ineffective eigenvectors. Finally, we briefly consider architectural geometry and isogeometric analysis as selected applications. [ABSTRACT FROM AUTHOR]

Hermite subdivision schemes act on vector valued data that is not only considered as functions values of a vector valued function from R to R r , but as evaluations of r consecutive derivatives of a function. This intuition leads to a mild form of level dependence of the scheme. Previously, we have proved that a property called spectral condition or sum rule implies a factorization in terms of a generalized difference operator that gives rise to a "difference scheme" whose contractivity governs the convergence of the scheme. But many convergent Hermite schemes, for example, those based on cardinal splines, do not satisfy the spectral condition. In this paper, we generalize the property in a way that preserves all the above advantages: the associated factorizations and convergence theory. Based on these results, we can include the case of cardinal splines in a systematic way and are also able to construct new types of convergent Hermite subdivision schemes. [ABSTRACT FROM AUTHOR]

Abstract Let X be any scheme defined over a Dedekind scheme S with a given section x ∈ X (S). We prove the existence of a pro-finite S -group scheme ℵ (X , x) and a universal ℵ (X , x) -torsor dominating all the pro-finite pointed torsors over X. Though ℵ (X , x) may not be unique in general it still can provide useful information in order to better understand X. In a similar way we prove the existence of a pro-algebraic S -group scheme ℵ alg (X , x) and a ℵ alg (X , x) -torsor dominating all the pro-algebraic and affine pointed torsors over X. The case where X → S has no sections is also considered. [ABSTRACT FROM AUTHOR]

Recently, several authors used linear codes to construct secret sharing schemes. It is known that if each nonzero codeword of a code C is minimal, then the dual code C ⊥ is suitable for secret sharing. To seek such codes Ashikhmin–Barg give a sufficient condition from weights; in [ n , k , d ] q code C , let w min and w max be the minimum and maximum nonzero weights, respectively. If w min w max > q − 1 q (*) then all nonzero codewords of C are minimal. In this paper, a necessary and sufficient condition is given for self-dual codes and for MDS codes to verify the inequality (*). Special codes are examined and applied for secret sharing schemes. [ABSTRACT FROM AUTHOR]

Let be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalisation of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp() of and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group G. To achieve this, we introduce the moduli functor M h G of G -marked Gorenstein canonical models with Hilbert polynomial h , and prove the existence of 𝔐 h [ G ] , the coarse moduli scheme for M h G . Then we show that 𝔐 h [ G ] has a proper and finite morphism onto 𝔐 h so that its image 𝔐 h (G) is a closed subscheme. In the end we obtain the canonical representation type decomposition 𝒟 h [ G ] of 𝔐 h [ G ] and use 𝒟 h [ G ] to study the structure of 𝔐 h [ G ]. [ABSTRACT FROM AUTHOR]

In this paper, we consider S-iteration to find fixed points of continuous mappings on an arbitrary interval. We give some necessary and sufficient conditions for the convergence of this iteration. Also, we proved that the rate of convergence of S-iteration is better than some other iterations for continuous and nondecreasing mappings. It is also noted that the method of proof of Lemma 3 using S-iteration is slightly different from that using the iteration schemes like Mann. [ABSTRACT FROM AUTHOR]

In the present paper, we give a full description of the jet schemes of the polynomial ideal ( x 1 ⋯ x n ) ∈ k [ x 1 , … , x n ] over a field of zero characteristic. We use this description to answer questions about products and intersections of ideals emerged recently in algorithmic studies of algebraic differential equations. [ABSTRACT FROM AUTHOR]

We prove that there is no non-trivial autoequvivalence of the category of schemes of finite type over Q . [ABSTRACT FROM AUTHOR]

In this paper, using the piecewise linear and quadratic Lagrange interpolation functions, we propose a novel numerical approximate method for the Caputo fractional derivative. For the obtained explicit recursion formula, the truncation error is investigated, which shows the involved convergence order isO(τ3−β) withβ∈(0,1). As an application, we use this proposed numerical approximation to solve the time fractional diffusion equations by the barycentric rational interpolations in space. The resultant systems of algebraic equations, truncation error, convergence, and stability are analyzed. Theoretical analysis and numerical examples show this constructed method enjoys accuracy of, wheredis the degree of the rational polynomial. [ABSTRACT FROM AUTHOR]

We consider repairable threshold schemes (RTSs), which are threshold schemes that enable a player to securely reconstruct a lost share with help from their peers. We summarise and, where possible, refine existing RTSs and introduce a new parameter for analysis, called the repair metric. We then explore using secure regenerating codes as RTSs and find them to be immediately applicable. We compare all RTS constructions considered and conclude by presenting the best candidate solutions for when either communication complexity or information rate is prioritised. [ABSTRACT FROM AUTHOR]

Motivated by the S-duality conjecture, we study the Donaldson–Thomas invariants of the 2-dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular curve. In the case where X is a K 3 fibration, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K 3 fiber and the Noether–Lefschetz numbers of the fibration. We prove that a certain generating function of these invariants is a vector modular form of weight − 3 / 2 as predicted in S-duality. [ABSTRACT FROM AUTHOR]

The complexity of the multiperiod dynamic unit commitment problem makes it difficult or even unviable to find the global optimal solution. Ordinal optimization provides a simulation-based approach suitable for solving this kind of problem. It uses crude models and rough estimates to derive a small set of unit commitment schemes for which simulations are necessary and worthwhile to find good enough solutions with drastically reduced computational burden. The 10-100 thermal units standard test example and the case of an actual provincial power system with 128 units verify the feasibility of ordinal optimization to solve the large-scale dynamic unit commitment problem. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

For the first time, we apply the sum-of-squares (SOS) decomposition technique for robust control of power systems. We propose an SOS L2 robust control scheme aiming at a power system characterized by exogenous disturbances. A set of states-related inequalities are utilized to guarantee L2 gain disturbance attenuation performance of the system. It involves semidefinite programming relaxations based on the SOS decomposition technique, which is employed to solve the inequalities that bring about robust control of the system. This method is superior to other traditional approaches. It is able to construct a robust controller that guarantees L2 gain disturbance attenuation performance of the system featuring exogenous disturbance by the SOS algorithm without solving Hamilton-Jacobi inequalities or using the recursive design of back-stepping. Then, the proposed approach is applied to derive a robust excitation controller for multimachine power systems. Moreover, a three-machine power system model is employed to test the robust excitation controller, which finally verifies its effectiveness and superiority. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

This paper presents 6-point subdivision schemes with cubic precision. We first derive a relation between the 4-point interpolatory subdivision and the quintic B-spline refinement. By using the relation, we further propose the counterparts of cubic and quintic B-spline refinements based on 6-point interpolatory subdivision schemes. It is proved that the new family of 6-point combined subdivision schemes has higher smoothness and better polynomial reproduction property than the B-spline counterparts. It is also showed that, both having cubic precision, the well-known Hormann-Sabin’s family increase the degree of polynomial generation and smoothness in exchange of the increase of the support width, while the new family can keep the support width unchanged and maintain higher degree of polynomial generation and smoothness. [ABSTRACT FROM AUTHOR]