Terms Of Multipliers Research Articles

Resource-Efficient Gradient Methods for Model Predictive Pulse Pattern Control on an FPGA

We demonstrate that an optimization-based model predictive pulse pattern controller can be designed with a complexity in terms of hardware resource usage on a field-programmable gate array (FPGA) that is comparable to that of a conventional controller. The keys to the superior performance and resource usage over existing solution methods for model predictive pulse pattern control are an appropriate problem reformulation and a newly derived result for the projection on the truncated monotone cone that composes the feasible set in this application. Using a coldstarted classic gradient method in fixed-point arithmetic, a numerically stable implementation is shown to require less than 300 clock cycles to meet the stringent accuracy specification for problems with at most three switching transitions per phase. For the case of four (five) transitions, only about 550 (690) cycles are required. At the same time, merely two digital signal processor (DSP)-type multipliers on an FPGA are used for all problem sizes. These results indicate a speed improvement of ten times and a resource reduction by 17 times in terms of DSP-type multipliers for the case of three transitions per phase compared with an existing solution method. When there are four or five transitions per phase, the resource reduction is even more impressive.

A Characterization of Multipliers of a Lau Algebra Constructed by Semisimple Commutative Banach Algebras

A necessary and sufficient condition for a Lau type binary operation defined by two mappings to be an algebra-operation is given in terms of multipliers. Also a characterization of multipliers of a Lau algebra constructed by semisimple commutative Banach algebras is given in terms of multipliers of original Banach algebras.

Resolution of Peller's problem concerning Koplienko–Neidhardt trace formulae

A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product S 2 ×S 2 of two copies of the Hilbert-Schmidt classes into the trace class S 1 is established in terms of linear Schur multipliers acting on the space S 1 of all compact operators. Using this formula, we resolve Peller's problem on Koplienko-Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function f with a bounded second derivative, a self-adjoint (unbounded) operator A and a self-adjoint operator B 2 S 2 such that f(A + B) f(A) d dt (f(A + tB)) � t=0 / 2 S 1 .

Optimality and duality for robust multiobjective optimization problems

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. We establish necessary/sufficient optimality conditions for robust (weakly) Pareto solutions of the considered problem. These optimality conditions are presented in terms of multipliers and limiting subdifferentials of the related functions. In addition, we address a dual (robust) multiobjective problem to the primal one, and explore weak/strong duality relations between them under assumptions of (strictly) generalized convexity.

Area Efficient Complex Floating Point Multiplier for Reconfigurable FFT/IFFT Processor Based on Vedic Algorithm

The need of complex multipliers in mathematics seems to be a very important aspect. The application used as a complex operation with respect to the real and imaginary numbers together. In many of the practical aspect the design substantiated to be a aiding hand for co-functionality units. Since to carry out the operations more correctly so as to elluct the technical peccadilloes. The results show that proposed FFT consumes very less resources in terms of slices, flip flops and multipliers to provide cost effective solution for DSP applications The proposed design has a desideratum for high efficacy eliciting structure in terms of accuracy. The device used in this proposed design is 7a30tcsg324-3.

A posteriori error control of [formula omitted]-finite elements for variational inequalities of the first and second kind

In this paper, residual-based a posteriori error estimates for variational inequalities, including those of the second kind, are proposed. The variational formulation and its discretizations are considered in an abstract framework of general Banach spaces. The main idea is to express the residual in terms of some Lagrange multipliers which can be obtained, for instance, by some post-processing. The residual itself is defined for an arbitrary element of the trial space. The error of this element and of the solution of the variational inequality is then estimated by the dual norm of the residual plus some computable remainder terms. This concept is applied to a variety of (frictional) contact problems, such as Signorini and obstacle problems as well as to the Bingham fluid problem. The applicability of the estimates is confirmed by several numerical experiments. In particular, the general framework allows for the discretization with hp-adaptivity which leads to nearly exponential convergence rates in most cases.

Resource optimised reconfigurable modular parallel pipelined stochastic approximation‐based self‐tuning regulator architecture with reduced latency

Present self-tuning regulator architectures based on recursive least-square estimation are computationally expensive and require large amount of resources and time in generating the first control signal due to computational bottlenecks imposed by the calculations involved in estimation stage, different stages of matrix multiplications and the number of intermediate variables at each iteration and precludes its use in applications that have fast required response times and those which run on embedded computing platforms with low-power or low-cost requirements with constraints on resource usage. A salient feature of this study is that a new modular parallel pipelined stochastic approximation-based self-tuning regulator architecture which reduces the time required to generate the first control signal, reduces resource usage and reduces the number of intermediate variables is proposed. Fast matrix multiplication, pipelining and high-speed arithmetic function implementations were used for improving the performance. Results of implementation demonstrate that the proposed architecture has an improvement in control signal generation time by 38% and reduction in resource usage by 41% in terms of multipliers and 44.4% in terms of adders compared with the best existing related work, opening up new possibilities for the application of online embedded self-tuning regulators.

Breakdown mechanisms of normally hyperbolic invariant manifolds in terms of unstable periodic orbits and homoclinic/heteroclinic orbits in Hamiltonian systems

We analyze the mechanism of breakdown of normally hyperbolic invariant manifolds (NHIMs) based on unstable periodic orbits, homoclinic and heteroclinic orbits in NHIMs for Hamiltonian systems. First, we classify the breakdown mechanism in terms of the characteristic multipliers (the eigenvalues of the phase space Jacobian matrix) of unstable periodic orbits in the NHIM and elucidate the classification for systems of three degrees of freedom. Second, we also present an index that provides a sufficient condition under which the NHIM ceases to exist in more global regions along the homoclinic and heteroclinic orbits in the NHIM. We demonstrate local and global features of the breakdown of the NHIM for a hydrogen atom in crossed electric and magnetic fields. Our analysis of unstable periodic orbits of shorter periods indicates that local features of the breakdown are highly inhomogeneous, depending on each periodic orbit. This manifests an inherent dynamical feature for systems of more than two degrees of freedom. Contrastingly, our analysis of homoclinic orbits indicates that the energy at which the NHIM breaks down does not depend on each homoclinic orbit. This result suggests the existence of a global breakdown of the NHIM behind these homoclinic orbits since these homoclinic orbits run through broader phase space regions.

Control and stabilization for the wave equation with variable coefficients in domains with moving boundary

The study of stabilization and control for PDEs with variable coefficients involves higher level of complexity than the corresponding case of constant coefficients. Further compounding the complexity are the concern and effects of dynamic boundary motion. The problem in its general form is extremely challenging to treat, but under certain specific physical and geometric conditions, such as the time-likeness of the boundary and a limited speed of domain expansion, energy decay estimates can be established and the exact controllability can also be obtained by control-theoretic and Riemannian-geometric methods. Our approach here is based on the Bochner technique of differential geometry in terms of Riemannian metric and geometric multipliers, by generalizing an energy identity method used earlier in Bardos and Chen (1981). Concrete examples are also given to illustrate the geometric conditions and the theorems.

Cost Analysis and Simulation of Decimator for Multirate Applications

In this paper, a decimator design has been presented for multirate digital signal processing.  The decimator design has been analysed and simulated for cost comparison in terms of multipliers and MPIS. Two structures  namely Transposed Direct form and Symmetric Direct form have been used performance and  resource consumption analysis. The decimators have been designed  & simulated using MATLAB. It can be observed from the simulated results that symmetric structure comsumes almost 50% less multipliers and MPIS compared to transposed structure. So the symmetric structure based decimator is suitable to provide cost effective solution

Reduced-order forward dynamics of multiclosed-loop systems

In this work, a reduced-order forward dynamics of multiclosed-loop systems is proposed by exploiting the associated inherent kinematic constraints at acceleration level. First, a closed-loop system is divided into an equivalent open architecture consisting of several serial and tree-type subsystems by introducing cuts at appropriate joints. The resulting cut joints are replaced by appropriate constraint forces also referred to as Lagrange multipliers. Next, for each subsystem, the governing equations of motion are derived in terms of the Lagrange multipliers, which are based on the Newton–Euler formulation coupled with the concept of Decoupled Natural Orthogonal Complement (DeNOC) matrices, introduced elsewhere. In the proposed forward dynamics formulation, Lagrange multipliers are calculated sequentially at the subsystem level, and later treated as external forces to the resulting serial or tree-type systems of the original closed-loop system, for the recursive computation of joint accelerations. Note that such subsystem-level treatment allows one to use already existing algorithms for serial and tree-type systems. Hence, one can perform the dynamic analyses relatively quickly without rewriting the complete model of the closed-loop system at hand. The proposed methodology is in contrast to the conventional approaches, where the Lagrange multipliers are calculated together at the system level or simultaneously along with the joint accelerations, both of which incur higher order computational complexities, and thereby a greater number of arithmetic operations. Due to the smaller size of matrices involved in evaluating Lagrange multipliers in the proposed methodology, and the recursive computation of the joint accelerations, the overall numerical performances like computational efficiency, etc., are likely to improve. The proposed reduced-order forward dynamics formulation is illustrated with two multiclosed-loop systems, namely, a 7-bar carpet scrapping mechanism and a 3-RRR parallel manipulator.

Enhanced Karush–Kuhn–Tucker condition and weaker constraint qualifications

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush–Kuhn–Tucker condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity on the constraint functions and the set constraint implies the existence of a local error bound. Finally we give a tighter upper estimate for the Frechet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. In particular we show that the value function of a perturbed problem is Lipschitz continuous under the perturbed quasinormality condition which is much weaker than the classical normality condition.

Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

We provide non-smooth atomic decompositions for Besov spaces Bp,qs(Rn), s>0, 0<p,q⩽∞, defined via differences. The results are used to compute the trace of Besov spaces on the boundary Γ of bounded Lipschitz domains Ω with smoothness s restricted to 0<s<1 and no further restrictions on the parameters p,q. We conclude with some more applications in terms of pointwise multipliers.

Sobol′’s sensitivity analysis for a distributed hydrological model of Yichun River Basin, China

Summary This paper aims to provide an enhanced understanding of the parameter sensitivities of the Soil and Water Assessment Tool (SWAT) using a variance-based global sensitivity analysis, i.e., Sobol′’s method. The Yichun River Basin, China, is used as a case study, and the sensitivity of the SWAT parameters is analyzed under typical dry, normal and wet years, respectively. To reduce the number of model parameters, some spatial model parameters are grouped in terms of data availability and multipliers are then applied to parameter groups, reflecting spatial variation in the distributed SWAT model. The SWAT model performance is represented using two statistical metrics – Root Mean Square Error (RMSE) and Nash–Sutcliffe Efficiency (NSE) and two hydrological metrics – RunOff Coefficient Error (ROCE) and Slope of the Flow Duration Curve Error (SFDCE). The analysis reveals the individual effects of each parameter and its interactions with other parameters. Parameter interactions contribute to a significant portion of the variation in all metrics considered under moderate and wet years. In particular, the variation in the two hydrological metrics is dominated by the interactions, illustrating the necessity of choosing a global sensitivity analysis method that is able to consider interactions in the SWAT model identification process. In the dry year, however, the individual effects control the variation in the other three metrics except SFDCE. Further, the two statistical metrics fail to identify the SWAT parameters that control the flashiness (i.e., variability of mid-flows) and overall water balance. Overall, the results obtained from the global sensitivity analysis provide an in-depth understanding of the underlying hydrological processes under different metrics and climatic conditions in the case study catchment.

Homogeneity Property of Besov and Triebel-Lizorkin Spaces

We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the studied function spaces, we present also some results on the entropy numbers of these embeddings. Moreover, we derive some applications in terms of pointwise multipliers.

Twenty Years of Rail Crowding Valuation Studies: Evidence and Lessons from British Experience

This paper reviews evidence from British experience of the valuation of rail crowding obtained over 20 years from 17 studies. It summarizes these studies, places some useful empirical evidence in the public domain and draws lessons from this considerable body of evidence and experience. Crowding valuations, both for standing and seated in crowding conditions, are summarized in terms of time multipliers, which are inherently more transferable than monetary equivalents. A meta‐analysis of 208 valuations is reported, finding the valuations to vary with load factor and journey purpose. The seating multiplier averages 1.19 and the standing multiplier averages 2.32. The latter is in line with widely used multipliers applied to walking and waiting time. The most recent evidence is based around the number of standing passengers per square metre, thereby providing a more accurate measure of the discomfort of standing since, unlike load factor, it allows for the layout of the carriage and ease with which crowding can be accommodated. As far as methodology is concerned, the paper covers issues such as presenting crowding in ‘stated preference’ exercises and the realism of the crowding levels offered, non‐linearities in the relationship between crowding multipliers and the severity and amount of crowding time, and probabilistic versus deterministic representations of crowding. The paper also identifies future areas for research.

Strong Duality for the CDT Subproblem: A Necessary and Sufficient Condition

In this paper, we consider the problem of minimizing a nonconvex quadratic function, subject to two quadratic inequality constraints. As an application, such a quadratic program plays an important role in the trust region method for nonlinear optimization; such a problem is known as the Celis, Dennis, and Tapia (CDT) subproblem in the literature. The Lagrangian dual of the CDT subproblem is a semidefinite program (SDP), hence convex and solvable. However, a positive duality gap may exist between the CDT subproblem and its Lagrangian dual because the CDT subproblem itself is nonconvex. In this paper, we present a necessary and sufficient condition to characterize when the CDT subproblem and its Lagrangian dual admits no duality gap (i.e., the strong duality holds). This necessary and sufficient condition is easy verifiable and involves only one (any) optimal solution of the SDP relaxation for the CDT subproblem. Moreover, the condition reveals that it is actually rare to render a positive duality gap for the CDT subproblems in general. Moreover, if the strong duality holds, then an optimal solution for the CDT problem can be retrieved from an optimal solution of the SDP relaxation, by means of a matrix rank-one decomposition procedure. The same analysis is extended to the framework where the necessary and sufficient condition is presented in terms of the Lagrangian multipliers at a KKT point. Furthermore, we show that the condition is numerically easy to work with approximatively.

Economic Impact/Forecast Model of Intelligent Transportation Systems in Michigan: An Input Output Analysis

This study aims to understand the impact that Intelligent Transportation Systems (ITS) may have on the state of Michigan's economy. Econometric aspects of ITS over other industries are sought because presently ITS is perceived as a contribution to transportation industry only. Leontief's Input-Output (I-O) model that establishes an economic measurement through industries is used to ascertain the ITS effects on Michigan. An aggregated industrial I-O model using RIMS II is utilized to compute the Michigan I-O table from the national I-O table. Savings in reduced time delays and fuel costs by employing full ITS products are forecasted to calculate an overall cost reduction factor pertaining to transportation industry. Impact of ITS on the intertwined industries in the I-O model is achieved by modifying the characteristics of Michigan I-O table and maximizing the effect on certain selected industries. Macroeconomic measures are then computed in terms of multipliers for all aggregated industries. These multipliers are obtained for the cases before ITS implementation, conventional improvement methods, and after ITS implementation. A sensitivity analysis is also carried out to gauge the forecast of ITS implementation in the state. Results suggest greater economic benefits that may be achieved for most industries by statewide implementation of the full ITS products.

Preduals of Qp -spaces II. Carleson imbeddings and atomic decompositions

In [Aleman, A., Carlsson, M. and Persson A., Preduals of Qp -spaces. Complex Variables (To appear).], we have obtained a representation of the Cauchy-predual of the space Qp on the unit disc as a weak product of weighted Dirichlet and Bergman spaces. The present article is a continuation of Aleman et al. and contains several applications and further developments of those results. We investigate the relation between Qp and Carleson inequalities for functions in weighted Dirichlet spaces and, in particular, we prove a characterization of bounded Qp -functions in terms of pointwise multipliers between such spaces. Moreover, we use our approach based on imbeddings in vector-valued sequence spaces to obtain atomic decompositions of the predual of Qp . This last result is then extended to the real variable setting where we prove atomic decomposition theorems for the preduals of certain function spaces that generalize .

Regional economic impacts of Grand Canyon river runners

Economic impact analysis (EIA) of outdoor recreation can provide critical social information concerning the utilization of natural resources. Outdoor recreation and other non-consumptive uses of resources are viewed as environmentally friendly alternatives to extractive-type industries. While outdoor recreation can be an appropriate use of resources, it generates both beneficial and adverse socioeconomic impacts on rural communities. The authors used EIA to assess the regional economic impacts of rafting in Grand Canyon National Park. The Grand Canyon region of northern Arizona represents a rural US economy that is highly dependent upon tourism and recreational expenditures. The purpose of this research is twofold. The first is to ascertain the previously unknown regional economic impacts of Grand Canyon river runners. The second purpose is to examine attributes of these economic impacts in terms of regional multipliers, leakage, and types of employment created. Most of the literature on economic impacts of outdoor recreation has focused strictly on the positive economic impacts, failing to illuminate the coinciding adverse and constraining economic impacts. Examining the attributes of economic impacts can highlight deficiencies and constraints that limit the economic benefits of recreation and tourism. Regional expenditure information was obtained by surveying non-commercial boaters and commercial outfitters. The authors used IMPLAN input–output modeling to assess direct, indirect, and induced effects of Grand Canyon river runners. Multipliers were calculated for output, employment, and income. Over 22,000 people rafted on the Colorado River through Grand Canyon National Park in 2001, resulting in an estimated $21,100,000 of regional expenditures to the greater Grand Canyon economy. However, over 50% of all rafting-related expenditures were not captured by the regional economy and many of the jobs created by the rafting industry are lower-wage and seasonal. Policy recommendations are given for increasing the regional retention of rafting expenditures and for understanding both the beneficial and adverse impacts that accompany outdoor recreation in rural areas.