Multiplier Function Research Articles

An MP-Newton method for computing nonlinear eigenpairs and its application for solving a semilinear Schrödinger equation

ln Yao and Zhou (2008), a minimax method for computing nonlinear eigenpairs by calculating critical points of the Lagrange multiplier function is presented. But, the method is slow and can find limited amount of eigenpairs. In this paper, a new general characterization, orthogonal-max characterization, for critical points of the Lagrange multiplier function is suggested. An MP-Newton method for finding orthogonal-max type critical points is designed through analyzing how the minimax method works. The new method becomes fast and able to calculate more nonlinear eigenpairs. Numerical experiment confirms these two progresses. Also, the MP-Newton method inherits the advantages of the minimax method. A convergence result for the method is established. Finally, an application for solving a semilinear Schrödinger equation is discussed.

Modifications to The Alcubierre Warp Field Metric in Anisotropic Matter and Implications to Detection of Warp Fields

The Alcubierre warp drive concept demonstrates a designed spacetime metric which enables hyperfast travel within the framework of known physics and has become one of the most widely studied spacetimes in the community. However, there has always been a singular issue with practical realization of the “warp drive” in that a large amount of matter with unattainable properties (such as negative or “exotic” matter/energy densities) are required. The negative matter-energy or “exotic” mass-energy density requirements violating the Averaged Weak and Null Energy Conditions mainly arise from solutions to the Einstein equations with little consideration of the matter content and characteristics within the metric. Recent efforts have shown that investigating details of the matter characteristics might offer new insights to practical warp field design and might lead to realizable solutions. This paper gives analysis of an anisotropic matter field solution, hypothetical applied variations to the Einstein coupling constant (via a multiplier function), and a multilayered warp bubble approach to reducing the warp field mass requirements to realizable forms and quantities. A discussion on the detection of such an advanced warp field is also given. Keywords: Alcubierre, Warp Drive, Spacetime Metric, Negative Energy, Einstein Equations, Anisotropic Matter

A design of multiplier based on Radix_4 Booth algorithm and 4-2 Wallace compression tree

In a multitude of computational and signal processing scenarios, the multiplier functions as a fundamental arithmetic component. Given the complex hardware arrangement of multipliers and their usual positioning within the crucial pathway of digital systems, their significance is substantial. Therefore, approximations of multipliers can greatly optimize system performance. This essay examines the fundamental ideas behind the Wallace tree, the Carry ahead adder, and the Radix-4 Booth algorithm. Additionally, instead of the more common 3-2 compressors, a Wallace tree structure with 4-2 compressors is used to compact these products for the manufacture of partial products. This reduction in compression stages to three significantly curtails delays along critical paths, thereby substantially improving overall performance. The compressed outcomes from the Wallace tree undergo processing via a 64 bit carry ahead adder, effectively addressing delays stemming from mutual carry propagation among sequentially connected regular full adders. Leveraging these principles and processes, a 32-bit signed multiplier is designed. Building upon this foundation, an approximate Booth multiplier is developed, enhancing both computational speed and reducing critical path delays. The functionality of the multiplier was validated using Vivado simulation, demonstrating its correctness. Additionally, the RTL-level circuitry of different segments of the multiplier was showcased.

Breast Cancer Diagnosis with Machine Learning Using Feed-Forward Multilayer Perceptron Analog Artificial Neural Network

An analog network classifier based on a multiplier and non-linear functions is presented in this paper, executing binary classification on breast cancer cells, and categorizing biopsies as benign or malignant tumors. An off-chip learning on-chip inference methodology is proposed for implementing a feed-forward analog artificial neural network based on fundamental design analog block circuits, realized with the aid of 90 nm CMOS technology. These circuits are meticulously designed and fine-tuned at the transistor scale to meet design criteria while minimizing power consumption. Through Spice simulations, the basic analog blocks were developed, leading to the specification of the full-chip hardware neural network. The Monte Carlo analysis of the final circuit reveals that the network achieves 96.85% accuracy and 0.9309 MCC on the Wisconsin breast cancer dataset, with a power consumption of 31.95 μW, and power supply rail of ±900 mV per analog circuit component and computational unit. The model effectively captures data patterns, providing stable, reliable, and robust predictions.

Some Estimates for the Jump of the Derivative of the Lagrange Multiplier Function in Optimal Control Problems with Second-order State Constraints

Some Estimates for the Jump of the Derivative of the Lagrange Multiplier Function in Optimal Control Problems with Second-order State Constraints

FPGA implementation of proficient Vedic multiplier architecture using hybrid carry select adder

ABSTRACT Nowadays, the application of computations and communications is needed for high performance, reduced size and lower power utilisation. The multiply and add functions are one of the frequently used operations in digital signal processing. Various types of multipliers are available in digital Various types of multipliers are available for various Signal processing applications.. Among these multipliers, Vedic multiplier is one of the most optimised multipliers used in a signal processing module. In the existing method, the Vedic multiplier is designed with conventional adders, which is having higher area utilisation, lower speed and higher power consumption. Hence, the modified Vedic multiplier is proposed to improve the speed of multiplication using hybrid technology. The partial products of the proposed multiplication are added using 2 × 2 Vedic multiplier and hybrid carry select adder (binary to excess one converter (BEC), Han-Carlson adder and Multiplexer). The critical path delays of hybrid 4 × 4 Vedic multiplier are the summation of 2 × 2 Vedic multiplier, two full adders, two multiplexers and two BECs for producing the final product. The proposed hybrid Vedic multiplier is operated at high speed with reduced size as compared to the existing multiplier techniques. The proposed hybrid Vedic multiplier is designed and simulated using Verilog HDL and implemented in Spartan 6 field-programmable gate array device. The implementation results showed that the delay of the proposed multiplier gets ameliorated as compared to array multiplication (30.84%), Wallace tree multiplication (29.52%), multiplication based on compressor (23.71%), Vedic multiplication by carry look-ahead adder (22.91%), Vedic multiplication by ripple carry adder (14.45%), revised booth multiplication (15.42%) and Vedic multiplication by Han-Carlson adder with BEC (13.95%) and hybrid multiplier (11.37%).

Integration Plasma Strategy Controlled Interfacial Chemistry Regulation Enabling Planar Lithium Growth in Solid‐State Lithium Metal Batteries

AbstractSolid‐state lithium metal batteries (SSLMBs) are identified as a highly promising candidate for next‐generation energy storage devices, yet they still face uncontrollable dendritic lithium (Li) growth originating from interfacial incompatibility. To address this issue, an “integration plasma (IP)” strategy for interlayer construction is proposed that integrates metal reduction and vapor deposition functions, featuring the ability to give a manipulable and quantifiable chemical regulation for controlling the surface concentration (Csurface) and the atomic ratio of the introduced metal element and electronegative element (ARE/M) on solid‐state electrolyte (SSE). This IP‐formed interlayer can in situ react with Li anode to synchronously produce metal‐Li alloy, Li salt and amorphous carbon, thus offering an “integrated function” to promote a spherical and hexagonal Li growth, preventing the dendrite propagation from SSE. When Csurface of metal elements and corresponding ARE/M is regulated as ≈1.13 nmol cm‐2 and ≈2.6, the IP‐modified SSE prolongs the lifespan of SSLMBs with LiNi0.8Co0.1Mn0.1O2 cathode to over 1000 cycles with a low‐capacity attenuation of 0.03% per cycle, highlighting the multiply functions of IP to accelerate the practical application of SSLMBs.

Research Progress on Bioactive Components and Their Functions of Fruits and Vegetables

Globally, humans are at the risk of increasing incidence of metabolic diseases, the occurrence of which is closely linked to people's daily diet. Fruits and vegetables are one of the important daily food types of people. Varieties of plant secondary metabolites are contained in fruits and vegetables, including phenolic acids, flavonoids, anthraquinones, terpenoids, alkaloids, steroidal saponins and polysaccharides. These metabolites usually have multiply bioactive functions, such as antioxidant, antitumor, hypoglycemic, hypolipidemic, neuroprotection, anti-inflammatory, antibacterial and disease prevention, which is of great importance in preventing the occurrence of human metabolic diseases. However, the composition and content, bioactive functions and mechanisms of action of these metabolites in different types of fruits and vegetables vary greatly. The research progress of the main bioactive components of fruits and vegetables and their multi-functions are reviewed in this paper to promote people's understanding and utilization of functional components of fruits and vegetables.

Sufficient Conditions for Convergence of Sequences of Henstock-Kurzweil Integrable Functions

The main aim of this paper is to present our approach of obtaining sufficient conditions for convergence of sequences of Henstock-Kurzweil integrable functions. Our approach involves the use of the concept of multiplier functions, where we define a class Φ of multipliers for the Henstock-Kurzweil integral. We consider a sequence (fn) of Henstock-Kurzweil integrable functions on a non-degenerate interval [a, b] and we assume that (fn) converges point wise to a function f. Then we show that f is Henstock-Kurzweil integrable and its integral is equal to the limit of the sequence (∫abfn) if there exists φ∈Φ such that the defined functionals of the type F (φ, fn) satisfy the imposed conditions. Beside the fact that the results regarding the convergence under the integral sign are always of great importance, the method introduced here can be imitated and used to obtain other results on the related areas.

Game-Theoretic Strategies for Cyber-Physical Infrastructures Under Component Disruptions

Networked infrastructures of recursively defined systems composed of discrete cyber and physical components are considered. The components of basic systems at the finest levels can be disrupted by cyber or physical means, and can be reinforced to survive at certain costs. A problem of ensuring the infrastructure performance is formulated as a game between a provider and an attacker, who probabilistically choose components to reinforce and attack, respectively. The disruptions of this infrastructure are characterized using the aggregate failure correlation function that specifies the conditional failure probability of the infrastructure given the failure of an individual system at that level. The survival probabilities of basic systems satisfy simple product-form, first-order differential equations expressed in terms of the multiplier functions. The utility functions of the provider and attacker are composed of the reward and cost terms, both expressed in terms of the component reinforcement and attack probabilities. The Nash equilibrium of this game is characterized, along with the sensitivity functions of the survival probabilities of basic systems that highlight their dependence individually on the cost-benefit terms, the correlation functions, and the multiplier functions. These results are illustrated using simplified models of a distributed cloud servers infrastructure, a 5G data network infrastructure, a high performance computing federation, and a smart energy grid infrastructure.

An efficient and robust Lagrange multiplier approach with a penalty term for phase-field models

In this paper, we propose and analyze a variant of Lagrange multiplier approach with a penalty term for phase-field models. More precisely, we develop two types of linear second-order decoupled and unconditionally energy stable time-stepping schemes for phase-field models based on the Crank-Nicolson (CN) and the second order backward differentiation formulations (BDF2), where the scalar multiplier variable is evaluated by solving a nonlinear algebraic equation. Comparing with the Lagrange multiplier method (Cheng et al. (2020) [6]) for phase-field models, a scalar penalty term is first introduced to improve the time-step size constraint for the convergence of Newton's iterative algorithm for the nonlinear algebraic equation, which allows us to obtain robust and efficient numerical schemes for phase-field models. Moreover, we only use first order time-stepping scheme to approximate the scalar multiplier variable, which will not affect the second order accuracy of the unknown phase function with some special Lagrange multiplier functions. Meanwhile, it plays an essential role in the derivation of energy stability of the proposed BDF2-based scheme on the nonuniform temporal mesh. In addition, the energy stability of the CN scheme is rigorously established. Furthermore, we deduce that the proposed BDF2 scheme is energy stable with the adjacent time-step ratios no more than 4.8645. Finally, a series of numerical tests are presented to numerically validate the efficiency and stability of our proposed Lagrange multiplier approach.

Uniform stabilization for a string/point mass system via arbitrary local memory effects versus frictional damping

In this paper, we investigate the stability of a string/point mass system with the interior complementary memory and frictional damping. Without the previously fundamental assumptions that the memory-effect region must include at least one of the ends of the interval and the active region of the frictional damping must cover the dynamic boundary, we eventually establish the uniform stabilization of the system by constructing some subtle multiplier functions. We also present the polynomial decay results under the classical assumption that the integral of the kernel is controlled by the kernel.

Сравнение способов аппроксимации функции множителей Лагранжа при решении контактных задач методом с независимой границей контакта

The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

R5hmCFDV: computational identification of RNA 5-hydroxymethylcytosine based on deep feature fusion and deep voting.

RNA 5-hydroxymethylcytosine (5hmC) is a kind of RNA modification, which is related to the life activities of many organisms. Studying its distribution is very important to reveal its biological function. Previously, high-throughput sequencing was used to identify 5hmC, but it is expensive and inefficient. Therefore, machine learning is used to identify 5hmC sites. Here, we design a model called R5hmCFDV, which is mainly divided into feature representation, feature fusion and classification. (i) Pseudo dinucleotide composition, dinucleotide binary profile and frequency, natural vector and physicochemical property are used to extract features from four aspects: nucleotide composition, coding, natural language and physical and chemical properties. (ii) To strengthen the relevance of features, we construct a novel feature fusion method. Firstly, the attention mechanism is employed to process four single features, stitch them together and feed them to the convolution layer. After that, the output data are processed by BiGRU and BiLSTM, respectively. Finally, the features of these two parts are fused by the multiply function. (iii) We design the deep voting algorithm for classification by imitating the soft voting mechanism in the Python package. The base classifiers contain deep neural network (DNN), convolutional neural network (CNN) and improved gated recurrent unit (GRU). And then using the principle of soft voting, the corresponding weights are assigned to the predicted probabilities of the three classifiers. The predicted probability values are multiplied by the corresponding weights and then summed to obtain the final prediction results. We use 10-fold cross-validation to evaluate the model, and the evaluation indicators are significantly improved. The prediction accuracy of the two datasets is as high as 95.41% and 93.50%, respectively. It demonstrates the stronger competitiveness and generalization performance of our model. In addition, all datasets and source codes can be found at https://github.com/HongyanShi026/R5hmCFDV.

Electronic skin based on cellulose/KCl/sorbitol organohydrogel

With the increasing interests in the fields of wearable devices, it is essential yet also challenging to develop electronic skin with customized functionalities, especially for harsh conditions. Herein, by using KCl as both anti-solvent for cellulose regeneration and ionic charge carrier in the cellulose gel network, cellulose/KCl/sorbitol organohydrogel (CKS) combining transparency (over 95% at 550 nm), stretchability (235%), high conductivity (3.88 S/m), and low temperature tolerance (−51.8 °C) was prepared. The CKS based electronic skin achieved simultaneous monitoring of object contact-separation/pressure, stretching/bending and thermal variation, with excellent reliability and stability even in harsh conditions, resembling the human skin with multiply functions. The CKS based electronic skin as efficient human-machine interface was also demonstrated. Furthermore, the CKS based triboelectric nanogenerator delivered a power density of 991 mW/m2, potential as mechanical energy harvesters for wearable devices. We believe the present work will inspire the development of cellulose based skin-like materials and contribute to the comprehensive utilization of naturel polymer in the field of smart devices.

Off-Diagonal Estimates for Bilinear Commutators

We find a minimal notion of non-degeneracy for bilinear singular integral operators T and identify testing conditions on the multiplying function b that characterize the Lp × Lq → Lr, 1<p,q<infty and r>frac {1}{2}, boundedness of the bilinear commutator [b, T]1(f, g) = bT(f, g) − T(bf, g). Our arguments cover almost all arrangements of the integrability exponents p, q, r with a single open problem presented in the end. Additionally, the arguments extend to the multilinear setting.

Polynomial stabilization of non-smooth direct/indirect elastic/viscoelastic damping problem involving Bresse system

We consider an elastic/viscoelastic problem for the Bresse system with fully Dirichlet or Dirichlet–Neumann–Neumann boundary conditions. The physical model consists of three wave equations coupled in certain pattern. The system is damped directly or indirectly by global or local Kelvin–Voigt damping. Actually, the number of the dampings, their nature of distribution (locally or globally) and the smoothness of the damping coefficient at the interface play a crucial role in the type of the stabilization of the corresponding semigroup. Indeed, using frequency domain approach combined with multiplier techniques and the construction of a new multiplier function, we establish different types of energy decay rate (see the table of stability results at the end). Our results generalize and improve many earlier ones in the literature (see El Arwadi and Youssef, in: On the stabilization of the Bresse beam with Kelvin–Voigt damping, Applied Mathematics and Optimization, pp. 1–27, 2019) and in particular some studies done on the Timoshenko system with Kelvin–Voigt damping (see for instance Ghader and Wehbe in A transmission problem for the Timoshenko system with one local Kelvin–Voigt damping and non-smooth coefficient at the interface, 2020. arXiv:2005.12756; Tian and Zhang in Z Angew Math Phys 68:20, 2017; Zhao et al. Acta Math Sin Engl Ser 21:655–666, 2005).

The Dilemma of Resolving the Low-Frequency Breakdown Problem in Microwave Components via Traditional and Improved Finite-Element Time-Domain Techniques

This paper developed an improved numerical methods for calculating electromagnetic field at low frequencies, and compared the performance with the traditional method. Traditional finite-element time-domain (FETD) is known to suffer from low frequency breakdown (LFB) problem, where system matrix becomes ill-conditioned, and leads to instability of small size electrical structures. In this paper, we proposed a mixed FETD (mFETD) method in resolving the LFB anomaly in the traditional FEM, with a particular reference to transmission line, inductor, and coaxial cable. We considered wave equation of E-field with incorporation of divergence constraint equation (DCE) as a function of Lagrange multiplier using current continuity equation (CCE) and Gauss’s law. For spatial discretization, both nodal basis functions and Curl conforming vector basis functions were selected, and we employed implicit Newmark beta algorithm (NBA) for integration of time. We describe how the components constructed via DCE in system matrix mitigate the singularity impact of the stiffness matrix, which consequently led to significant improvement of the system matrix. Numerical experiment and results demonstrate how the mFETD obtains stable numerical solution and attains faster rate of convergence while using an iterative solver, as such, improves the computational efficiency. Therefore, the mFETD method handles the transient problems in transmission line, which causes LFB anomaly in the traditional FETD, but not efficient in terms of computational time and iteration at solving the coaxial cable problem.

Confidence interval of parameters in multiresponse multipredictor semiparametric regression model for longitudinal data based on truncated spline estimator

In this paper, we provide a theoretical discussion on estimating confidence interval of parameters in a multiresponse multipredictor semiparametric regression (MMSR) model for longitudinal data. The MMSR model consists of two components namely a parametric component and a nonparametric component. In consequently, estimating the MMSR model is equivalent to estimating the parametric and nonparametric components. Estimating the parametric component is equivalent to estimating parameters of the model, while estimating the nonparametric component is estimating unknown smooth function. In this paper, we estimate the parametric and nonparametric components using a weighted least square method and a smoothing technique namely truncated spline, respectively. Next, we estimate the confidence interval of parameters in the MMSR model using pivotal quantity and Lagrange multiplier functions. The results of this study can be applied to the Covid-19 data that is to model the case growth rate (CGR) and case fatality rate (CFR) of Covid-19 which are influenced by many variables including comorbid, age, gender, temperature, self-isolation, isolation in hospital, and others.

Modeling of thermal stresses during hardening the product surface by thermal pulse

A particular solution of a linear variant of the dynamic thermal elasticity problem is considered in application to modeling the conditions of surface hardening of metal products by an energy pulse. The authors determined the equation of medium motion with the model of temperature pulse tested earlier for compatibility with special cases of the equations of parabolic and hyperbolic thermal conductivity. The problem of loading a flat plane of a short circular cylinder (disk) with a temperature pulse is presented. Pulse is a consequence of adopted structure of the volumetric power density of the heat flux, the time multiplier of which has the form of a single wave of the Heaviside function. Classical thermoelastic displacement potential and the method of its division into the product of independent variables functions were used to construct the thermal stress tensor. Differential equations for multiplier functions and their general solutions were found. Natural boundary conditions were set for the components of thermal stress tensor, and their tasks were solved. The obtained solutions are in the form of segments of functional series (the Bessel function in radial coordinate and the exponential function in axial coordinate). The article considers a numerical example of loading a disk made of 40KhN steel which has the mechanical properties sensitive to temperature treatment. Maple computer mathematics package was used in the calculations. Approximate solutions take into account the first 24 terms of the functional series. Estimation of the example makes it possible to explain the presence of stress peaks and stress intensity as a consequence of mutually inverse processes of temperature stress growth and reduction of elasticity coefficients with temperature rise. The numerical example warns against relying only on estimates of solutions to thermoelasticity problems without taking into account the plastic and viscous properties of the material.