Multiplier Function Research Articles

Influence of Two-Frequency Radiation Intensity Fluctuations on the Output Signal of a Vortex Optical Fiber Forming OAM Address in Polyharmonic Sensor Technology

A schematic diagram of a RoF radio-optic system with vortex signals is presented, in which the radio frequency is determined by the difference between the wavelengths of two lasers. It is assumed that the generation of a vortex signal can be performed through a vortex fiber-optic periodic structure, which can be obtained using a technology similar to the manufacture of long-period fiber Bragg gratings. The parameters of the grating are modeled assuming that the fundamental light-guide mode (LP01) is applied to the specified vortex element, and the higher-order mode (LP11) is reflected. It was found that the distortion of the vortex signal can be reduced by introducing apodization and chirping of this periodic structure. The following optimal parameters have been estimated: the apodization and chirp multiplier functions, at which the distortions of the amplitude and phase of the vortex signal, as well as the appearance of an unwanted angle distortion, will be minimal. It is shown that such gratings can be exploited in addressed sensors systems using the orbital angular momentum (OAM) of a lightwave as a unique sensor address.

Research on The Optimal Solution of Lagrangian Multiplier Function Method in Nonlinear Programming

For the general nonlinear constrained optimization model, this article will propose a new nonlinear Lagrange function, discuss the properties of the function at the KKT point, and prove that under appropriate conditions, the iterative point generated by the dual algorithm based on the function The column is locally convergent, and then an error estimate of the solution related to the penalty parameter is given. This provides a new way to solve nonlinear constrained optimization problems.

Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions.

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Trajectory shaping guidance law design using constraint-combining multiplier

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

An Updated Formalism for Line-driven Radiative Acceleration and Implications for Stellar Mass Loss

Abstract Radiation contributes to the acceleration of large-scale flows in various astrophysical environments because of strong opacity in the spectral lines. Quantification of the associated force is crucial to understanding these line-driven flows, and a large number of lines (due to the full set of elements and ionization stages) must be taken into account. Here we provide new calculations of the dimensionless line strengths and associated opacity-dependent force multipliers for an updated list of approximately 4.5 million spectral lines compiled from the NIST, CHIANTI, CMFGEN, and TOPbase databases. To maintain generality of application to different environments, we assume local thermodynamic equilibrium, illumination by a Planck function, and the Sobolev approximation. We compute the line forces in a two-dimensional grid of temperatures (i.e., values between 5200 and 70,000 K) and densities (varying over 11 orders of magnitude). Historically, the force multiplier function has been described by a power-law function of optical depth. We revisit this assumption by fitting alternate functions that include saturation to a constant value (Gayley’s Q ¯ parameter) in the optically thin limit. This alternate form is a better fit than the power-law form, and we use it to calculate example mass-loss rates for massive main-sequence stars. Because the power-law force multiplier does not continue to arbitrarily small optical depths, we find a sharp decrease, or quenching, of line-driven winds for stars with effective temperatures less than about 15,000 K.

On inequalities of Kolmogorov type for classes of functions that are multiply monotonic on a finite interval

We solve the problem about exact constants in additive Kolmogorov-type inequalities on the class of multiply monotonic functions, defined on a finite interval.

A comparative study to assess surface water's anthropic and natural vulnerability using the DKPR and RUSLE approaches. Case of the watershed of the Joumouaa dam (Coastal basin of Ghiss, North East Morocco)

The salinization of surface water in a coastal context leads to a qualitative degradation of this resource by various sources of anthropogenic and natural pollution. In this context, we present the results of a comparative study using "DKPR" and "RUSLE" models to evaluate the degree of surface water vulnerability against pollution, especially in the sub-watershed of the Joumouaa dam, a hydraulic infrastructure providing drinking water for the Targuist city. The "DKPR" model adopted as a qualitative approach involves four parameters: Accessibility of the aquatic environment (D), Water functioning of the soil and subsoil (K), Physiography watershed (P), Rainfall erosivity (R). The final result is a resource vulnerability map obtained by combining index maps of these four parameters using remote sensing and GIS. The "RUSLE" model applied as a quantitative approach integrates five factors in a multiplying function, namely: rainfall erosivity (R), soil erodibility (K), slope length and steepness (LS), cover-management (C), and soil conservation practices (P) in a remote sensing and GIS environment. The analysis of the final vulnerability maps of the approaches mentioned above will be helpful support for water resource managers and decision-makers better identify areas of high risk and their protection.

RECON: Resource-Efficient CORDIC-Based Neuron Architecture

Contemporary hardware implementations of artificial neural networks face the burden of excess area requirement due to resource-intensive elements such as multiplier and non-linear activation functions. The present work addresses this challenge by proposing a resource-efficient Co-ordinate Rotation Digital Computer (CORDIC)-based neuron architecture (RECON) which can be configured to compute both multiply-accumulate (MAC) and non-linear activation function (AF) operations. The CORDIC-based architecture uses linear and trigonometric relationships to realize MAC and AF operations respectively. The proposed design is synthesized and verified at 45nm technology using Cadence Virtuoso for all physical parameters. Implementation of the signed fixed-point 8-bit MAC using our design, shows 60% less area, latency, and power product (ALP) and shows improvement by 38% in area, 27% in power dissipation, and 15% in latency with respect to the state-of-the-art MAC design. Further, Monte-Carlo simulations for process-variations and device-mismatch are performed for both the proposed model and the state-of-the-art to evaluate expectations of functions of randomness in dynamic power variation. The dynamic power variation for our design shows that worst-case mean is $189.73\mu W$ which is 63% of the state-of-the-art.

Boundedness of Pseudo-Differential Operator for S0 Class

Pseudo-differential operator in a function space is obtained from the Fourier transform of this function space with a multiplier function. This paper will discuss and prove the boundedness of pseudo-differential operator in Lebesgue space with the multiplier function is in the class S0. The evolution of the pseudo-differential theory was then rapid. Based on development from this history, it has gave birth to the general definition of pseudo-differential operator that explain in this paper The general definition of pseudo-differential, of course has an applied or representation. One of them is the problem of partial differential equations in the Poisson equation have the solution , and using Fourier transforms is obtained. In this case the form can be carried in the general form of a pseudo-differential operator. The solution can be estimated for every if operator is a bounded operator. In this paper, the operator defined with correspondes some symbol that describe this operator is more interest. The conclusion of this paper is the boundedness pseudo-differential operator , so we can estimated this number.©2020 JNSMR UIN Walisongo. All rights reserved.

Dry Clutch Control of Two-Speed Electric Vehicles by Using an Optimal Control Scheme With Persistent Time-Varying Disturbance Rejection

A novel two-speed inverse automatic mechanical transmission (I-AMT) is proposed to eliminate the torque interruption in conventional AMT and improve the working performance of electric vehicles (EVs). However, due to the intrinsic structural characteristics of I-AMT, the requirements for clutch slip control are different from current AMT. Besides, clutch slip control is sensitive to internal uncertainties and external persistent time-varying disturbances during gear shifting. This study proposes a unified framework to build a clutch slip model for gear upshift and downshift. A high-order disturbance observer-based optimal controller is developed to reject persistent time-varying disturbances in a dry clutch system. During controller deduction, a novel multiplier function λ is introduced, and the optimal control law is presented as a feedback form of system states, the disturbance, and the derivatives of the disturbance. The controller is then applied to the clutch slip processes during gear shifting of an EV equipped with I-AMT. Simulation and experimental results under gear upshift and downshift demonstrate that the controller guarantees consistent performance under various working scenarios with different kinds of disturbances. The rapidity and smoothness of the clutch slip process are ensured without large speed or torque fluctuation, thus improving the overall gear shift quality.

The Various Definitions of Multiple Differentiability of a Function f: ℝn→ ℝ

Since the 17-th century the concepts of differentiability and multiple differentiability have become fundamental to mathematical analysis. By now we have the generally accepted definition of what a multiply differentiable function f:Rn→R is (in this paper we call it standard). This definition is sufficient to prove some of the key properties of a multiply differentiable function: the Generalized Young’s theorem (a theorem on the independence of partial derivatives of higher orders of the order of differentiation) and Taylor’s theorem with Peano remainder. Another definition of multiple differentiability, actually more general in the sense that it is suitable for the infinite-dimensional case, belongs to Fréchet. It turns out, that the standard definition and the Fréchet definition are equivalent for functions f:Rn→R. In this paper we introduce a definition (which we call weak) of multiple differentiability of a function f:Rn→R, which is not equivalent to the above-mentioned definitions and is in fact more general, but at the same time is sufficient enough to prove the Generalized Young’s and Taylor’s theorems.

Theoretical evaluation of the performance of greases with additives

The formation of protective films under the action of additives on friction surfaces is a rather complicated process. In the first approximation, when the materials of the additive present in the lubricant interact with the substrate material, physicochemical processes should occur, as a result of which the near-surface structure of the metal changes, etc. The stability of a structured lubrication system depends on the strength of the structural framework, the forces of interaction between its individual particles, the dispersion medium at the interface, and the number of particle contacts per unit volume. The efficiency of the lubrication with additives from graphite and graphene components is considered. It was found that if we know the binding energy of 1 mole of the film and its thickness, it is possible to determine the separation pressure. As a result of a theoretical analysis of the processes occurring during the interaction of graphene particles with the surface of the substrate or metal, the dependence of the multiplier function on the number of layers in the film was established. An equation is obtained that characterizes the total area of separation of film fragments over the entire surface of the part, taking into account the pressure in the nodes and mechanisms and the stochastic nature of this phenomenon. It has been determined that the functioning of a new assembly or mechanism, pressure fluctuations are minimal due to minimal wear and optimal part tolerances. In the interaction of metal - metal additives, the electrons of the metal atoms are able to form an electron cloud in the crystal lattice, partially extending beyond the lattice. This can lead to the appearance of a dipole moment, the negatively charged pole of which is outside the metal lattice, and the positively charged pole is inside it. Metal nanoparticles that make up additives to lubricants, in contrast to graphenes, are nanosized 3D objects with a full-fledged crystal lattice, and therefore have higher dipole moments, which reduces the adhesive properties of the film, but in general does not contradict the known theories of their formation at certain conditions.

Iterated commutators under a joint condition on the tuple of multiplying functions

We present a pair of joint conditions on the two functions b 1 , b 2 b_1,b_2 strictly weaker than b 1 , b 2 ∈ BMO b_1,b_2\in \operatorname {BMO} that almost characterize the L 2 L^2 boundedness of the iterated commutator [ b 2 , [ b 1 , T ] ] [b_2,[b_1,T]] of these functions and a Calderón-Zygmund operator T T . Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.

Multiply monotone functions for radial basis function interpolation: Extensions and new kernels

In this article, we focus on the connections of monotonicity properties and the strict positive definiteness of functions on Rd. We collect the existing results known for the Euclidean space and present a new technique to construct positive definite functions from multiply monotone functions. Further, we collect properties of multiply monotone functions which allow us to construct new positive definite functions.

Regularization of linear ill-posed problems involving multiplication operators

ABSTRACT We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise from equations based on non-compact self-adjoint operators in Hilbert space, after applying unitary transformations arising out of the spectral theorem. For classical regularization theory, when noisy observations are given and the noise is deterministic and bounded, then non-compactness of the ill-posed equations is a minor issue. However, for statistical ill-posed equations with non-compact operators less is known if the data are blurred by white noise. We develop a theory for spectral regularization with emphasis on this case. In this context, we highlight several aspects, in particular, we discuss the intrinsic degree of ill-posedness in terms of rearrangements of the multiplier function. Moreover, we address the required modifications of classical regularization schemes in order to be used for non-compact statistical problems, and we also introduce the concept of the effective ill-posedness of the operator equation under white noise. This study is concluded with prototypical examples for such equations, as these are deconvolution equations and certain final value problems in evolution equations.

Pólya-type criteria for conditional strict positive definiteness of functions on spheres

Identifying (conditionally) strictly positive definite functions is of great importance as they allow the unique solution of certain interpolation problems. We introduce new sufficient (and some necessary) conditions for functions to be conditionally strictly positive definite on all spheres Sd−1, d>2, only employing monotonicity properties. For strictly positive definite and conditionally negative definite functions on all spheres we give a characterisation in terms of monotonicity properties. Further, we prove that multiply monotone functions are positive definite on spheres up to a certain dimension.

Novel probabilistic model for searching most probable point in structural reliability analysis

The Most Probable Point (MPP) is typically searched by transforming the basic random variables from original to standard normal space in the traditional first order reliability method (FORM). However, the FORM formulation may provide inaccurate MPP for those reliability problems with several local MPPs. The FORM based probabilistic model is a computational method and it may provide inaccuracy and unstable results for complex problems. In this paper, a probabilistic model is proposed to evaluate the MPP using cumulative distribution function (CDF) of basic random variables. The MPP is determined by solving an optimization problem in the original space which maximizes a multiplier function in terms of the CDF of the random variables. The performance of the proposed probabilistic model, usual FORM and first order saddle point approximation method (FOSAM) using SQP optimization solver is demonstrated by several numerical and engineering problems with normal and non-normal variables. The results of the numerical study illustrate that the proposed model provides an efficient approach to obtain the MPP which is simpler and more accurate than the usual FORM and FOSAM; particularly for reliability problems with non-normal random variables.

Design of 3D multi-layered electrospun membranes embedding iron-based layered double hydroxide for drug storage and control of sustained release

Nowadays polymer dressings are expected to possess multiply functions. Besides acting as physical barriers, dressings may provide for the injured tissue species able to turn wound healing process faster and painless. In this way, dressings can be designed aiming to enable the release of drugs. The possibility to modulate drug release kinetics is a desired characteristic to be achieved in order to turn drug delivery systems adequate to specific treatments. However, hydrophilic drugs and hydrophobic polymers incompatibility hinders such modulation and a long-term release cannot be achieved efficiently. Here we present the design of poly(lactic acid) (PLA) membranes containing iron-based Layered Double Hydroxide (LDH) particles able to storage a hydrophilic anionic drug (derived from the non-steroidal anti-inflammatory naproxen). LDH particles are excellent candidates to compose multifunctional composites. They may present diverse biocompatible compositions, possess an elevated encapsulation capacity and tends to promote drugs sustained release by its own, besides assisting tissues regeneration process. Nanofibrous membranes were prepared by the combination of electrospun PLA and electrosprayed LDH as alternated layers (approach A) and also by both technics performed at the same time (approach B). In approach A, by varying the thickness of the PLA fibrous layers, it was possible to easily modulate the drug release rate. Half of drug content was released after 1, 4 and 17 days for the membranes containing the thinnest, the intermediate and the thicker PLA layers, respectively, and after 56 h for the membrane prepared by the approach B. Naproxen release was kept for 18 days for the thinnest membrane, 59 days for the membrane prepared by the approach B and 66 days for the thicker membranes. We believe that this work can inspire the development of new functional membranes with tunable drug release profile thanks to the versatile electrospinning and electrospraying techniques.

On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO

It is known that the compactness of the commutators of point-wise multiplication with bilinear homogeneous Calderón–Zygmund operators acting on product of Lebesgue spaces is characterized by the multiplying function being in the space CMO. This space is the closure in BMO of its subspace of smooth functions with compact support. It is shown in this work that for bilinear Calderón–Zygmund operators arising from smooth (inhomogeneous) bilinear Fourier multipliers or bilinear pseudodifferential operators, one can actually consider multiplying functions in a new subspace of BMO larger than CMO.

Analog Vector-Matrix Multiplier Based on Programmable Current Mirrors for Neural Network Integrated Circuits

We propose a CMOS Analog Vector-Matrix Multiplier for Deep Neural Networks, implemented in a standard single-poly 180 nm CMOS technology. The learning weights are stored in analog floating-gate memory cells embedded in current mirrors implementing the multiplication operations. We experimentally verify the analog storage capability of designed single-poly floating-gate cells, the accuracy of the multiplying function of proposed tunable current mirrors, and the effective number of bits of the analog operation. We perform system-level simulations to show that an analog deep neural network based on the proposed vector-matrix multiplier can achieve an inference accuracy comparable to digital solutions with an energy efficiency of 26.4 TOPs/J, a layer latency close to 100 μs and an intrinsically high degree of parallelism. Our proposed design has also a cost advantage, considering that it can be implemented in a standard single-poly CMOS process flow.