On the continuity of a Lagrangian multiplier function in input optimization

1986 ◽  
Vol 34 (3) ◽  
pp. 362-369 ◽  
Author(s):  
J. Semple ◽  
S. Zlobec
Keyword(s):  
Lagrangian Multiplier ◽  
Input Optimization ◽  
Multiplier Function

scholarly journals User Clustering and Power Allocation for Energy Efficiency Maximization in Downlink Non-Orthogonal Multiple Access Systems

2021 ◽  
Vol 11 (2) ◽  
pp. 716
Author(s):  
Ruibiao Chen ◽  
Fangxing Shu ◽  
Kai Lei ◽  
Jianping Wang ◽  
Liangjie Zhang
Keyword(s):  
Energy Efficiency ◽  
Power Allocation ◽  
Multiple Access ◽  
Spectrum Efficiency ◽  
Lagrangian Multiplier ◽  
Efficiency Gain ◽  
Optimal Power Allocation ◽  
Optimal Power ◽  
User Clustering ◽  
Cluster Dynamic

Non-orthogonal multiple access (NOMA) has been considered a promising technique for the fifth generation (5G) mobile communication networks because of its high spectrum efficiency. In NOMA, by using successive interference cancellation (SIC) techniques at the receivers, multiple users with different channel gain can be multiplexed together in the same subchannel for concurrent transmission in the same spectrum. The simultaneously multiple transmission achieves high system throughput in NOMA. However, it also leads to more energy consumption, limiting its application in many energy-constrained scenarios. As a result, the enhancement of energy efficiency becomes a critical issue in NOMA systems. This paper focuses on efficient user clustering strategy and power allocation design of downlink NOMA systems. The energy efficiency maximization of downlink NOMA systems is formulated as an NP-hard optimization problem under maximum transmission power, minimum data transmission rate requirement, and SIC requirement. For the approximate solution with much lower complexity, we first exploit a quick suboptimal clustering method to assign each user to a subchannel. Given the user clustering result, the optimal power allocation problem is solved in two steps. By employing the Lagrangian multiplier method with Karush–Kuhn–Tucker optimality conditions, the optimal power allocation is calculated for each subchannel. In addition, then, an inter-cluster dynamic programming model is further developed to achieve the overall maximum energy efficiency. The theoretical analysis and simulations show that the proposed schemes achieve a significant energy efficiency gain compared with existing methods.

Determinants of audit fees in quoted financial and non-financial firms

2021 ◽  
Vol 3 (2) ◽  
pp. 30-40
Author(s):  
Wasiu Ajani Musa ◽  
Ramat Titilayo Salman ◽  
Ibrahim Olayiwola Amoo
Keyword(s):  
Financial Reporting ◽  
Audit Quality ◽  
Secondary Data ◽  
Sampling Technique ◽  
Audit Fees ◽  
Three Dimensions ◽  
Annual Reports ◽  
Lagrangian Multiplier ◽  
Financial Firms ◽  
Lm Test

Regulators have ensured the compulsory disclosure of audit fees in the financial statement to overcome abnormal fees and instill credibility in the financial report since audit pricing is contingent upon audit quality. However, discrepancies between audit fee dimensions are evidenced in the abnormal audit fees, resulting in accounting scandals. Hence, this study assessed the determinants of audit fees in quoted financial and non-financial firms by building a model underpinned by agency theory (Mitnick, 2006) and economic theory of product differentiation (Beath & Katsoulacos, 1991). Secondary data were utilized from companies’ annual reports between 2009 and 2018 using the purposive sampling technique. Furthermore, Breusch-Pagan Lagrangian multiplier (LM) test and the Hausman test indicated the consistency of the models. The static panel regression estimations showed that auditee size, risk, auditor size, reputation, engagement lag, and International Financial Reporting Standards (IFRS) implementation significantly affect audit fees in both sectors. This study concluded that the three dimensions largely determine audit fees. This study instructively proposed that assurance clients should devise an outline of guidelines and practices to guide activities in the sectors by monitoring the variables that impact audit fees

Study On Energy Dissipation Mechanism of an Impact Damper System

2022 ◽  
Author(s):  
Vinayaravi R ◽  
Jayaraj Kochupillai ◽  
Kumaresan D ◽  
Asraff A. K
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Fundamental Frequency ◽  
Low Frequency ◽  
High Amplitude ◽  
Lagrangian Multiplier ◽  
Impact Damper ◽  
Contact Algorithm ◽  
Dissipation Of Energy ◽  
Excitation Time

Abstract The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behaviour of an impact damper system using a MDOF system with Augmented Lagrangian Multiplier contact algorithm. Mathematical modelling and numerical simulations are carried out using ANSYS FEA package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behaviour of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

scholarly journals On Relatively Invariant Measures

1960 ◽  
Vol 12 ◽  
pp. 367-373
Author(s):  
Mark Mahowald
Keyword(s):  
Invariant Measure ◽  
Invariant Measures ◽  
Locally Compact Groups ◽  
Major Portion ◽  
Compact Groups ◽  
Locally Compact ◽  
Multiplier Function ◽  
Baire Measure

In this note we will discuss the question of the measurability of the multiplier function of a relatively invariant measure on a group. That is, for a group G, σ-ring S, and a measure μ defined on the sets of S, we assume: E in S, x in G implies xE is in S and μ(XE) = σ(x)μ(E) and study the measurability of the function σ(x).The problem was discussed by Halmos (1, p. 265), on locally compact groups and there the situation proved to be as nice as it could be, that is, if the measure is a non-trivial, relatively invariant Baire measure then the multiplier function is continuous. We prove two theorems for groups in which no topology is assumed. In the first theorem we assume a shearing condition and answer the question completely. The second theorem places a condition on the measure and weakens the shearing assumption. Its proof is complicated and occupies the major portion of this paper.

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