scholarly journals Regularization methods for ill-posed problems of general physics

2021 ◽  
pp. 148-155
Author(s):  
Vyacheslav Starkov
Keyword(s):  
Operator Equation ◽  
Background Radiation ◽  
Mathematical Formulation ◽  
Regularization Methods ◽  
Dark Counts ◽  
Ill Posed ◽  
Definition Of ◽  
Borel Measurable ◽  
The Mathematical Model ◽  
Theoretical Foundations

On the example of a specific physical problem of noise reduction associated with losses, dark counts, and background radiation, a summary of methods for regularizing ill-posed problems is given in the statistics of photocounts of quantum light. The mathematical formulation of the problem is presented by an operator equation of the first kind. The operator is generated by a matrix with countable elements. In the sense of Hadamard, the problem of reconstructing the number of photons of quantum light is due to the compactness of the operator of the mathematical model. A rigorous definition of a regularizing operator (regularizer) is given. The problem of stable approximation to the exact solution of the operator equation with inaccurately given initial data can be overcome by one of the most well-known regularization methods, the theoretical foundations of which were laid in the works of A.N. Tikhonov. The selection of an important class of regularizing algorithms is based on the construction of a parametric family of functions that are Borel measurable on the semiaxis and satisfy some additional conditions. The set of regularizers in this family includes most of the known regularization methods. The main ones are given in the work.

CONSUMER CREDIT: THEORY AND PRACTICE

2020 ◽  
Vol 3 (3) ◽  
pp. 32-37
Author(s):  
Shavkat Abdullayev ◽  
Keyword(s):  
Consumer Credit ◽  
Theory And Practice ◽  
Current Status ◽  
Consumer Lending ◽  
Definition Of ◽  
Theoretical Foundations

The article discusses the theoretical foundations, current status and ways of improving consumer lending in Uzbekistan. It were studied the views of foreign and domestic scientists on the definition of consumer credit. There are analyzed the disadvantages of consumer credits and are proposed ways to improve them

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

The Use of Photogrammetry in Piping Design

1983 ◽  
Vol 197 (2) ◽  
pp. 125-138 ◽  
Author(s):  
P A Bracewell ◽  
U R Klement
Keyword(s):  
Information Retrieval ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cost Effective ◽  
Process Industry ◽  
Process Plant ◽  
Definition Of ◽  
High Degree ◽  
Positional Data

Piping design for ‘revamp’ projects in the process industry requires the retrieval of large amounts of ‘as-built’ data from existing process plant installations. Positional data with a high degree of accuracy are required. Photogrammetry, the science of measurement from photographs, was identified in Imperial Chemical Industries plc (ICI) as a suitable tool for information retrieval. The mathematical formulation enabling the definition of three-dimensional positions from photographic information is described. The process of using ICI's photogrammetric system for the definition of complete objects such as structures and pipes is illustrated. The need for specialized photogrammetric software for design purposes is explained. A case study describing how the photogrammetric system has been applied is described and graphical outputs from this exercise are shown. It is concluded that this particular photogrammetric system has proved to be a cost effective and accurate tool for the retrieval of ‘as-built’ information.

THEORETICAL AND METHODOLOGICAL FUNDAMENTALS OF PUBLIC-PRIVATE PARTNERSHIP

2021 ◽  
Vol 4 (8) ◽  
pp. 11-18
Author(s):  
Dinara Atadjanova ◽  
Keyword(s):  
Public Sector ◽  
Scientific Basis ◽  
Public Private Partnership ◽  
Infrastructure Investment ◽  
Private Partnership ◽  
Definition Of ◽  
Theoretical Foundations ◽  
Practical Nature

This article examines the theoretical foundations and content of public-private partnership. It also presents the research of scientists who have analyzed the content, scientific basis and practical nature of public-private partnership. As a result of the research, the author gave an author definition of the concept of public-private partnership.Keywords: public, business entity, public-private partnership, public sector, infrastructure, investment, innovation, private partner.

Energy Shaping Control of Electrostatic Membrane Vibrations

1999 ◽  
Author(s):  
Andreas Kugi ◽  
Kurt Schlacher ◽  
Manfred Kaltenbacher ◽  
Reinhard Lerch
Keyword(s):  
Nonlinear Distortion ◽  
Supply Voltage ◽  
Mathematical Formulation ◽  
Voltage Source ◽  
Membrane Electrode ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Electrostatic Transducers ◽  
Membrane Vibrations ◽  
The Mathematical Model

Abstract A strong analytical mathematical formulation of electrostatic transducers is the necessary prerequisite for the design of feedback controllers. Based on the theory of Hamiltonian systems the mathematical model of a typical electrostatic transducer configuration with a moving membrane electrode and a rigid backplate electrode is derived. It is a well known fact that an increase in the sensitivity of the transducer often brings about also an increase in the nonlinear distortion and may occur a sticking of the membrane to the backplate electrode. In this paper, we propose a concept that gives a possible solution for these undesirable effects by using a controlled voltage source for the supply voltage of the transducer. The controller is designed by shaping the potential energy of the closed loop system. The change of the capacity of the transducer due to the motion of the membrane is considered as the sensor output.

Formal Metamodeling for Secure Model-Driven Engineering

2021 ◽  
Vol 12 (2) ◽  
pp. 46-67
Author(s):  
Liliana Maria Favre
Keyword(s):  
Cloud Computing ◽  
Formal Specifications ◽  
Model Driven Engineering ◽  
Model Driven ◽  
Transformation Rules ◽  
Systematic Development ◽  
Definition Of ◽  
Context Specific ◽  
Theoretical Foundations

Systems and applications aligned with new paradigms such as cloud computing and internet of the things are becoming more complex and interconnected, expanding the areas in which they are susceptible to attacks. Their security can be addressed by using model-driven engineering (MDE). In this context, specific IoT or cloud computing metamodels emerged to support the systematic development of software. In general, they are specified through semiformal metamodels in MOF style. This article shows the theoretical foundations of a method for automatically constructing secure metamodels in the context of realizations of MDE such as MDA. The formal metamodeling language Nereus and systems of transformation rules to bridge the gap between formal specifications and MOF are described. The main contribution of this article is the definition of a system of transformation rules called NEREUStoMOF for transforming automatically formal metamodeling specifications in Nereus to semiformal-MOF metamodels annotated in OCL.

scholarly journals Mathematical formulation of energy efficient routing with constraint in mobile ad hoc network

2018 ◽  
Vol 7 (2) ◽  
pp. 674
Author(s):  
Rakesh Sahu ◽  
Narendra Chaudhari
Keyword(s):  
Energy Consumption ◽  
Energy Efficient ◽  
Ad Hoc Network ◽  
Ad Hoc ◽  
Mobile Ad Hoc Network ◽  
Mathematical Formulation ◽  
Energy Efficient Routing ◽  
Optimization Function ◽  
Mobile Ad Hoc ◽  
The Mathematical Model

Energy consumption of nodes during the transmission is an important factor for the efficiency and lifetime of a mobile ad hoc network. The reduction in consumption of energy can be achieved, only when its consumption at each step is known. The purpose of this paper is to formulate the mathematical model of energy consumption of network on the basis on links and available nodes in order to formulate the energy optimization function. The probability of link failure in route and innetwork have been taken into consideration as constraints while formulating the objective function of estimated energy consumption, as the low connectivity is one of the challenges due to mobility in ad hoc network.

scholarly journals ECONOMIC SECURITY OF SMALL AGRICULTURAL ENTERPRISES

2019 ◽  
Vol 1 (15) ◽  
pp. 181-185
Author(s):  
M.V. Boiko
Keyword(s):  
Economic Security ◽  
Risk Level ◽  
Economic Science ◽  
Economic Stability ◽  
Economic Space ◽  
Agricultural Enterprises ◽  
Basic Approaches ◽  
Definition Of ◽  
Theoretical Foundations ◽  
Single Approach

The article “Economic Security of Small Agricultural Enterprises” aims at exploring the theoretical foundations of economic security for small agricultural enterprises. The basic approaches to definition of the category "economic security of the enterprise" are investigated. The theoretical bases of the definition of "economic security" are considered. The integration of Ukraine into the global economic space implies the modernization of the modern financial and economic system, which envisages the transition of market entities to a new level of relations and the leveling of traditional geographical boundaries. At the same time, the conditions of functioning of enterprises in a market environment become more stringent due to the expansion of the range of probable threats and dangers, which increase the risk level of conducting business activities, increasing uncertainty, and increasing competition. It is economic security that can provide the enterprise with effective functioning, economic stability, development and improvement of its competitiveness level. The main purpose of this work is to research and analyze the major achievements of economic science in the economic security of a small business and to present the author's vision of the essence of this concept. The set of research methods is the methodology of analysis and organization of major publications, legislation and laws, namely methods of generalization, comparison, chronologization, analysis and generalization. The author's vision of interpreting the concept of "economic security of enterprises" is a scientific novelty. The practical value of the study is to analyze the main publications on the definition of the essence of the concept of “economic security of the enterprise”, because today there is no single approach that would clearly interpret this concept.

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