scholarly journals Application of Two-Channel Principle in Measuring Devices to Compensate for Disturbing Influences of Unknown Physical Nature

2020 ◽  
Vol 11 (3) ◽  
pp. 228-235
Author(s):  
V. N. Nesterov ◽  
A. R. Li
Keyword(s):  
A Priori ◽  
Sufficient Conditions ◽  
Physical Nature ◽  
Physical Principle ◽  
External Disturbances ◽  
Technological Method ◽  
Acceptable Accuracy ◽  
Measuring Devices ◽  
Measurement Results ◽  
Necessary And Sufficient

The article notes the advantages of the method of constructing absolutely invariant measuring transducers for working in conditions with disturbing influences. However, this method is not universal. Its limitations are due to the impossibility of "symmetric" transmission of all disturbing influences into parallel measuring channels. A broader interpretation of the two-channel principle is proposed to overcome these limitations. The aim of the study was to substantiate and implement a method for constructing quasi-invariant measuring transducers and systems that retain their metrological characteristics under external disturbances of unknown physical nature.The theory that develops the two-channel principle to a full-fledged technological method is presented in the article. The theory includes the necessary and sufficient conditions for physical feasibility this method. Two fundamental tasks have been solved in the work. The first task is to identify signs that reflect the essence of the technological method in to specific cases and the second is to implement a methodology that allows these signs to be effectively applied in practice.In the examples, a complex of technologies is defined for groups of elements of quasi-invariant transducers that provide compensation of the influencing factors acting on them with acceptable accuracy.There are significant advantages in discussed method. It gives hope for acceptable measurement results under conditions when character and even physical principle of influencing a priori are unknown.

scholarly journals An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions

2019 ◽  
Vol 50 (3) ◽  
pp. 207-221 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Differential Operators ◽  
A Priori ◽  
Sufficient Conditions ◽  
Robin Boundary Conditions ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Robin Boundary

The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.

Consensus and Consensualization of High-Order Swarm Systems With Time Delays and External Disturbances

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Jianxiang Xi ◽  
Zongying Shi ◽  
Yisheng Zhong
Keyword(s):  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
External Disturbances ◽  
Consensus Function ◽  
Design Problems ◽  
Consensus Analysis ◽  
Analysis And Design ◽  
Time Varying Delay ◽  
Necessary And Sufficient

By using dynamic output feedback consensus protocols, consensus analysis, and design, problems for swarm systems with external disturbances and time-varying delays are dealt with. First, two subspaces, namely, a consensus subspace and a complement consensus subspace, are defined. Based on the state projection onto the two subspaces, L2-consensus and L2-consensualization problems are introduced. Then, a necessary and sufficient condition for consensus is presented and an explicit expression of the consensus function is given. Especially, it is shown that the time-varying delay does not influence the consensus function. Finally, in terms of linear matrix inequalities, sufficient conditions for L2-consensus and L2-consensualization are presented, respectively, which possess less calculation complexity, since they are independent of the number of agents, and numerical simulations are shown to demonstrate theoretical results.

scholarly journals INFORMATION AND OPTIMAL INVESTMENT IN DEFAULTABLE ASSETS

2014 ◽  
Vol 17 (08) ◽  
pp. 1450050 ◽  
Author(s):  
GIULIA DI NUNNO ◽  
STEFFEN SJURSEN
Keyword(s):  
Counting Process ◽  
Partial Information ◽  
A Priori ◽  
Sufficient Conditions ◽  
Random Measure ◽  
Optimal Investment ◽  
Terminal Time ◽  
Necessary And Sufficient ◽  
Forward Integration ◽  
Different Levels

We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modeled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.

scholarly journals An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel

2019 ◽  
Vol 27 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Partial Information ◽  
A Priori ◽  
Sufficient Conditions ◽  
Convolution Kernel ◽  
Dirac System ◽  
Integral Term ◽  
Necessary And Sufficient ◽  
The Uniqueness Theorem

AbstractAn integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of the spectrum. We prove the uniqueness theorem, provide an algorithm for the solution of the inverse problem together with necessary and sufficient conditions for its solvability.

scholarly journals Generalized Keller-Osserman Conditions for Fully Nonlinear Degenerate Elliptic Equations

2018 ◽  
Vol 64 (1) ◽  
pp. 74-85
Author(s):  
I Capuzzo Dolcetta ◽  
F Leoni ◽  
A Vitolo
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
Sufficient Conditions ◽  
Degenerate Elliptic Equations ◽  
Fully Nonlinear ◽  
Degenerate Elliptic ◽  
Whole Space ◽  
Necessary And Sufficient ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

We discuss the existence of entire (i.e. defined on the whole space) subsolutions of fully nonlinear degenerate elliptic equations, giving necessary and sufficient conditions on the coefficients of the lower order terms which extend the classical Keller-Osserman conditions for semilinear elliptic equations. Our analysis shows that, when the conditions of existence of entire subsolutions fail, a priori upper bounds for local subsolutions can be obtained.

scholarly journals Optimality conditions for systems with insufficient data

1990 ◽  
Vol 41 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
A Priori ◽  
Sufficient Conditions ◽  
Distributed Parameter ◽  
Not Given ◽  
Cost Criterion ◽  
Distributed Parameter Control ◽  
Recent Theorem ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient ◽  
Distributed Parameter Control System

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.

scholarly journals Locally undetermined states, generalized Schmidt decomposition, and application in distributed computing

2009 ◽  
Vol 9 (11&12) ◽  
pp. 997-1012
Author(s):  
Y. Feng ◽  
R. Duan ◽  
M. Ying
Keyword(s):  
Distributed Computing ◽  
Quantum State ◽  
Fault Tolerant ◽  
A Priori ◽  
Sufficient Conditions ◽  
Quantum States ◽  
Consensus Problem ◽  
Schmidt Decomposition ◽  
Pure States ◽  
Necessary And Sufficient

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.

scholarly journals Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Nedyu Popivanov ◽  
Todor Popov ◽  
Allen Tesdall
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Generalized Solution ◽  
Generalized Solutions ◽  
Singular Solutions ◽  
Priori Estimates ◽  
Characteristic Cone ◽  
Equation Boundary ◽  
Necessary And Sufficient

For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertexOof the boundary light characteristic cone and does not propagate along the bicharacteristics. The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance toO. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained.

Terminal Control with Guaranteed Accuracy Based on the Interval System Model

Vestnik MEI ◽  
2021 ◽  
pp. 115-121
Author(s):  
Nikita V. Skribitsky ◽  
Keyword(s):  
Control Problem ◽  
A Priori ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Problem Solution ◽  
Terminal Control ◽  
Interval System ◽  
Interval Model ◽  
Necessary And Sufficient ◽  
Solution Accuracy

The problem of optimal terminal control of a linear stationary system the parameters of which are known with accuracy up to intervals is formulated, and the necessary and sufficient conditions for its stability and controllability are determined. A set of control actions that guarantee the specified accuracy of solving the optimal control problem given an interval model of the initial data is obtained. The necessary and sufficient conditions for the existence of this set are determined, and algorithms for its construction and obtaining its rectangular subset of the maximum volume are developed. A priori requirements for the accuracy of identifying the system parameters are formulated taking into account the requirements for the control problem solution accuracy.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document