Iteration Principle Research Articles

Relational Quantum Mechanics, quantum relativism, and the iteration of relativity

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.

Technological Machines Operation by Identification Method

In order to effectively organize the process of agricultural enterprises, it is reasonable to involve management tools to build optimal models of interaction of individual components of the production process. The most significant part concerning the technical and economic efficiency is the technological process. However, the harvesting and postharvesting process is of the highest priority. The current stage of the management paradigm development includes the attraction of mathematical modeling in the organizational process. The construction of mathematical models is necessary at the stage of planning, organization, control, and is aimed at choosing such parameters of the technological process that will ensure the highest economic efficiency. At the same time, the validation process of the optimal parameters of machines and equipment that separate the grain receiving is of the most importance. While solving this problem, it is necessary to consider various efficiency criteria, the main of which are “loss volumes” and “reduced costs”. The criteria for the efficiency of the technical equipment of postharvesting grain process are the permissible values of agrotechnical requirements that consider the time of safe storage of freshly harvested grain mass without pretreatment and grain shatter losses due to its overripe. It is necessary to consider the maximum allowable volumes of losses during the postharvesting technological process. In order to define the best organizational solutions the iteration principle is used until a solution that meets the restrictions on the reduced costs level is found. The mathematical modeling in technological processes is carried out with the involvement of regression models that allow predicting the qualitative indicators of the operation of the pre-cleaning machine. As a result, it is possible to choose such a mode of equipment operation that ensures the production of grain that meets the regulatory requirements for the quality of the resulting product. The novelty of this study lies in the development of optimal ways for combine harvesters functioning. The article presents the methodology and procedure of optimizing the technological process during the postharvesting process of grain. The characteristics received as a result of experiments allow us to organize the technological process in an agricultural enterprise in the most optimal way so that it is economically and technically efficient.

Investigation on surface evolution and subsurface damage in abrasive lapping of hard and brittle materials using a novel fixed lapping tool

Novel fixed abrasive lapping (NFAL) is used in this study to quickly remove the surface damage layer and control the depth of subsurface damage (SSD), thus saving overall machining time and reducing the costs of large-aperture optical manufacturing. The influence of lapping parameters on the surface and subsurface state is studied through a series of experiments to better understand the material removal and damage mechanisms during NFAL. A surface evolution model for NFAL was established based on indentation fracture mechanics, mathematical statistics, abrasive wear theory and convolution iteration principle. Experimental results show that the model can predict the surface topography well. Further simulation experiments were also conducted to study the effects of the tool load and particle size on the microscopic removal characteristics of the NFAL process. The results show that NFAL can quickly produce submicron-level surface roughness and restrain SSD with the reasonable selection of lapping parameters.

Analysis of fractional hybrid differential equations with impulses in partially ordered Banach algebras

In this paper, we investigate a class of fractional hybrid differential equations with impulses, which can be seen as nonlinear differential equations with a quadratic perturbation of second type and a linear perturbation in partially ordered Banach algebras. We deduce the existence and approximation of a mild solution for the initial value problems of this system by applying Dhage iteration principles and related hybrid fixed point theorems. Compared with previous works, we generalize the results to fractional order and extend some existing conclusions for the first time. Meantime, we take into consideration the effect of impulses. Our results indicate the influence of fractional order for nonlinear hybrid differential equations and improve some known results, which have wider applications as well. A numerical example is included to illustrate the effectiveness of the proposed results.

Dhage iteration principle for IVPs of nonlinear first order impulsive differential equations

In this paper we prove the existence and approximation theorems for the initial value problems of first order nonlinear impulsive differential equations under certain mixed partial Lipschitz and partial compactness type conditions. Our results are based on the Dhage monotone iteration principle embodied in a hybrid fixed point theorem of Dhage involving the sum of two monotone order preserving operators in a partially ordered Banach space. The novelty of the present approach lies the fact that we obtain an algorithm for the solution. Our abstract main result is also illustrated by indicating a numerical example.

(Un)knowability and knowledge iteration

Abstract The KK principle states that knowing entails knowing that one knows. This historically popular principle has fallen out of favour among many contemporary philosophers in light of putative counterexamples. Recently, some have defended more palatable versions of KK by weakening the principle. These revisions remain faithful to their predecessor in spirit while escaping crucial objections. This paper examines the prospects of such a strategy. It is argued that revisions of the original principle can be captured by a generalized knowledge iteration principle, Weak-KK, which states that knowing entails the possibility of knowing that one knows. But Weak-KK is vulnerable to an unknowability result and therefore must be rejected. The arguments here suggest that retreating to weaker iteration principles is not an option for the KK enthusiast.

ITERATION PRINCIPLE FOR IVPS OF NONLINEAR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATIONS

In this paper we prove the existence and approximation theorems for the initial value problems of first order nonlinear impulsive differential equations under certain mixed partial Lipschitz and partial compactness type conditions. Our results are based on the Dhage monotone iteration principle embodied in a hybrid fixed point theorem of Dhage involving the sum of two monotone order preserving operators in a partially ordered Banach space. The novelty of the present approach lies the fact that we obtain an algorithm for the solution. Our abstract main result is also illustrated by indicating a numerical example.

A policy iteration algorithm for the American put option and free boundary control problems

We develop a solution method for American put options that directly employs the policy iteration principle of dynamic programming. The method iteratively improves exercise policies, obtains monotonically increasing value functions and converges quadratically under reasonable assumptions. We present a numerical implementation that exhibits these features. The same principle is also applied to obtain a monotonically improving policy iteration scheme for general free boundary optimal control problems.

Indicative conditionals without iterative epistemology

AbstractThis paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail that it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles.

Analytical model for the winding process-induced residual stresses of the multilayered filament wound cylindrical composite parts

The residual stresses due to winding tensions have significant influence on the product quality of the filament wound composite parts. In this paper, an analytical model is proposed to calculate the winding process-induced residual stresses for the multilayered filament wound composite parts with metal linear based on the three-dimensional thick-walled cylinder theory. In the modeling of winding process, the contribution of the current outmost winding tension to the residual stresses of the previously wound composite layers is first calculated and then the total residual stresses is obtained based on the elastic superposition principle. Moreover, the winding tensions are modified for equal residual stress in fibers based on the inverse iteration principle. Compared with the results in other work and obtained by finite element method, it shows that the proposed analytical model is of high accuracy and can be used to calculate the residual stresses due to winding tensions for the multilayered filament wound composite parts. The expected winding tensions for the equal residual fiber stresses can be quickly obtained after several iterations. Moreover, the effects of thickness of metal linear on the winding tensions distributions are further investigated based on the proposed model and the iterative algorithm.

Approximating Solutions of Nonlinear Hybrid Caputo Fractional Integro-Differential Equations via Dhage Iteration Principle

In this article, we prove the existence and approximation of solutions of the initial value problems of nonlinear hybrid Caputo fractional integro-differential equations. The main tool employed here is the Dhage iteration principle in a partially ordered normed linear space. An example is also given to illustrate the main results.

Robust Analog Precoding Designs for Millimeter Wave MIMO Transceivers With Frequency and Time Division Duplexing

Millimeter wave (mmWave) communication provides high data rates thanks to large arrays at the transmitter and receiver, coupled with large bandwidth channels. Exploiting the arrays is challenging due to the need to configure precoding at the transmitter based on the large frequency selective channel. In this paper, we exploit the power iteration principle and propose a robust analog precoding training algorithm that can be applied in both frequency division duplex transmission systems and time division duplex transmission systems with or without RF calibration. We further analyze the convergence of the proposed algorithm and show how it converges to the singular value decomposition optimality exponentially. We propose null space projection on top of the power iteration to form multiple orthogonal beams at the transmitter and receiver. Strongest tap selection with proper energy pruning is used to collect as much precoding gain as possible from a frequency selective fading channel. The exponential effective SINR mapping performance is evaluated and demonstrates that the overall approach works smoothly. Numerical simulation results demonstrate algorithm robustness and the algorithm works not only for the simplified mmWave directional channels, but also for more general rich scattering channels.

Approximating solutions of nonlinear second order ordinary differential equations via Dhage iteration principle

In this paper the authors prove algorithms for the existence as well as approximation of the solutions for an initial and a periodic boundary value problem of nonlinear second order ordinary differential equations. The main results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2013) in the partially ordered normed linear spaces and the numerical solution of the considered equations is obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and results are also illustrated by some numerical examples.

Iteration Principles in Epistemology II: Arguments Against

The prequel to this paper introduced the topic of iteration principles in epistemology and surveyed some arguments in support of them. In this sequel, I'll consider two influential families of objection to iteration principles. The first turns on the idea that they lead to some variety of skepticism, and the second turns on ‘margin for error’ considerations adduced by Timothy Williamson (2000).

Iteration Principles in Epistemology I: Arguments For

AbstractEpistemic iteration principles are principles according to which some or another epistemic operator automatically iterates‐‐‐e.g., if it is known that P, then it is known that P, or there is evidence that P, then there is evidence that there is evidence that P. This article provides a survey of various arguments for and against epistemic iteration principles, with a focus on arguments relevant to a wide range of such principles.

Lewis on iterated knowledge

The status of the knowledge iteration principles in the account provided by Lewis in “Elusive Knowledge” is disputed. By distinguishing carefully between what in the account describes the contribution of the attributor’s context and what describes the contribution of the subject’s situation, we can resolve this dispute in favour of Holliday’s (2015) claim that the iteration principles are rendered invalid. However, that is not the end of the story. For Lewis’s account still predicts that counterexamples to the negative iteration principle ( $$\lnot Kp\rightarrow K\lnot Kp$$ ) come out as elusive: such counterexamples can occur only in possibilities which the attributors of knowledge are ignoring. This consequence is more defensible than it might look at first sight.

Concurrent Dynamic Algebra

We reconstruct Peleg’s concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an axiomatization of concurrent dynamic algebras from that basis. In this context, sequential composition is not associative. It interacts with parallel composition through a weak distributivity law. The modal operators of concurrent dynamic algebra are obtained from abstract axioms for domain and antidomain operators; the Kleene star is modelled as a least fixpoint. Algebraic variants of Peleg’s axioms are shown to be derivable in these algebras, and their soundness is proved relative to the multirelational model. Additional results include iteration principles for the Kleene star and a refutation of variants of Segerberg’s axiom in the multirelational setting. The most important results have been verified formally with Isabelle/HOL.

Initiality for Typed Syntax and Semantics

In this thesis we give an algebraic characterization of the syntax and semantics of simply–typed languages. More precisely, we characterize simply–typed binding syntax equipped with reduction rules via a universal property, namely as the initial object of some category. We specify a language by a 2–signature (Σ, A), that is, a signature on two levels: the syntactic level Σ specifies the sorts and terms of the language, and associates a sort to each term. The semantic level A specifies, through inequations, reduction rules on the terms of the language. To any given 2–signature (Σ, A) we associate a category of “models” of (Σ, A). We prove that this category has an initial object, which integrates the terms freely generated by Σ and the reduction relation — on those terms — generated by A. We call this object the programming language generated by (Σ, A). Initiality provides an iteration principle which allows to specify translations on the syntax, possibly to a language over different sorts. Furthermore, translations specified via the iteration principle are by construction type–safe and faithful with respect to reduction. To illustrate our results, we consider two examples extensively: firstly, we specify a double negation translation from classical to intuitionistic propositional logic via the category–theoretic iteration principle. Secondly, we specify a translation from PCF to the untyped lambda calculus which is faithful with respect to reduction in the source and target languages. In a second part, we formalize some of our initiality theorems in the proof assistant Coq. The implementation yields a machinery which, when given a 2–signature, returns an implementation of its associated abstract syntax together with certified substitution operation, iteration operator and a reduction relation generated by the specified reduction rules.

Approximating positive solutions of PBVPs of nonlinear first order ordinary quadratic differential equations

In this paper the authors prove the existence as well as approximations of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic differential equations under some suitable mixed hybrid conditions. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. A numerical example is also provided to illustrate the abstract theory developed in the paper.

Stability and turing instability in a diffusive predator–prey system with Beddington–DeAngelis functional response

A diffusive two-species predator–prey system with the Beddington–DeAngelis functional response and subject to homogeneous Neumann boundary conditions is considered. In the region of parameters where the positive constant steady state is globally asymptotically stable when there exists no diffusion, the impact of the diffusion on the stability is analyzed in detail. The global asymptotic stability of the positive constant steady state is also considered by means of the upper and lower solutions method and the monotone iteration principle.