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If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different dimensions, the one of higher dimension must ruled. A ruled system is one whose equations define at each point in the state manifold, a ruled submanifold of the tangent space. Dynamic equivalence is also known as equivalence by endogenous dynamic feedback, or by a Lie-B\"acklund transformation when control systems are viewed as underdetermined systems of ordinary differential equations; it is very close to absolute equivalence for Pfaffian systems. It was already known that a differentially flat system must be ruled; this is a particular case of the present result, in which one of the systems is assumed to be "trivial" (or linear controllable).

In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.

In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.

Up until now we've focused our attention on the text of Scripture.  We took five episodes looking at the Hebrew Bible, including it's sources, transmission, and how textual scholars go about deciding the initial text.  Then for the last seven episodes we did the same for the New Testament, examining the surviving source material and looking at the work of textual criticism.  Now, we are in a good position to shift gears and turn to the whole world of translation.  As it turns out, English Bible translators divide into two broad styles of translation: formal equivalence and dynamic equivalence.  In this episode we'll explore these two translation philosophies and the trade offs each makes in order to produce English Bibles. https://www.youtube.com/watch?v=OTalda3J_eQ —— Books —— The Complete Guide to Bible Translations by Ron Rhodes Essential Guide to Bible Versions by Philip W. Comfort The Journey from Texts to Translations by Paul D. Wegner How to Choose a Translation for All Its Worth by Gordon Fee and Mark Strauss The Art of Bible Translation by Robert Alter How We Got the Bible by Neil Lightfoot The Theory and Practice of Translation by Eugene Nida —— Links —— Andi Wu, “ A Quantitative Evaluation of the Christian Standard Bible ” Check out all the lectures in How We Got the Bible See what other classes are available here or on the Restitutio Classes podcast (subscribe in Apple , Spotify , RSS feed ) If you’d like to support Restitutio, you can donate here . Intro music: Good Vibes by MBB Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) Free Download / Stream : Music promoted by Audio Library

Translation is an act of communication across dissimilar cultures. In as such, cultural expressions or idioms are a particularly salient translation challenge, especially when translating between two distinct languages spoken by two different nations. Idioms convey rich cultural connotations, and so require consideration of both cultural and linguistic dissimilarities when providing for translation. This article describes findings for idiomatic expressions within the sewing frame and their Persian equivalences in the framework of Nida's Dynamic Equivalence theory to answer such questions of translation. Specifically, to what extent Persian idiomatic expressions overlap this frame in English connotatively is explored on one hand; as compared to their differences in using source domains, on the other. To do so, twenty seven sewing frame idiomatic expressions in English were collected from the work of Uberman (2008), website of http://www.UsingEnglish.com/idiom.asp , http://goenglish.com/idiom.asp and http://www.idiomeanings.com. Next their Persian equivalences were searched for and directly compared. The results show that the overlapping of idioms in this frame is mostly connotatively oriented and that there are some English expressions that have zero idiomatic equivalence in Persian.

We report a qualitative analysis of elementary school students engaged in collaborative problem solving involving mathematical equivalence tasks. We build on previous research showing that students often use strategies based on either operational or relational understandings of the equal sign. We closely analyze three cases and identify nuanced aspects of the social interaction that influence whether and how students develop and use operational or relational strategies toward a final solution. Students' demonstrated understandings of the equal sign during collaboration aligned with those identified in past research. We argue that a social-mathematical power dynamic was co-constructed in each of the dyads, and the ways students navigated that dynamic affected the quality of individual engagement and therefore learning. [For the complete proceedings, see ED583608.]

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among mathematically equivalent states. In the fall of 2019, 475 middle-school students participated in a randomized control trial where they worked in either FH2T or online problem sets with hints and feedback in ASSISTments over four 30-minute sessions during their math class. We found that (a) students in both conditions improved their understanding of mathematical equivalence from pretest to posttest; (b) students in the FH2T condition performed better on posttest compared to students in the problem set condition; and (c) the condition effect was comparable between students with high versus low prior knowledge. Together, the findings suggest that From Here to There! is an effective intervention for improving middle-school students' understanding of mathematical equivalence. The implications for research and practice on the usefulness of digital environments in mathematics education are discussed. [This is the online version of an article published in "Journal of Educational Psychology."]

Approximate Dynamic Inversion (ADI) has been established as a method to control minimum-phase, nonaffine-incontrol systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear Proportional-Integral (PI) realization that is largely independent of the nonlinear function that defines the system. In this report, we first present an extension of the ADI method for single-input nonaffine-in-control systems that renders the closed-loop error dynamics independent of the reference model dynamics. The equivalent PI controller will be derived and both of these results are then extended to multi-input nonaffine-in-control systems.

This paper uses an unsteady strained flame in the stagnation point configuration to examine the effect of temporal gradients of mixture equivalence ratio on combustion in a premixed methane/air mixture. An inexact Newton backtracking method, coupled with a preconditioned Krylov subspace iterative solver, was used to improve the efficiency of the numerical solution and expand its domain of convergence in the presence of detailed chemistry. Results indicate that equivalence ratio variations with timescales lower than 10 ms have significant effects on the burning process, including reaction zone broadening, burning rate enhancement, and extension of the flammability limit toward leaner mixtures. While the temperature of a flame processing a stoichiometric-to-lean equivalence ratio gradient decreased slightly within the front side of the reaction zone, radical concentrations remained elevated over the entire flame structure. These characteristics are linked to a feature reminiscent of back-supported flames in which a stream of products resulting from burning at higher equivalence ratio is continuously supplied to lower equivalence ratio reactants. The relevant feature is the establishment of a positive temperature gradient on the products side of the flame which maintains the temperature high enough and the radical concentration sufficient to sustain combustion there. Unsteadiness in equivalence ratio produces similar gradients within the flame structure, thus compensating for the change in temperature at the leading edge of the reaction zone and accounting for an observed flame inertia. For sufficiently large equivalence ratio gradients, a flame starting in a stoichiometric mixture can burn through a very lean one by taking advantage of this mechanism.

In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e. systems dynamically equivalent to linear control systems, the advantage of this approach is that it allowed us to consider control affine systems as well. Through this context we are able to classify all control affine systems of three states and two controls under dynamic equivalence of the type (x,u) |-> y(x,u).

The starting point of this work is a framework allowing to model systems with dynamic process creation, equipped with a procedure to detect symmetric executions (ie., which differ only by the identities of processes). This allows to reduce the state space, potentially to an exponentially smaller size, and, because process identifiers are never reused, this also allows to reduce to finite size some infinite state spaces. However, in this approach, the procedure to detect symmetries does not allow for computationally efficient algorithms, mainly because each newly computed state has to be compared with every already reached state. In this paper, we propose a new approach to detect symmetries in this framework that will solve this problem, thus enabling for efficient algorithms. We formalise a canonical representation of states and identify a sufficient condition on the analysed model that guarantees that every symmetry can be detected. For the models that do not fall into this category, our approach is still correct but does not guarantee a maximal reduction of state space.

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient D_S in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with D_S, will indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio D_L/ D_S of the long-time to the short-time self-diffusion coefficients must then be the same for both, an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids[Phys. Rev. Lett. 70, 1557 (1993)]. We corroborate these predictions by comparing molecular and Brownian dynamics simulations on (soft- and hard-sphere) model systems, representative of what we may refer to as the "hard-sphere" dynamic universality class.

The direct scheme of Model Reference Adaptive Control System (MRACS) may have several disadvantages; (i) the current state of the plant cannot be easily grasped from values of adjustable adaptive controller parameters, (ii) it has often inferior conditions to an indirect scheme, with respect to the persistent excitation (PE) conditions of adjustable controller parameters for convergence to optimal values. Indirect MRACS based on Dynamic Certainty Equivalent (DyCE) principle hasnot been well studied though the importance of indirect scheme is recognized in an actual field using adaptive control. This paper presents new two design schemes of indirect MRACS based on DyCE principle. These are realized by recursive identifiers and new high order tuners.