Academic literature on the topic 'Doubly chained tree structures'

AbstractThe first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in [28] by improving both the lower and the upper bounds.

Graphs are one of the most fundamental and widely used non-linear hierarchical structures of linked nodes. Problems in sciences and engineering can be formulated and solved by the graph model. This paper develops a comprehensive design pattern of formal digraphs using the Doubly-Linked List (DLL) architecture. The most complicated form of graphs known as the weighted digraph is selected as a general graph model, based on it simple graphs such as nondirected and/or nonweighted ones can be easily derived and tailored. A rigorous denotational mathematics, Real-Time Process Algebra (RTPA), is adopted, which allows both architectural and behavioral models of digraphs to be rigorously designed and implemented in a top-down approach. The architectural models of digraphs are created using RTPA architectural modeling methodologies known as the Unified Data Models (UDMs). The physical model of digraphs is implemented using nodes of DLL dynamically created in the memory. The behavioral models of digraphs are specified and refined by a set of 18 Unified Process Models (UPMs) in three categories namely the management operations, traversal operations, and node manipulation operations. This work has been applied in a number of real-time and nonreal-time system designs and specifications such as a Real-Time Operating System (RTOS+), graph-based and tree-based applications, and the ADT library for an RTPA-based automatic code generation tool.

In this paper, a curve-shaped based doubly clamped piezoelectric energy harvester (CD-PEH) is explored for improving the energy harvesting performance. The harvester consists of a composed beam constructed with two arc-shaped structures and a flat beam, as well as two proof masses. A method based on chained beam constraint model theory (CBCM) is first applied to build the nonlinear restoring force model of the CD-PEH, the developed analytical model is validated by the finite element analysis (FEA). Then the electromechanically coupled model for the CD-PEH is built to investigate the effect of excitation amplitudes, geometric parameters and load resistance on the output characteristics. Due to the geometric nonlinearity caused by the arc-shaped configuration, the CD-PEH orderly exhibits quasi-linear, softening nonlinear and mixed hardening & softening nonlinearity behavior with the increasing of excitation level, which could effectively extend the frequency bandwidth of the system. For the excitation of A = 8 m/s2, the effective working bandwidth of the CD-PEH is increased by 633% compared with the effective bandwidth in the case of A = 2 m/s2. Moreover, comparison experiments demonstrate that the output voltage and the effective bandwidth are increased by 225 and 450%, respectively, compared with the typical doubly-clamped piezoelectric energy harvester (T-PEH) under the same excitation amplitude. Overall, this study provides a new way and theoretical framework for the design of high-efficiency doubly clamped piezoelectric energy harvester.

Recursive data structures are abstractions of simple records and pointers. They impose a <em> shape</em> invariant, which is verified at compile-time and exploited to automatically generate code for building, copying, comparing, and traversing values without loss of efficiency. However, such values are always tree shaped, which is a major obstacle to practical use. We propose a notion of <em> graph types </em>, which allow common shapes, such as doubly-linked lists or threaded trees, to be expressed concisely and efficiently. We define regular languages of <em> routing expressions</em> to specify relative addresses of extra pointers in a canonical spanning tree. An efficient algorithm for computing such addresses is developed. We employ a second-order monadic logic to decide well-formedness of graph type specifications. This logic can also be used for automated reasoning about pointer structures.

In self-determination theory (SDT), multiple conceptual regulations of motivation are posited. These forms of motivation are especially qualitatively viewed by SDT researchers, and there are situations in which combinations of these regulations occur. In this article, instead of the commonly used numerical approach, this is modeled more versatilely by sets and relations. We discuss discrete mathematical models from the theory of knowledge spaces for the combinatorial conceptualization of motivation. Thereby, we constructively add insight into a dispute of opinions on the unidimensionality vs. multidimensionality of motivation in SDT literature. The motivation order derived in our example, albeit doubly branched, was approximately a chain, and we could quantify the combinatorial details of that approximation. Essentially, two combinatorial dimensions reducible to one were observed, which could be studied in other more popular scales as well. This approach allows us to define the distinct, including even equally informative, gradations of any regulation type. Thus, we may identify specific forms of motivation that may otherwise be difficult to measure or not be separable empirically. This could help to dissolve possible inconsistencies that may arise in applications of the theory in distinguishing the different regulation types. How to obtain the motivation structures in practice is demonstrated by relational data mining. The technique applied is an inductive item tree analysis, an established method of Boolean analysis of questionnaires. For a data set on learning motivation, the motivation spaces and co-occurrence relations for the gradations of the basic regulation types are extracted, thus, enumerating their potential subforms. In that empirical application, the underlying models were computed within each of the intrinsic, identified, introjected, and external regulations, in autonomous and controlled motivations, and the entire motivation domain. In future studies, the approach of this article could be employed to develop adaptive assessment and training procedures in SDT contexts and for dynamical extensions of the theory, if motivational behavior can go in time.