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The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of star-free languages is the smallest class containing the finite languages and closed under boolean operations and concatenation. We prove that the tight bounds on the quotient complexities of union, intersection, difference, symmetric difference, concatenation and star for star-free languages are the same as those for regular languages, with some small exceptions, whereas 2ⁿ-1 is a lower bound for reversal.

We present the integration and accuracy and power improved hearing aid system that proposes the triple oscillation-based loops (TOL) technique. Compared with the conventional techniques, the technique replaces the interface capacitors, A/D and D/A convertors with the oscillation-based closed loop and the calibration/operation feedback paths, which are able to enhance the integration of the system and improve the system's accuracy and power performance. Specifically, the technique achieves the only once of the second-order delta-sigma modulation with an integrator and an oscillator. To realize the architecture, the current mode blocks with calibration and successive subtraction are presented on the circuit design. Simulated with a 0.13 μm standard CMOS process in Cadence, with the 16 ohm loudspeaker impedance under the 1 V supply voltage, the input referred DC offset voltage with interface capacitor free is achieved below 2.5 mV; and the signal-to-noise and distortion rate (SNDR) achieves 50 dB@400 mV_p-p output voltage. Moreover, the power consumption with no load is maintained within 350 μW.

This paper defines a new operation through extending the idea of the 0-dimensional crossing change and Shimizu’s 2-dimensional region crossing change [A. Shimizu, Region crossing change is an unknotting operation, J. Math. Soc. Jpn. 66(3) (2014) 693–708, doi:10.2969/jmsj/06630693] to a 1-dimensional version called the arc crossing change. We will also prove that the arc crossing change is an unknotting operation with the help of Gauss diagrams.

Dorsal wrist pain with or without a palpable dorsal wrist ganglion is a common complaint. Watson developed the concept of the dorsal wrist syndrome (DWS) which is an entity encompassing pre-dynamic rotary subluxation of the scaphoid and the overloaded wrist. We reviewed 20 cases of DWS treated surgically. There were nine males (11 wrists) and nine females (nine wrists). Post-operative follow-up ranged from five to 67 months (mean, 37 months). At operation, we observed SLL tears in eight wrists and dorsal ganglia in 12 cases. Following surgery, 12 cases reported being pain free, five had mild pain, two moderate pain and one case reported severe pain. Post-operative extension/flexion was 73/70 average. Post-operative grip strength was 28 kg average. We believe that excision of the posterior interosseous nerve and the dorsal capsule including the ganglion, if present, provides pain relief in DWS.

Today’s smart and sustainable agricultural enterprises are founded on the intercorrelation between Industry 4.0 (I4) technologies and circular economy (CE) fundaments. At the industrial level, it is mandatory to constrain the design, operation, and control of the next generation of manufacturing, logistics, and supply chain systems that respect economic, environmental, and social aspects. At the individual level, behaviours and preferences require re-do (as recycling) and a re-do-not (as rethinking) actions to reduce human inefficiencies and excesses in the economy and impacts on the environment. Both industrial and individual levels are responsible for the growth of a harmonious industry and society into a new I4–CE mandate intertwined with sustainable development concerns. Particularly, this paper reveals how the state-of-the-art I4 technologies could promote CE initiatives in the agriculture industry by addressing such technologies as a foundation for the so-called precision agriculture (PA). The outcomes of this paper are as follows: (a) address the mutually advantageous linkage between PA and CE; (b) detailed knowledge of the potential contributions of PA technologies to the regenerate, share, optimise, loop, virtualise, and exchange (ReSOLVE) as a CE model; (c) propose an action plan for future study integrating smart PA and CE principles based on green supply chain management theories.

This paper considers the problems of scheduling N jobs of the same family, each manufactured in a number of operations, in order, on three CNC machining centres which are equipped with automatic tool changers. A generalized procedure to minimize tool changeovers has been developed and tested on real industrial problems considering a set of possible constraints. The procedure suggested in this paper results in minimal changeovers. Validity of the heuristics suggested is borne out of the fact that when the same case-problem is considered as a Travelling Salesman problem and solved using Hungarian Method, identical result is attained. The procedure is simple and easy to implement in a CNC environment.

A set $C$ of operations defined on a nonempty set $A$ is said to be a clone if $C$ is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the $n$-ary operations defined on set $A$ for all natural numbers $n\ge 1$ and the operations are the so-called superposition operations $S_m^n$ for natural numbers $m,n\ge 1$ and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set $A$ and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.

For fixed integers $1\le i<j\le n$ and $\sigma \in S_n$, we study the faithful representation of superassociative algebras by two kinds of functions of the arity $n$, the so called $(i,j)$-commutative and $\sigma$-commutative. The automorphism on the algebra of all $(i,j)$-commutative functions is determined. In general, an isomorphism from a superassociative system which consists of a family of nonempty sets and a family of operations satisfying the axiom of superassociativity to a system of full multiplace functions is discussed. Particularly, we also provide necessary and sufficient conditions under which a superassociative system and a system of $\sigma$-commutative functions are isomorphic. With these results, a close connection with the theory of terms and tree languages is described.

A term which is a formal expression defined by variables and operation symbols can be described by tree diagram. The class of terms under which the longest distance from the root to each vertex is equal is called completely expanded. In this paper, we consider the partial many-sorted operation defined on the family of all completely expanded terms of type $\tau$ and construct the partial algebra satisfying the clone axioms. The partial operations on arbitrary algebra generated by completely expanded terms and their related structures are obtained.

The current Communication-based Train Operation Control (CBTC) system adopts the adhesion, closed system architecture and autonomous safety model. It only makes the brakes respond to the train operation speed, train position, the input of the front-back train relationship and other input states. With the rapid development of urban rail transit, train operations are becoming more and more complex, and operators need to respond to more external events. However, since the current data acquisition equipment of CBTC system only has basic functions but has neither data acquisition nor data interface for other emergencies, the system has no response stored or is unable to respond in time for exogenous emergencies. Therefore, based on the current CBTC system, this article presents a new generation of global cooperative signaling for train control. Through increasing acquisition of external environment data acquisition equipment and interface, the safety cooperative function of wayside subsystem, carborne subsystem and other subsystem can be improved. Also, the new generation of global cooperative signaling for train control is able to have a timely and efficient response to fail-safe information. Improving the safety and reliability of train operation system brings about the fail-safe of the whole rail transit system.