REPRESENTASI SIMBOLIK SISWA DALAM MENYELESAIKAN SOAL HOTS MATERI RELASI DAN FUNGSI KELAS VIII SMP

This study aims to describe the symbolic representation of students in solving HOTS questions on the relation material and functions of class VIII SMP. Qualitative descriptive research method with case research form. The research subjects consisted of six grade VIII students of SMP N 22 Palembang, namely two high-ability students, two medium-ability students and two low-ability students. The data was collected by providing test questions, interviews and documentation. The results of data analysis show that high-ability students have errors in the function symbols, function equations, curly braces, and in determining the results. Students with abilities have several errors that cannot function, are incomplete in brackets, errors in curly braces, there are unacceptable problems and errors in the same symbol as low-ability students there are errors in the function symbol, complete in brackets not curly braces on the set as well as errors in completion.Keywords: Representation, Ability, Error, symbol, Equation

Bounded ACh unification

We consider the problem of the unification modulo an equational theory associativity and commutativity (ACh), which consists of a function symbol h that is homomorphic over an associative–commutative operator +. Since the unification modulo ACh theory is undecidable, we define a variant of the problem called bounded ACh unification. In this bounded version of ACh unification, we essentially bound the number of times h can be applied to a term recursively and only allow solutions that satisfy this bound. There is no bound on the number of occurrences of h in a term, and the + symbol can be applied an unlimited number of times. We give inference rules for solving the bounded version of the problem and prove that the rules are sound, complete, and terminating. We have implemented the algorithm in Maude and give experimental results. We argue that this algorithm is useful in cryptographic protocol analysis.

Extensions of unification modulo ACUI

The theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, that is, unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, that is, consider approximate ACUI-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

PURE INDUCTIVE LOGIC WITH FUNCTIONS

We consider the version of Pure Inductive Logic which obtains for the language with equality and a single unary function symbol giving a complete characterization of the probability functions on this language which satisfy Constant Exchangeability.

Sedentary behavior is associated with disability status and walking performance, but not cognitive function, in multiple sclerosis

Eighty-two persons with multiple sclerosis wore an accelerometer as a measure of sedentary time (min/day) and completed measures of disability status (self-reported Expanded Disability Status Scale), walking performance (timed 25-foot walk and 6-min walk), and cognitive function (symbol digit modalities test). Accelerometry-measured sedentary time was significantly correlated with disability status scores (r = 0.31, p < 0.01), 6-min walk distance (r = –0.40, p < 0.01), and timed 25-foot walk performance (r = 0.35, p < 0.01), but not cognitive function performance (r = –0.12, p = 0.29).

THE NON-AXIOMATIZABILITY OF O-MINIMALITY

Fix a language extending the language of ordered fields by at least one new predicate or function symbol. Call an L-structure R pseudo-o-minimal if it is (elementarily equivalent to) an ultraproduct of o-minimal structures. We show that for any recursive list of L-sentences , there is a real closed field satisfying which is not pseudo-o-minimal. This shows that the theory To−min consisting of those -sentences true in all o-minimal -structures, also called the theory of o-minimality (for L), is not recursively axiomatizable. And, in particular, there are locally o-minimal, definably complete expansions of real closed fields which are not pseudo-o-minimal.

Performance Analysis of Multi-Antenna Relay Networks over Nakagami-m Fading Channel

In this chapter, the authors present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent and identically distributed (i.i.d) Nakagami-m fading channels. The outage probability, moment generation function, symbol error probability and average channel capacity are derived in closed-form using the Signal-to-Noise-Ratio (SNR) statistical characteristics. After that, the authors formulate the outage probability problem, optimize it with an approximated problem, and then solve it analytically. Finally, for comparison with analytical formulas, the authors perform some Monte-Carlo simulations.

On bounded arithmetic augmented by the ability to count certain sets of primes

Over 25 years ago, the first author conjectured in [15] that the existence of arbitrarily large primes is provable from the axioms IΔ0(π) + def(π), where π(x) is the number of primes not exceeding x, IΔ0(π) denotes the theory of Δ0 induction for the language of arithmetic including the new function symbol π, and def(π) is an axiom expressing the usual recursive definition of π. We prove a modified version in which π is replaced by a more general function ξ that counts some of the primes below x (which primes depends on the values of parameters in ξ), and has the property that π is provably Δ0(ξ) definable.