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Advances in 1D Materials
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Javier Palomino, Brad R. Weiner, Gerardo Morell
From the 1950s through the 1970s, several researchers have found involuntarily the occurrence of CNFs in metallic catalysts used for the conversion of carbon-containing gases into olefins (Melechko et al., 2005). Hence, the CNFs have attracted the attention of experimentalists and theoreticians, producing comprehensive studies to control its properties such as surface structure, diameter, length, chemical and mechanical properties. The studies revealed that CNFs possess high mechanical strengths and moduli, high stiffness, excellent electrical and thermal conductivities, as well as strong fatigue and corrosion resistance (Zhou et al., 2009). Presently, CNF is a material of great interest due to its modern potential applications including tips for scanning microscopy and field emission devices, biological probes, and nanoelectronics (Merkulov et al., 2001).
Equivalence Checking
Published in Louis Scheffer, Luciano Lavagno, Grant Martin, EDA for IC Implementation, Circuit Design, and Process Technology, 2018
Andreas Kuehlmann, Fabio Somenzi
A SAT solver returns an assignment to the variables of a propositional formula that satisfies it if such an assignments exists. A literal is either a variable or its negation, a clause is a disjunction of literals from distinct variables, and a CNF formula is a conjunction of clauses. We shall use the following simple CNF formula as a running example: () (¬a∨b∨c)∧(a∨¬b∨c)∧(¬c∨d)∧(¬c∨¬d)
Electrospun Bio Nanofibers for COVID-19 Solutions
Published in K.M. Praveen, Rony Thomas Murickan, Jobin Joy, Hanna J. Maria, Jozef T. Haponiuk, Sabu Thomas, Electrospun Nanofibers from Bioresources for High-Performance Applications, 2023
Akhila Raman, A.S. Sethulekshmi, Appukuttan Saritha
Cellulose is the most abundant and renewable biopolymer on earth. Cellulose nanofibers have a low coefficient of thermal expansion [18], good mechanical properties [19], environmental friendliness, low densities [20], and higher surface areas [21] and can be extracted from various renewable sources. CNF has potential applications in electronic devices, food packaging, food additives, in the biomedical area [22], gas barrier films [23], cosmetic products [24], and nanocomposites [25]. Cellulose nanofibers can be obtained from various natural sources such as cotton [26] banana rachis [27], sugar beet pulp, bamboo [28], coconut husk fibers [29], sugarcane bagasse, sisal [30], pineapple leaf fibers [31], and the like.
On black-box optimization in divide-and-conquer SAT solving
Published in Optimization Methods and Software, 2021
O. S. Zaikin, S. E. Kochemazov
A Boolean variable x is a variable that can take only two values , often represented by respectively. A literal is either a Boolean variable or its negation . A sequence of literals connected by logical ‘or’, eg , is called a disjunction or a clause. It takes the value of if and only if any of the literals takes this value. A conjunction (logical ‘and’) of clauses is called a Conjunctive Normal Form (CNF). Any Boolean formula can be represented in CNF [59]. The Boolean satisfiability problem (SAT) in its decision variant is then formulated as follows: for a CNF C over Boolean variables from set , to answer the question whether there exists such an assignment of variables from X that once each variable is set to , the CNF C becomes . If such an assignment exists, then it is called satisfying assignment and C is called satisfiable. If there are no assignments satisfying the formula, then the formula is called unsatisfiable.
Medical diagnosis and treatment is NP-complete
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2021
Jeffrey. E. Arle, Kristen W. Carlson
The problem that helped establish the NPC class is ‘satisfiability’ (SAT): Given a Boolean expression in conjunctive normal form (CNF), does a given assignment of truth values satisfy it, i.e. result in a value of TRUE (Cook, 1971; Hopcroft & Ullman, 1979)? A Boolean expression in CNF is a set of OR clauses connected to each other by AND conditions; therefore, all the OR clauses in the entire expression must be true to satisfy a truth statement. SAT embodies the structure of constraint satisfaction problems in diverse domains such as planning and scheduling, computer chip validation, protein folding, and fibre optic routing (Arora & Barak, 2009) (Gomes & Selman, 2002). An algorithm to satisfy a CNF expression must backtrack when it hits a conflict in order to re-test a new truth assignment on all clauses against which it was not previously tested (Moskewicz et al., 2001). Conversely, satisfying decidability of Boolean expressions in disjunctive normal form (DNF), which is a set of AND clauses connected by ORs, is tractable – trivial, by constructing a truth assignment to satisfy any clause.
A MaxSAT based approach for QoS cloud services
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
Abderrahim Ait Wakrime, Said Jabbour, Nabil Hameurlain
We first introduce the satisfiability problem (SAT) and some necessary notations. SAT corresponds to the problem of deciding if a formula of propositional classical logic is consistent or not. It is one of the most studied NP-complete decision problem. We consider the conjunctive normal form (CNF) representation for the propositional formulas. A CNF formula Φ is a conjunction of clauses, where a clause is a disjunction of literals. A literal is a positive (p) or negated () propositional variable. The two literals p and are called complementary. We denote by the complementary literal of l, i.e. if l=p, then and if , then . For a set of literals L, is defined as . A CNF formula can also be seen as a set of clauses, and a clause as a set of literals. Let us recall that any propositional formula can be translated to CNF using linear Tseitin's encoding [5]. We denote by (respectively ) the set of propositional variables (respectively literals) occurring in Φ.