We study the space required by Polynomial Calculus refutations of random k-CNFs. We are interested in how many monomials one needs to keep in memory to carry on a refutation. More precisely we show that for k ≥ 4 a refutation of a random k-CNF of ∆n clauses and n variables requires monomial space Ω(n∆− 1+ k−3− ) with high probability. For constant ∆ we prove that monomial space complexity is Θ(...

This work investigated the redispersion and setting behavior of highly loaded (~ 18 wt.% solids in water) pastes cellulose nanofibrils (CNFs) with carboxymethyl (CMC). A single-screw extruder was used to continuously process CNF + CMC into cord. The adsorption onto CNFs assessed through zeta potential titration which revealed a surface charge change ~ 61% from ? 36.8 mV 0.094 mmol/g COOH for pu...

The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiablity algorithms, and lastly average-case hardness over this distribution has also been linked to hardness of approximation via Feige’s hypothesis. In this paper, we prove that any Cutting Planes refutation for ran...

Recent algorithms for model counting and compilation work by decomposing a CNF into syntactically independent components through variable splitting, and then solving the components recursively and independently. In this paper, we observe that syntactic component analysis can miss decomposition opportunities because the syntax may hide existing semantic independence, leading to unnecessary varia...

Abstract The petroleum‐based materials are widely used in daily life, which inherently tough to degrade, increasingly polluting the environment and affecting human health. Cellulose fibrous membrane, ubiquitous, low‐cost, biodegradable material, can serve as a promising substitute. Herein, cellulose membranes were constructed with microfibers made from wood particle fibers (WPF) mechanical prop...

In this work, a composite of cellulose nanofibers (CNFs) and boron nitride nanosheets (BNNSs) with high dispersity in water is prepared via the combination ball-milling high-pressure homogenization, which then transformed into paper-like film by vacuum assisted filtering drying. The obtained CNF/BNNS dispersions can stably exist over 30 days without observation sediments. CNFs as medium protect...

Thick carbon nanofiber (CNF) films were uniformly grown on metal wires with the assistance of pre-deposited NiO nanowalls. The as-prepared wire-shaped composites that integrate the capacitance of CNFs and Ni particles were directly used as electrodes to construct high capacitive fiber supercapacitors for micro-power supplies.

Cellulose nanofibrils (CNFs), which are generated from abundant, environmentally friendly natural plant resources, display numerous interesting properties such as outstanding mechanical strength, negligible light scattering, and low thermal expansion (Zimmermann et al., 2010). These nanofibers are usually created by mechanical fibrillation or chemical oxidation of pulp fibers. CNFs have previou...