Boolean functions play an important role in symmetric ciphers. One of important open problems on Boolean functions is determining the maximum possible resiliency order of n-variable Boolean functions ...with optimal algebraic immunity. In this letter, we search Boolean functions in the rotation symmetric class, and determine the maximum possible resiliency order of 9-variable Boolean functions with optimal algebraic immunity. Moreover, the maximum possible nonlinearity of 9-variable rotation symmetric Boolean functions with optimal algebraic immunity-resiliency trade-off is determined to be 224.
Cryptographic Boolean functions play an important role in the design of symmetric ciphers. Many cryptographic criteria such as balancedness, nonlinearity, correlation immunity and transparency order ...are connected with the Walsh support of a Boolean function. However, we still know little about the possible structure of the Walsh supports of Boolean functions. In 2005, Carlet and Mesnager studied the Walsh supports of Boolean functions and constructed a class of n-variable Boolean functions whose Walsh support is F2n∖{0}, for n≥10. For n≤6, it can be verified using the computer that there is no Boolean function with the Walsh Support F2n∖{0}. However, concerning the values of n=7,8,9, it has been an open problem for many years. In this paper, we construct two classes of balanced Boolean functions with the maximum possible Walsh support F2n∖{0}, and partially solve this problem. The first class of functions are of odd variables with n≥9, and the second class of functions are constructed based on the Maiorana–McFarland bent functions, which are of even variables with n≥8. As a result, the above open problem has been settled for n=8,9, and the only unsolved case is n=7.
The weight spectra of the Reed-Muller codes $RM(r,m)$ were unknown for
$r=3,...,m-5$. In IEEE Trans. Inform. Theory 2024, Carlet determined the weight
spectrum of $RM(m-5,m)$ for $m\ge10$ using the ...Maiorana-McFarland construction,
where the result was tried to be extended to $RM(m-6,m)$, but many problems
occurred and much work needed to be done. In this paper, we propose a novel way
of constructing Reed--Muller codewords and determine the weight spectrum of
$RM(m-6,m)$ for $m\ge12$, which gives a positive answer to an open question on
the weight spectrum of $RM(m-c,m)$ for $c=6$. Moreover, we put forward a
conjecture and verify it for some cases. If the conjecture is true, then that
open question can be completely solved.
A nanoscale, synthetic perturbation was all that was required to nudge a natural, self-assembly process toward significantly higher order. Metallic thin film strips were transformed into nanoparticle ...arrays by nanosecond, liquid-phase dewetting. Arrays formed according to an evolving Rayleigh–Plateau instability, yet nanoparticle diameter and pitch were poorly controlled. However, by patterning a nanoscale sinusoid onto the original strip edge, a precise nanoparticle diameter and pitch emerged superseding the naturally evolving Rayleigh–Plateau instability.
This paper presents a study of a quasi-zero-stiffness (QZS) isolator. A unique relationship between the geometry configuration and the stiffness of the spring elements is obtained in order to design ...the property of high-static-low-dynamic stiffness. Analytical solutions of the nonlinear QZS system are derived with the harmonic balance method for the characteristic analysis of the force transmissibility and critical conditions for occurring jump-down and jump-up phenomena. The effects of damping and excitation force on the system behaviors are discussed. A series of experimental tests demonstrate that the QZS system greatly outperforms a corresponding linear isolation system. The former enables vibration to be attenuated at 0.5 Hz, while the latter can only execute attenuation after 4.2 Hz. The QZS system is especially effective for vibration isolation in the low-frequency range.
In the present study, non-crosslinked lanthanum-chitosan (La-CTS-0X) and crosslinked lanthanum-chitosan (La-CTS-1X/2X) composites were prepared as new complex biosorbents for effective phosphate ...removal from wastewater. Batch adsorption experiments were investigated by varying the influencing parameters, viz., pH, initial concentration of phosphate ions, contact time, temperature and co-existing anions. Experimental data were well fitted to the Langmuir isotherm model (R2 = 0.9998) as well as the pseudo-second-order model (R2 = 1.000), indicating that the phosphate adsorption process was homogeneous, mono-layered and chemisorption dominated. Besides, the maximum phosphate adsorption capacity for La-CTS-0X/1X/2X was 47.28, 57.84 and 31.01 mg g−1 at pH 6, respectively. Thermodynamic parameters including ΔH° (−43.7 kJ mol−1), ΔS° (−132 J mol−1 K−1) and ΔG° (−4.60 kJ mol−1) revealed that the essence of adsorption was spontaneous and exothermic. The regenerated materials could be repeatedly used for three cycles without obvious degradation of performance. Characterization of the adsorbent using FTIR, SEM, EDS and XPS techniques suggested that the possible adsorption mechanisms were electrostatic attraction as well as ligand exchange. More importantly, the La-CTS-1X had rapid removal rate for phosphate within 10 min and the remained P concentration met the permissible limit by the U.S. Environmental Protection Agency (EPA).
•La-CTS-(0–2)X were successfully synthesized by controlling the cross-linking agent.•Fast removal of phosphate (removal rate > 95%) within 10 min.•La-CTS-1X exhibits high adsorption capacity (57.84 mg g−1) for phosphate.•Electrostatic attraction and ligand exchange mechanisms occurred on La-CTS surface.
The effect of three nanocellulose (various in crystalline allomorph and morphology) on lipid in vitro gastrointestinal digestibility was investigated. Corn oil-in-water emulsions were prepared by ...CNCs-I, CNCs-II and CNFs respectively. The variations of droplets diameter D4,3, zeta potential, and microstructure were measured during gastrointestinal digestion (mouth, stomach and small intestine), and the free fatty acid (FFA) released in the small intestine phase were examined. The FFA-released test results indicated that both crystalline allomorph and morphology of nanocellulose affected the degree of lipid digestion, especially the morphology. FFA released amount was ranked in the order of CNCs-I (56.60%), CNCs-II (48.67%) and CNFs (28.21%). This is mainly due to the difference in the self-assembly behavior of nanocellulose at the interface. Our findings provide an innovative solution that using nanocellulose as food-grade particle stabilizer to modulate the digestion of Pickering emulsified lipids, which would benefit the development of given functional foods.
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Nanolithographically patterned copper rings were synthesized, and the self-assembly of the rings into ordered nanoparticle/nanodrop arrays was accomplished via nanosecond pulsed laser heating above ...the melt threshold. The resultant length scale was correlated to the transport and instability growths that occur during the liquid lifetime of the melted copper rings. For 13-nm-thick rings, a change in the nanoparticle spacing with the ring width is attributed to a transition from a Raleigh−Plateau instability to a thin film instability because of competition between the cumulative transport and instability timescales. To explore the competition between instability mechanisms further, we carried out experiments with 7-nm-thick rings. In agreement with the theoretical predictions, these rings break up in both the azimuthal and radial directions, confirming that a simple hydrodynamic model captures the main features of the processes leading to the breakup.
We study the instability of nanometric Cu thin films on SiO2 substrates. The metal is melted by means of laser pulses for some tens of nanoseconds, and during the liquid lifetime, the free surface ...destabilizes, leading to the formation of holes at first and then in later stages of the instability to metal drops on the substrate. By analyzing the Fourier transforms of the SEM (scanning electron microscope) images obtained at different stages of the metal film evolution, we determine the emerging length scales at relevant stages of the instability development. The results are then discussed within the framework of a long-wave model. We find that the results may differ whether early or final stages of the instability are considered. On the basis of the interpretation of the experimental results, we discuss the influence of the parameters describing the interaction of the liquid metal with the solid substrate. By considering both the dependence of dominant length scales on the film thickness and the measured contact angle, we isolate a model which predicts well the trends found in the experimental data.
The complete mitochondrial genome (mitogenome) of an important medicinal insect Hydrillodes repugnalis (Lepidoptera: Noctuoidea) was sequenced and analyzed. The mitogenome is circular with 15,570 bp ...long, and shows typical gene content and arrangement. Nucleotide composition is highly biased toward A + T nucleotides (81.1%). All protein-coding genes (PCGs) initiate with canonical start codon ATN, except for cox1 being CGA. The typical stop codon TAA is used for most PCGs, while the nad4l uses the TAG, and cox1 and cox2 use incomplete termination codon T. All tRNAs have a typical clover-leaf structure, except for trnS1 (AGN) lacking the dihydrouridine arm. Comparative mitogenome analysis showed that the motif “ATGATAA” between atp8 and atp6, and the motif “ATACTAA” between trnS2 and nad1 are commonly present in noctuoid mitogenomes. In A + T-rich regions, the motif “ATAGA” and subsequent poly-T structure, the motif “ATTTA” and followed macrosatellite (AT)n element and an “A”-rich 3′ end upstream of the trnM gene can be recognized across noctuoid mitogenomes. Phylogenetic analyses showed that H. repugnalis is nested into the Erebidae clade, consistently being sister to the Aganainae. Within Noctuoidea, the (Notodontidae + (Erebidae + (Nolidae + (Euteliidae + Noctuidae))) was consistently recovered firstly based on multiple mitochondrial datasets.
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