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 Magnus Gausdal Find Computer Science , 2014, Abstract: We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time $2^{O(n)}$ given the truth table of length $2^n$, in fact under the same assumption it is impossible to approximate the multiplicative complexity within a factor of $(2-\epsilon)^{n/2}$. When given a circuit, the problem of determining the multiplicative complexity is in the second level of the polynomial hierarchy. For nonlinearity, we show that it is #P hard to compute given a function represented by a circuit.
 Archives of Materials Science and Engineering , 2007, Abstract: Purpose: This paper presents investigation results of the properties of the multicomponent (Ti,Al)N and gradient Ti(C,N) wear resistant coatings, deposited with the PVD process onto the substrate from the cemented carbides, cermets and Al2O3+TiC type oxide tool ceramics.Design/methodology/approach: The methodology includes analysis of the mechanical and functional properties. The Ra parameter was assumed to be the value describing surface roughness. The microhardness tests using the Vickers method were made with use of dynamic ultra microhardness tester. The measurements were made in the load - unload” mode. Tests of the coatings adhesion to the substrate material was made with use of the scratch test. Surface roughness tests were done both before depositing the coatings and after completing the PVD process. Cutting properties of the investigated materials were determined based on the technological continuous cutting tests of the EN-GJL-250 grey cast iron.Findings: Main properties of the investigated materials were introduced. It has been stated, that properties of the cemented carbides, cermets and oxide tool ceramics with deposited multicomponent (Ti,Al)N and gradient Ti(C,N) PVD coatings increase in comparison with uncoated material. Multiple increase of tool life result among other things from almost double increase of microhardness of PVD coated materials in comparison with uncoated cemented carbides, cermets and oxide tool ceramics, increasing of thermal and chemical wear resistance and improving of chip formation and removing process’ conditions.Practical implications: Pro-ecological dry cutting processes without the use of the cutting fluids and in the Near-Net-Shape” technology.Originality/value: Application of multicomponent (Ti,Al)N and gradient Ti(C,N) types of coatings onto sintered tool materials in order to improve cutting properties of tools.
 Journal of Achievements in Materials and Manufacturing Engineering , 2009, Abstract: Purpose: The paper presents investigation results of the structure and mechanical properties of gradient coatings deposited by cathodic arc evaporation - physical vapour deposition (CAE-PVD) techniques onto the X40CrMoV5-1 hot work tool steel, HS6-5-2 high speed steel and SiAlON tool ceramics. The Ti(C,N), (Ti,Al)N and (Al,Si,Cr) N coatings were investigated.Design/methodology/approach: Microstructure was characterised using scanning and transmission electron microscopy. The phase composition of the investigated coatings was determined by means of the X-ray diffractometer. The chemical concentration changes of the coating components, and the substrate material were evaluated in virtue of tests carried out in the GDOS spectrometer. Tests of the coatings’ adhesion to the substrate material were made using the scratch test method.Findings: It was found out that the structure of the PVD coatings deposited onto all substrates is composed of fine crystallites. The investigations made by use of the glow discharge optical emission spectrometer indicate to the existence of the transition zone between the substrate material and the coating. The results show that all coatings present good adhesion. The critical load LC2, which is in the range 35-90 N, depends on the coating type and substrate. Good adhesion of the coatings deposited to the substrate should be connected with the existence of the transition zone. All the coatings are demonstrated by high hardness.Research limitations/implications: Ti(C,N), (Ti,Al)N and (Al,Si,Cr) N gradient coatings can be applied for cutting tools and hot working tools.Originality/value: Working out and testing PVD coatings obtained by tool ceramic and tool steels is a special future of development direction in a domain of thin coatings.
 Jan Chabrowski Opuscula Mathematica , 2009, Abstract: We investigate the solvability of the Neumann problem (1.1) involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side $f$ of the equation belongs to $L^m(\Omega )$ with $1 \leq m < 2$.
 Archives of Materials Science and Engineering , 2011, Abstract: Purpose: The paper presents investigation results of properties of the sintered tool materials: cemented carbides, cermets and Al2O3 type oxide tool ceramics with gradient (Ti,Al)N and Ti(C,N) coatings deposited with the cathodic arc evaporation CAE-PVD method.Design/methodology/approach: Analysis of the mechanical and functional properties: surface roughness, microhardness, adhesion, and wear. Analysis of the structure (SEM). Computer simulation of stresses carried out in ANSYS environment, using the FEM method.Findings: The wear resistant gradient coatings of the type (Ti,Al)N and Ti(C,N) deposited on the investigated sintered tool materials yield a considerable increase of microhardness in the surface area, which, combined with good adhesion of the coating to the substrate, obtained in effect of the application of gradient structure of the coating, has the influence on the applicability properties of these materials during machining tests. A more advantageous distribution of stresses in gradient coatings influence on better mechanical properties. The distribution of stresses on the coating surface has the influence on microhardness, while distribution of stresses in the contact area between the coating and substrate has the influence on the adhesion of coatings.Practical implications: Deposition of hard, thin, gradient coatings on materials surface by PVD method features one of the most intensely developed directions of improvement of the working properties of materials.Originality/value: Techniques of gradient coatings deposition is one of the most spectacular aspect of the materials engineering development in the last years. Uunique combination of substrates and coatings is presented in the paper.
 Kai-Uwe Schmidt Computer Science , 2013, Abstract: The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order nonlinearity of a random Boolean function converges strongly for all r\ge 1. This extends results by Rodier for r=1 and by Dib for r=2. The methods in the present paper are mostly of elementary combinatorial nature and also lead to simpler proofs in the cases that r=1 or 2.
 Journal of Achievements in Materials and Manufacturing Engineering , 2008, Abstract: Purpose: The main aim of researches was investigation of structure and properties of the (Ti,Al,Si)N gradient wear resistant coatings.Design/methodology/approach: The structural investigations include the metallographic analysis on the transmission and scanning electron microscope. Examinations of the chemical compositions of the deposited coatings were carried out using the X-ray energy dispersive spectrograph EDS, glow-discharge optical emission spectroscope GDOES, auger electron spectroscope (AES) and using the X-ray diffractometer. The investigations include also analysis of the mechanical and functional properties of the materials: substrate hardness tests and microhardness tests of the deposited coatings, surface roughness tests, evaluation of the adhesion of the deposited coatings as well as cutting properties.Findings: Deposition of the multicomponent gradient coatings with the PVD method, based on the Al and Si solid secondary solution in the TiN titanium nitride, isomorphous with the alternating pure titanium nitride TiN, on tools made from oxide, nitride ceramics and tool cermets, results in the increase of mechanical properties in comparison with uncoated tool materials, deciding thus the improvement of their working properties.Practical implications: Deposition of (Ti,Al,Si)N nanocrystalline coatings by the use of PVD method causes the increase of cutting properties of tools made of cermets for ca. 300% and of Al2O3+ZrO2 for ca. 100% comparing to adequately uncoated tools.Originality/value: Comparison of the wide range of modern sintered tool materials with wide unique set of PVD coatings.
 Journal of Achievements in Materials and Manufacturing Engineering , 2008, Abstract: Purpose: The paper presents investigation results of structure and properties of the multilayer and gradientTiN+(Ti,Al,Si)N+TiN nanocrystalline coatings deposited with the PVD method (CAE -Cathodic Arc Evaporationprocess) and in the combination of Al2O3 and TiN coatings in the CVD process on the substrate of cemented carbides,cermets, Al2O3+ZrO2, Al2O3+TiC, Al2O3+SiC(w) oxide ceramics and Si3N4 nitride ceramics.Design/methodology/approach: The structural investigation includes the metallographic analysis on thetransmission and scanning electron microscope, confocal microscope. Examinations of the chemicalcompositions of the deposited coatings were carried out using the X-ray energy dispersive spectrograph EDS,glow-discharge optical emission spectroscope GDOS, and using the X-ray diffractometer. The investigationincludes also analysis of the mechanical and functional properties of the material: substrate hardness testsand microhardness tests of the deposited coatings, surface roughness tests, evaluation of the adhesion of thedeposited coatings, cutting properties of the investigated materials.Findings: Deposition of the multicomponent gradient coatings with the PVD method, based on the Al and Si solidsecondary solution in the TiN titanium nitride, isomorphous with the alternating pure titanium nitride TiN, on toolsmade from oxide, nitride ceramics and tool cermets, results in the increase of mechanical properties in comparisonwith uncoated tool materials, deciding thus the improvement of their working properties.Practical implications: Deposition of (Ti,Al,Si)N nanocrystalline coatings by the use of PVD method causesthe increase of cutting properties of tools made of cermets for ca. 300% and of Al2O3+ZrO2 for ca. 100%comparing to adequately uncoated tools.Originality/value: Comparison of the wide range of modern sintered tool materials with wide unique set ofPVD coatings.
 Physics , 1999, DOI: 10.1103/PhysRevE.55.5443 Abstract: The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number of typical data problems. The main result is that the ratings of the different measures vary from example to example. It seems therefore preferable to use an algorithm with good overall performance, that is, higher order autocorrelations or nonlinear prediction errors.
 Computer Science , 2015, Abstract: Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the policy gradient method to the whole class of coherent risk measures, which is widely accepted in finance and operations research, among other fields. We consider both static and time-consistent dynamic risk measures. For static risk measures, our approach is in the spirit of policy gradient algorithms and combines a standard sampling approach with convex programming. For dynamic risk measures, our approach is actor-critic style and involves explicit approximation of value function. Most importantly, our contribution presents a unified approach to risk-sensitive reinforcement learning that generalizes and extends previous results.
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