Max-min fuzzy reasoning


The take-home lesson is that the vast majority of high-pressure studies are on solids or other rigid media and are not done under hydrostatic conditions. The stresses and stress-related properties may vary throughout the sample. Unless the probes are very local and focus on a small region of the sample, measurements are averages over a range of, often uncharacterized, conditions.  [c.1956]

Another way to overcome the step-size restriction fc < is to use multiple-time-stepping methods [4] or implicit methods [17, 18, 12, 3). In this paper, we examine the latter possibility. But for large molecular systems, fully implieit methods are very expensive. For that reason, we foeus on the general class of scmi-implicit methods depicted in Fig. 1 [12]. In this scheme. Step 3 of the nth time step ean be combined with Step 1 of the (n - - l)st time step. This then is a staggered two-step splitting method. We refer to [12] for further justification.  [c.289]

We focus on so-called symplectic methods [18] for the following reason It has been shown that the preservation of the symplectic structure of phase space under a numerical integration scheme implies a number of very desirable properties. Namely,  [c.412]

Starting from this situation, we have applied total energy calculations, using the first principles Cax-Parrinello method, to a crystal unit cell of orthorhombic polyethylene (see Fig. 4). Because of the application of periodic boundary conditions the system may be considered as an infinite, perfect, crystal. The Car-Parrinello method employs the density functional formalism. Basis set convergence may be demonstrated by increasing the plane-wave cut-off energy, as we will show below. The fact that the calculation of the Young s modulus involves elongation of the unit cell box in one direction, one may anticipate problems with the use of a finite plane wave basis at the interfaces between the boxes. Indeed, when not accounting for this problem a significant scatter of the energy is found as a function of box length a correction due to Francis and Payne [18] resolves this problem. The resulting total energy curve as function of elongation of the box length is shown in Fig. 5, and from the curvature at the minimum the Young s modulus can be obtained [19,20]. Basis set convergence was tested and the calculated Young s moduli for a crystal structure slightly different from that displayed in Fig. 4 are shown in Fig. 6. It is observed that the value for the modulus initially fluctuates as a function of basis set size, which might be the reason that some Hartree-Fock based values were found to be low compared to the highest experimental value reported. For the correct experimental geometry of orthorhombic polyethylene at T = 4 K we evaluated a value for the Young s modulus of 334 GPa, whereas optimization of the crystal structure with the computational tools led to a value of 366 GPa. The difference is acceptable and, more importantly, the values are above the available experimental values, and in the range usually found when attempting to extrapolate experimental values to the ideal, perfectly drawn, material.  [c.438]

Quantitative analysis. Spectroscopic analysis is widely used in the analysis of vitamin preparations, mixtures of hydrocarbons (e.y., benzene, toluene, ethylbenzene, xylenes) and other systems exhibiting characteristic electronic spectra. The extinction coefficient at 326 mp, after suitable treatment to remove other materials absorbing in this region, provides the best method for the estimation of the vitamin A content of fish oils.  [c.1149]

Inspired by the many hydrolytically-active metallo enzymes encountered in nature, extensive studies have been performed on so-called metallo micelles. These investigations usually focus on mixed micelles of a common surfactant together with a special chelating surfactant that exhibits a high affinity for transition-metal ions. These aggregates can have remarkable catalytic effects on the hydrolysis of activated carboxylic acid esters, phosphate esters and amides. In these reactions the exact role of the metal ion is not clear and may vary from one system to another. However, there are strong indications that the major function of the metal ion is the coordination of hydroxide anion in the Stem region of the micelle where it is in the proximity of the micelle-bound substrate. The first report of catalysis of a hydrolysis reaction by me tall omi cell es stems from 1978. In the years that  [c.138]

Instead of probability distributions it is more common to represent orbitals by then-boundary surfaces, as shown m Figure 1 2 for the Is and 2s orbitals The boundary sur face encloses the region where the probability of finding an electron is high—on the order of 90-95% Like the probability distribution plot from which it is derived a pic ture of a boundary surface is usually described as a drawing of an orbital  [c.8]

Let s focus our attention on a portion of Figure 3 4 The region that lies between a torsion angle of 60° and 180° tracks the conversion of one staggered conformation of ethane to the next one Both staggered conformations are equivalent and equal m energy but for one staggered conformation to get to the next it must first pass through an eclipsed conformation and needs to gam 12 kJ/mol (2 9 kcal/mol) of energy to reach it This amount of energy is the activation energy for the process Molecules must become energized m order to undergo a chemical reaction or as m this case to undergo rotation around a carbon-carbon bond Kinetic (thermal) energy is absorbed by a molecule from collisions with other molecules and is transformed into potential energy When the potential energy exceeds the unstable arrangement of atoms that exists at that instant can relax to a more stable structure giving off its excess potential energy m collisions with other molecules or with the walls of a container The point of maximum potential energy encountered by the reactants as they proceed to products is called the transition state The eclipsed conformation is the transition state for the conversion of one staggered conformation of ethane to another  [c.108]

Let s begin by choosing a simple quantitative problem requiring a single measurement. The question to be answered is—What is the mass of a penny If you think about how we might answer this question experimentally, you will realize that this problem is too broad. Are we interested in the mass of United State pennies or Canadian pennies, or is the difference in country of importance Since the composition of a penny probably differs from country to country, let s limit our problem to pennies minted in the United States. There are other considerations. Pennies are minted at several locations in the United States (this is the meaning of the letter, or absence of a letter, below the date stamped on the lower right corner of the face of the coin). Since there is no reason to expect a difference between where the penny was minted, we will choose to ignore this consideration. Is there a reason to expect a difference between a newly minted penny not yet in circulation, and a penny that has been in circulation The answer to this is not obvious. Let s simplify the problem by narrowing the question to—What is the mass of an average United States penny in circulation This is a problem that we might expect to be able to answer experimentally.  [c.54]

Although gas chromatography is widely used, it is limited to samples that are thermally stable and easily volatilized. Nonvolatile samples, such as peptides and carbohydrates, can be analyzed by GC, but only after they have been made more volatile by a suitable chemical derivatization. For this reason, the various techniques included within the general scope of liquid chromatography are among the most commonly used separation techniques. Although simple column chromatography, first introduced by Tswett, is still used in large-scale preparative work, the focus of this section is on high-performance liquid chromatography (HPLC).  [c.578]

A magnetic-sector instrument separates ion.s according to their m/z values but, unlike the quadrupole, by dispersing them in space (Figure 28.1b). Having dispersed the ions, their arrival can be recorded over a region of space (array detection) or, by increasing (or decreasing) the magnetic field, the ions can be brought sequentially to a focus (point detection). Either point or array detectors are used with magnetic instruments.  [c.201]

In the third field-free region, all of the fields affecting the motion of an ion have been passed through on its way to the collector. A metastable ion mj fragmenting in this region gives an ion mj as before, but, because all ion separations have been done, the mj ions arrive at the same focus as their precursor ions m,. There is only one way to differentiate them, and that is to make use of their kinetic energies. A normal ion mj arriving at the collector has kinetic energy zeV, but a product ion mj from decomposition of metastable m, ions has only kinetic energy (m2/m,)zeV = zeV, in which V < V. A special ion collector can be used to differentially reflect normal and metastable ions by control of an ion repeller voltage. Both normal and metastable ion spectra can be scanned by adjusting the repeller voltage. However, because this method requires a different ion collector than those normally used in mass spectrometry, it is a little-used technique, especially as more convenient linked scanning gives similar information on connections between ions.  [c.240]

Extreme Uv (Euv) Lithography. This term denotes a projection hthography system designed to use light of wavelength near 13 nm (the soft x-ray region), produced by irradiation of a metal target with a pulsed uv laser (129). At this wavelength, high resolution imaging can be achieved while maintaining acceptable depth of focus if imaging optics with a low numerical aperture are used. However, this is accompanied by a number of technical challenges, including the development of new x-ray sources, an ah-redective optical design and a new type of redective mask suitable for soft x-ray imaging (Fig. 40). Proponents of euv Hthography predict resolution scalable to 0.07 microns while maintaining a large depth of focus.  [c.135]

Pressed wheels are heat-treated to fuse the ceramic bond or cure the resin bond. Ceramic-bonded wheels are fired to about 1250°C in continuous tunnel or periodic kilns, and resin-bonded ones are baked in periodic ovens at 175 to 200°C. After firing or baking, the wheels are checked for proper dimension, density, and modulus of elasticity, and sometimes for sandblast resistance to assure proper grade. These slightly oversize wheels are then finished, ie, machined to final size. To achieve desired thickness, the wheel sides are mbbed under heavy pressure on large rotating steel tables charged with steel shot. Diameter reduction is accompHshed using rotating conical steel cutters mounted in a lathe post holder. Holes may be tmed using conical cutters or diamond tools but many times they are simply bushed with a plastic, lead, or sulfur compound by pouring or injection mol ding.  [c.15]

Crush-Form Grinding Wheels. In cmsh-form grinding, a rotating, contoured cmshing wheel is forced into the face of a revolving vitrified wheel, cmshing the face to the exact contour needed on the metal object to be ground. The contoured wheel is then placed in production and when wear or dulling occurs, the face is again cmshed to regain proper contour. Many parts formerly turned with metal-cutting tools and then surface ground are now shaped and surface finished in one pass of a cmsh-formed wheel.  [c.15]

Now, breakthrough technology for creating computer-synthesized holograms, including the flat optical element for forming hidden images, has been developed in Russia. We have created devices both for visualization of hidden images and for automatic, indestructible control of computer-synthesized holograms The principles of automatic control of hidden images are based on pattern recognition theory. The technology is the result of cooperation between Moscow State University and the Federal Agency for Government Communication and Information under the President of the Russian Federation (FAGCI).  [c.268]

Fig. XV-11. Electron micrograph of a freeze fracture replica of a region inside a mul-tivesicular liposome. Note the tetrahedral coordination nearly every vertex has three edges, and each face is connected to three others. The average number of edges per face is 5.1. (From Ref. 77.) Fig. XV-11. Electron micrograph of a freeze fracture replica of a region inside a mul-tivesicular liposome. Note the tetrahedral coordination nearly every vertex has three edges, and each face is connected to three others. The average number of edges per face is 5.1. (From Ref. 77.)
The rather complicated issues raised in the preceding paragraph are central to the subject of quantum mechanics, and their resolution fonus the basis of one of the most unportant postulates associated with the Schrodinger fomuilation of the subject. In the example above, discussion focuses entirely on the eigenvalues of the momentum operator. What significance, if any, can be attached to the eigenfiinctions of quantum-mechanical operators In the interest of simplicity, the remainder of this subsection will focus entirely on the quantum mechanics associated with operators that have a finite number of eigenvalues. These are said to have a discrete spectrum, in contrast to those such as the linear momentum, which have a continuous spectrum. Discrete spectra of eigenvalues arise whenever boundaries limit the region of space in which a system can be. Examples are particles in hard-walled boxes, or sofi-walled shells and particles attached to springs. The results developed below can all be generalized to the continuous case, but at the expense of increased mathematical complexity. Readers interested in these details should consult chapter 1 of Landau and Lifschitz (see additional reading).  [c.8]

Since the pseudopotential does not bind the core states, it is a very weak potential. Simple basis functions can be used to describe the pseudo-wavefiinctions. For example, a simple grid or plane wave basis will yield a converged solution [25]. The simplicity of the basis is important as it results in an unbiased, flexible description of the charge density. Also, since the nodal structure of the pseudo-wavefunctions has been removed, the charge density varies slowly in the core region. A schematic model of tire pseudopotential model is illustrated in figure Al.3.10. The pseudopotential model describes a solid as a sea of valence electrons movmg in a periodic background of cores (composed of nuclei and inert core electrons). In this model many of the complexities of all-electron calculations, calculations that include the core and valence electrons on an equal footing, are avoided. A group IV solid such as C with 6 electrons per atom is treated in a similar fashion to Sn with 50 electrons per atom since both have 4 valence electrons per atom. In addition, the focus of the calculation is only on the accuracy of the valence electron wavefunction in the spatial region away from the chemically inert core.  [c.108]

Although the primary focus of this article is on quantum scattermg theory, it is unportant to note that classical and semiclassical approximations play an important role in the application of scattering theory to problems in chemical physics. The primary reason for this is that the de Broglie wavelength associated witii motions of atoms and molecules is typically short compared to the distances over which these atoms and molecules move during a scattering process. There are exceptions to this of course, in the limits of low temperature and energy, and for light atoms such as hydrogen atoms, but for a very broad sampling of problems the dynamics is close to the classical limit.  [c.994]

The total depth of focus is the sum of both. It mcreases with the wavelength of the light, depends on the numerical aperture and the magnification of the microscope. For X = 550 mn, a refractive index of 1 and a numerical aperture of 0.9, the depth of focus is in the region of 0.7 pm with a numerical aperture of 0.4 it increases to about 5 pm. Fligh-resolution objectives exclude the observation of details in the axial direction beyond their axial resolution. This is tnie for conventional microscopy, but not for scaiming confocal microscopy, since optical sectioning allows successive layers in the bulk to be studied. Similarly, the field of view decreases with increasing resolution of the objective in conventional microscopy, whereas it is independent of resolution in scaiming microscopy.  [c.1660]

Infrared spectroscopy has also been widely employed in electrochemistry [105. 106. and 107]. Spectra aid the identification of reactants, of products and of long-lived intennediates and allow changes in the interfacial solvent to be tracked. A variety of spectral sampling and data acquisition methods have been developed to approach in situ detection of species. In external reflection sampling methods, the infrared beam is directed tlnough a polarizer onto the front surface of a highly polished disc-shaped working electrode witli high reflectivity in the infrared spectral region, such as Pt, An or Ag. A special, thin-layer electrochemical cell is used that pennits the infrared beam to enter and strike the disc, where it is reflected out of the cell and detected. In contrast, in attenuated total internal reflection sampling methods, the working electrode is a thin film of metal deposited on one surface of an ATR crystal. The metal film must be sufiBciently thin to allow penetration of the IR evanescent wave beyond the metal solution interface. The ATR crystal fomis the bottom of a chamber that holds the electrolyte solution and the counter and reference electrodes and the crystal is positioned so that the metal film is inside the chamber. This method has not been widely used in electrochemistry partly due to the diflSculty in the preparation of the thin metal film working electrodes. Nonetheless, the latter design overcomes molecular transport limitations imposed by external reflection methods, where a thin solution layer of the order 1-5 pm between the front face of the working electrode and the infrared transparent window is required to minimize absorption of infrared radiation by tlie solvent. In fact, diflfiision of species into and out of the thin-layer region is restricted and can lead to reactant depletion or product accumulation.  [c.1948]

Foggi P, Pettini L, Santa I, Righini R and Califano S 1995 Transient absorption and vibrational relaxation dynamios of the lowest exoited singlet state of pyrene in solution J. Phys. Chem. 99 7439-45  [c.3049]

In this section there is an attempt to give a compact overview of currently available force fields however, it is by no means complete, as in this context it is not possible to mention every feature or functionality (minimization, dynamics, polarization, periodic boundaries, free energies, treatment of long-range electrostatics, water models, NMR restraints, QM/MM capabilities, etc.) implemented in the various packages. For further information, readers should consult the references or web sites dted. Mindful readers may recognize that the well-known, mainly commercial modeling packages, which all include implementations of one or more force fields, have largely been omitted. The reason is that the focus of this compilation is on the different parameterizations, and not on their implementation.  [c.349]

When Lhe Direct SCT calciihilion option is chosen, the Lwo-elec-iroii integrals are recoin pined in every iteraLion. A Direct SCT calculation will be con siderably slower th an a regn lar SCFcalculation which computes all the two-electron integrals and then saves them, retrieving the saved in tegrals every iteration to form the Fock matrices. The Direct SCF calculation avoids using disk space or a large main memory. This option may be practical for large molecular systems run on a desk-top PC where there is little available space on th e disk.  [c.115]

Method 1. Twenty-three grams of clean sodium (most conveniently weighed under sodium-dried ether after the surface coating has been cut away with a knife) are introduced into a 750 or 1000 ml. round-bottomed Pyrex fiask containing about 200 ml. of sodium-dried xylene or at least suflScient xylene to cover the sodium completely. The flask is placed on a sand bath supported on a ring burner. Two or three thiclmesses of dry cloth (or a thick towel), sufficient to envelop the whole fiask, are placed in a convenient position on the bench. The sand bath is heated cautiously and the ring of condensed vapour of the xylene is carefully watched. When the ring of condensed vapour has risen to wdthin one inch from the neck of the flask, the flame beneath the burner is extinguished, a well-fitting rubber stopper or good quality bark cork is rapidly introduced, the flask is completely wrapped in the previously prepared cloth and shaken vigorously for 30-60 seconds or until the molten sodium is converted into a fine powder. The flask is then placed on a suberite ring and the stopper is removed. The sodium is thus obtained in the form of small spheres, the size of which is controlled by the time and rapidity of the shaking. Any particles of sodium adhering to the sides of the fiask are washed under the xylene. When the contents of the fiask have cooled to room temperature, the xylene may be decanted and the sodium washed twice with 100 ml. of sodium-dried ether to remove traces of xylene finally the finely-divided sodium is covered with absolute ether. A bucket, half-full of dry sand, should be kept at hand in case of breakage of the fiask. Not more than 25-30 g. of sodium should be powdered at one time by this procedure.  [c.193]

But this method has been generating more rabid attention than any other in the underground. Feck sent Strike some articles on it. Osmium emailed Strike some of the same references [56, 57]. Everyone is talking about it. And for good reason. It is essentially the second generation of reductive amination using superclean, gentle catalysts. Just think of it as Method 1 - except that the NaBHaCN has been replaced by a more workable catalyst Sodium Triacetoxyborohydride [NaBH(OAc)3].  [c.120]

The relative amounts of the two products however are not equal more as 1 2 dimethyl cyclohexane is formed than trans The reason for this is that it is the less hindered face of the double bond that approaches the catalyst surface and is the face to which hydro gen IS transferred Hydrogenation of 2 methyl(methylene)cyclohexane occurs preferen tially at the side of the double bond opposite that of the methyl group and leads to a faster rate of formation of the cis stereoisomer of the product  [c.309]

Arc lamps are more efficient than incandescent light sources and radiate from a small region of space, so the light is much easier to focus or collimate than is the light from a heated filament. For that reason — and the possibility of obtaining an intense light beam — arc lamps are used for many purposes, as in photolithography, photocuring of polymers, or theater lighting, but they cannot match the laser for the amount of energy deposited into a small space in a short time.  [c.123]

Radiotelescopes are used to scan the universe for radiation in the radioffequency region of the spectrum (see Figure 3.1). As illustrated in Figure 5.11 such a telescope consists of a parabolic reflecting dish which focuses all parallel rays reaching it onto a radiofrequency detector supported at the focus of the paraboloid. The surface of such a dish must be constructed accurately but only sufflciently so that the irregularities are small compared with the wavelength of the radiation, which is of the order of 0.5 m.  [c.119]

Limitations. The number of transistors present on a chip has doubled approximately every 18 months skice the kitegrated ckcuit was fkst developed (a rate of kicrease predicted by Gordon Moore of Intel Corporation ki 1960 that has become known as Moore s law). The main reason for this continuing decrease ki the minimum feature sizes of transistors (and consequent kicrease ki density of transistors on the chip) has been the development of photohthography, the prototypical reductive method (7,15,16,81—83). PhotoUthography creates patterns ki layers of siUcon, kisulators, and metals to produce the kitegrated ckcuit. For the accurate reproduction of features onto the siUcon wafer, the wavelength of light used must be at least as small as the smallest feature size (eg, feature resolution varies as the wavelength of light used and is kiversely proportional to the aperture of the objective lens and the depth of focus (DOF), requiring innovative solutions in planarization technologies and mask design). Other issues related to further scaling down of integrated ckcuits include the effects of power supply and threshold voltage of the transistors, short channel lengths, thickness of the gate oxide, high electric fields, fluctuations in the number of dopant atoms, and interconnect delays (7,84). The most important limitation for further size reduction, however, remains the development of new photo- and other Hthographic techniques.  [c.203]


See pages that mention the term Max-min fuzzy reasoning : [c.3031]    [c.307]    [c.437]    [c.678]    [c.1229]    [c.1976]    [c.2277]    [c.2492]    [c.499]    [c.279]    [c.113]    [c.154]    [c.174]    [c.357]    [c.473]    [c.516]    [c.309]    [c.347]    [c.395]    [c.203]   
Advanced control engineering (2001) -- [ c.333 ]