Cardinal functions

By this requirement this polynomial is uniquely defined though there are many different ways to represent it. For theoretical purposes the Lagrange formulation is convenient. There, Trj is combined of basis polynomials, so-called cardinal functions l t)... 

An important property of a fuzzy set is its cardinality. While for crisp sets the cardinality is simply the number of elements in a set, the cardinality of a fuzzy set A, CardA, gives the sum of the values of the membership function of A, as in Eq. (9). 

A trivial reversible CA consists of a collection of completely isolated systems each site contains only itself in its neighborhood. Since a7 = 1, the rule table and site value sets have the same cardinality. In particular, if the function 21,—> Z is invertible (i.e. if 4> serves merely to permute the elements of the set Zk) then the global CA system is itself reversible. More formally, writing < = tt H/ci where... 

Criteria 1-3 are the cardinal characteristics of Fickian diffusion and disregard the functional form of D(ci). Violation of any of these is indicative of non-Fickian mechanisms. Criterion 4 can serve as a check if the D(ci) dependence is known. As mentioned, it is crucial that the sorption curve fully adhere to Fickian characteristics for a valid determination of D from the experimental data. At temperatures well above the glass transition temperature, 7 , Fickian behavior is normally observed. However, caution should be exercised when the experimental temperature is either below or slightly above 7 , where anomalous diffusion behavior often occurs. 

GM Zentner, JR Cardinal, J Feijen, S-Z Song. Progestin permeation through polymer membranes. IV. Mechanism of steroid permeation and functional group contributions to diffusion through hydrogel films. J Pharm Sci 68 970-975, 1979. 

A cardinal role for IL-4 in host protection against intestinal nematode infection was first shown in the H. polygyrus challenge model. Worm expulsion was delayed following treatment with anti-IL-4 or anti-IL-4 receptor monoclonal antibodies, while control treated animals successfully cleared infection (Urban et al., 1991b). Blockade of the IL-4 receptor effectively prevents the in vivo function of IL-4 and IL-13, as these two cytokines share the IL-4 receptor a-chain for signalling functions (Lin et al, 1995). In... 

Theory Cortisol (or hydrocortisone) was introduced in the year 1951, for the treatment of rheumatoid arthritis. It has a significant effect on protein metabolism. It also exerts widespread effects on carbohydrates, lipid and protein synthesis (or anabolism). The cardinal side effects such as excessive potassium excretion and sodium retention, enhanced gastric acidity, oedema, psychosis and negative nitogen balance are some of the exaggerated manifestations of the normal metabolite functions of cortisol. 

Idzko M. Hammad H, van Nimwegen M, Kool M, Vos N, Hoogsteden HC, Lambrecht BN Inhaled iloprost suppresses the cardinal features of asthma via inhibition of airway dendritic cell function. J Clin Invest 2007 II7 464-472. 

Dunning s correlation consistent basis sets cc-pVAZ [27] augmented with diffuse functions [28] were used in the calculations. We considered cardinal numbers X—D, T, Q, 5, 6 and single (s), double (d), triple (t), and quadruple (q) augmentations. The orbitals were not allowed to relax in the coupled cluster response calculations. 

Cell migration and invasion are cardinal properties of NSCs and CSCs, respectively. Assessing the effect of drugs on these functional parameters is therefore of paramount preclinical relevance. A Matrigel invasion assay, performed in Transwell chambers, represents the most advantageous and efficient method. 

The extreme forms, but not the intermediate forms, of asymmetric similarity defined by Tversky (6) given in Eqs. 2.26 and 2.27 can be transformed into two symmetric measures by taking the maximum and minimum of the set cardinalities in the denominators of the two equations. The forms of these equations are obtained in analogy to those developed by Petke (33) for vectors and field-based functions (see Subheadings 2.3. and 2.4. for further details) ... 

Alzheimer s disease, the most prevalent form of dementia, afflicts approximately 10% of the population over age 65. The cardinal features of Alzheimer s disease are progressive loss of memory and disordered cognitive function. Alterations in behavior and a decline in Ian-... 

Parkinson JA, Dailey JW, Cardinal RN, Bamford A, Fehnert B, Lachenal G, Rudarakanchana N, Halkerston KM, Robbins TW, Everitt BJ (2002) Nucleus accumbens dopamine depletion impairs both acquisition and performance of appetitive Pavlovian approach behavior implications for mesoaccumbens dopamine function. 

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