Contiguous Functions Research Articles

The contiguous function relations for the basic hypergeometric series

De facon analogue aux developpements de Rainville de relations contigues pour la fonction hypergeometrique generalisee on etablit ce type de relations pour la q-extension de cette fonction, la fonction hypergeometrique de base. On donne des applications a des polynomes q-orthogonaux

ChemInform Abstract: Evaluation of the Polar‐Inductive and Mesomeric Effects Exerted by para‐Substituted Phenyl Rings on Contiguous Functionalities.

ChemInformVolume 18, Issue 48 Physical Organic Chemistry ChemInform Abstract: Evaluation of the Polar-Inductive and Mesomeric Effects Exerted by para-Substituted Phenyl Rings on Contiguous Functionalities. E. BARCHIESI, E. BARCHIESI Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this authorS. BRADAMANTE, S. BRADAMANTE Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this authorG. A. PAGANI, G. A. PAGANI Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this author E. BARCHIESI, E. BARCHIESI Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this authorS. BRADAMANTE, S. BRADAMANTE Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this authorG. A. PAGANI, G. A. PAGANI Dip. Chim. Org. Ind., Univ., 20133 Milano, ItalySearch for more papers by this author First published: December 1, 1987 https://doi.org/10.1002/chin.198748042Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume18, Issue48December 1, 1987 RelatedInformation

ChemInform Abstract: Evaluation of the Polar‐Inductive and Mesomeric Effects Exerted on Contiguous Functionalities by N‐Oxidopyridinium Groups

The polar–inductive and mesomeric effects (and mixtures thereof) of N-oxidopyridinium-2-, -3-, and 4-yl functionalities have been evaluated in terms of the σIB, σR–, and σ scales previously defined. Values were generated from the phenyl para-13C shifts of PhCH2C5H4NO and PhNHC5H4NO, respectively. The parameters obtained successfully account for the phenyl para-13C shifts of the sodium salts of anilinopyridine 1-oxides (VII), prepared in turn by deprotonation of the corresponding precursor nitrogen acids by sodium methylsulphinylmethanide. Results show that the N-oxidopyridinium ring exerts considerably more electron-withdrawing power, by both polar–inductive and mesomeric mechanisms, than in the absence of the N-oxide function.

On some generalizations of Ramanujan’s continued fraction identities

In this note we establish continued fraction developments for the ratios of the basic hypergeometric function2ϕ1(a,b;c;x) with several of its contiguous functions. We thus generalize and give a unified approach to establishing several continued fraction identities including those of Srinivasa Ramanujan.

Evaluation of the polar-inductive and mesomeric effects exerted by para-substituted phenyl rings on contiguous functionalities

The para C-13 shifts of the phenyl ring in PhCH2Ar (I) is used as a monitor to evaluate, in terms of the previously defined σIB constants, the polar-inductive effect exerted by some para-substituted aryl rings. Analogously, the para C-13 shift of the phenyl ring in PhNHAr (IV) is used as a monitor to evaluate, in terms of the previously defined σC– constants, the blended polar-inductive and mesomeric effects exerted by such para-substituted aryl rings. The same para C-13 data offer access, through a biparametric (DSP) treatment, to σR– constants, which account for the mesomeric effects exerted by the same substituents. C-13 Shifts data are also reported for the 4′-substituted sodium aryl(phenyl)amides PhN–Ar (VII) which have been prepared in Me2SO by deprotonation of PhNHAr. The σC– values just obtained account successfully for the para C-13 shifts of the phenyl ring of (VII), for the para C-13 shifts of the phenyl ring of phenylhydrazones of para-substituted benzaldehydes, and for the acidity of aryl(phenyl)amines measured in Me2SO–H2O by Dolman and Stewart. The success of the biparametric treatment is limited by the small range of the σIB values of the para-substituted aryl derivatives and by the scarcity of data. The σIB set is linearly related to the set of σI constants obtained from substituted acetic acids. Both the σIB and the σC– sets account successfully for the acidity of para-substituted benzoic acids in H2O, in Me2SO, and in the gas phase: a rationale is given.

Evaluation of the polar–inductive and mesomeric effects exerted on contiguous functionalities by N-oxidopyridinium groups

The polar–inductive and mesomeric effects (and mixtures thereof) of N-oxidopyridinium-2-, -3-, and 4-yl functionalities have been evaluated in terms of the σIB, σR–, and σ scales previously defined. Values were generated from the phenyl para-13C shifts of PhCH2C5H4NO and PhNHC5H4NO, respectively. The parameters obtained successfully account for the phenyl para-13C shifts of the sodium salts of anilinopyridine 1-oxides (VII), prepared in turn by deprotonation of the corresponding precursor nitrogen acids by sodium methylsulphinylmethanide. Results show that the N-oxidopyridinium ring exerts considerably more electron-withdrawing power, by both polar–inductive and mesomeric mechanisms, than in the absence of the N-oxide function.

Substituent effects in α-substituted carbanions

The para13C shifts of benzylcarbanions PhCH–X (VI) in Me2SO, acidities of toluene carbon acids PhCH2X (I) in Me2SO, and gas-phase acidities of methane carbon acids CH3X (VIII) are submitted to mono- and bi-parametric substituent treatment using previously defined sets of σc–, σIB, and σR– constants. It is confirmed that these scales are appropriate for describing interactions between contiguous functionalities, as opposed to literature values which account for remote interactions. Gas-phase acidities respond excellently to substituent effect treatment, while solution data show deviations for the SO2R and CN substituents. Such deviances are accounted for as a manifestation of SSSAR (Stabilization due to Specific Solvent Assisted Resonance) for groups which exhibit extensive charge transfer from the carbanionic carbon to the π-accepting substituent (COR, CO2R, CONMe2, NO2, etc.). The mesomeric component of substituent effects is about three times more important than the polar–inductive one in governing the acidities of carbon acids in Me2SO solution and in affecting the chemical shift of the para monitor in PhCH–X. Relative to the gas phase, the solvent enhances by a factor of 2 the sensitivity of acidities of carbon acids to the mesomeric components of substituent effects. The sensitivity of the para monitor in PhCH–X to polar–inductive components of substituent effects shows, relative to the neutral precursor PhCH2X (I), a three-fold increase and, relative to the PhNHX family, a two-fold increase. The sensitivity of the para monitor in PhCH–X to mesomeric components of substituent effects shows a three-fold increase relative to the PhNHX family.

Additions and Corrections - Substituent Effect Treatment of Interactions between Contiguous Functionalities G-X. Remote Response to Polar and Inductive Influence of X on G = C(sp3) and -N<.

Additions and Corrections - Substituent Effect Treatment of Interactions between Contiguous Functionalities G-X. Remote Response to Polar and Inductive Influence of X on G = C(sp³) and -N<.

ChemInform Abstract: SUBSTITUENT EFFECT TREATMENT OF INTERACTIONS BETWEEN CONTIGUOUS FUNCTIONALITIES G‐X. PART 1. REMOTE RESPONSE TO POLAR AND INDUCTIVE INFLUENCE OF X ON G = C(SP(3)) AND ‐N.LTBBRAC.

Chemischer InformationsdienstVolume 11, Issue 25 Physical Organic Chemistry ChemInform Abstract: SUBSTITUENT EFFECT TREATMENT OF INTERACTIONS BETWEEN CONTIGUOUS FUNCTIONALITIES G-X. PART 1. REMOTE RESPONSE TO POLAR AND INDUCTIVE INFLUENCE OF X ON G = C(SP(3)) AND -N.LTBBRAC. S. BRADAMANTE, S. BRADAMANTESearch for more papers by this authorG. A. PAGANI, G. A. PAGANISearch for more papers by this author S. BRADAMANTE, S. BRADAMANTESearch for more papers by this authorG. A. PAGANI, G. A. PAGANISearch for more papers by this author First published: June 24, 1980 https://doi.org/10.1002/chin.198025082Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume11, Issue25June 24, 1980 RelatedInformation

Substituent effect treatment of interactions between contiguous functionalities G-X. 2. Remote response to polar-inductive and mesomeric influence of X on G = -O- and -NH-

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSubstituent effect treatment of interactions between contiguous functionalities G-X. 2. Remote response to polar-inductive and mesomeric influence of X on G = -O- and -NH-Silvia Bradamante and Giorgio A. PaganiCite this: J. Org. Chem. 1980, 45, 1, 114–122Publication Date (Print):January 1, 1980Publication History Published online1 May 2002Published inissue 1 January 1980https://doi.org/10.1021/jo01289a022RIGHTS & PERMISSIONSArticle Views830Altmetric-Citations19LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts

Sequential contiguity and short-term memory in children's discrimination learning

In two experiments preschool children's performance on a successive discrimation was an increasing function of sequential contiguity (the probability that presentation of a given stimulus is followed by another presentation of that same stimulus rather than by presentation of a different stimulus). An explanation of this sequential contiguity effect in terms of short-term memory processes received considerable support.

Coupling of three angular momenta

Some earlier results on the coupling of two angular momenta are extended in the present paper to three angular momenta. As in the previous case, the eigenfunctions with sharp total angular momentum are obtained in closed forms which do not contain the Clebsch-Gordan coefficients explicitly. The occurrence of the hypergeometric function in the present formulation renders the treatment highly flexible and makes it possible to derive a number of alternative expressions for the 6 —j symbol. Moreover, recursion relations between contiguous 6 —j symbols are derived more easily from Gauss’s relations between contiguous hypergeometric functions.

Concept attainment as a function of instance contiguity and number of irrelevant dimensions.

Concept attainment as a function of instance contiguity and number of irrelevant dimensions.

On the representations of the group SU(3)

By a generalization of techniques developed earlier for dealing with the three-dimensional rotation group O3 the generators of the group SU(3) are expressed as differential operators involving four independent variables. The reduction in the number of variables simplifies the mathematical problem and makes it easier to study the properties of the group and its irreducible representations. From the forms of the new operators it becomes apparent that the basic states of an irreducible representation of SU(3) are linear combinations of Clebsch-Gordan series of SU(2) (or O3). A convenient expression for the latter, which simplifies the derivation and also brings out the significance of certain steps more clearly, is obtained here by a proper interpretation of the results given in an earlier paper by the author. Besides this certain recursion relations for the Clebsch-Gordan coefficients of SU(2) are also found to be helpful for studying the SU(3) representations. These relations are derived in a novel way from Gauss's relations between contiguous hypergeometric functions.

Recurrence relations for oscillator-well radial integrals

ABSTRACTThe general radial integral between oscillator-well wave-functions with a Gauss interaction potential is expressed as a generalized hypergeometric function. A relation between contiguous functions is found and used to obtain a recurrence relation between these integrals.

Effect of Lack of Visual Stimulus Variation on Exploratory Behavior in the Adult White Rat

The idea that organisms often are motivated to seek external stimulation for its own intrinsic value, apart from serving any apparent biological need, is not a new one. However, present day explanations of the mechanism behind exploratory behavior are at sharp variance with one another. . Myers and Miller (6) conceive of exploratory behavior as a function of an internal drive stimulus rather than one external to the organism. As tension-reductionists, they argue that exploratory behavior is motivated by a disequilibrium within the organism and can be categorized with the primary drives of hunger, thirst, and sex. They maintain that a monotonous environment produces a tension state called boredom which is capable of initiating motor behavior leading to new stimuli, thereby increasing sensory variation. Boredom, as a persistent stimulus, is consequently reduced, and the behavior is reinforced. However, Harlow ( 3 ) contends that exploratory and manipulatory behaviors are functions of drives unlike the classical ones of sex, hunger, and thirst. He argues that they are not homeostatic and that their source of stimulation originates outside the organism. This stimulation initiates the behavior, sustains it, and also serves as a reward. Any resultant learning is a function of contiguity rather than drive reduction. Hence his explanation of exploratory behavior emphasizes the role of externally elicited motives. One way of testing the foregoing hypotheses is to deprive the animal of those stimuli which are assumed to reward or establish exploratory behavior. Berlyne ( 1) reported that 10 min. of confinement had no effect on exploratory behavior in the rat. In a developmental type study, Montgomery and Zimbardo (5) found that depriving rats of stimulus variation for relatively long periods after weaning had no effect on subsequent exploratory behavior. Butler (2) discovered that short stimulus-deprivation periods served to increase exploratory behavior in the Rhesus monkey. The conflicting results reveal clearly the necessity of further investigation. The purpose of this experiment was to determine whether a relatively

The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)

The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)