Top PDF Advanced second order functional differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University
ferential equations is well-posed, but the same problem for the advancedfunctionaldifferentialequations is ill-posed. In other words, while the initial value problem with a retarded equation has a unique solution, the initial value problem with an advanced equation has an infinite number of infinitely differentiable solutions. This makes it possible to prescribe additional conditions for advancedequations. Another fundamental difference between the equations is that there is an entire solution to the retarded problem, but there is no solution to the advanced problem which is holomorphic at the origin. Whereas the retarded problem has power series solu tions, the advanced problem can have (among other solution forms) Dirichlet series solutions. The asymptotics, as x -t 00, of the retarded and the advanced problem
The no t ion o f d i s course i s advanced by Habermas as t he mos t approp r i a t e form of argumen t a t ion . The ac t of par t i c i pa t i ng i n any d i scourse car r i es wi t h i t the suppos i t ion that there is a communi ty of inqui rers and fur thermore , that a genu ine agreemen t or consensus among t he par t i c i pan t s i s poss ible . I f we did no t suppose that a grounded consensus were poss ible and could in some way be d i s t i ngu i shed from a false consensus , then the very mean ing of d i scourse would be cal led i n t o ques t i on . In at temp t i ng to arr ive at a ra t i onally mo t i va t ed unders tanding we assume that everyone who speaks a na tural language i s i n t u i t ively fam i l iar wi th i t and t rus t h i m o r hersel f t o d i s t ingu ish a t rue f rom a false consensus ( 62 ) . To come to a ra t i onal dec i s ion about such ma t ters we mus t presume t hat t he ou t come of d i s course w i l l res t on the force of the be t ter argumen t and no t upon acc iden tal or sys t ema t i c cons t rain t s o n d iscuss ion . Habermas main tains that the s t ructure o f communi ca t ion i s free f rom cons t raint when all par t i c i pan ts have t he s ame oppor tuni ty to selec t and employ speech ac t s , and when there i s an e f fec t ive equali ty in the assump t i on of dialogi cal roles ( 63 ) . I t i s t h i s commi tment t o consider all individuals as po t ent ial par t i c i pan t s i n d i s course whi ch presupposes a universal commi tmen t to the i nheren t equal i ty , au t onomy , and ra t ional i ty , of human beings .
1 9 6 5 ) . Whi le some s h r i nkage of nerve f i bres ha s been observed at the u l t r a s tructural leve l , a s a resul t of f i x a t i on and subsequent proce s s ing of nerve , i t ha s been conc luded that no appre c iable change in morphology occur s , a s a l l components of nerve f i bres are a f fected to a s im i lar degree ( Arbuthnot t e t a � 1 9 8 0 ) . The preservat ion of nerve f i bres in e l ectron m i cros copy is cons idered to be adequa te if no s pl i t t ing of the mye l i n s heath has occurred , apart f rom the Schmidt-Lantermann i n c i sure s , if the axo lemma adhere s c l o s e ly to the i nner turns of the mye l i n sheath , and i f the f i ne structure of mitochondria , neurof i l aments and mi crotubu l e s is pre served . Some spl i t t i ng of the mye l i n i s l ikely i n the large s t f ibres w i th the thick e s t mye l i n shea th s ( Arbuthnott e t aL , 1 9 8 0 ) . Unmy? l i na ted nerve f i bre s may be v i s ible on l i ght mi croscopy , but can on ly be examined in deta i l by e lectron m i croscopy . Observat ion of the f i ne s tructure of axona l organe l le s may prov ide informa t ion l i nk i ng s t ructural changes of the various s ubce l lu l a r components w i th unde r l y i ng bi ochemi ca l d i s turbance s , a s we l l a s provid ing an extreme ly sen s i t ive method of detect ing minima l patho log i c a l change ( Dayan , 1 9 7 9 ) . Aga in , care mu s t be taken not to m i s take damage induced by inadequate care in the co l l ect i on a nd proc e s s ing of t he nerve , for true pa t holog i ca l change s .
Now comes the question of why the study of the quotient between the length and the multiplicity is of interest. The motivation behind this question comes primar ily from  by again analysing several of the generalisations of Bezout's Theorem given by W. Vogel and his colleagues (Stiickrad, Flenner and others) . In  W. Vogel asked whether the degree of the intersection of two projective varieties can be bounded above using the degree of these varieties. This finally leads to the consideration of the ratio
interest--binary phylogenetic trees--it is sometimes n ecessary to work with more g en e ral classes of trees, a theme that reappears in later sections. C learly the re is fu rthe r work to be done i n e n u me rating binary trees by the weight of r-colourings, for r>2. While the appropriate set of (2r- "1 ) simultaneous q uadratic equations can be written down for the generating functions, (as in theore m "1 .2"1 for r=2) it is not clear how they cou ld be solved , o r i ndeed whether there is a convenient expression for their soluti o n . lt is possible that structural approaches, such as
Ang l icans continued to fo l l ow British d e v e l opments c l os e l y. The Church Gazette , for instance , reported eminent Br itish sci entist Dr Carpenter 's 1 87 3 assertion that evo lution presented 'a far grand e r notion o f Creat i v e Des ign , than the idea of specia l interpositions required to remed y the irregu l ar working o f a machine irregu l ar l y constructed in the first instance1•22 High Churchman Canon H.P. Liddon was reported in the same year as asserting that e v o l ut ion ' from a Theistic point o f v iew, i s mer e l y our way o f describing what we c an observe of God ' s cont inuous action upon the physical wor l d 1 •23 By the end of the decade Canon Curteis articu l ated the Br itish trend whi ch co loni a l Ang l i cans undoubted l y fo l l owed : 'To a l arge and increasing number of Churchmen the e v o l ution hypothes i s appears , not on l y
The principal stero ids secreted in the cycl ic ewe are progesterone and o e s t radi ol - 1 7b ( Pant e t al . , 1 9 7 7 ) . On the day before o e s trus one or more f ol l i c l e s grow rapidl y and the c oncent rat i on of o e s tradiol - 17b i n the bl ood increases from about 1 0 to 20 pg/ml . The o e s trogen cau s e s behavi oural oestrus . A pos i t ive f eedback f r o m oestradi ol , al ong with hypothal amic GnRH , s t imul ate s r e l e a s e of LH and FSH from the p i tuitary . The conc entrat ion of LH in the bl ood ri ses t o a peak of about 80 ngjml 1 0 h after the beginning of oestrus , and then both LH and e s t radiol c oncentra t i ons fal l rapidl y . LH st imul ates ovul ation , which occurs about 14 h after the LH peak , i . e . about 24 h after the beg inning of o e s t rus. Throughout the r e s t of the oestrous cycl e , the LH c onc entra t i on r e ma ins ve ry l ow ( 2 to 3 ng/ml ) . At the s ame t ime a s the LH peaks , FSH reaches a maximum of about 170 ng/ ml and then fal l s rapidl y . Unl ike LH , it r i s e s to a second peak 24 h after the f i r s t . Af ter o e s trus , FSH c oncentra t i on i s el evated at day 3 and from day 8 to 1 2 i t r i s es to about 80 ng/ml and then decl ine s to about 40 ngjml before the next o e s t rus . At ovulation , s t i mul ated by LH and prolac t in , the granul osa c e l l s form the corpus luteum ( CL) , which s e c r e t e s proge sterone . Maximum c onc entrations of proge s t er one are reached in the blood at days 8 - 9 of the cyc l e and rema in high unt il days 1 3-14 when the corpus l uteum starts t o regre s s ( Ward , 198 6 ) .
Additionally, it was reported in this thesis that treatment of isolated CD23+CD25- B cells, which were characterised to be FO-I B cells, with rShh, lead to an increased death. Hence, it is possible, that FO-I B cells may have lost the ability to respond to a Hh signal or no longer express the receptors for Hh. It is also possible that they require the presence of another B cell subset to secrete Hh protein. Thus, it would be important to characterise the different peripheral B cell subset including, T1, T2, FO-I, FO-II, T2- MZP and MZ in terms of their expression for the Hh signalling component including Ptch, Smo and Gli proteins. Using, flow cytometry, the expression of Ptch and Smo could be investigated in the peripheral B cell subsets. Using RT-PCR, the expression of the Gli proteins in the different peripheral subsets could be investigated. Also, it was observed that treatment of B cells with exogenous rShh, could increase the expression of genes including Bnip3, Traf2, Btk, Nfatc1 and Bmp2/4. It would be important to investigate whether these genes are induced differently in the different peripheral subsets observed in our culture including CD23+CD25-, (subset I) CD23+CD25+ (subset II) and CD23-CD25+ (subset III). Thus, it would be important to sort the subsets, and examine them in isolation for their expression of these genes. A pilot experiment has been carried out, although inconclusive, it remains very promising.
The plots of Fig. 7, show frequency and phase proﬁles of two inverse ﬁlters derived from the data from the El-Centro 18/5/1940 N and E component seismic events. The fre- quency responses were obtained after the data was wavelet de-noised. The x-axis is a log-plot to reveal details at the low frequencies of interest and to emphasise the fact that de-convolution ﬁlters perform in a manner consistent with the single degree of freedom accelerometer model. Fig. 7 also shows the results of modelling the accelerometer by a perfect single degree of freedom system with natural fre- quency 10 Hz and ratio of critical damping 0.552. These parameter value where recorded with the accelerogram data in the header information . The plots show that at low frequencies to approximately 40 Hz for the El-Cen- tro Eastern component the RLS inverse ﬁlter show an approximately ﬂat response (0 dB) in the region of interest. The El-Centro Northern component is approximately ﬂat to about 75 Hz and the phase plots are approximately lin- ear. However, there is an element of uncertainty in both of the de-convolution methods. It is not known whether at the time the instrument behaved as a perfect secondorder SDOF system or that given its years in situ its calibration parameters were still correct; nor indeed whether the RLS characterises the instrument response to a better degree. The characteristic of the anti-alias ﬁlter is also unknown. However, both give similar response characteris- tics and the RLS provides a means of estimating the instru- ment response without any assumptions about the instrument. The RLS approach does perform quite well in the pass band region in Fig. 2, which is, for the engineer- ing, the region of interest. The diﬀerences in magnitude between the two approaches are small in this region. In
. Birger Langkjær designates what he deems “four different levels of realism” that are discernible in and of film in his essay, “Realism and Danish Cinema” (Ed. Anne Jerslev. Realism and 'Reality' in Film and Media.. Northern Lights Film and Media Yearbook. Copenhagen: Museum Tusculanum Press, 2002. 15-40). This includes: “perceptual realism”, “realism of style”, “narrative realism”, and recognitional realism or what Langkjær calls “realism as recognition”. Whereas, Gregory Currie and Torben Grodal each delineate their own respective categories of realism drawing upon the experiential – that is the psychological and affective – dimensions of realism. Currie identifies three “doctrines of cinema, all of which have been called ‘realism’ in his essay “Film Reality and Illusion” (Post-Theory: Reconstructing Film Studies. Eds. David Bordwell and Noël Carroll. Madison and London: The University of Wisconsin Press, 1996. 325-344). The first doctrine he invokes, the “transparency” thesis, has already been mentioned above. The other two categories are “perceptual realism” and “illusionism”. Like Hallam and Marshment, Currie’s thesis acknowledges the competing traditions and epistemologies that form the various precepts of realism, albeit in a far more consolidated manner that is distinctly
Whatever the reasons, research specifically on teacher questioning is relatively limited and has tended to be generic rather than specific to mathematics. Such research has often focused on the product, or outcome, of questioning rather than the process and been conducted in an individual-psychological paradigm and based on quantitative methodologies. Quasi-experiments have been used to explore the relationship between the type of question (for example open/closed or higher/lower order) and learning outcomes. Meta-analysis of such research is inconclusive with some studies reporting a correlation between learning outcomes and cognitive level, but with others indicating no significant difference (see Redfield and Rousseau 1981; Samson et al 1987; Winne 1979). Given the complexity of interrelated factors that are involved in a context for questioning indicated above perhaps this variation is not surprising. More conclusively, a positive relationship has been between of wait time and the following factors: the frequency of student responses, the correctness of responses and the level of cognitive engagement (see Tobin 1987 for a meta-analysis). James Dillon’s analysis of questioning and other discursive practices outside the classroom support this. In other questioning situations or discussion, pauses are frequent and lengthy, indicating that breaks in speech are a necessary part of the process of talking. Evidence from situations such as therapeutic interviews indicates that waiting and silence are not only important cognitively for the responder but emotionally as well (Dillon 1990).
The t re atment s were 4 diet s , l abe l led 1 through t o 4 , cont a ining guan idinated ge l at in ( GG ) and a b a s e in the rat i o s o f 0 . 5 : 1 , 1 : 1 , 1 . 5 : 1 and 2 : 1 respect i ve l y . The base was the s ame a s that used in exper iment 3 and c ompr i sed a cel l u l o s e to c o rnstarch mixture in the rat i o o f 3 : 1 . Bi rds were fed 2 0 g ( ai r dry ) o f e ach diet mixed with water in the rat i o of 1 g diet to 5 cc of water . The wate r was added immediat e l y p r i o r to feeding us ing cal ibrated 3 5 ml di spo s ab l e syringes . The t reatments were a l l o c ated randomly ove r the 3 2 b i rds to give 4 treatment each o f 8 bi rds . Intubat i on equ ipment and procedures were tho s e out l ined in exper iment 3 . I ntubat ion was comp leted within 2 hours and birds were s a c r i f i ced s ome 3 to 7 hour s fol lowing intubat i on on the b a s i s of degree o f crop empt ine s s and on the appearance of Cr in the droppings . The b i rds were sacr i fi c e d and digest a s amp l e s obt a ined u s ing the s ame procedures a s those de s c r ibed in experiment 3 . D ige s t a s amp l e s were col lected in sma l l p l a s t ic b a g s and s t o red overnight in a free zer before they were tran s ferred to the fre e z e dryer .