Development of the female flower and gynecandrous partial inflorescence of Myrica californica

1979 ◽  
Vol 57 (2) ◽  
pp. 141-151 ◽  
Author(s):  
Alastair D. Macdonald
Keyword(s):  
Fourth Order ◽  
Female Flower ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Unique Structure ◽  
Inflorescence Axis ◽  
Definition Of ◽  
Fifth Order ◽  
Partial Inflorescence

Organogenesis of the female flower and gynecandrous partial inflorescence is described. Approximately 25 first-order inflorescence bracts are formed in an acropetal sequence. A second-order inflorescence axis, the partial inflorescence, develops in the axil of each bract. Third-, fourth-, and fifth-order axes arise in the axils of second-, third-, and fourth-order bracts. A gynoecium terminates a second-order axis and sometimes a distal third-order axis. A gynoecium consists of two stigmas and one basal, unitegmic, orthotropous ovule. The wall enclosing the ovule, the circumlocular wall, is comprised distally of gynoecial tissue and proximally of tissue of the inflorescence axis and its appendages. The latter portion of the wall is formed by zonal growth. Androecial members, formed proximal to the gynoecium on the partial inflorescence, are carried onto the circumlocular wall by zonal growth. A stamen may develop from the last-formed primordium before gynoecial inception or from a potentially stigmatic primordium. The papillae of the flower and fruit arise as emergences and from potentially bracteate, axial, and staminate primorida during the development of the circumlocular wall. The term circumlocular wall is used in a neutral sense to describe this unique structure. Since the gynoecium is composed of gynoecial appendages and inflorescence axis and appendages, a functional definition of gynoecium must be expanded to include any tissue, including an inflorescence, that surrounds the ovule(s) and forms the fruit(s).

Inception of the cupule of Quercus macrocarpa and Fagus grandifolia

1979 ◽  
Vol 57 (17) ◽  
pp. 1777-1782 ◽  
Author(s):  
Alastair D. Macdonald
Keyword(s):  
Female Flower ◽  
Fagus Grandifolia ◽  
Second Order ◽  
The Other ◽  
Third Order ◽  
Quercus Macrocarpa ◽  
First Order ◽  
Female Inflorescence ◽  
Inflorescence Axis ◽  
Morphological Nature

The female inflorescence of Fagus grandifolia comprises two flowers; one flower terminates the first-order inflorescence axis, the other flower terminates the second-order inflorescence axis. Each flower is flanked by two cupular valves each of which arise in the axil of a bract. The two valves flanking the flower terminating the first-order inflorescence axis represent second-order inflorescence axes and the two valves flanking the flower terminating the second-order inflorescence axis represent third-order inflorescence axes. The four valves remain discrete. Each female flower of Quercus macrocarpa terminates a second-order inflorescence axis and is surrounded by a continuous cupule. The cupule first forms as two primordia in the axils of each of the two transversal second-order bracts. These cupular primordia represent third-order inflorescence branches. The cupule primordia become continuous about the pedicel by meristem extension. The cupules of Fagus and Quercus are homologous to the extent that they are modified axes of the inflorescence. This serves as a model to interpret the morphological nature of the fagaceous cupule.

Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed K. Elboree
Keyword(s):  
Symbolic Computation ◽  
Fourth Order ◽  
Bilinear Form ◽  
Rogue Waves ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear

Abstract Based on the Hirota bilinear form for the (3 + 1)-dimensional Jimbo–Miwa equation, we constructed the first-order, second-order, third-order and fourth-order rogue waves for this equation using the symbolic computation approach. Also some properties of the higher-order rogue waves and their interaction are explained by some figures via some special choices of the parameters.

scholarly journals Generalised Algebraic Continued Fractions related to Definite Integrals

1958 ◽  
Vol 9 (4) ◽  
pp. 170-182
Author(s):  
L. R. Shenton
Keyword(s):  
Recurrence Relation ◽  
Fourth Order ◽  
Continued Fractions ◽  
Recurrence Formula ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Definite Integrals ◽  
Image Position ◽  
Remarkable Relation

The present paper is a continuation of the work initiated in [l]-[5]. In [5] I gave an expansion of the formfor the second order C.F. associated withwhere U8, V8, W8 satisfy a fourth-order recurrence relation, there being a similar expansion for third order C.F.'s. I shall now give simple expressions for U8, V8, W8 (or related forms) in terms of χ2s(Z1), χ2s (Z2), ω2s(Z1), ω2s(Z2), whereand show that there is a remarkable relation between the recurrence formula for the first order C.F. and that satisfied by U3, V3, W3. The generalised form of these results will be stated and proved.

Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong
Keyword(s):  
Second Order ◽  
Base Catalysis ◽  
Substitution Reactions ◽  
Third Order ◽  
Methoxy Derivative ◽  
First Order ◽  
General Base ◽  
Protic Solvents ◽  
Kinetics Of ◽  
Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

Panicle, spikelet, and floret development in orchardgrass (Dactylis glomerata)

1993 ◽  
Vol 71 (4) ◽  
pp. 523-532 ◽  
Author(s):  
Joanna Fraser ◽  
Eric G. Kokko
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Unique Feature ◽  
Dactylis Glomerata ◽  
Bilateral Symmetry ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Lateral Branches ◽  
Scanning Electron

The initial stages of panicle, spikelet, and floret development in field-grown 'Kay' orchardgrass were examined using scanning electron microscopy. Spikelets arose from a complex multilevelled sequence of initiation from branch apices. Spikelets developed indirectly in a two-tiered progression: (i) an acropetal and basipetal sequence of first order, second-order, and third-order inflorescence apices, and (ii) an acropetal development within subclusters of higher-order lateral branch inflorescence apices. The panicle had the unique feature of dorsiventrality as well as bilateral symmetry. The basal apex from first-order, second-order, or third-order apices developed on the same side of the main axis as the first-order apex. The two glumes subtending each spikelet primordium developed alternately and acropetally. Development and initiation of florets within spikelets was basipetal within the panicle, basipetal within clusters and subclusters of spikelets on lateral branches, and acropetal within spikelets. Within florets, paleas developed later than lemmas. Key words: Dactylis glomerata, cocksfoot, scanning electron microscopy, development, panicle.

Incommensurately modulated structure of TaGe0.354Te2: application of crenel functions

1996 ◽  
Vol 52 (1) ◽  
pp. 100-109 ◽  
Author(s):  
F. Boucher ◽  
M. Evain ◽  
V. Petříček
Keyword(s):  
Detailed Analysis ◽  
Fourth Order ◽  
X Ray Diffraction ◽  
Third Order ◽  
Modulated Structure ◽  
X Ray ◽  
First Order ◽  
Germanium Telluride ◽  
Orthorhombic Cell ◽  
Orthogonalization Procedure

The incommensurately modulated structure of tantalum germanium telluride, TaGe0.354Te2, was determined by single-crystal X-ray diffraction. The dimensions of the basic orthorhombic cell are a = 6.4394 (5), b = 14.025 (2), c = 3.8456 (5) Å, V = 347.3 (1) Å3 and Z = 4. The (3 + 1)-dimensional superspace group is Pnma(00γ)s00, γ = 0.3544 (3). Refinements on 1641 reflections with I ≥ 3σ(I) converged to R = 0.065 and 0.044 for 526 main reflections and R = 0.061, 0.12, 0.28 and 0.32 for 782 first-order, 237 second-order, 37 third-order and 59 fourth-order satellites, respectively. Since the structure exhibits a strong occupational modulation of both Ta and Ge atoms, along with important displacive modulation waves, crenel functions were used in the refinement in combination with an orthogonalization procedure. Such an approach is shown to be the most convenient and to give reliable coordinations and distances. A detailed analysis of some Te...Te distances is performed, in connection with already known commensurately and incommensurately modulated MAx Te2 structures.

A Note on Homogeneous Dendrites

1968 ◽  
Vol 11 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Z. A. Melzak
Keyword(s):  
Branch Point ◽  
Rooted Tree ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Graph Theoretic ◽  
Order Branch

In graph - theoretic terms a homogeneous p-dendrite, p ≥ 2, is defined as a finite singly-rooted tree in which the root has valency 1 while every other vertex has valency 1 or p. More descriptively, a homogeneous p-dendrite may be imagined to start from its root as the main, or 0th order, branch which proceeds to the first - order branch point where it gives rise top first - order branches. Each of these either terminates at its other end (which is a second-order branch point) or it splits there again into p branches (which are of third order), and so on. The order of the dendrite is the highest order of a branch present in it. For completeness, a 0-th order dendrite is also allowed, this consists of the 0-th order branch alone.

Attenuated microvascular alterations in coarctation hypertension

1989 ◽  
Vol 256 (1) ◽  
pp. H213-H221 ◽  
Author(s):  
D. L. Stacy ◽  
R. L. Prewitt
Keyword(s):  
Fourth Order ◽  
Vascular Tone ◽  
Structural Parameters ◽  
Renal Hypertension ◽  
Second Order ◽  
Hypertensive Rats ◽  
Third Order ◽  
Flow Dependence ◽  
Vascular Beds ◽  
Microvascular Alterations

Arteriolar vasoconstriction, structural reductions in dilated diameter, and rarefaction have been observed in vascular beds with chronic renal hypertension. To determine their pressure or flow dependence, these functional and structural parameters were studied in the developing and chronic stages of coarctation hypertension in the cremaster muscle, a normotensive skeletal muscle bed that is protected from the effects of elevated microvascular pressures. Hypertension was produced in rats by placing a silver clip around the abdominal aorta above the branches of the renal arteries. In hypertensive rats, resting diameters were reduced in second-order arterioles after 4 and 8 wk, in third-order arterioles after 2, 4, and 8 wk, and in fourth-order arterioles after 4 and 8 wk, vs. controls. Vascular tone was elevated in second-order arterioles after 2, 4, and 8 wk and in third- and fourth-order arterioles after 8 wk in hypertensive rats. No increases in medial-intimal area were found at any stage of hypertension in any arteriolar order. The density of small arterioles (3rd-5th orders) was reduced by 20% in hypertensive rats at 8 wk but was unchanged at the other time periods. These arteriolar alterations, especially the absence of structural reductions in diameter, are attenuated compared with those observed in one-kidney, one-clip hypertension and suggest that most of the arteriolar alterations that occur in renal hypertension are pressure or flow dependent.

On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures

2018 ◽  
Vol 14 (03) ◽  
pp. 383-401
Author(s):  
Song-Ping Zhu ◽  
Guang-Hua Lian
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Second Order ◽  
Approximation Technique ◽  
Third Order ◽  
Numerical Examples ◽  
Taylor Expansions ◽  
Vix Futures ◽  
Validity Condition

Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

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