Use of the Maple System in Math Tuition at Universities

The following article explores the application of educational technologies at a University level and their contribution in enhancing the educational effectiveness. It discusses the capabilities of computer algebra systems, such as Maple. It is integrated in the math tuition of the Technical University (TU) in Varna and is used by its students during laboratory exercises.

Using Physical Quantities in Applied Mathematical Problems with Maple

The present article discusses units of measure and their base units, work environments built in the Units package of the computer algebra system Maple. An analysis is drawn of the tools of the application in connection with the use of physical quantities and their features. Maple’s main commands are arranged in groups depending on the function. Some applied mathematical problems are given as examples making use of derivative, integral and differential equations.

Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.

Shade promotes thorn development in a tropical liana, Artabotrys hexapatalus (Annonaceae)

The liana Artabotrys hexapetalus (L.f.) Bhand., which is widely planted in the Tropics and native to African rain forests, produced new reiterations (new leader shoots) normally and after damage induced by Hurricane Andrew (August 24, 1992). In each new orthotropic shoot, there is a gradient in lateral branch structures from basal thorns, to vegetative leafy branches, to distal leafy flowering branches. We noted that reiterations developing in shade had more thorns than similar reiterations developing in full sun. Tents with clear (66% photosynthetically active radiation [PAR]) and shaded plastic film (12%–14% PAR) were placed over nodes when the axillary buds began to expand to produce reiteration shoots. After 2 mo of growth inside the tents and in the open, the types of lateral outgrowths (thorn vs. branch) were recorded. Shoots in spectrally neutral shade (red to far red of full sun) and spectrally altered shade (red to far red of canopy shade) produced significantly more thorns at the lower nodes of the shoots as compared to those in full sun. Shoots in control clear plastic tents were the same as those in full sun. We conclude that the fate of lateral bud development is controlled by irradiance (light level) but not by light quality. Increased thorn production in shade could be advantageous to plants growing in the deep shade of rain forests. Thorns in the self-shaded regions of the plant, and well below the forest canopy, could aid in protection from herbivory and in climbing by acting as hooks.

The developmental responses of papaya leaves to simulated canopy shade

The developmental responses of plants to shade underneath foliage are influenced by reductions in irradiance and shifts in spectral quality (characterized by reductions in the quantum ratio of red to far-red wavelengths, R:FR). Previous research on the influence of shadelight on leaf development has neglected the reductions in R:FR characteristic of foliage shade, and these studies have almost certainly underestimated the extent and array of developmental responses to foliage shade. We have studied the effects of reduced irradiance and R:FR on the leaf development of papaya (Carica papaya L., Caricaceae). Using experimental shadehouses, replicates of plants grown in high light conditions (0.20 of sunlight and R:FR = 0.90) were compared to low light conditions (0.02 of sunlight) with either the spectral quality of sunlight (R:FR = 0.99) or of foliage shade (F:FR = 0.26). Although many characteristics, such as leaf thickness, specific leaf weight, stomatal density, palisade parenchyma cell shape, and the ratio of mesophyll air surface/leaf surface were affected by reductions in irradiance, reduced R:FR contributed to further changes. Some characters, such as reduced chlorophyll a/b ratios, reduced lobing, and greater internode length, were affected primarily by low R:FR. The reduced R:FR of foliage shade, presumably affecting phytochrome equilibrium, strongly influences the morphology and anatomy of papaya leaves.

Correlates of leaf optical properties in tropical forest sun and extreme-shade plants

Thirteens hade-adaptedr ain forest species were comparedw ith twelve sun-adaptedt ropical forest species for correlates to leaf optical properties (described previously in Amer. J. Bot. 73: 1100-1108). The two samples were similar in absorptance of quanta for photosynthesis, but the shade-adaptedt axa: 1) had significantlyl ower specificl eaf weights,i ndicatinga more metabolically efficient production of surface for quantum capture; 2) synthesized less chlorophyll per unit area; and 3) used less chlorophyll for capturing the same quanta for photosynthesis. The anatomical features that best correlate with this increased efficiency are palisade cell shape and chloroplast distribution. Palisade cells with more equal dimensions have more chloroplasts on their abaxial surfaces. This dense layer of chloroplasts maximizes the light capture efficiency limited by sieve effects. The more columnar palisade cells of sun-adapted taxa allow light to pass through the central vacuoles and spaces between cells, making chloroplasts less efficient in energy capture, but allowing light to reach chloroplasts in the spongy mesophyll. Pioneer species may be an exception to these two groups of species. Three pioneer taxa included in this study have columnar palisade cells that are extremely narrow and packed closely together. This layer allows little penetration of light, but exposure of the leaf undersurface may provide illumination of spongy mesophyll chloroplasts in these plants.

Simulating Forest Shade to Study the Developmental Ecology of Tropical Plants: Juvenile Growth in Three Vines in India

Both light quantity and quality affect the development and autoecology of plants under shade conditions, as in the understorey of tropical forests. However, little research has been directed towards the relative contributions of lowered photosynthetic photon flux density (PPFD) versus altered spectral distributions (as indicated by quantum ratios of 660 to 730 nm, or R:FR) of radiation underneath vegetation canopies. A method for constructing shade enclosures to study the contribution of these two variables is described. Three tropical leguminous vine species (Abrus precatorius L., Caesalpinia bondicela Fleming and Mucuna pruriens (L.) DC.) were grown in two shade enclosures with 3-4% of solar PPFD with either the R:FR of sunlight (1.10) or foliage shade (0.33), and compared to plants grown in sunlight. Most species treated with low R:FR differed from those treated with high R:FR in (1) percent allocation to dry leaf weight, (2) internode length, (3) dry stem weight/length, (4) specific leaf weight, (5) leaf size, and (6) chlorophyll a/b ratios. However, these plants did not differ in chlorophyll content per leaf dry weight or area. In most cases the effects of low R:FR and PPFD were additional to those of high R:FR and low PPFD. Growth patterns varied among the three species, but both low PPFD and diminished R:FR were important cues in their developmental responses to light environments. This shadehouse system should be useful in studying the effects of light on the developmental ecology of other tropical forest plants.

Leaf Optical Properties of Rainforest Sun and Extreme Shade Plants

The opticalp ropertieso f the leaves of twelve tropicals un speciesa nd thirteent ropicale xtreme shade species were examinedw ith an integratings pherea ttachedt o a spectroradiometerM. easurements of diffuse reflectance and transmittance allowed calculations of absorptance, 350- 1,100 nm. Althoughs ome shade species absorbedh igherp ercentageso f quantumf lux densities for photosynthesis (400-700 nm, PPFD) than the mean for the sun species, the sun and shade species as groups were not significantly different from each other: 90.2, S.D. 3.6% for shade species and 88.6, S.D. 2.4% for the sun species. The groups of species did not differ in total absorptance of energy 350-1,100 nm. Furthermore, the sun and shade species were identical in theirs hifto f absorptancea t wavelengthsb etween6 50 and 750 nm. The anthocyanicc oloration of the leaf undersurfaceso f two species polymorphicf or this characteristic( Trionela hirsuta and Ischnosciphonp ruinosus)i s correlatedw ith increaseda bsorptancea t the uppere nd of the action spectrum of photosynthesis. Although sun and shade species have similar optical properties, the energy investment (as documented by dry wt per unit area of leaf surface) is much less for the shade species.