# Volume 5 No. 1

January 2002## On Minimal Rigidity of Prisms

**pp 51-55 (Vol 5 No. 1 2002)**

**Gloria A. Rosalejos ^{1} and Severino V. Gervacio ^{2}**

^{1} Department of Mathematics, Mindanao State University, Marawi City

^{2} Department of Mathematics, De La Salle University, 2401 Taft Avenue, Manila

**ABSTRACT**

The Cartesian product *Cm X Pn* of a cycle *Cm* and a path *Pn, n ~ 2,* is called a prism. It can be checked from [2] that points in the Euclidean space *R 3* can be chosen to represent the vertices of the prism such that the distance between points representing adjacent vertices is 1. Thus, *Cm X Pn* is a so called unit graph in R 3 . Clearly, this graph is flexible(not rigid) in *R 3* . We can flex the prism so that the distance between some non-adjacent vertices will be equal to 1. Then, a new unit edge can be added to join such a pair of vertices. This paper will show how to do such addition of edges, using only the minimum number of edges, to transform the prism to a rigid unit graph in *R 3 .*

## The Spectra of Some Asymmetric, Circulant and r-regular Digraphs and their Complements

**pp 40-50 (Vol 5 No. 1 2002)**

**lsagani B. Jose
**

*Department of Mathematics*

*De La Salle University*

*2401 Taft Avenue, 1004 Manila*

*josi@dlsu.edu.ph*

**ABSTRACT**

Let G be a digraph and A( G) be its adjacency matrix. The spectrum of G, denoted by Spec G is where Ao, AI, … , Ap-l are the eigenvalues of A( G) and mo, m1, … , m – 1 are their corresponding multiplicities. This paper discusses some properties of the spectrum of four different classes of asymmetric, circulant, and r-regular digraphs and their complements. The digraphs considered in this paper are orientations of the rth power of a cycle, a complete graph, a complete bipartite graph, and a digraph whose adjacency matrix is circulant with first row entries all zeros exc~t the ( d + 1) st and nth column entries which are’ both 1’s.

## On Topologies and Reflexive Transitive Relations On Finite Sets

pp 36-39 (Vol 5 No. 1 2002)

Severino Docto Diesto, Ph.D.

*Department of Mathematics *

*De La Salle University-Manila *

*2401 Taft Avenue, Manila*

ABSTRACT

**For finite sets, the concepts of topology and reflexive transitive relations are shown to be equivalent; thus a topology on a **

**finite set can be represented by an incidence relation, and a function between finite topological spaces has a matrix representation. A theorem on when and only when this matrix representation is a representation for a continuous friction is then given. **

## Conceptual Understanding of Forces Among Physics Majors

pp 20-35 (Vol 5 No. 1 2002)

Robert C. Roleda

*Science Education Department, De La Salle University *

*2401 Taft Avenue, 1004 Manila*

ABSTRACT

Conceptual understanding of forces among physics majors at De La Salle University were evaluated using the Force Concept Inventory (FCI). The FCJ scores were found to vary from an average of 23.0% for freshmen to 39. 74% for seniors. Only one out of 81 physics majors of all year levels was found to be a clearly Newtonian thinker. While there is a marked difference in the understanding of inertia and falling bodies between freshmen and seniors, conceptual understanding of kinematics, Newton’s 2nd and 3,d Laws, and force identification did not reach the 50% level from first to fourth year.

## Acetamide as potential C- and N-source of the extremely acid and heavy metal resistant filamentous fungus, Bispora sp.

pp 9-19 (Vol 5 No. 1 2002)

Hartmut Gimmler ^{1}, Astrid Boots ^{1}, Josefina de Jesus ^{2
}

^{1} Julius-von-Sachs-lnstitute of Bioscience, University of Wurzburg, Germany

^{2} Department of Biology, De La Salle University, 2401 Taft Avenue, 1004 Manila Philippines

**ABSTRACT**

*The extremely acid resistant filamentous fungus Bispora sp. (possessing two distinct growth optima at pH 1 and pH 7) is able to utilize metal complexed cyanides as N-source and to grow with acetamide as the only nitrogen and carbon source at both pH 1. 0 and 7. 0, whereas little growth is observed with formamide as N-source. The nitrogen content of the fungus grown with acetamide is similar tp ·that of the control grown with NH4 + as N-source but higher than those cultures deprived of nitrogen. In the absence of appropriate substrates the fungus did not express amidases such, as urease, formamidase, acetamidase, whereas in the presence of formamide and acetamide, formamidase activity, but no acetamidase activity was observed. Since the fungus is able to grow with acetamide as the only C- and N-source, data imply the involvement of an enzyme in acetamide metabolism which is different from a normal acetamidase. The incorporation of 14C-acetamide into the fungus and the subsequent utilization of the substrate, as analyzed by TLC, support the view that inducible enzymes related to CJ-metabolism are of importance for the nutrition of Bispora sp. grown at pH 1.0 with acetamide as C- and N-source.*

## Air Borne Lead Contamination of Trees in Metro Manila-A Study of Environmental Hazards Related to Leaded Fuels

**pp 1-8 (Vol 5 No. 1 2002)**

**Josefina de Jesus ^{1}, Markus Woitke ^{2}, Hartmut Gimmler ^{2}, Astrid Boots ^{2}, Elena Ragragio ^{3}**

^{1} Biology Department, De La Salle University, Taft Avenue, Manila, Philippines

^{2} Julius-van-Sachs-Institute of Bioscience, University of WUrzburg, Germany

^{3} Biology Department, University of the Philippines, Padre Faura, Manila

**ABSTRACT**

The environmental hazards originating from the use of leaded fuel in Afetro lvfanila were analyzed indirectly by investigating the Ph content and contamination of leaves of trees exposed to heavy traffic along Taft Avenue in comparison ,with three sites with less or no traffic in the countryside. Both the internal Pb content and the external Pb load of plans were measured. Internal Pb content of samples along Taft Avenue and the countrysides yielded an average o/6.5 mJ; and 0.6 mg Pb per kg dry weight respectively ,while that of external Pb load were 18. 9 mg and 2. 74 mg Pb per kg dry weight respectively. These values from the two sampling areas ·were significantly different. The impact of Pb pollution was discussed in terms of *phytotoxicity* of Pb to plants and possible effects on the food chain. and consequently, on human health.