PUP Journal of Science and Technology

Includes bibliographical references.

Taxonomic Survey of Butterflies in Ninoy Aquino Parks and Wildlife Center, Quezon City -- A Method for obtaining the state equations of Electrical Circuits bases on network theorems: its analytical and practical implementations and verification by computer simulations -- On a Family of power-associative and alternative nafils of order n = 3m + 1 -- Community Structure of Zooplankton at Sampaloc Lake, San Pablo City, Laguna, Philippines -- On the singularity of the Cartesian product of graphs -- Tentacles of the Octonions.

[Article Title: Taxonomic Survey of Butterflies in Ninoy Aquino Parks and Wildlife Center, Quezon City / Lourdes V. Alvarez, Anne Loraine A. Cordero and Gennelyn A. De Mesa, p. 1-8]

Abstract: Butterflies are important not only for their aesthetic value but for the essential role they are playing in the environment such as food for preda-tors, reproduction of plants and as important bio-indicators of climate change. They are also considered as indicators of ecological balance due to their sensitivity to toxins and pesticides. This study documents the butterflies found within the vicinity of Ninoy Aquino Parks and Wildlife Center. Twenty-two subspecies belonging to five families and fifteen genera were found occurring in the area. Four belong to genus Troides (T. rhadamantus) and Papilio (P. poly-tes pasikrates, P. polytes ledebouria and P. demoleus), while the rest belong to the genera Delias (D. hyparete luzonensis), Appias (A. olferna peducaea), Leptosia (L. nina malayana), Pareronia (P. boebera boebera), Eurema (E. hecabe hecabe and E. blanda vallivolans), Catopsilia (C. pomona pomona and C. scylla asema), Hypolimnas (H. bolina philippinensis), Junonia (J. hedonia ida, J. atlites atlites, Joritya wallacei and J. almana javana), Parthenos (P. slyvia philippinensis), Cethosia (C. biblis insularis), and Ypthima (Y. pandocus corticaria).

[Article Title: A Method for obtaining the state equations of Electrical Circuits bases on network theorems: its analytical and practical implementations and verification by computer simulations/ Alexander S. Carrascal, p. 9-30]

Abstract: This paper presents an alternative method for obtaining the state equations of a dynamic but passive RLC network (resistive-inductive-capacitive network) using DC analysis by deriving from it a resistive multiple-port network and then applying on the derived network the well-known network theo-rems, such as the Superposition, Thevenin's, and Norton's Theorems to compute network functions that correspond to certain two-port network parameters such as z-, y-, h-, and g-parameters. The network functions are then used together with the parameters of the energy-storage elements to determine the coefficients of the required state equations. A significant advantage of this method is that it is readily amenable to practical implementations using DC test input signals and meter instruments. Calculations of the network functions can also be done using standard software packages such as PSpice, Circuit Maker, and Electronic Workbench. Once the state equations are determined, the solution or output can then be obtained either analytically or by computer simulations using Matlab.

[Article Title: On a Family of power-associative and alternative nafils of order n = 3m + 1/ Raoul E. Cawagas, p. 31-42]

Abstract: The existence of an interesting family of power-associative abelian NAFILs of order n = 3m + 1, where m ≥ 3, has been established by construction with the aid of the software FINITAS. This family includes a subfamily of order n = 3(2' -1) +1, r ≥ 2, whose members have the alternative property. Any member of this subfamily has subsystems all of which are Klein groups of order 2'. Its first three members are of orders n = 10, 22, 46. Using FINITAS, the order n = 46 member has been found to have 424 proper subsystems.

[Article Title: Community Structure of Zooplankton at Sampaloc Lake, San Pablo City, Laguna, Philippines/ Armin S. Coronado, John G. S. Mallari and Sarah J. M. Balana, p. 43-50]

Abstract: The zooplankton distribution and productivity are directly affected by the physical and chemical conditions of freshwater systems. This study assessed the composition of zooplankton community in Sampaloc Lake, San Pablo City, Laguna in an attempt to determine the trophic status of the lake. Among the environmental parameters measured, only the dissolved oxygen gave significant differences (a0.05 > 0.04) among five stations, which can be explained by the varying levels of organic compounds that each station is receiving. The zooplankton community of the lake consists three major groups namely Rotifera, Cladocera and Copepoda. Although rotifers gave the highest species richness (42 taxa), copepods were the most abundant (53.60%). Zoo-plankters within the lake showed high diversity (H' = 2.034; 1 - D = 0.7581) but no taxa drastically dominated (D = 0.2419) the community. During the sampling period, the average measurements of the various physico-chemical parameters (pH = 7.97 ÷ 0.09; transparency = 32.40 ÷ 4.57 in; DO = 7.50 ÷ 0.40 mg/L) indicated mesotrophic condition of the lake. Moreover, the presence of Brachionus, Filinia, Bosmina and Ceriodaphnia supported the eutrophic condition of Sampaloc Lake.

[Article Title: On the singularity of the Cartesian product of graphs/ On the singularity of the Cartesian product of graphs, p. 51-56]

Abstract: A graph G is singular if and only if the adjacency matrix of G is singular. If G and H are graphs, we show that the cartesian product GOH is singular if and only if G has an eigenvalue 1 such that - 1 is an eigenvalue of H.

[Article Title: Tentacles of the Octonions/ Alexander S. Carrascal, p. 57-68]

Abstract: This article presents a "mathematical monster" with many names, faces and tentacles. It is notoriously famous for being non-commutative and non-associative and stands in the crossroads of several disciplines. The alias it assumes and the mask it wears depends on which direction it faces. It is associated with names such as Cayley numbers, Hadamard matrix, Heawood graph, and Steiner loops, quasigroups, and triple systems. It can appear variously as an alternative algebra, a combinatorial design, a finite projective plane, a graph, a nonlinear code, to cite just a few. Only those with eyes trained for seeing mathematical patterns are able to discern its presence and recognize its appearance upon encounter. Thus, it is the aim of this article to expose its identity, that is, unmask its face, describe its tentacles, and reveal its name: the octonions!