Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n

The Coprime graph is a graph from a finite group that is defined based on the order of each element of the group. In this research, we determine the coprime graph of generalized quaternion group Q_(4n) and its properties. The method used is to study literature and analyze by finding patterns based on some examples. The first result of this research is the form of the coprime graph of a generalized quaternion group Q_(4n) when n = 2^k, n an odd prime number, n an odd composite number, and n an even composite number. The next result is that the total of a cycle contained in the coprime graph of a generalized quaternion group Q_(4n) and cycle multiplicity when is an odd prime number is p-1.Keywords: Coprime graph, generalized quaternion group, order, path AbstrakGraf koprima merupakan graf dari dari suatu grup hingga yang didefiniskan berdasarkan orde dari masing-masing elemen grup tersebut. Pada penelitian ini akan dibahas tentang bentuk graf koprima dari grup generalized quaternion Q_(4n). Metode yang digunakan dalam penelitian ini adalah studi literatur dan melakukan analisis berdasarkan pola yang ditemukan dalam beberapa contoh. Adapun hasil pertama dari penelitian adalah bentuk graf koprima dari grup generalized quaternion Q_(4n) untuk kasus n = 2^k, n bilangan prima ganjil ganjil, n bilangan komposit ganjil dan n bilangan komposit genap. Hasil selanjutnya adalah total sikel pada graf koprima dari grup generalized quaternion dan multiplisitas sikel ketika bilangan prima ganjil adalah p-1.Kata kunci: Graf koprima, grup generalized quternion, orde

Quantum algorithms for computing general discrete logarithms and orders with tradeoffs

We generalize our earlier works on computing short discrete logarithms with tradeoffs, and bridge them with Seifert's work on computing orders with tradeoffs, and with Shor's groundbreaking works on computing orders and general discrete logarithms. In particular, we enable tradeoffs when computing general discrete logarithms. Compared to Shor's algorithm, this yields a reduction by up to a factor of two in the number of group operations evaluated quantumly in each run, at the expense of having to perform multiple runs. Unlike Shor's algorithm, our algorithm does not require the group order to be known. It simultaneously computes both the order and the logarithm. We analyze the probability distributions induced by our algorithm, and by Shor's and Seifert's order-finding algorithms, describe how these algorithms may be simulated when the solution is known, and estimate the number of runs required for a given minimum success probability when making different tradeoffs.

Species composition, relative abundance, and distribution of land snail species in Mt. Lantoy Key Biodiversity Area, Cebu, Philippines

Rosales R, Lillo E, Alcazar SM, Colita L, Caballero J, Malaki AB. 2020. Species composition, relative abundance, and distribution of land snail species in Mt. Lantoy Key Biodiversity Area, Cebu, Philippines. Biodiversitas 21: 5438-5447. This study aimed to establish an inventory of land snails in Mt. Lantoy, Cebu Island, Philippines. A two-person team conducted sampling on eight permanent plots with an elevation range of 182 m-691 m. The study has listed a total of 872 individuals represented by 25 species belonging to 15 genera and nine families. Seven families belong to the air-breathing pulmonate group, Order Stylommatophora: Bradybaenidae, Camaenidae, Trochomorphidae, Achatinidae, Ariophantidae, Helicarionidae, Helicinidae. Two families were under the prosobranch group, Order Caenogastopoda: Cyclophoridae, and Pupinidae. The Cyclophoridae was the richest family with five species, followed by Bradybaenidae, Camaenidae, Helicinidae, having four species. The Trochomorphidae and Helicarionidae have three species. The Pupinidae has two species, while the Achatinidae and Ariophantidae has one species each. There were three (3) endemic and ten (10) new island record species collected and identified with four (4) species that were classified as rare. Rysotta otaheitana Ferussac 1821 was the most abundant, representing 25.22% of the total number of individuals. The Leptoma nitidum ancilis Bartsch 1918 has the widest geographical distribution with a constancy rate of 100%. Widespread species appear to be more abundant, while other species were geographically restricted in few study areas.

Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds

In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi–Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi–Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.

A New Characterization of PSL(2, q) by Group Order and the Set of Vanishing Element Orders

An element g in a finite group G is called a vanishing element if there exists some irreducible complex character χ of G such that [Formula: see text]. Denote by Vo(G) the set of orders of vanishing elements of G, and we prove that [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text] is a prime power.

Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order

In a finite group G, let {\pi_{e}(G)} be the set of orders of elements of G, let {s_{k}} denote the number of elements of order k in G, for each {k\in\pi_{e}(G)} , and then let {\operatorname{nse}(G)} be the unordered set {\{s_{k}:k\in\pi_{e}(G)\}} . In this paper, it is shown that if {\lvert G\rvert=\lvert L_{2}(q)\rvert} and {\operatorname{nse}(G)=\operatorname{nse}(L_{2}(q))} for some prime-power q, then G is isomorphic to {L_{2}(q)} .

Local interactions and global properties of wild, free-ranging stickleback shoals

Collective motion describes the global properties of moving groups of animals and the self-organized, coordinated patterns of individual behaviour that produce them. We examined the group-level patterns and local interactions between individuals in wild, free-ranging shoals of three-spine sticklebacks, Gasterosteus aculeatus . Our data reveal that the highest frequencies of near-neighbour encounters occur at between one and two body lengths from a focal fish, with the peak frequency alongside a focal individual. Fish also show the highest alignment with these laterally placed individuals, and generally with animals in front of themselves. Furthermore, fish are more closely matched in size, speed and orientation to their near neighbours than to more distant neighbours, indicating local organization within groups. Among the group-level properties reported here, we find that polarization is strongly influenced by group speed, but also the variation in speed among individuals and the nearest neighbour distances of group members. While we find no relationship between group order and group size, we do find that larger groups tend to have lower nearest neighbour distances, which in turn may be important in maintaining group order.