The influence of finger-counting strategies (pointing, keep track, montring) on number representations is supported by several empirical facts. However, even the above mentioned strategies have been object of studies during childhood, little is known about how finger-counting could interact with the semantic representation of numbers in adulthood. To address this issue, we conducted a first experiment in which participants had to identify Arabic digits by pressing the keyboard with one between their ten fingers. Results showed that responses were faster and more accurate when the finger assigned to each digit was congruent with the finger-counting habits of the participants (Di Luca, Granà, Semenza, Seron and Pesenti, 2006). Subsequently, in a numerosity detection task, we showed that the numerosities expressed by canonical configurations are named faster than those expressed by non-canonical ones, even when no motors responses were needed (Di Luca and Pesenti, in press). Moreover, when used as unconsciously presented primes, both types of configurations speeded up comparative judgments of Arabic digits, but only the priming effect induced by canonical configurations generalized to new, never consciously seen, numerosities, which implies an automatic semantic access for these one only. Finally, we showed that these differences cannot be ascribed to simple visual features, but they stem from two distinct semantic processes. Specifically, canonical configurations are processed as a symbolic system and activate a place coding semantic representation of magnitude, whereas non-canonical configurations activate a summation coding semantic representation.

In Libellulidae there are two types of egg-laying behaviour, non-contact guarding where the male accompany the female during oviposition and tandem guarding where the male is physically coupled with the female. These egg laying strategies also shows differences in egg size distribution and egg size. In species which perform non-contact guarding the egg size is inversely proportionate to the order of laying. In tandem species on the other hand, the egg size is more randomly distributed and the eggs are slightly larger than in non-contact species. To see if there is a difference in the female internal reproductive organs between the two guarding types, the ovariole number was counted. The result shows that species which perform tandem guarding during oviposition have a fewer number of ovarioles compared to the non-contact species. This difference in ovariole number was also species specific. Increasing impact on ecosystems, the survival of dragonflies or any other insects can no longer be taken for granted. Therefore can this information be valuable in conservation biology when new habitats are created for preservation of species.

Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of Erdös-Kac states that the quantity (ω(m)-loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φ-function. Erdös and Pomerance proved that the quantity(ω(φ(m)-(1/2)(loglog m)^2)\((1/√(3)(loglog m)^(3/2)) also distributes normally. In this thesis, we prove these two results. We also prove a function field analogue of the Erdös-Pomerance Theorem in the setting of the Carlitz module.

Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of Erdös-Kac states that the quantity (ω(m)-loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φ-function. Erdös and Pomerance proved that the quantity(ω(φ(m)-(1/2)(loglog m)^2)\((1/√(3)(loglog m)^(3/2)) also distributes normally. In this thesis, we prove these two results. We also prove a function field analogue of the Erdös-Pomerance Theorem in the setting of the Carlitz module.

Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been improved upon by number theorists several times. The theorem can also be generalized to finite abelian groups. In 1994 Meshulam worked on finding an upper bound for subsets containing only trivial 3-APs based on the number of components in a finite abelian group. Meshulam’s bound holds for finite abelian groups of odd order. In 2003 Lev generalised Meshulam’s result for almost all finite abelian groups. In 2009 Liu and Spencer generalised the concept of a 3-AP to a linear equation and obtained a similar bound depending on the number of components of the group. In 2011, Liu, Spencer and Zhao generalised the 3-AP to a system of linear equations. This thesis is an overview of these results.

When the paper web and press felt enter a nip in the press section of a paper machine, both the paper web and felt are compressed. Water is forced from the paper sheet into the press felt due to a hydrodynamic pressure gradient between the sheet and felt. Water not only flows through the felt in the transversal z-direction, but also flows through the felt in the machine and cross-machine directions. On the exit side of the nip, the pressure imposed on the sheet-felt system by the rolls begins to decrease. Both the paper web and press felt begin to expand, and a vacuum is created in the web and felt. The vacuum in the web is stronger than that in the felt, and thus water and air tend to flow from the felt back into the sheet, causing rewet. Three mechanisms that contribute to rewet have been proposed: 1) film splitting between the paper web and press felt, 2) capillary forces in the web drawing water from the felt into the web, and 3) the pressure differential between the web and felt during expansion. The objective of this project was to design and test under flow conditions similar to those in a press nip a smart water receiver to be used in the press section of a paper machine. In this manner, the feasibility of such a water receiver was to be determined. The purpose of this water receiver is to accept water that is pressed from the paper web in a nip and prevent the return of this water to the paper web upon exit from the nip. Thus, the smart water receiver allows flow through the felt in the positive z-direction of the felt (away from the paper web) and not in the negative z-direction (towards the paper web). The smart water receiver concept utilizes a layer of micro-check valves incorporated into the press felt to perform in the desired manner. A mathematical model and lab-scale prototype were created in order to predict the behavior of such a design in the press nip.

Bingo game is a popular and interesting game. This paper considers some interesting properties of the Bingo game played in Taiwan. We discuss how to use the computer to calculate some interesting probability value for various sizes of bingo games. For example, the expectation of the calls to hit a Bingo and the expectation of the Bingo number after the $k$th number is called. Some interesting results are also discussed.

Let S be a set of k distinct elements. An oriented k coloring of an oriented graph D is a mapping f:V(D)¡÷S such that (i) if xy is conatined in A(D), then f(x)¡Úf(y) and (ii) if xy,zt are conatined in A(D) and f(x)=f(t), then f(y)¡Úf(z). The oriented chromatic number Xo(D) of an oriented graph D is defined as the minimum k where there exists an oriented k-coloring of D. For an undirected graph G, let O(G) be the set of all orientations D of G. We define the oriented chromatic number Xo(G) of G to be the maximum of Xo(D) over D conatined by O(G). In this thesis, we determine the oriented chromatic number of complete bipartite graphs and complete k-partite graphs. A grid G(m,n) is a graph with the vertex set V(G(m,n))={(i,j) | 1¡Øi¡Øm,1¡Øj¡Øn} and the edge set E(G(m,n))={(i,j)(x,y) | (i=x+1 and j=y) or (i=x and j=y+1)}. Fertin, Raspaud and Roychowdhury [3] proved Xo(G(4,5))¡Ù7 by computer programs. Here, we give a proof of Xo(D(5,6)=7 where D(5,6) is the orientation of G(5,6).

Let $gamma(G)$ be the domination number of a graph $G$. For any permutation $pi$ of the vertex set of a graph $G$, the prism of $G$ with respect to $pi$ is the graph $pi G$ obtained from two copies $G_{1}$ and $G_{2}$ of $G$ by joining $uin V(G_{1})$ and $vin V(G_{2})$ iff $v=pi(u)$. We prove that $$gamma(pi C_{n})geq cases{frac{ n}{ 2}, &if $n = 4k ,$ cr leftlceilfrac{n+1}{2} ight ceil, &if $n eq 4k$,} mbox{and } gamma(pi C_{n}) leq leftlceil frac{2n-1}{3} ight ceil mbox{for all }pi.$$ We also find a permutation $pi_{t}$ such that $gamma(pi_{t} C_{n})=k$, where $k$ between the lower bound and the upper bound of $gamma(pi C_{n})$ in above. Finally, we prove that if $pi_{b}C_{n}$ is a bipartite graph, then $$gamma(pi_{b}C_{n})geq cases{frac{n}{2}, &if $n = 4k ,$cr leftlceilfrac{n+1}{2} ight ceil, &if $n = 4k+2$,} mbox{and } gamma(pi_{b}C_{n})leq leftlfloor frac{5n+2}{8} ight floor.$$

Thesis (doctoral)--Georg-August-Universität zu Göttingen, 1913. / Cover title. Vita.