Abstract:
Let $\boxplus$, $\boxtimes$ and $\uplus$ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure $\mu$ on $[0,\infty)$ with finite second moment, we find the scaling limit of $(\mu^{\boxtimes N})^{\boxplus N}$ as $N$ goes to infinity. The $\mathcal{R}$--transform of the limit distribution can be represented by the Lambert's $W$ function. We also find similar limit theorem by replacing the free additive convolution with the boolean convolution.

Abstract:
We give a complete list of the Lebesgue-Jordan decomposition of Boolean and monotone stable distributions and a complete list of the mode of them. They are not always unimodal.

Abstract:
We will prove that: (1) A symmetric free L\'evy process is unimodal if and only if its free L\'evy measure is unimodal; (2) Every free L\'evy process with boundedly supported L\'evy measure is unimodal in sufficiently large time. (2) is completely different property from classical L\'evy processes. On the other hand, we find a free L\'evy process such that its marginal distribution is not unimodal for any time $s>0$ and its free L\'evy measure does not have a bounded support. Therefore, we conclude that the boundedness of the support of free L\'evy measure in (2) cannot be dropped. For the proof we will (almost) characterize the existence of atoms and the existence of continuous probability densities of marginal distributions of a free L\'evy process in terms of L\'evy--Khintchine representation.

Abstract:
We find necessary and sufficient conditions for the free additive infinite divisibility of some free multiplicative convolutions with the Wigner, the arcsine, the free Poisson and other distributions, including explicit examples.

Abstract:
We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We prove that the class of free regular measures is closed under the free multiplicative convolution, t-th boolean power for $0\leq t\leq 1$, t-th free multiplicative power for $t\geq 1$ and weak convergence. In addition, we show that a symmetric distribution is freely infinitely divisible if and only if its square can be represented as the free multiplicative convolution of a free Poisson and a free regular measure. This gives two new explicit examples of distributions which are infinitely divisible with respect to both classical and free convolutions: \chi^2(1) and F(1,1). Another consequence is that the free commutator operation preserves free infinite divisibility.

Abstract:
It is known that in many cases distributions of exponential integrals of Levy processes are infinitely divisible and in some cases they are also selfdecomposable. In this paper, we give some sufficient conditions under which distributions of exponential integrals are not only selfdecomposable but furthermore are generalized gamma convolution. We also study exponential integrals of more general independent increment processes. Several examples are given for illustration.

Abstract:
The N-body problem is an active research topic in physics for which there are two major algorithms for efficient computation, the fast multipole method and treecode, but these algorithms are not popular in financial engineering. In this article, we apply a fast N-body algorithm called the Cartesian treecode to the computation of the integral operator of integro-partial differential equations to compute option prices under the CGMY model, a generalization of a jump-diffusion model. We present numerical examples to illustrate the accuracy and effectiveness of the method and thereby demonstrate its suitability for application in financial engineering.

Abstract:
ABSTRACT
The molecular signaling pathway linked to hyper-trophy of the anti-gravity/postural soleus muscle af-ter mechanical overloading has not been identified. Using Western blot and immunohistochemical analy-ses, we investigated whether the amounts of NFATc3, GSK-3?, NFATc1, and neonatal MHC change in the mechanically overloaded soleus muscle after cyc-losporine A (CsA) treatment. Adult male ICR mice were subjected to a surgical ablation of the gas-trocnemius muscle and treated with either CsA (25 mg/Kg) or vehicle once daily. They were sacrificed at 2, 4, 7, 10, and 14 days post-injury. Mechanical over-loading resulted in a significant increase in the wet weight and the cross-sectional area of slow and fast fibers of the soleus muscle in placebo-treated mice but not CsA-treated mice. After 4 days of mechanical overloading, we observed a similar co-localization of neonatal MHC and NFATc3 in several myotubes of both mice. The placebo-treated mice possessed larger myotubes with neonatal MHC than CsA-treated mice. At 7 days, mechanical overloading induced marked expression of neonatal MHC in myotubes and/or myofibers. Such neonatal MHC-positive fibers emerged less often in the hypertrophied soleus mus-cle subjected to treatment with CsA. CsA treatment did not significantly change the amount of GSK-3? protein in the soleus muscle. The modulation of growth in neonatal MHC-positive myofibers by CsA treatment may inhibit the hypertrophic process in the soleus muscle after mechanical overloading.

A quantitative
analysis of capillary supply to skeletal muscle is important for understanding
the upper limit of the capacity for delivery of oxygen and substrates to muscle
cells. It has been well documented that the number of capillaries is altered
by several factors including development, aging, and alteration of muscle
activity level such as exercise training and inactivation. There is, however,
a contradiction in animal studies for aging-related change in the number of
capillaries. Human studies using biopsy technique also displayed an
inconsistency on that point, in which capillary supply was not influenced or
decreased with aging. This review discussed an inconsistency among studies for
aging-related change in muscle capillary supply. In conclusion, the
relationship between capillary supply and muscle fiber size is similar for both
young and elderly population, and the morpho- logical balance between
capillaries and each muscle fiber was maintained with advancing age.

Abstract:
multiple range tests according to kramer, 1956 were performed on 3 meristic and 15 morphometric characters of "pescada-foguete" (macrodon ancylodon) samples collected off coast near concei？？o da barra (espirito santo state), atafona, macaé, ubatuba cities, bom abrigo island and rio grande do sul state coast. it was also observed morphological differences in otoliths collected at each region. the number of statistical differences among samples and different morphological characteristics presented by otoliths suggested the existence of four populations along the studied area: (1) along espírito santo state coast; (2) near the region between atafona and macaé coasts; (3) along s？o paulo, paraná and north santa catarina states coasts and (4) along rio grande do sul state coast. probably the differentiation was caused by different environmental conditions observed among regions. other papers about life history corroborate these results except for the espírito santo population about which there is no biological information up to the moment.