Abstract:
This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that our Greeks converge to Malliavin Greeks in the continuous time model. The computation algorithm of Greeks for American options using the binomial tree is also given in this article. There are three advantageous points to use binomial tree approach for the computation of Greeks. First, mathematics is much simpler than using the continuous time Malliavin calculus approach. Second, we can construct a simple algorithm to obtain the Greeks for American options. Third, this algorithm is very efficient because one can compute the price and Greeks (delta, gamma, vega, and rho) at once. In spite of its importance, only a few previous studies on the computation of Greeks for American options exist, because performing sensitivity analysis for the optimal stopping problem is difficult. We believe that our method will become one of the popular ways to compute Greeks for options.

Abstract:
In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\'al "the reciprocal of (the number) n", which is often abbreviated to igi-n, and igi-te-en whose meaning is somewhat abstract, that is, "a proportion (of something)" or "the ratio (of something to another)"(1). Thus the mathematical meanings of the two terms are quite clear, but we have not been able to clarify their literal meanings or their origins so far. In the present paper I shall offer a most probable interpretation of the early term, igi-n-g\'al, and a definite solution to the etymology of the later term, igi-te-en, both of which are based on my analysis of several mathematical terms that concern multiplication or division.

Abstract:
In the middle of the third millennium BC the Sumerians must have noticed that the reciprocal of the number 7,in contrast to the numbers 1,2,3,4,5,and 6,could not be expressed by a finite sexagesimal fraction but it recurred every three places.Since the number 7 is the first natural number that has such a property, it was of particular interest to them and became the representative of their number mysticism.

Abstract:
In the present paper I shall clarify that the origin of compound interest goes back 4400 years to Sumer by showing the Sumerian scribe of Enmetena Foundation Cone calculated seventh power of four-thirds.

Abstract:
In the present paper I shall reveal two circular figures hidden behind the Susa mathematical text no.3,lines 5 and 6 with my own analysis of the text.

Abstract:
Introduction: The surgical management of lateral lymph nodes in differentiated thyroid carcinoma is controversies. Therefore, we analyzed whether sentinel lymph nodes (SLN) biopsy of the first draining nodes in the jugulo-carotid chain is an accurate technique to select patients with true-positive but nonpalpable lymph nodes for selective lateral node dissection. Materials and Methods: From January 2009 to December 2009, 12 patients with solitary papillary carcinoma measuring 2 cm by ultrasonography were included in this study. After the thyroid gland was exposed to avoid injuring the lateral thyroid lymphatic connection, approximately 0.2 ml of 5mg/ml indocyanine green was injected into the parenchyma of upper and lower thyroid gland. Some stained lymph nodes in the jugulo-carotid chain could be identified following the stained lymphatic duct and dissected as the SLN. After that, thyroidectomy with modified neck dissection was performed. Results: The mean tumor size was 22.1 ± 4.6 mm. Identification and biopsy of stained SLN in the ipsilateral jugulo-carotid chain was successful in all 12 cases. In 6 cases, histopathological analysis of SLNs revealed metastases of the papillary thyroid carcinoma. Among them, 2 cases had additional metastatic lymph nodes in the ipsilateral compartment. Of the 6 patients who had negative lymph node metastasis (LNM) in SLNs, all patients had negative LNM in the ipsilateral compartment. Conclusions: The method may be helpful in the detection of true-positive but nonpalpable lymph nodes and may support a decision to perform a selective lateral node dissection in patients with papillary thyroid carcinoma.

Abstract:
Argentine ant invasion changed colour-polymorphic composition of ant-mimetic jumping spider Myrmarachne in southwestern Japan. In Argentine ant-free sites, most of Myrmarachne exhibited all-blackish colouration. In Argentine ant-infested sites, on the other hand, blackish morph decreased, and bicoloured (i.e. partly bright-coloured) morphs increased in dominance. Invasive Argentine ant drives away native blackish ants. Disappearance of blackish model ants supposedly led to malfunction of Batesian mimicry of Myrmarachne.

Abstract:
We have developed a computational method that predicts the positions of active compounds, making it possible to increase activity as a fragment evolution strategy. We refer to the positions of these compounds as the active position. When an active fragment compound is found, the following lead generation process is performed, primarily to increase activity. In the current method, to predict the location of the active position, hydrogen atoms are replaced by small side chains, generating virtual compounds. These virtual compounds are docked to a target protein, and the docking scores (affinities) are examined. The hydrogen atom that gives the virtual compound with good affinity should correspond to the active position and it should be replaced to generate a lead compound. This method was found to work well, with the prediction of the active position being 2 times more efficient than random synthesis. In the current study, 15 examples of lead generation were examined. The probability of finding active positions among all hydrogen atoms was 26%, and the current method accurately predicted 60% of the active positions.

Abstract:
We investigate the correspondence between the D2-brane, which is described by the abelian Born-Infeld action, and multiple D0-branes, which are done by the nonabelian Born-Infeld action. We construct effective actions for the fuzzy cylinder, sphere and plane formed via D0-branes and compare these actions with those for the cylindrical, spherical and planar D2-brane. We show that in the continuous limit, the effective actions for the fuzzy D0-branes precisely coincide with those for the single D2-brane if both the fuzziness of the D0-brane and the area occupied per a unit of magnetic flux on the D2-brane are equal to $(2\pi\ell_s)^2$.