An elementary proof of Peng’s central limit theorem under sub-linear expectations

Motivated by studies in mathematical finance, S. Peng established a central limit theorem (CLT) under sub-linear expectations by using partial differential equations (PDEs). In this paper, we provide a novel proof of Peng’s CLT in the frame of sub-linear expectation. Our method is not only elementary in the sense that it does not use PDEs, but also more applicable because we only require the random variables to satisfy a reasonable condition which coincides with the classical Lindeberg’s condition when the sub-linear expectation reduces to a linear expectation.

H-Mode Power Threshold Studies on MAST

Analysis of the L–H and H–L transition power thresholds (Pth) and pedestal parameters are presented for the mega ampere spherical tokamak (MAST). The dependencies of Pth on the average, core plasma electron density, X-point height, and plasma current are described. Increasing X-point distance from the divertor floor over 10–12 cm is found to increase Pth by a factor of three, while X-point heights greater than this have no further influence. The X-point height dependence of Pth is also observed to be sensitive to the plasma current. An Ip decrease from 0.77 MA to 0.65 MA, is observed to lower Pth by a factor of three across the X-point height scan and increases the maximum X-point height at which Pth stops increasing by 3 cm. Finally, a comparison of the experimental results with the predictions by the finite beta drift wave model is made, which provides a reasonable condition for the transition into and out of the H-mode.

Polynomial Interpolation of Normal Conditional Expectation

In this paper we are interested in approximating the conditional expectation of a given random variable X with respect to the standard normal distribution N(0, 1). Actually we have shown that the conditional expectation E(X|Z) could be interpolated by an N degree polynomial function of Z, φN(Z) where N is the number of observations recorded for the conditional expectation E(X|Z = z). A pointwise error estimation has been proved under reasonable condition on the random variable X.

PARADIGMA PENELITIAN KOMUNIKASI

Current researches tend to accommodate environment factors and are often dominantly influenced by them. This is a reasonable condition since the nature of communication Science is a contextual one so that it cannot be separated from the facts in its surroundings. The discussion on the development and trends in communication Science will be more interesting to study because in the present time there are many methods and analysis which are applied to understand the elements of communication Science. In accordance to this fact, it is expected that in the near future, communication Science will be more developed and has more complete fields of study in order to give more benefits to society.

Reducibility study of Rossetta ilmenite ore briquettes and powder with coke breeze at 800-1100°C

Ilmenite ore fine and coke breeze as reduced material were briquetted with different amounts of organic materials such as molasses or pitch were studied in this investigation. The produced briquettes at reasonable condition were reduced in nitrogen atmosphere at temperature range 800 - 1100oC to determine the factors controlling the reduction and to determine the controlling mechanism. Also ilmenite ore fine with coke breeze were reduced at the same temperature range in nitrogen atmosphere without briquetting process, for the sake of comparison.

Microencapsulation Exploration of Squalene by Ultrasonic Spraying and Freeze-Drying

Squalene, a natural antioxidant, was microencapsulated by the method of ultrasonic spraying and freeze-drying using shell materials of gelatin and arabic gum. The suitable condition for ultrasonic emulsification before ultrasonic spraying and freeze-drying was frequency 28 kHz and running time 20 min. The reasonable condition for microencapsulation of squalene by ultrasonic spraying and freeze-drying was gelatin 3.0 %, arabic gum 5.0 %, maltodextrin 6.0 % and sucrose ester 0.9 %. The appearance and size of microcapsules of squalene were measured by scanning electron microscope and metallographic microscope. The microcapsules of squalene were smonth spheres at the diameter of about 10 μm.

FRACTAL STRUCTURE ON k-SAT

The k-SAT (k ≥ 3) is a typical NP-complete problem in computer science. To visualize k-SAT, we embed the Boolean expressions in k-CNF, with variables in an infinite list, into cube [0, 1]k of Euclidean space. In this paper, we find fractal structure of the visualized image of satisfiable expressions, we also prove that the image has full Hausdorff dimension k under some reasonable condition, by constructing some Moran subset. The results show this image is quite different from that with respect to a finite list of Boolean variables as in Refs. 1 and 2.

BORN–INFELD LAGRANGIAN USING CAYLEY–DICKSON ALGEBRAS

We rewrite the Born–Infeld Lagrangian, which is originally given by the determinant of a 4×4 matrix composed of the metric tensor g and the field strength tensor F, using the determinant of a (4·2n)×(4·2n) matrix H4·2n. If the elements of H4·2n are given by the linear combination of g and F, it is found, based on the representation matrix for the multiplication operator of the Cayley–Dickson algebras, that H4·2n is distinguished by a single parameter, where distinguished matrices are not similar matrices. We also give a reasonable condition to fix the parameter.

Optimal Underwriting Contracts and Underpricing of New Issues

The purpose of this paper is to analyze a new issue process in a model that focuses on the contractual relationship between an issuing firm and its investment banker, when the latter is assumed to have superior information regarding the market demand for the new securities. A “firm commitment” contract induces first-best choices of marketing effort and offer price by the banker, but is shown to be suboptimal for the issuer when the information asymmetry exists prior to contracting. The issuer's selection of a second-best underwriting contract is shown to result, under certain conditions, in the offer price set below the first best level. This “underpricing” result is explicitly explained and related to the empirical literature on underpricing. Finally, it is shown that, under a reasonable condition, the issuer does not lose value by delegating the pricing decision to the better informed investment banker.

Proper morphisms and excellent schemes

Let f: X → Y be a finite type morphism of locally noetherian schemes. It is well known ([3, IV, 7.8.6]) that the excellent property ascends from Y to X. On the other side there are counter-examples where X is excellent and Y is not. First of all it is easy to show that the condition on chains of prime ideals does not descend (see [3, IV, 7.8.4]), even by finite morphisms. Secondly in [2] it is produced an example where X is excellent while Y is not a G-scheme (i.e. it has not the good properties of formal fibers). However in [2] it is also proved that the property concerning the openness of regular loci (the so called “J-2”) descends by finite type surjective morphisms. Therefore we are led to the following question: When does the G-scheme property descend? I.e. what conditions do we need on f? A reasonable condition is conjectured (in [2]) as the following: f is proper surjective. The aim of the present paper is precisely to give an answer to such a question. What we really prove is the following. If X is a G-scheme and J-2 (quasi-excellent), then the same is true for Y, provided that f is proper surjective and moreover all the residue fields of Y have characteristic 0. We remark that the result is strongly based on Hironaka’s desingularization for quasi-excellent schemes defined over a field of characteristic 0.