Abstract:
In their paper, “On the Cross-sectional Relation between Expected Returns and Betas”, Roll and Ross (1994) demonstrated that the expected returns and betas can have zero relationship even when the underlying market portfolio proxies are nearby the efficient frontier. In this note, we provide the mathematical details that lead to their conclusion and further show that their claim needs not hold for the entire set of MV portfolios.

Abstract:
In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a
homomorphism. The results which proved for generalized left *-derivation of R in[1] are extended by using
generalized left *-α

Abstract:
The theory of Relativity is consistent with the Lorentz transformation. Thus Pr. Lévy proposed a simple derivation of it, based on the Relativity postulates. A reply is provided: Some related results (five ones) are found and developed step by step which would invalid it. So Lorentz transformation would not be simply derived by this way. Finally an alternative demonstration of Lorentz transformation is reminded, consistent with Quantum Mechanics.

Abstract:
Let R be a 2-torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n ￠ ’2)-torsion free or if R is an inner derivation of R, then d2n ￠ ’1=0.

Abstract:
Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving combinatorics problems. Furthermore, we formally derive combinatorics problems by PAR method, which cannot only simplify the process of algorithmic program's designing, but also improve its automatization, standardization and correctness. We develop algorithms for two typical combinatorics problems, the number of string scheme and the number of error per-mutation scheme. Lastly, we obtain accurate C++ programs which are transformed by automatic transforming system of PAR platform.

The
western thoughts have brought many new ideas to China in 19^{th} century, and influenced the words’ meanings of Chinese words system. The
Chinese-English translated terms and their different derivations bridge the gap
between different cultures. The scholar translated English word “civilization”
into Chinese word “wenming”. “Wenming” is derived from “wen” and “ming”. “Wen”
means “People feel and experience the nature by heart, and then painting and
describing things, at last, one can obtain knowledge through this process”. “Ming”
means “based on wen, people are conducted to the correct direction, and become
enlightened and civilized”. “Civilization” is derived from “civil”. And “civil”,
“civis”, “civitas” and “civilitas” have the same word origin. The radical factors
of the meaning of the word “civilization” are “make” and “development”. They
focused on the “town” and “city”, namely, the process of cumulating wealth and
remolding the nature through human being intervening in nature actively. The
different word derivations between “wenming” and “civilization” disclose the
differences of the location and culture when the modern thought of civilization
was pervading the whole world. At the same time, with the semantic developing
of “wenming”, it has the similar concept connotation with “civilization”, so it
displays the compatible property and makes it possible for translation between
two language units.

Explore the new way of product derivation by integrating the interaction design thinking into the product derivation method. It analyzes the thinking mode of interaction design, describes how to make the product provide better experience for the user, from the perspective of the four elements of people, activity, context and technology, and shows how to combine interaction thinking for product derivation through the cases. Good products in addition to the realization of the function also need to meet the needs of the user experience. Product derived can get new methods and ideas from the interaction design of systematic thinking, so that products can provide better service for users in the digital era.

Abstract:
let a be an algebra. a sequence {dn} of linear mappings on a is called a higher derivation if for each a, b ? a and each nonnegative integer n. jewell [pacific j. math. 68 (1977), 91-98], showed that a higher derivation from a banach algebra onto a semisimple banach algebra is continuous provided that ker(d0) ? ker(dm), for all m = 1. in this paper, under a different approach using c*-algebraic tools, we prove that each higher derivation {dn} on a c*-algebra a is automatically continuous, provided that it is normal, i. e. d0 is the identity mapping on a.

Abstract:
Let A be an algebra. A sequence {d n} of linear mappings on A is called a higher derivation if for each a, b ? A and each nonnegative integer n. Jewell [Pacific J. Math. 68 (1977), 91-98], showed that a higher derivation from a Banach algebra onto a semisimple Banach algebra is continuous provided that ker(d0) ? ker(d m), for all m = 1. In this paper, under a different approach using C*-algebraic tools, we prove that each higher derivation {d n} on a C*-algebra A is automatically continuous, provided that it is normal, i. e. d0 is the identity mapping on A.