Abstract:
Using the theory of coincidence degree, the authors have studied the existence of periodic solutions of a type of higher order with restoring terms delay functional differential equations with neutral type, and some new results for the existence of periodic solutions have been obtained.

Abstract:
The author has studied the existence of periodic solutions of a type of higher order delay functional differential equations with neutral type by using the theory of coincidence degree, and some new sufficient conditions for the existence of periodic solutions have been obtained. 1. Introduction and Lemma With the rapid development of modern science and technology, functional differential equation with time delay has been widely applied in many areas such as bioengineering, systems analysis, and dynamics. Functional differential equation with complex deviating argument is an important type of the above function. Because the property of the solution to this kind of equation is impossibly estimated, so the literature on the functional differential equation with complex argument is relatively rare [1]. In recent years, with the maturity of the theory of nonlinear functional analysis and algebraic topology, we have the powerful tools of the study on the functional differential equation with complex deviating argument, so it is possible to study the above equation. Furthermore, the study on the periodic solutions of functional differential equation is always one of the most important subject that people concerned for its widespread use. Many results of the study of Duffing-typed functional differential equation and Liénard-typed functional differential equation have been obtained, for example, the literatures [2–18]. Hitherto, the literature of the discussion of higher order functional differential equations has not been found a lot [19]. In this paper I have studied and derived some sufficient conditions that guarantee the existence of periodic solutions for a type of higher order functional differential equations with complex deviating argument as the following: and some new results have been obtained. In order to establish the existence of -periodic solutions of , we make some preparations. Definition 1.1. Let , are Banach spaces, and let be an open and bounded subset in , and let be linear mapping; the mapping will be called a Fredholm mapping of index zero if and is closed in . Definition 1.2. Let , let be projectors, and let be nonlinear mapping; the mapping will be called -compact on if and are compact. Lemma 1.3 (see [20]). Let , be Banach spaces; is a Fredholm mapping of index zero ; are continuous mapping projectors; is an open bounded set in ; is -Compact on , furthermore suppose that:(a) ; (b) ; (c) , then the equation has at least one solution on , where is Brouwer degree. 2. Main Results and Proof of Theorems Theorem 2.1. Suppose that , , , are

Abstract:
Based on the mathematical model of one dimension transient flow of the polymer foam in porous media, the numerical calculation method of the flow mentioned above by using the finite difference method is given. Through the experiments of one dimension transient flow of HPAM (Hydrolytic Polyacrylamide) foam in the artificial sandstone core, the HPAM foam generation and coalescence coefficient of the mathematical model mentioned above are determined. The profiles of the liquid phase saturation, the pressure drop and the number density of one dimension transient flow of HPAM foam with the dimensionless time in artificial sandstone core are numerically calculated and analyzed by using the numerical calculation method.

Abstract:
The mathematical models of the flow of polymer foam in porous media under three injection modes are established and the relevant numerical calculation methods are given. The profiles of the liquid phase saturation, the pressure drop and the number density of the flowing HPAM foam in artificial sandstone cores with the dimensionless distance under three injection modes are numerically calculated and analyzed. The results show that, compared with the injection mode 2 and 3, HPAM foam flows in a piston-like fashion in the artificial sandstone core under the injection mode 1 and produces the biggest pressure drop. Obviously, the flood efficiency is the highest under the injection mode 1.

Abstract:
As an application of artificial intelligence and expert system technology to database design,this paper presents an intelligent design tool NITDT,which comprises a requirements specification language NITSL,a knowledge representation language NITKL,and an inference engine with uncertainty reasoning capability.NITDT now covers the requirements analysis and conceptual design of database design.However,it is possible to be integrated with another database design tool,NITDBA,developed also at NIT to become an integrated design tool supporting the whole process of database design.

Abstract:
We introduce the sequence given by generating function and establish some explicit formulas for the sequence . Several identities involving the sequence , Stirling numbers, Euler polynomials, and the central factorial numbers are also presented. 1. Introduction and Definitions For a real or complex parameter , the generalized Euler polynomials are defined by the following generating function (see [1–4]) Obviously, we have in terms of the classical Euler polynomials , being the set of positive integers. The classical Euler numbers are given by the following: The so-called the generalized Euler numbers are defined by (see [3, 5]) In fact, are the Euler numbers of order , being the set of integers. The numbers are the ordinary Euler numbers. Zhi-Hong Sun introduces the sequence similar to Euler numbers as follows (see [6, 7]): where (and in what follows) is the greatest integer not exceeding . Clearly, for . The first few values of are shown below The sequence is related to the classical Bernoulli polynomials (see [8–11]) and the classical Euler polynomials . Zhi-Hong Sun gets the generating function of and deduces many identities involving . As example, (see [6]), Similarly, we can define the generalized sequence . For a real or complex parameter , the generalized sequence is defined by the following generating function: Obviously, By using (10), we can obtain We now return to the Stirling numbers of the first kind, which are usually defined by (see [2, 5, 8, 11, 12]) or by the following generating function: It follows from (13) or (14) that and that The central factorial numbers are given by the following expansion formula (see [3, 5, 13]): or by means of the generating function It follows from (17) or (18) that with We also find from (18) that The main purpose of this paper is to prove some formulas for the generalized sequence and . Some identities involving the sequence , Stirling numbers , and the central factorial numbers are deduced. 2. Main Results Theorem 1. Let and Then, Remark 2. By (15), (19), (20), and Theorem 1, we know that is a polynomial of with integral coefficients. For example, by setting in Theorem 1, we get Taking in Theorem 1, we can obtain the following. Corollary 3. Let . Then, From Corollary 3, we may immediately deduce the following results. Corollary 4. Let . Then, Theorem 5. Let . Then, Theorem 6. Let . Suppose also that is defined by (22). Then, Theorem 7. Let . Then, Theorem 8. Let . Then, Theorem 9. Let . Then, 3. Proofs of Theorems Proof of Theorem 1. By (10), (13), and (18), we have which readily yields This completes the

The load varies periodically, but the peak current of
power cable is controlled by its continuous ampacity in China, resulting in the
highest conductor temperature is much lower than90℃,
the permitted long-term working temperature of XLPE. If the cable load is
controlled by its cyclic ampacity, the cable transmission capacity could be
used sufficiently. To study the 10kV XLPE cable cyclic ampacity and its factor, a
three-core cable cyclic ampacity calculation software is developed and the
cyclic ampacity experiments of direct buried cable are undertaken in this
paper. Experiments and research shows that the software calculation is correct
and the circuit numbers and daily load factor have an important impact on the
cyclic ampacity factor. The cyclic ampacity factor of 0.7 daily load factor is
1.20, which means the peak current is the 1.2 times of continuous ampacity. If
the continuous ampacity is instead by the cyclic ampacity to control the cable
load, the transmission capacity of the cable can be improved greatly without
additional investment.

Abstract:
The selection of power transformer is very important to power sector. Most methods are utilized according to the initial cost and don’t consider the synthetical evaluation of economy and technology. Based on previous research, this paper addresses a new practical probabilistic life cycle cost model. Then, in order to demonstrate the practicability of probabilistic life cycle cost for the
power transformer, illustrative investment alternatives of actual power transformers are discussed. From the result of the numerical investigation, it may be positively stated that the optimum investment alternative for the power transformer based on the probabilistic life cycle cost model proposed in this study will lead to a more rational, economical and effective procedure compared with the conventional method only considering the initial cost.