In the present article generalization of Weierstrass’s preparation theorem and the division theorem for germs of holomorphic functions at a point of ^{n }-dimensional complex space are considered. The author formulates the global theorem about division in terms of existence and continuity of the linear operator.

The Hypoexponential distribution is the distribution of the sum of m≥2 independent Exponential random variables. This distribution is used in modeling multiple exponential stages in series. This distribution can be used in many domains of application. In this paper we find a modified and simple form of the probability density function for the general case of the Hypoexponential distribution when its parameters do not have to be distinct. This modified form is found by writing the probability density function of this distribution as a linear combination of the probability density function of the known Erlang distribution. Also, this modified form generates a simple form of the cummulative distribution function, moment generating function, reliability function, hazard function, and moment of order k for the general case of the Hypoexponential distribution. Moreover, new identities are established. Finally, we consider the coefficients of this linear combination and propose an algorithm to compute them.

In recent years, uncertain textual data has become ubiquitous because of the latest technology used for data collection. As the existing technology can only collect data in an imprecise way. Furthermore, various technologies such as privacy-preserving data mining create data which is inherently uncertain in nature. So this paper propose a frequent pattern mining technique for mining termsets from uncertain textual data. This technique has conducted a study on uncertain textual data using the Karnaugh Map concept. The paper describes the approach in a three step procedure. First, we review existing methods of finding frequent termsets from document data. Second, a new method UTDKM ( Uncertain Textual Data Mining using Karnaugh Map) is proposed for finding frequent termset from uncertain textual data. Finally, we carried out experiments to evaluate the performance of the proposed method. The experimental results demonstrate that the prominent feature of this method that is it requires only a single database scan for mining frequent patterns. It reduces the I/O time as well as CPU time.

In this paper, we study the summations P _{(a,b,c)EN3 } (f(a + b) + f(b + c) + f(c + a)) and P_{(a;b;c;d)2N4 }(f(a + b + c) + f(b + c + d) + f(c + d + a)). Especially, for the first summation we obtain some relations related to Bernoulli and Euler polynomials.

Tuberculosis is an infectious disease which can be fatal. Hence, availability of models predicting its potential outbreak can be very useful in its preventative strategies. This paper finds the best mathematical model which fits onto the tuberculosis occurrence data of Ashanti Region of Ghana, and uses the model to predict the future epidemiology and incidence of the disease in the region to enhance anti-tuberculosis campaigns. The data used for the study was obtained from the Ashanti Health Services and spans January 2001 to March 2013. It is evident from the analysis that tuberculosis occurrence in the region studied can best be modeled with ARMA (1, 0) or AR(1), i.e. a stochastic time series linear model, and that tuberculosis epidemic in the Ashanti Region is expected to be stable between April 2013 and April 2015. The Mean Absolute Error (MAE) and the Mean Squared Error (MSE) are used to compare the in-sample forecasting performance of three selected competing models, and the result shows that it is not always true that the best selected model gives the best results so far as the mean square error (MSE) is concerned. The forecasting accuracies for the obtained model, i.e. AR (1), using MAE and MSE are respectively 16.3171 and 461.3148.

Let X be a graph on n vertices and let B = {P(x) : x ∈ V (X)} be a collection of n subgraphs of X, one for each vertex, B is an orthogonal double cover (ODC) of X if every edge of X occurs in exactly two members of B and any two members share an edge whenever the corresponding vertices are adjacent in X and share no edges whenever the corresponding vertices are nonadjacent in X. The main question is: given the pair (X, G), is there an ODC of X by G? An obvious necessary condition is that X is a regular. In this paper, we are almost exclusively concerned with the starter maps of the orthogonal double covers of cayley graphs and using this method to construct ODCs by a complete bipartite graph, a complete tripartite graph, caterpillar, and a connected union of a cycle and a star whose center vertex belongs to that cycle.

In this paper, a Susceptible - Exposed - Infected - Recovered (SEIR) epidemiological model is formulated to determine the transmission of tuberculosis. The equilibrium points of the model are found and their stability is investigated. By analyzing the model, a threshold parameter R_{0} was found which is the basic reproductive number. It is noted that when R_{0} < 1 the disease will fail to spread and when R_{0} > 1 the disease will persist in the population and become endemic. The model has two non–negative equilibria namely the disease – free equilibrium and the endemic equilibrium. The graphical solutions of the differential equations were developed using Matlab as well as the computer simulations.

We consider the class E of endo-Noetherian modules, i.e. the modules M which satisfying the ascending chain condition for endomorphic kernels: any ascending chain Kerf1 Kerf2 Kerfn is stationary, where fi 2 End(M). Let N be the class of Noetherian modules. It is clear that every Noetherian R-module M is endo-Noetherian, so N E, but the converse is not true. Indeed, Q is a non-Noetherian Z-module which is endo-Noetherian. The aim of this work, is to characterize commutative rings for which E and N are identical.

In this paper we introduce a new subclass of multivalent analytic functions defined by fractional calculus operator. Such results as subordination and superordination properties, convolution properties, inequality properties and other interesting properties of this subclass are proved.