MCA has gained a reputation for being a very useful statistical method for determining the association between two or more categorical variables and their graphical description. For performance this method, we must calculate the singular vectors through (SVD). Which is an important primary tool that allows user to construct a low-dimensional space to describe the association between the variables categories. As an alternative procedure to use (SVD), we can use the (BMD) method, which involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, the (HD) is formed. The aim of study is to use alternative method of (MCA) that is appropriate with order

Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.

By- products of corn starch industry were used to prepare media for propagation the lactic acid bacteria as a natural auxotroph. The by- products used were the corn steep water (S) and gluten extract (G) after a proper treatment to get them ready for media preparation. The results showed that it was possible to replace the peptone and meat extract by gluten extract in MRS medium. The growth was approximately similar to that obtained in standard MRS media. Corn steep water (S) was used as well and the growth enhanced by including Tween – 80 at 1% level. The later media named MZ, which was superior for growing standard and local strains and starters. The MZ medium modified by adding acetate and glacial acetic acid similarly to

The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never  approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-vers

     . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

Facial emotion recognition finds many real applications in the daily life like human robot interaction, eLearning, healthcare, customer services etc. The task of facial emotion recognition is not easy due to the difficulty in determining the effective feature set that can recognize the emotion conveyed within the facial expression accurately. Graph mining techniques are exploited in this paper to solve facial emotion recognition problem. After determining positions of facial landmarks in face region, twelve different graphs are constructed using four facial components to serve as a source for sub-graphs mining stage using gSpan algorithm. In each group, the discriminative set of sub-graphs are selected and fed to Deep Belief Network (DBN) f

Wheat straw was modified with malonic acid in order to get low cost adsorbent have a good ability to remove copper and ferric ions from aqueous solutions, chemical modification temperature was 120°C and the time was 12 h. Parameters that affect the adsorption experiments were studied and found the optimum pH were 6 and 5 for copper and iron respectively and the time interval was 120 min and the adsorbent mass was 0.1 g. The values for adsorption isotherms parameters were determined according to Langmuir [qmax were 54.64 and 61.7 mg/g while b values were 0.234 and 0.22 mg/l] , Freundlich [Kf were 16.07 and 18.89 mg/g and n were 2.77 and 3.16], Temkin [B were 0.063 and 0.074 j/mol and At were 0.143 and 1.658 l/g] and for Dubinin-Radushkev

The destruction and protection of cultural property has been a feature of armed conflicts for thousands of years and it has received increasing international focus over the past two decades. This feature was clearly appeared during the recent armed conflict in Iraq. During the conflict, cultural property was subjected to intentional and organised destruction by members of ISIS. Although there are international legal norms to protect cultural property during armed conflict, however, this destruction has proven the failure of those rules to effectively deter these criminal acts. This Article analyses the framework of international law relevant to the protection of cultural property during of armed conflict in the light of that destruction,