Let E be a uniformly smooth and uniformly convex real Banach space and A : E → E* be a generalized Φ-strongly monotone and bounded map with A-1(0) ≠ θ. A new iterative process is constructed and proved to converge strongly to the unique solution of the equation Au = 0. An application to convex minimization problem is given. Furthermore, the technique of proof is of independent interest.
Recently, a new symbolic algorithm for solving comrade linear systems is given by Karawia [A. A. Karawia, Symbolic algorithm for solving comrade linear systems based on a modi fied Stair-Diagonal Approach, Appl. Math. Lett. 2013; 26:913-918.]. This paper introduces different numerical and symbolic algorithms for solving comrade linear systems via transformations. Our symbolic algorithm removes the cases where the numerical algorithms fail. The computational cost of these algorithms is given. It gives better absolute error than the other methods. The algorithm is implementable to the Computer Algebra System (CAS) such as MAPLE and MATLAB. Some illustrative examples are presented for the sake of illustration.
In this paper the author(s) present derivations for the mean and variance of the nth power transformation of the error component of the multiplicative time series model. as a general rule to any power transformation. Some of the published transformations like the square root and the inverse were used to validate the results obtained. The results showed that they conformed to the general rule.
Fast image retrieval has been a fundamental problem in the area of image processing for a long time. This paper proposes a rapid image retrieval algorithm by improving the conventional nearest neighbor search through the implementation of vector product quantization and inverted indexing structure. Vector product quantization can efficiently accomplish the fast nearest neighbor search task, and has many great advantages in terms of storage requirements, retrieval speed and accuracy. In order to further reduce the search time, an approximate threshold-based distance estimation technique is introduced into the retrieval algorithm. Moreover, the quick sort method is implemented to reorder the image search results, which can significantly improve the performance of our retrieval algorithm.
This short paper offers an example of possibly fruitful interactions between modal logic and number theory. In the paper, Conway's remark that p and p.2p + 1 can both be prime numbers is formulated as a formula of modal logic and then analyzed for its decidability.
Let us call a ring R to be right permeable if for any α ∈ R; Rα = 0, thenαR = 0. Left permeable and permeable rings are defined analogously. These rings are generalized reversible rings with a privileging role that permeability inherited in its several extensions where reversibility seized to be inherited. It will be proved that full matrix ring, polynomial ring, Laurent polynomial ring, Dorroh extension, group ring and Ore extensions of a right (left) permeable ring are right (left) permeable rings. Moreover, the same holds for Barnett matrix rings with their extensions in different quotient polynomials and matrix forms.
The concept of fuzzy versions of Simpson’s rule and Runge-Kutta method of order four are introduced. In this paper, the solution of fuzzy ordinary differential equation of the first order by Simpson’s rule and Runge-Kutta method of order four is presented without converting them to crisp form. The results from these two methods are proved identical by complete error analysis. The accuracy and efficiency of the proposed methods are illustrated by an example with a trapezoidal fuzzy number and triangular fuzzy number.