Abstract:
The aim of the present work was to develop controlled release matrix formulation of nifedipine and investigate the effects of both hydrophilic and hydrophobic polymers on in vitro drug release. Matrix tablets were prepared by wet granulation technique using different concentration of hydroxy propyl methyl cellulose (HPMC), ethyl cellulose (EC), compressible Eudragits (RSpo and RLpo) and their combination in different ratios to examine their influence on tablet properties and drug release profile. Tablets were evaluated by measurement of hardness, friability, content uniformity, weight variation and drug release pattern. Release studies were carried out using USP type II apparatus in 900 ml of sodium phosphate buffer (pH 7.4) with 0.5% (w/v) SDS. The amount of drug released was determined at 238 nm by UV-visible spectrophotometer.In vitro dissolution studies indicated that hydrophobic polymers significantly reduced the rate of drug release compared to hydrophilic ones in 12 hrs and combination of both polymers exhibited the best release profile to sustain the drug release for prolong period of time. As a result, the tablet containing HPMC:EC in ratio of 0.75:1 showed better controlled release pattern over a period of 12 hrs. In selected formulation, the calculated regression coefficients for release models fitted best to zero-order models.

A
semimicroscopic analysis of a set of experimental data of elastic α + ^{12}C scattering was performed at several laboratory energies. The
Woods-Saxon parameters were adjusted to obtain the best χ^{2} fit to the scattering data. The energy systematics of
the positions of Airy minima was constructed, and it was shown that their
positions depend linearly on the inverse center of mass energy. The parameters
of the model potential have been determined unambiguously. It has been shown
that the energy dependence of the volume integrals satisfies the dispersion
relation and agrees well with the results obtained within a phenomenological
analysis. Also, it has been shown that the found positions of the Airy minima
satisfy the rule of the quadratical dependence of the position of the Airy
minima on the reduced mass of the colliding nuclei.

Abstract:
This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods. 1. Prerequisites One of the important and challenging problems in numerical analysis is to find the solution of nonlinear equations. In recent years, several numerical methods for finding roots of nonlinear equations have been developed by using several different techniques; see, for example, [1, 2]. We herein consider the nonlinear equations of the general form where is a real valued function on an open neighborhood and a simple root of (1.1). Many relationships in nature are inherently nonlinear, in which their effects are not in direct proportion to their cause. Accordingly, solving nonlinear scalar equations occurs frequently in scientific works. Many robust and efficient methods for solving such equations are brought forward by many authors; see [3–5] and the references therein. Note that Newton’s method for nonlinear equations is an important and fundamental one. In providing better iterations with better efficiency and order of convergence, a technique as follows is mostly used. The composition of two iterative methods of orders and , respectively, results in a method of order , [6]. Usually, new evaluations of the derivative or the nonlinear function are needed in order to increase the order of convergence. On the other hand, one well-known technique to bring generality is to use weight function correctly in which the order does not die down, but the error equation becomes general. In fact, this approach will be used in this paper. Definition 1.1. The efficiency of a method is measured by the concept of efficiency index, which is given by where is the convergence order of the method and is the whole number of evaluations per one computing process. Meanwhile, we should remember that by Kung-Traub conjecture [7] as comes next, an iterative multipoint scheme without memory for solving nonlinear equations has the optimal efficiency index and optimal rate of convergence . Higher-order methods are widely referenced in

Abstract:
The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.

Abstract:
Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation ()=0. New techniques can be taken into account as the generalizations of the one-step method of Steffensen. Theoretical proofs of the main theorems are furnished to reveal the eighth-order convergence. Per computing step, the derived methods require only four function evaluations. Experimental results are also given to add more supports on the underlying theory of this paper as well as lead us to draw a conclusion on the efficiency of the developed classes.

Abstract:
This study has proposed two classes of without memory iterative derivative-free methods for solving nonlinear equations. The first class includes three evaluations of the function per full iteration to reach the local order of convergence four. And the second class of methods carries out one more function evaluation than the first one to achieve seventh-order of convergence. The suggested schemes are useful when the calculation of derivatives of the functions is expensive. To show their easy implementations and efficiencies, this study has applied them to solve some numerical examples by comparing with the existing derivative-free methods in literature.

Abstract:
In this note, after presenting a new root-finder family of local order four and obtaining two new one-point iterative schemes, we compare some different fourth-order methods by some numerical examples. Subsequently, we specify that the methods of the same order and the same efficiency index have different computational cost and also conclude that the existed methods are less efficient than the proposed iterative schemes in this work. This is because of that, per iteration all of the evaluations have not the same computational cost, while it had been considered in the past papers in this field.

Abstract:
e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for one the interaction is two-body

Abstract:
We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified and not arbitrary couplings. We also compute in closed forms the one and two-point functions and the explicit form of the ground state. The degeneracy structure of the ground state is also discussed.

Abstract:
In medical applications such as recognizing the type of a tumor as Malignant or Benign, a wrong diagnosis can be devastating. Methods like Fuzzy Support Vector Machines (FSVM) try to reduce the effect of misplaced training points by assigning a lower weight to the outliers. However, there are still uncertain points which are similar to both classes and assigning a class by the given information will cause errors. In this paper, we propose a two-phase classification method which probabilistically assigns the uncertain points to each of the classes. The proposed method is applied to the Breast Cancer Wisconsin (Diagnostic) Dataset which consists of 569 instances in 2 classes of Malignant and Benign. This method assigns certain instances to their appropriate classes with probability of one, and the uncertain instances to each of the classes with associated probabilities. Therefore, based on the degree of uncertainty, doctors can suggest further examinations before making the final diagnosis.