Hardy-Littlewood-Type Theorem for Mixed Fractional Integrals in Hölder Spaces

We study mixed Riemann-Liouville fractional integration operators and mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The obtained are results generalized to the case of Hölder spaces with power weight.

On Symmetric Riemann-Derivatives

The basic properties like monotoni city, Darboux property, mean value property of symmetric Riemann-derivatives of order n of a real valued function f at a point x of its domain (a closed interval) is studied. In some cases, function is considered to be continuous or semi-continuous.

Effectiveness of Oral Tests in Improving Learners’ Mathematical Performance

The main purpose of this paper is, the effect of guided oral questions in mathematics lessons on evaluation formative testing in Increase academic achievement. The sample of the Research consisted of two 23-person classes from computer students at the University of Dr. Moien Rasht. Both classes took pre-test, with a common question from the semester’s lessons. Randomly, Class A was selected as the control, and Class B was selected as the experiment .In Class A, after 6 weeks of teaching, evaluation formative the classical test was formally written (paper-and-pencil) .Group B students, with the same content of Class A teaching, received group Oral (participatory) instead of, formative tests. Group members were selected based on formula, According to the attention, pre-test scores value, and other Indicators. At the end of the semester, both classes were aggregated with the same question, and the scores of both classes were analyzed by descriptive and inferential statistics, t and ES .Statistical analysis showed that learning rate increased in both control and experimental groups. But in cumulative Evaluation, the mean scores of the experimental group were higher than the Average scores of the control group. While in the pre-test, the control group scores were higher than the experimental group. The area under the corresponding curve, ES = .96, is / 831. That is, the area under the curve corresponding to the test group members, on whom the developmental test was orally administered, their mathematics lesson scores were83.15 higher than the control group.

Comparative Analysis of Similarities and Differences between Null Hypotheses, Assumption of Breach

The main purpose of this paper is to comparatively study the similarities and differences between of the , null hypothesis and assumption of breach .The null hypothesis , in applied researches, particularly experiments for confirm or rejection .a hypothesis, regard to inferential statistics That used in many different fields of humanities researchers, particularly psychology, education, management and sociological placed assumption of breach, to prove geometric proposition( theorems), which hypothetical temporary, that with the help of reasoning, the false statements, it we conclude. Such a statement may deny our hypotheses or assume reduction ad absurdum. The use of these two words separately and hypothesis alternative in abundance, the world of science and research, has been discussed, but the relationship between these words, mention, yet. Isn’t .This article describes the relation of these assumptions. Likewise, in writing, to the similarity, their differentiation, are mentioned. Including the results, that is, the achieve results null hypothesis, researcher with the error is encountered, but In the Reduction ad absurdum the achieve results, not an error.

The Triple Product Rule is Incorrect

The triple product rule, also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler’s chain rule, relates the partial derivatives of three interdependent variables, and often finds application in thermodynamics. It is shown here that its derivation is wrong, and that this rule is not correct; hence, the Mayer’s relation and the heat capacity ratio, which describe the difference between isobaric and isochoric heat capacities, are also untrue. Also, the relationship linking thermal expansion and isothermal compressibility is wrong. These results are confirmed by many experiments and by the previous theoretical findings of the author.

Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis

This paper presents fourth order Adams predictor corrector numerical scheme for solving initial value problem. First, the solution domain is discretized. Then the derivatives in the given initial value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of difference equations is developed. The starting points are obtained by using fourth order Runge-Kutta method and then applying the present method to finding the solution of Initial value problem. To validate the applicability of the method, two model examples are solved for different values of mesh size. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results of the solution for small value of mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.

On Symmetric Riemann-Derivatives

The basic properties like monotoni city, Darboux property, mean value property of symmetric Riemann-derivatives of order n of a real valued function f at a point x of its domain (a closed interval) is studied. In some cases, function is considered to be continuous or semi-continuous.

Effectiveness of Oral Tests in Improving Learners' Mathematical Performance

The main purpose of this paper is, the effect of guided oral questions in mathematics lessons on evaluation formative testing in Increase academic achievement. The sample of the Research consisted of two 23-person classes from computer students at the University of Dr. Moien Rasht. Both classes took pre-test, with a common question from the semester's lessons. Randomly, Class A was selected as the control, and Class B was selected as the experiment .In Class A, after 6 weeks of teaching, evaluation formative the classical test was formally written (paper-and-pencil) .Group B students, with the same content of Class A teaching, received group Oral (participatory) instead of, formative tests. Group members were selected based on formula, According to the attention, pre-test scores value, and other Indicators. At the end of the semester, both classes were aggregated with the same question, and the scores of both classes were analyzed by descriptive and inferential statistics, t and ES .Statistical analysis showed that learning rate increased in both control and experimental groups. But in cumulative Evaluation, the mean scores of the experimental group were higher than the Average scores of the control group. While in the pre-test, the control group scores were higher than the experimental group. The area under the corresponding curve, ES = .96, is / 831. That is, the area under the curve corresponding to the test group members, on whom the developmental test was orally administered, their mathematics lesson scores were83.15 higher than the control group.

Numerical Method of the Line for Solving One Dimensional Initial- Boundary Singularly Perturbed Burger Equation

In this Research Method of Line is used to find the approximation solution of one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable x is replaced into the functional values at each grid points by using the central finite difference method. Then, the resulting first-order linear ordinary differential equation is solved by the fifth-order Runge-Kutta method. To validate the applicability of the proposed method, one model example is considered and solved for different values of the perturbation parameter ‘ε’ and mesh sizes in the direction of the temporal variable, t. Numerical results are presented in tables in terms of Maximum point-wise error, EN,Δt and rate of convergence, Pε N,Δt. The stability of this new class of Numerical method is also investigated by using Von Neumann stability analysis techniques. The numerical results presented in tables and graphs confirm that the approximate solution is in good agreement with the exact solution.

Special Diophantine Triples InvolvingSquare Pyramidal Numbers

In this communication, we accomplish special Diophantine triples comprising of square pyramidal numbers such that the product of any two members of the set added by their sum and increased by a polynomial with integer coefficient is a perfect square.