In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

A progressive increase in the desire for environmentally friendly lubricants by users and strict government regulations for the use of these lubricants has provided an opportunity to use plant oils as biodegradable lubricants, therefore vegetable oils have been investigated to replace oil lubricants because of their maintaining the conditions of nature (environment) properties. In this paper, the influences of the blending ratio of mustard seeds oil with commercial mineral oil (SAE40) on the tribological characteristics were investigated and compared with mineral oil using the four-ball tribotester. Mustard seeds oil was blended with mineral oil at a volumetric ratio ranging from 22.5 to 90%. All experimental works were

The interest in pre-service teacher training has become influential in teaching English as a foreign language, and the purpose of this training course is to prepare qualified teachers to teach effectively through the application of this technique by undergraduate students. This research aims to find out the effect of using the seven principles of good practice as a teaching technique on the fourth stage student-teachers’ performance at the College of Education for Women/University of Baghdad, during the academic year 2017-2018. The sample includes (60) students selected according to the stratified sampling method. The observational checklist used by the department to assess the student teachers’ performance during the practicum perio

In this paper, we introduce a method to identify the text printed in Arabic, since the recognition of the printed text is very important in the applications of information technology, the Arabic language is among a group of languages with related characters such as the language of Urdu , Kurdish language , Persian language also the old Turkish language " Ottoman ", it is difficult to identify the related letter because it is in several cases, such as the beginning of the word has a shape and center of the word has a shape and the last word also has a form, either texts in languages where the characters are not connected, then the image of the letter one in any location in the word has been Adoption of programs ready for him A long time.&

A simple, rapid and sensitive spectrophotometric method has been proposed for the determination of La (III) using 3-hydroxy -4-(2-hydroxy-phenyl azo) naphthalene -1- sulfonic acid as a chromogenic reagent. This method is based on the formation of a red-pink colored complex, upon the reaction of La(III) with the reagent in an alkaline medium (pH= 9.50), having a maximum absorbance at 459 nm. Beer's law is valid in the concentration range 0.512 µg.ml-1 with a Sandell's sensitivity value of 0.0188 µg.cm-2 and molar absorptivity of 7376.12 L.mol-1.cm-1. The stoichiometric composition of the chelate is 1:3. The effect of the presence of different cations as interferants in the determination of La(III) under the given optimum conditions

Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.

many painters tried to mix colors with Music by direct employment through colorful musical pieces or the use of multiple instruments and techniques , or vice versa, including the French artist )Robert Stroben(, he transferred the piece of music to be depicted on the painting and worked on the tones of music (Johann Sebastian Bach) by dropping the color on the lines of the musical scale, for example (the C tone) ranging from brown to red ( Tone La A) from gray to orange, and so on, the presence of links and similarity factors between the world of music and the world of colors facilitated the process of linking musical notes with colors, the most famous of which was presented by the world (Newton) in the circle of basic colors and linking

Resumen

    Sotileza , localismo santandrino de sutileza , es la parte más fina del aparejo de pescar donde va el anzuelo. Es la obra maestro de José María de Pereda.Su ambiente , el Santander viejo, anterior al año 50,evocado emocionadamente - emociόn romántica contenida en los trazos sobrios y firmes de un naturalism psicolόgico y paisajista,el Santander que el autor confiesa poseer en el fondo de su corazόn,«y tenerlo esculpido en la memoria de tal suerte que ,a ojos cerrados,me atrevería a trazarle con todo su perímetro y sus calles, y el color de sus piedras, y el número, y los nombres, y hasta las caras de sus habitantes».Dentro de la grandeza primaria de las criaturas de Pere

The research is a vision of the future of industry in Iraq, so it is may be outside the ceiling of the capabilities of the Iraqi economy, and therefore it is exaggerated. Therefore, future plans must be applicable through the availability of capabilities. Everyone knows that the financial and administrative corruption and mismanagement of resources are the main cause of the inefficiency of the industrial sector, and the failure to exercise its real role in achieving economic development.; as well as the political situation and the dominance of parties and their insistence on addressing positions that have a strong relationship in managing the economic sector that has a significant impact on drawing the economic map in its current

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a