On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique

On the solution of integral equations with strongly singular kernels

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

On the solution of integral equations with strong ly singular kernels

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

Higher Education Institutions and the Accounting Education In The Second Half of XIXth Century on the Ottoman Empire

The aim of this study to examine, the higher education institutions’ development and the paid attention on the accounting education in the Ottoman Empire as a consequence of efforts on conforming to the politic and economic developments of the 19th century Westernization movements and transiting to European based double-entry bookkeeping methodology. After summarizing economic and politic annals of the second half of the 19th century, founded-in the term higher education institutions are mentioned. Handout especially dwelled on the subject of accounting education in the higher education. Sample accounting doctrine books used in the education of accounting are given on the final section of the paper.

The mode 3 crack problem in bonded materials with a nonhomogeneous interfacial zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations

The crack problem in bonded nonhomogeneous materials

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors

Toward Developing a Valid and Reliable Assessment of Learners’ Nature of Engineering Views

Nature of Engineering (NOE) refers to the epistemological beliefs pertaining to engineering (Antink-Meyer & Brown, 2019; Deniz et al., 2019; Hartman & Bell, 2018; Kaya et al., 2017; Pleasants & Olson, 2019). Given that a person’s engineering values and beliefs can affect how that individual perceives not only certain tasks, but also his/her ability to accomplish them, it is important to support pre-college teachers and students in improving their NOE understanding. This continues to be one of the main goals of pre-college Science, Technology, Engineering, and Math (STEM) education, and has become particularly relevant since the release of the Next Generation Science Standards (NGSS) in 2013. NGSS elevated the engineering design process to the level of scientific inquiry and focused on the aspects of NOE implicitly. Just as researchers have been calling for a greater emphasis on the understanding the Nature of Science (NOS) during the last fifty years, including the need for K-12 students to develop adequate NOS views, students today need to be better informed on the key NOE aspects in order to appreciate and understand engineering. Recently, some researchers have attempted to explore relevant NOE aspects for K-12 students with the aim of generating more sophisticated views of NOE among students. However, at present, assessment of NOE understanding, which is a fundamental part of NOE research, is a challenge, due to the absence of a reliable instrument. It is therefore imperative to develop a NOE instrument that can be adopted in pre-college engineering instruction, as the findings yielded can help close the gap between learners’ NOE conceptions and the actual engineering practice. Most importantly, pre-college engineering education can be modified by using a spectrum of instructional methods geared toward enhancing learners’ NOE understanding. This was the aim of the proposed study, and it was achieved by accomplishing the following two goals: (a) describing the NOE aspects relevant to K-12 education based on the NGSS and the National Research Councils’ Framework for K-12 Science Education; (b) developing a new empirical, reliable, and valid open-ended Nature of Engineering Instrument – Version B (VNOE-B), in part derived from a Views of the Nature of Engineering (VNOE) questionnaire designed to assess learners’ NOE perceptions. This research mainly focused on the development and validation of the VNOE-B questionnaire while also discussing the implications of the use of the new VNOE-B questionnaire in educational practice. It is envisaged that the findings yielded by this investigation will guide the science and engineering education community in devising the most appropriate ways to help students and teachers develop fully-informed NOE views

Applications of Glass Fibers in 3D Preform Composites

E-glass three dimensional (3D) stitched preform composites have been developed for several industrial applications due to their high mechanical performance and damage tolerance properties. Although some in-plane properties of the stitched E-glass composite structure are slightly lower than in laminated composite, its mode-I delamination failure is improved. This was achieved by using the out-of-plane directional stitched fibers. Recently, some nanoparticles as single-walled nanotubes (SWNT) or multiwalled nanotubes (MWNT) or nanofibers (NF) were added to the glass fabric structure or stitched preform during consolidation process. This further enhances the thermo-mechanical impact properties of the E-glass fiber composites

Remembering Thirty-five Years of Social Accounting: A Review of the Literature and the Practice

The purposes of this paper are to briefly review the past thirty-five years of social accounting literature and to examine social accounting practices within the choosen time period. Further, this paper contributes to the limited literature of researchs exploring social accounting literature and literature’s effect on social disclosures and corporate reporting. We use three time periods of Mathews (1997) as 1970-1980,1981-1990, 1991-1995 and adds one more period as 1995-2006 to undertake a general review of the literature within social and enviromental accounting. As concluded, we find that, in spite of growing interest for social accounting practices and literature, there are still major problems related social accounting practices that researchers may undertake