introduction. students' evaluation of teaching is a major concern in higher education. in this regard, during the past 30 years hundreds of papers have been published which because of various grounds from valid, reliable to useless, such papers cannot be easily summarized. the present study investigated for two purposes, first was to out line opinions of two groups of advocates and opposit...

Every good introduction to set-theoretic forcing starts with basic forcing algebras like ”adding a Cohen real” or ”adding a Cohen subset of ω1”. It seems that these algebras are particularly simple mainly because they contain a dense subtree, so we might as well pretend we are forcing with a tree. Such a forcing is especially easy to visualize as the generic object will be a branch through the ...

Exercise 1 (10 Points). Prove or give a counterexample for each of the following: (a) If A ⊆ B and B ⊆ C, then A ⊆ C. (b) If A ∈ B and B ∈ C, then A ∈ C. Solution: (a) Consider any element a ∈ A. Since A ⊆ B every element of A is also an element of B, so a ∈ B. By same reasoning, a ∈ C since B ⊆ C. Thus every element of A is an element of C, so A ⊆ C. (b) Let A = {1}, B = {1, {1}}, and C = {{1,...

In the present work, we have developed a mild, efficient, and environmentally benign method for the synthesis of tetrahydrobenzo[b]pyran derivatives via a three-component cyclocondensation of aldehydes, malononitrile and dimedone utilizing ammonium chloride as a simple, easily available and cost effective catalyst under microwave irradiation. This method has several attracting features such as ...

An interaction potential at different orientation for the CH4 and CO2 complex was derived at theB3LYP level of theory and 6-31+G* basis sets. The potential energy surface was computed on somemolecular geometries. The complete basis set limit of the interaction energies were fitted to wellknownanalytical functions. To determine the second virial coefficients B, U(r) is used to obtain themodel’s ...

Bipolar neutrosophic set theory and rough neutrosophic set theory are emerging as powerful tool for dealing with uncertainty, and indeterminate, incomlete, and inprecise information. In the present study we develop a hybrid structure called “rough bipoar neutrsophic set”. In the study, we define rough bipoar neutrsophic set and define union, complement, intersection and containment of rough bip...