Solving the Quintic: A New Approach to Bring's Transformation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

Solving the Quintic: A New Approach to Bring's Transformation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

Solution of the Quintic and Sextic by Radicals

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

Solution of the Quintic and Sextic by Radicals

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its Bring-Jerrard binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

Simulations of surface corrugations of graphene sheets through the generalized graphene thermophoretic motion equation

In the current decade, nanomaterials have attracted great attention due to the wide range of applications in various disciplines and nanotechnology. Graphene is the best nanoscale material and one of the thinnest elastic films and has various applications. The thermophoretic motion system describes the diffusion of solitaries into substrate-supported graphene sheets. Lie group transformation of the motion equation is used to reduce the equation into solvable equation which is solved through the Bernoulli approximation method and some properties of the solutions are discussed.

Investigation of relativistic fermions with various energy–momentum distributions in q-deformed approach

In this paper, we investigate the [Formula: see text]-deformed Dirac equation. We obtain a quasi-exactly solvable equation. The energy–momentum distribution is considered using Landau–Lifshitz, Einstein and Papapetrou complexes and the results are discussed.

Insightful Solution of a Geometry Problem with Instructional Cues: II. Individual Studies

As a sequel to a group experiment, this paper reports a study of the effects of instructional cues on individuals' insightful solutions to a problem in geometry. 96 college freshmen, 28 men and 68 women, were selected from hundreds of volunteers, carefully matched for mathematical background and divided into four equal groups who were given varying graded amounts of suggestive instructional cues. Group I, a control without cues, yielded the lowest percentage of insightful solutions but consumed the longest time; Group II, with an unworkable equation, gave more solutions in shorter time upon stratified analysis, but seemed to show some detrimental effect of the misleading cue on the whole group's gross mean time; Group III, with a solvable equation, produced still better scores both in amount and speed as well as four correct answers by computation; Group IV, with a direct cue that diagonals of a rectangle are equal, achieved the best performance. By manipulating the variables of sampling and procedure, the pooled mean score has been raised from the less than 9% obtained earlier in a group experiment to 50% insightful solutions.