[The work of Etienne Sergent extolled in Algeria]

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...

Alkenes like 1-butene and 2-butene exhibit constitutional isomerism, as they differ in the position of the double bond. Further, 2-butene exhibits stereoisomerism and exists as two distinct compounds differing in spatial arrangement.
An isomer is called cis-2-butene when the methyl groups are on the same side of the double bond, and the other stereoisomer, in which methyl groups are on the opposite side of the double bond, is called trans-2-butene. The cis and trans stereoisomers are not...

The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam is...

Oxymercuration–reduction of alkenes is one of the major reactions converting alkenes to alcohols. It involves the hydration of alkenes with mercuric acetate in a mixture of tetrahydrofuran and water, forming an organomercury adduct. This is followed by a demercuration step in which the adduct is reduced to an alcohol using sodium borohydride.

The IUPAC naming system for alkenes replaces -an- with -en- in the corresponding parent alkanes. Accordingly, a simple alkene replaces the -ane suffix of the alkane with -ene.
As per the IUPAC rules, the longest carbon chain containing the maximum number of double bonds is identified as the parent chain and is numbered such that the doubly bonded carbon atoms receive the lowest possible numbers. The location of the double bond is indicated by the number of its first carbon atom. In branched...

The principle of Saint-Venant postulates that the stress distribution within a structural member does not rely on the precise method of load application except in the vicinity of the load application points. Consider a scenario where loads are centrally applied on two plates. In this case, the plates move toward each other without any rotation. This movement causes the member to contract in length and expand in width and thickness. Uniform deformation across all elements and maintaining...