Some new inequalities for continuous fusion frames and fusion pairs

Frames are essential components of various mechanical and structural systems used daily. These structures are known for their stability and ability to bear heavy loads. A frame is constructed using two-force and multi-force members, interconnected using pin joints. In contrast, trusses are made entirely of two-force members.
Frames are versatile and widely used in various applications such as structural supports for beams and columns, automobile chassis construction, and in the construction...

Proteins are involved in several cellular processes and biochemical reactions. Analyzing a specific protein of interest requires it to be isolated from the other proteins in the cell. This is achieved by overexpressing the specific gene in a suitable host to produce large quantities of the target protein. A tag or label is recombined with the gene to produce a fusion protein containing the target protein and the tag. The tags on these fusion proteins can then be used for easy detection and...

A composite body is a body made up of multiple parts, connected to form a larger, unified object. Each part has its own weight and center of gravity, which must be considered to determine the center of gravity of the composite body. In cases where the density or specific weight is constant, the center of gravity coincides with the centroid.
Composite bodies have widespread applications in mechanical engineering, from automobiles to aircraft to rockets. For example, an automobile wheel comprises...

Consider a hydraulic hoist supporting a load of 1 kN. Assuming a simplified schematic representation of this frame structure, the force acting on BD and BF members can be determined.

Fibrous joints are a type of joint where the bones are connected by fibrous connective tissue. These joints provide stability and minimal to no movement between the articulating bones. There are three types of fibrous joints.
Suture
All the bones of the skull, except for the mandible, are joined to each other by a fibrous joint called a suture. The fibrous connective tissue found at a suture strongly unites the adjacent skull bones and thus helps to protect the brain and form the face. In...

Consider a jib crane with an external load suspended from the pulley. The dimensions of the crane members are shown in the figure. A systematic analysis of the frame structure is required to determine the reaction forces at the pin joints, assuming that the pulleys are frictionless.