Persistent left superior vena cava as a perpetuator of atrial fibrillation: Frequency analysis using continuous...

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

Amyloid fibrils are aggregates of misfolded proteins.  Under most circumstances, misfolded proteins are either refolded by chaperone proteins or degraded by the proteasome. However, in the case of a mutation or a disease, these proteins can accumulate to form large clusters and often further assemble to form elongated fibers, called fibrils. 
Amyloid deposits were observed as early as 1639 in the liver and the spleen.   In 1854, Rudolph Virchow performed iodine staining,...

For solutions containing mixtures of different cations, the identity of each cation can be determined by qualitative analysis. This technique involves a series of selective precipitations with different chemical reagents, each reaction producing a characteristic precipitate for a specific group of cations. Metal ions within a group are further separated by varying the pH, heating the mixture to redissolve a precipitate, or adding other reagents to form complex ions.
For instance, group IV...

Fibril-associated collagens are a type of collagens present in the extracellular matrix with interrupted triple helices or FACIT (Fibril-associated collagens interrupted triple-helices). FACIT help connect and attach the collagen fibrils with each other as well as with other proteins of the extracellular matrix.
For example, the type II collagen fibrils in cartilage have covalently bound type IX fibril-associated collagens at regular intervals. Other types of fibril-associated collagens are...

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...