Intraoperative assessment of corneal injuries using microscope-integrated optical coherence tomography

Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
Electron tomography can be performed either in TEM or STEM (scanning transmission...

Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...

Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...

Op-amp circuits have significant applications in various fields, including automotive engineering. One such application is cruise control systems in cars, where op-amp circuits are integral for maintaining a constant speed. In these systems, op-amps function as both integrators and differentiators.
An integrator within an op-amp circuit produces an output directly proportional to the integral of the input signal. This is achieved by replacing the feedback resistor in a typical inverting...

Consider a real-valued function defined on a closed interval. One of the fundamental objectives in calculus is to determine the area under the graph of such a function. When an exact computation is not readily available, this area can be estimated by dividing the interval into a finite number of equal subintervals. Each subinterval corresponds to a rectangle whose width is the length of the subinterval and whose height is determined by the value of the function at a selected point within that...