What do nodules on the lungs signify?

Commonly called a “spot on the lung” or a “shadow,” a nodule is a round area that is more dense than normal lung tissue. It shows up as a white spot on a CT scan. Lung nodules are usually caused by scar tissue, a healed infection that may never have made you sick, or some irritant in the air.

What are lung nodules made of?

Hamartomas are the most common type of benign lung tumor and the third most common cause of solitary pulmonary nodules. These firm marble-like tumors are made up of tissue from the lung’s lining as well as tissue such as fat and cartilage. They are usually located in the periphery of the lung.

How many lung nodules turn into cancer?

About 40 percent of pulmonary nodules turn out to be cancerous. Half of all patients treated for a cancerous pulmonary nodule live at least five years past the diagnosis. But if the nodule is one centimeter across or smaller, survival after five years rises to 80 percent.

When are lung nodules serious?

Lung nodules are usually about 0.2 inch (5 millimeters) to 1.2 inches (30 millimeters) in size. A larger lung nodule, such as one that’s 30 millimeters or larger, is more likely to be cancerous than is a smaller lung nodule.

What kind of infections cause lung nodules?

Causes and Diagnoses of Lung Nodules

  • Bacterial infections, such as tuberculosis and pneumonia.
  • Fungal infections, such as histoplasmosis, coccidioidomycosis or aspergillosis.
  • Lung cysts and abscesses.
  • Small collections of normal cells, called hamartoma.
  • Rheumatoid arthritis.
  • Sarcoidosis.

What is the tensor product of Hilbert spaces?

In mathematics, and in particular functional analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product.

Is the Hilbert space a symmetric monoidal category?

It is essentially the same universal property shared by all definitions of tensor products, irrespective of the spaces being tensored: this implies that any space with a tensor product is a symmetric monoidal category, and Hilbert spaces are a particular example thereof. . i = 1 , 2. {\\displaystyle i=1,2.}

Is there a topology for Hilbert spaces with inner products?

Since Hilbert spaces have inner products, one would like to introduce an inner product, and therefore a topology, on the tensor product that arise naturally from those of the factors. Let H1 and H2 be two Hilbert spaces with inner products

What is the tensor product of H1 and H2?

That this inner product is the natural one is justified by the identification of scalar-valued bilinear maps on H1 × H2 and linear functionals on their vector space tensor product. Finally, take the completion under this inner product. The resulting Hilbert space is the tensor product of H1 and H2 .