I have been studying differential equations, and developed a theorem about linear second order equations. I have not been able to find it anywhere else on the web or in my textbooks, and so I thought I would post it up here. Click "read more" to see the theorem.

Several times a week, astronomers detect the violent death cry of a massive star -- an extraordinarily energetic release of gamma rays that takes place in just a matter of seconds to minutes, called a gamma-ray burst (GRB). The GRB's ejecta, which is thought to be beamed in narrow jets, slams into interstellar gas at near light speed. This violent collision shocks the material and produces a bright afterglow that can radiate brightly at X-ray and other wavelengths for several days, or even a few weeks.

Like a piece of chalk dissolving in vinegar, marine life with hard shells is in danger of being dissolved by increasing acidity in the oceans.

Ocean acidity is rising as sea water absorbs more carbon dioxide released into the atmosphere from power plants and automobiles. The higher acidity threatens marine life, including corals and shellfish, which may become extinct later this century from the chemical effects of carbon dioxide, even if the planet warms less than expected.

A new study by University of Illinois atmospheric scientist Atul Jain, graduate student Long Cao and Carnegie Institution scientist Ken Caldeira suggests that future changes in ocean acidification are largely independent of climate change.

Acrux announced positive results from its Phase 1 clinical studies
using two unique contraceptive skin sprays, each containing a progestin and an estrogen.

The first study was a Phase I, pharmacokinetic study, investigating the delivery of a formulation combining Nestorone® and the synthetic estrogen, Ethinyl Estradiol. A single dose of the combination formulation was applied to the forearm of healthy volunteers.

The results showed that the dosing of the contraceptive spray provided effective delivery of both contraceptive agents, with blood concentrations of Nestorone® and Ethinyl Estradiol in the target range expected to provide effective contraception.

The spray was well tolerated, with no serious adverse events recorded.

Could you survive a day like Jack Bauer has on the Fox television show "24?" Maybe not, and it might not be just because you lack counter-terrorism training.

People are known to differ markedly in their response to sleep deprivation, but the biological underpinnings of these differences have remained difficult to identify. Researchers have now found that a genetic difference in a so-called clock gene, PERIOD3, makes some people particularly sensitive to the effects of sleep deprivation. The findings, reported by Antoine Viola, Derk-Jan Dijk, and colleagues at the University of Surrey's Sleep Research Center, appear online this week in the journal Current Biology.

Let’s say a college student enters a classroom to take a test. She probably already has an idea how she will do—knowledge available before she actually takes out a pencil. But do animals possess the same ability to think about what they know or don’t know?

A new study by researchers from the University of Georgia, just published in the journal Current Biology, shows that laboratory rats do.

University College London researchers have found the first physiological evidence that invisible subliminal images do attract the brain's attention on a subconscious level. The wider implication for the study, published in Current Biology, is that techniques such as subliminal advertising, now banned in the UK but still legal in the USA, certainly do leave their mark on the brain.

Using fMRI, the study looked at whether an image you aren't aware of ¬– but one that reaches the retina – has an impact on brain activity in the primary visual cortex, part of the occipital lobe. Subjects' brains did respond to the object even when they were not conscious of having seen it.

A protein known as the "master watchman of the genome" for its ability to guard against cancer-causing DNA damage has been found to provide an entirely different level of cancer protection: By prompting the skin to tan in response to ultraviolet light from the sun, it deters the development of melanoma skin cancer, the fastest-increasing form of cancer in the world.

In a study in the March 9 issue of the journal Cell, researchers at Dana-Farber Cancer Institute report that the protein, p53, is not only linked to skin tanning, but also may play a role in people's seemingly universal desire to be in the sun – an activity that, by promoting tanning, can reduce one's risk of melanoma.

Patients admitted to hospitals for ischemic stroke on weekends had a higher risk of dying than patients admitted during the week, in a Canadian study published in Stroke: Journal of the American Heart Association.

A "weekend effect" has been previously documented when looking at other conditions such as cancer and pulmonary embolism; however, little is known of its impact on stroke death.

"What is really novel in our work beyond the discovery of the 'weekend effect' on ischemic stroke is the subgroup analysis in other settings/characteristics and the identification of variables associated with the 'weekend effect,'" said Gustavo Saposnik, M.D., M.Sc., lead author of the study.

Two new studies by University of California, Berkeley, scientists highlight the amazing promiscuity of genes, which appear to shuttle frequently between organisms, especially more primitive organisms, and often in packs.

Such gene flow, dubbed horizontal gene transfer, has been seen frequently in bacteria, allowing pathogenic bacteria, for example, to share genes conferring resistance to a drug. Recently, two different species of plants were shown to share genes as well.