We study the regularity of the extremal solution of the semilinear biharmonic equation β∆u−τ∆u = λ (1−u)2 on a ball B ⊂ R , under Navier boundary conditions u = ∆u = 0 on ∂B, where λ > 0 is a parameter, while τ > 0, β > 0 are fixed constants. It is known that there exists a λ∗ such that for λ > λ∗ there is no solution while for λ < λ∗ there is a branch of minimal solutions. Our main result asse...

The authors apply bootstrap methods to the half-BPS Wilson line with local operator insertions (defects) in four-dimensional maximally supersymmetric (N = 4) Yang-Mills theory. They extract analitically scaling dimension of lightest non-protected scalar fourth order strong coupling expansion (t'Hooft coupling).

Alzheimer's disease (AD) is a progressive neurodegenerative disease characterized by synapse dysfunction and cognitive impairment. Understanding the development and progression of AD is challenging, as the disease is highly complex and multifactorial. Both environmental and genetic factors play a role in AD pathogenesis, highlighted by observations of complex DNA modifications at the single gen...

This article considers the role of mental time travel in human evolution. A central thesis is that other primates, although having memory and expectation, do not possess the same ability to live in the past or in the future. The first half of this paper argues that reconstructive access to the past (i.e. episodic memory) is dependent on other advanced cognitive capabilities (e.g. self-awareness...

We investigate the asymptotic behavior as k → +∞ of sequences (uk)k∈N ∈ C (Ω) of solutions of the equations ∆uk = Vke 4uk on Ω, where Ω is a bounded domain of R and limk→+∞ Vk = 1 in C 0 loc (Ω). The corresponding 2-dimensional problem was studied by Brézis-Merle and Li-Shafrir who pointed out that there is a quantization of the energy when blow-up occurs. As shown by Adimurthi, Struwe and the ...

The unrelenting progress of laboratory techniques is rapidly unleashing the huge potential of palaeomicrobiology. That bodies are often found in poor condition is common to both palaeomicrobiology and forensic medicine, and this might stimulate them towards a joint quest to extract reproducible data for reliable specimens.

The nature of time has long been an obsession for philosophers, scientists, and laymen. This nearly universal interest in time is encapsulated by the fact that the quotation “Time is nature’s way of keeping everything from happening at once” has been attributed to both Woody Allen and Albert Einstein! Although some argue that time is an illusion, ongoing work has revealed that most organisms po...