Conjecture 1 (Weak PFR over ) Let be a finite non-empty set whose doubling constant is at most . Then there is a subset of of density that has affine dimension (i.e., it is contained in an affine space of dimension ). Conjecture 2 (PFR over ) Let be a non-empty set whose dou...
An equivalent form of this statement is that any measurable function which is locally essentially constant in the sense that for -almost every , is necessarily globally essentially constant in the sense that there is a constant such that for -almost every . A basic consequence of ergodicity is ...
PINNs leverage the power of deep learning while improving compliance with physical laws, making them a versatile tool for applications where physics is fully or partially known, such as the case of a PDE or ODE with unknown coefficients. Applications of PINNs include: Heat transfer, specifically f...
To our knowledge, there is nothing like the marginal value theorem in partial differential equation (PDE) models or other ecological models involving continuous space. However, there is a strong foundation for the ideal-free distribution in continuous space models (Arditi and Dacorogna 1988; ...
find an explicit solution of the PDE above, or at least prove existence and uniqueness of a solution; Q2: find some of its qualitative properties; Q3: in particular, what is the distribution ofXT/2? In the recent paper [4], which was written concurrently with and independently of this wo...
Both drugs are referred to as “PDE5 inhibitors.”The medications efficiently encourage blood flow to the genital region by blocking the PDE5 enzyme which signals the body when an erection is about to end, allowing normal, healthy erections of appropriate duration. These prescription drugs alleviat...
if you remember you FEM theory: if D(w,x,t)=0 is a differential equation for w(x,t) then the weak form of the PDE is 'integral over volume of v(x,t)*D(w,x,t) dV = 0' where v(x,t) are unrestricted weight functions. the FE method approximates the differential operator D(...
Male UltraCore is backed by a proprietary technology developed exclusively for their Supplement. VI-PEX is the secret behind Male UltraCore’s vasodilating technology, with its precise combination of nitric oxide boosters and PDE-5 inhibitors. ...
) is non-decreasing (resp. non-increasing) in for any fixed . In principle one should be able to establish these monotonicity claims directly from the PDE (7) or from the implicit solution (9), but it was not clear to me how to do so. An interesting example of such a limiting ...
Let be a function whose norm is at least 1/K. Then there exists a quadratic polynomial such that . Note that the quadratic phases are the only functions taking values in [-1,1] whose norm attains its maximal value of 1. It is conjectured that the exponentially weak correlation here can...