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Dear mathoverflowers. Just wondering if the following inequality is true. For all $p >1$ there is some $C$ such that | |x+1|^p-|y+1|^p -p(x-y)| \le C ( |x|+|y| + |x|^{p-1} … 0answers 3 views ### Solving systems of integral equations using Volterra series I came across this problem when trying to solve the following integral equations arising in direct scattering: \begin{align} n_{11}(x,z)=1+\int_{-\infty}^xe^{-izy}u(y)n_{21}(y,z … 3answers 60 views ### How many Perfect Matchings in a regular bipartite Graph Hi Guys, We have a d-regular bipartite Graph G = (X,Y,E) with |X| = |Y| = n and |E| = nd. i want to know a Upper Bound of the number of Matching Thankx 0answers 407 views +150 ### Orders in number fields Let K be a degree n extension of {\mathbb Q} with ring of integers R. An order in K is a subring with identity of R which is a {\mathbb Z}-module of rank n. Quest … 9answers 370 views ### objects which can’t be defined without making choices but which end up independent of the choice It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure … 4answers 146 views ### Surfaces ruled over elliptic curves Ground field \Bbb{C}. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose E … 0answers 20 views ### What is the meaning of the cospecialization map? This question comes from the same place as my other one. In reading SGA 4 1/2, but not SGA4 itself (at least, not the obvious sections xv + xvi), one can learn about the "cospecia … 0answers 39 views ### Is a Lie group equivariantly formal under conjugation by a maximal torus? Given an action of a group G on a topological space X, the associated homotopy quotient isX_G := (EG \times X)/G,$where$EG$is the total space of a universal principal$G …
The quick definition of a map $f \colon X \to B$ of schemes being acyclic is that the natural unit of adjunction $\def\id{\operatorname{id}}\id \to f_* f^*$ is an isomorphism, wher …