General Formula for SHE Problem Solution

Solution formula for an inverse problem with underdetermining data

A General Solution for the 2-Pyridyl Problem**

Problem solved: an air-stable 2-pyridyl borane that can effectively couple to a wide range of aryl and heteroaryl halides and pseudohalides has evaded the synthesis community for decades. The discovery that Cu(DEA)(2) powerfully enables palladium-mediated cross-couplings with air-stable boronates 1 has finally provided a general solution to this problem. DEA=diethanolamine, DMF=N,N'-dimethylfor...

A general Plücker formula

We prove a formula which compares intersection numbers of conormal varieties of two projective varieties and their dual varieties. When one of them is linear, we can recover the usual Plücker formula for the degree of the dual variety. The basic strategy of the proof is to study a category of Lagrangian subvarieties in the cotangent bundle of a projective space under a birational transformation.

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

A general formula for channel capacity

Abrlracr-A h u l a for the cppecity et arbitrary sbgle-wer chrurwla without feedback (mot neccgdueily Wium" stable, stationary, etc.) is proved. Capacity ie shown to e i p l the supremum, over all input processts, & the input-outpat infiqjknda QBnd as the llnainl ia praabiutJr d the normalized information density. The key to thir zbllljt is a ntw a"c sppmrh bosed 811 a Ampie II(A Lenar trwrd eu...