Isoperimetric properties of condenser capacity

On the Capacity of a Condenser

An isoperimetric inequality for logarithmic capacity

We prove a sharp lower bound of the form capE ≥ (1/2)diamE · Ψ(areaE/((π/4)diam 2E)) for the logarithmic capacity of a compact connected planar set E in terms of its area and diameter. Our lower bound includes as special cases G. Faber’s inequality capE ≥ diamE/4 and G. Pólya’s inequality capE ≥ (areaE/π)1/2. We give explicit formulations, functions of (1/2)diamE, for the extremal domains which...

Capacity of a condenser whose plates are circular arcs

We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear plate condenser found by Simonenko and Chekulaeva in 1972 and sheds light on the problem of finding an asymptotic formula for the capacity of condenser whose p...

An isoperimetric inequality for logarithmic capacity of polygons

We verify an old conjecture of G. Pólya and G. Szegő saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...