A generalization of the Sherman–Morrison–Woodbury formula

a generalization of strong causality

در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...

A Generalization of Macmahon’s Formula

We generalize the generating formula for plane partitions known as MacMahon’s formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald’s symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon’s formula for strict plane partitions.

A Generalization of the Itô Formula

A Generalization of the Auslander-buchsbaum Formula

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.

Generalization of Garsia’s Formula

Notice that Bk a is a sum of terms σ1σ2 . . . σk where σi ∈ Sn is a term of the ith copy of Ba. Each σi will be called an a-shuffle, because it shuffles the first a cards back into the deck. We can thus denote σi = (b(i−1)a+1, b(i−1)a+2, . . . , bia) where b(i−1)a+m = σi(m) (i.e. σi acted on the mth card of the deck). Thus, the sequence (σ1, . . . , σk) gives rise to the ka-tuple (b1, b2, . . ....