A Generalization of Lerch?s 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.

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, . . ....

Improvements in Formula Generalization

From 01.10. to 05.10.2007, the Dagstuhl Seminar 07401 Deduction and Decision Procedures was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar are put together in this paper.

A Generalization of the Itô Formula