Gradients are natural first order differential operators depending on Riemannian metrics. The principal symbols of them are related to the enveloping algebra and higher Casimir elements. We give certain relations in the enveloping algebra, which induce not only identities for higher Casimir elements but also all Bochner-Weitzenböck formulas for gradients. As applications, we give some vanishing...

The role of dynamical cosmological Casimir effect to phantom (constant w ) and oscillating universe is discussed. It is shown explicitly that its role is not essential near to Big Rip singularity. However, the account of Casimir fluid makes the scale factor approach to Rip time to be faster. Rip time itself maybe changed too.

We discuss the renormalisation of the ground state energy of massive fields obeying boundary conditions, i.e., of the Casimir effect, and emphasise the role of the mass for its understanding. This is an extended abstract of a talk given at the topical group meeting on Casimir Forces at the Harvard-Smithsonian Center for Astrophysics on March 15-29, 1998. Renormalisation is a key to the understa...

– We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential μ = 0 has the standard asymptotic form with universal Casimir terms. In contrast to the well-known Casimir effect for the photon gas, see e.g. [1], this effect for the massive quantum partic...

برای دستیابی به مزیت رقابتی در شرایط عدم‌­اطمینان که آن تغییر ضروری است، یکی از چالش‌های بزرگ سازمان‌ها کاهش ریسک طریق ایجاد زنجیره‌های تأمین تاب‌آور است. تاب‌آوری زنجیره ‌تأمین توانایی مقابله با اختلال اشاره دارد یک رویداد غیرقابل‌پیش‌بینی بوده و دارای منابع داخلی خارجی مختلفی ازجمله بلایای طبیعی ریسک‌های عملیاتی پژوهش حاضر شبیه‌سازی توسط نرم‌افزار ارنا زنجیره‌ سنگ ساختمانی «کارخانه سنگبری آسم...

– We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, shor...