As we have seen in Chapter 2, the partition function of the Ising model on a planar graph G with positive boundary conditions is proportional to the even subgraph generating function ZG⇤(x), where G⇤ is the weak dual of G and x is the weight vector defined by the low-temperature expansion. Similarly, the partition function of the model with free boundary conditions is proportional to ZG(x), whe...

Consider a finite classical system in contact with a heat reservoir. A central concept in thermodynamics is that of the work performed on such a system, when some external parameters of the system are made to change with time. (These parameters may represent, for instance, the strength of an external field, or the volume of space within which the system is confined, or, more abstractly, some pa...

a water soluble, bronsted acid, 5-sulfosalicylic acid as an efficient organocatalyst was used for the synthesis of physiologically active 2-substituted benzimidazole derivatives from o-phenylenediamine and aromatic aldehydes in ethanol at reflux condition. cost-effectiveness, use of non-hazardous solvents, metal free and commercially available catalyst, single-step, environmentally friendly gre...

Chitosan was used for nanoencapsulation of Lactobacillus acidophilus as probiotic bacteria. In vitro experiments were done with the objective of investigating the survival of the bacteria cells in gastro-intestinal conditions. The results demonstrated that the size of chitosan nanoparticles noticeably increases by increasing chitosan concentration from 0.05 to 0.5 g/mL. Encapsulation of the cel...

one of important conditions of capital, is the condition to guarantee profit. with due attention of illegality of the free- interest and forbidding of the usury under the islamic and iranian law, it is necessary that; the legal status of this condition and it’s legal sanction to be considered it seems that, the condition to guarantee profit is a condition about the performance of act by witch t...

A bstract The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as positivity condition second null shape derivative of relative entropy S rel ( ρ || σ ) an arbitrary state with respect to vacuum . natural one-parameter family generalization, Sandwiched Rényi divergence n...