Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspec...

results for error analysis of finite element methodWe consider the following four problems: 1:(E)w: Find u ∈ V such thata(u, v) = (f, v) for all v ∈ V .2:(Eh)w: Find uh ∈ Vh such thata(uh, vh) = (f, vh) for all vh ∈ Vh.3:(E)w: Find u ∈ V such thata (u , v) = (f, v) for all v ∈ V . DDM APPLIED TO RADIATION PROBLEMS389 4:(Eh )w: Find u Nh ∈ Vh such ...

We examine thermoelastic equations of state for silicate perovskite based on data from recent static compressiori studies. We analyze trade-offs among the fitting parameters arid examine data sets for possible effects of metastability and of Mg-Fe solid solution. Significant differences are found between equations of' state based on low pressure measurements obtained for perovskite outside of i...

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically,...

The electrical potential difference (P.D.) across the cell membrane was measured in monolayers of HeLa cells. At 37°C in the cells' growth medium, the mean P.D. was found to be —1 5.45 ±0.57 my, the cell interior being negative. In Tris buffer the P.D. was —17.10 ±0.71 my. The PD. was tempera ture sensitive, falling to —11.9 my at 27°Cand —9.12my at 17°C.Increasing extracellular K ...

The relation between the special relativity and quantum mechanics is discussed. Based on the postulate that space-time inversion is equa-valent to particle-antiparticle transformation, the essence of special relativity is explored and the relativistic modification on Stationary Schrödinger Equation is derived. The 20th century is coming to an end. Many people wish to speculate on the developmen...

— The common method of computing atomic transition probabilities involves the expansion of atomic wavefunctions in terms of single-configuration, LS-coupled basis functions. Calculated values are frequently rendered very unreliable by cancellation effects resulting from intermediate-coupling and configuration-interaction mixing of basis functions. Examples are discussed in the spectra of Ar I, ...

which has a matrix Lax pair [, ] and is shown to be related to a negative flow in the Sawada-Kotera hierarchy. Several conservation quantities and a bi-Hamiltonian structure were found in []. Himonas and Holliman [] applied the Galerkin-type approximation method to prove the well-posedness of strong solutions for Eq. () in the Sobolev space Hs(R) with s >  on both the line and the circle....