We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d = 2 and b = 3, 4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.

We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T = 0 in the thermodynamic limit, their density vanishes asymptotically along the curve approaching the origin. This phenomenon explains the coincidence of the low temper...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by χ′a(G). Sierpinski graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpinski gasket graphs Sn are the graphs naturally defined ...

The sealing performance of end fittings is very important for offshore oil and gas pipelines. To investigate the sealing behavior of a ring-shaped wedge seal, global and local numerical models of the ring–pipe interaction have been developed based on the finite-element method. First, the sealing process of the ring under pressure is simulated. Second, a criterion for the penetration of fluid pr...

Some problems related to the transition density u(t, x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory’s formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t, x) on the Sierpinski gask...

Picoliter droplets actuated on an electrowetting-on-dielectric (EWD) actuator are demonstrated. In this study, the physical scaling of electrodes for 33 μm and 21 μm EWD devices resulted in droplets of 12 pl and 5 pl being dispensed respectively in conjunction with 3 μm SU8 gaskets. The stacked multi-layer insulators in the actuators consisted of 200 nm tantalum pentoxide (Ta2O5) and 200 nm par...

The present paper is concerned with the study of vector-valued interpolation functions on Sierpiński gasket by certain classes fractal functions. This extends known results real-valued and a compact interval in $${\mathbb {R}}$$ gasket. We smoothness property interpolants A few elementary properties approximants operator that emerge connection are indicated. Some constrained approximation aspec...

We apply a recently obtained three-critical-point theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti an...

This is an expository paper which includes several topics related to the Dirichlet form analysis on the Sierpiński gasket. We discuss the analog of the classical Laplacian; approximation by harmonic functions that gives a notion of a gradient; directional energies and an equipartition of energy; analysis with respect to the energy measure; harmonic coordinates; and non self-similar Dirichlet fo...