Elliptic and hyperbolic cylindrical curves satisfying Tzitzeica condition are obtained via the solution of the forced harmonic equation. Mathematics Subject Classification: 53A04, 34A05.

We construct Dirac operators and spectral triples for certain, not necessarily selfsimilar, fractal sets built on curves. Connes’ distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the construction, we address Kigami’s measurable Riemannian geometry, which is a metric realization of the Sierpinski gasket as a self-affine space with continuously dif...

Investigators who have devised practical forms of manometers recording by optical registration have experienced considerable difficulty in selecting the constants so that an adequate natural frequency and a sufficient degree of sensitivity exist at the same time. Frank’s equation 2’ = M 1 2R ---y iE makes it clear why this is so. The natural period, T, is decreased by reducing the effective mas...

We determine the harmonic volumes for all the hyperelliptic curves. This gives a geometric interpretation of a theorem established by A. Tanaka [10].

Motivated by Gauss’s first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a...

We consider a non-interacting gas under the inverted harmonic potential and present infinitely degenerate non-stationary orthogonal states. discuss that it has an infinite entropy at absolute zero temperature. show uncertainty in position of particle can be as there exists solution which asymptotes to Dirac delta function. obtain new free wave packet using eigenstates for potential. It unique s...

Numerous theoretical physics and chemistry problems can be modeled using Mathieu’s equations (MEs). They are crucial to the theory of potential energy in quantum systems, which is equivalent Schrödinger equation. According mentioned applications, thus, current study investigates stability behavior nonlinear-coupled MEs. The analysis coupled harmonic resonance cases imposes two solvability condi...