Related papers: Oscillations and their applications in partition c…
A layered material structure in a monochromatic neutrino beam produces interference effects that could be used for the measurement of features of the neutrino mass matrix. The phenomenon would be most useful at high energies.
We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defined by the oscillatory integral depend on the type of a…
Oscillons are extremely long-lived, spatially-localized field configurations in real-valued scalar field theories that slowly lose energy via radiation of scalar waves. Before their eventual demise, oscillons can pass through (one or more)…
Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion…
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction. Presented results hold both for systems with and without…
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and…
We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems:…
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
Unitary rotations of polychromatic images on finite two-dimensional pixellated screens provide invertibility, group composition, and thus conservation of information. Rotations have been applied on monochromatic image data sets, where we…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to non-linear oscillators can improve the measurement conditions. Here, this effect of…
Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures…
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial…
In important work on the parity of the partition function, Ono related values of the partition function to coefficients of a certain mock theta function modulo 2. In this paper, we use M\"obius inversion to give analogous results which…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
The oscillations of the test particles on circular orbits in field of super-extremal charged central object are researched. The formulae for oscillation frequencies are obtained in cases of circular orbits perturbations caused by small…
We investigate the complexity of generalizations of colourings (acyclic colourings, $(k,\ell)$-colourings, homomorphisms, and matrix partitions), for the class of transitive digraphs. Even though transitive digraphs are nicely structured,…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…
We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.