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We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…

In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

We give a new proof of Chen-Lin result with Li-Zhang method.

We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.

A simplified model of the bird skeleton along with elongation parameters for the flight feathers is used to explore the diversity of bird shapes. Varying a small number of parameters simulates a wide range of observed bird silhouettes. The…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.

In this paper, in the context of the ``Dessins d'enfants'' theory, we give a combinatorial criterion for a plane tree to cover a tree from the classes of "chains" or "stars''. Besides, we discuss some applications of this result which are…

Li-Zinger's hyperplane theorem states that the genus one GW-invariants of the quintic threefold is the sum of its reduced genus one GW-invariants and 1/12 multiplies of its genus zero GW-invariants. We apply the Guffin-Sharpe-Witten's…

We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial…

In double field theory, the equation of motion for a point particle in the background field is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by the analysis on the particle motion, we…

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.

Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…

We consider a class of bi-parameter kernels and related square functions in the upper half-space, and give an efficient proof of a boundedness criterion for them. The proof uses modern probabilistic averaging methods and is based on…

Production of energy (metabolism) and its distribution is vital for living organisms, both at individual level - between different functions of an organism, as well as between species of communities at different organizational levels,…

We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…

In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.