Subexponential Computation of Truncated Theta Series

ABSTRACT.  We describe an algorithm to compute in $O(e^{c\sqrt{ k\log k}})$ binary operations, for some absolute constant $c>0$, expressions like $\sum_{1\leq n\leq 2^\alpha} e^{\frac{2\pi i n^2}{2^k}} n^a$ and $\sum_{\substack{1\leq n\leq 2^\alpha\\ 1\leq m\leq...

Fuzzy Bi-Quasi-Interior Ideals of Semirings

ABSTRACT.  In this paper, we introduce the notion of a fuzzy bi-quasi interior ideal as a generalization of fuzzy ideals, fuzzy bi-quasi ideals, fuzzy quasi-interior ideals and fuzzy bi-interior ideals of a semiring. We prove that every fuzzy right quasi-interior...

Solution of the Millennium Problem for the Navier-Stokes Equations

ABSTRACT.  One of the millennium problems can be stated as follows: can there be smooth, not vanishing identically initial data for the Navier-Stokes equations in R such that the corresponding solution to the NSP (Navier-Stokes problem) exists for all times t ≥ 0? We...

Tribonacci Cordial Labeling of Some Snake Graphs

ABSTRACT.  An injective function f : V (G) → {T0, T1, T2, . . . , Tn}, where n = |V (G)| − 1, is said to be a Tribonacci cordial labeling if the induced function f ∗ : E(G) →{0, 1} defined by f∗(uv) = (f(u) + f(v)) mod 2 satisfies the condition |ef (0) − ef (1)| ≤ 1...

On Some Trigonometric and Inverse Trigonometric Integral Formulas

ABSTRACT.  This paper presents a new collection of trigonometric and inverse trigonometric integral formulas based on a known integral result. Some of these formulas evaluate to zero, while others are notable for their connection to well-known mathematical constants,...