Related papers: An elementary proof of the halting property for Ch…

The problem of existence and stability of equilibria of DC microgirds with constant power loads methods is addressed in this paper. Constant power loads (CPLs) often cause instability due to its negative impedance characteristics. What is…

We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…

Consider a symmetric function $\mathcal{C}(x,y)$ on $[0,1]\times[0,1]$ which is twice continuously differentiable up to the boundary, and which satisfies $ \mathcal{C}(x,y)=\mathcal{C}(1-x,1-y)$. Let $A^{(n)} = \big(a^{(n)}_{i,j}\, :\, i,j…

In an earlier work [K. Castillo et al., J. Math. Anal. Appl., 514 (2022) 126358], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail concerning the characterization of the continuous $q$-Jacobi…

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of…

We consider triangular P\'olya urns and show under very weak conditions a general strong limit theorem of the form $X_{ni}/a_{ni}\to \mathcal{X}_i$ a.s., where $X_{ni}$ is the number of balls of colour $i$ after $n$ draws; the constants…

The arrest of Langmuir-wave collapse by quantum effects, first addressed by Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz trial-function method is revisited, using rigorous estimates and systematic asymptotic…

Balancing a matrix is a preprocessing step while solving the nonsymmetric eigenvalue problem. Balancing a matrix reduces the norm of the matrix and hopefully this will improve the accuracy of the computation. Experiments have shown that…

In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…

In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is…

This paper establishes an equivalence between the halting problem in computability theory and the convergence of power series in mathematical analysis.

We revisit J. Shallit's minimization problem from 1994 SIAM Review concerning a two-term asymptotics of the minimum of a certain rational sum involving variables and products of their reciprocals, the number of variables being the large…

We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show…

In 1959, Erd\H{o}s and Gallai proved that every graph G with average vertex degree ad(G)\geq 2 contains a cycle of length at least ad(G). We provide an algorithm that for k\geq 0 in time 2^{O(k)} n^{O(1)} decides whether a 2-connected…

Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…

Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links…

Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These…

We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…

We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically conjectures}, and then {\it automatically proves}, closed-form…

The vivid contrast between two competing algorithms for solving Abel's equation $g(\theta(x)) = g(x) + 1$, given $\theta(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal…