The n crossing number of a graph G, denoted crn(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a > b > 0, there exists a graph G for which cr0(G) = a, cr1(G) = b, and cr2(G) = 0. This provides support for a conjecture of Archdeacon et al. and resolves a problem of Salazar.

This paper proposes a new equation to show the time domain features of jitter: Jitter = (Ti+1-Ti)/Ti. The subjects are tonal language speakers. Jitter is extracted from EGG signals. The results show that: (1) jitter does not obey Gaussian distribution but multimodal distribution; (2) the first peak position near zero of the jitter distribution curve increases with the pitch; (3) each peak posit...

Abstract The purpose of the research was to study inheritance trait oleic acid content in oil winter rapeseed seeds reciprocal F1 hybrids. We carried out 2019-2020 under field and greenhouse conditions. used two high lines for hybridization: BH 1844 (82.2 %) 1848 (83.0 %), high-yielding from varieties Sarmat Selegor with a standard level 62.1 60.5 %, respectively. Analysis C18:1 hybrids, condit...

A detailed structured backward error analysis for four kinds of Palindromic Polynomial Eigenvalue Problems (PPEP) ( d ∑ l=0 Alλ l ) x = 0, Ad−l = εA ⋆ l for l = 0, 1, . . . , ⌊d/2⌋, where ⋆ is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}. Each of them has its application background with the case ⋆ taking transpose and ε = 1 attracting a great deal of attention lately ...

We prove an analog of the Szemerédi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field R. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.

Parent-of-origin effects have long been recognized and exploited in plant breeding genetic studies. These can be conferred by preferential expression of an allele from one parent, organellar effects, or altered organellar-nuclear interaction. The goal this work was to evaluate parent-of-origin on seed, cotyledon, early growth traits cucumber using a full eight-by-eight diallel crossing two doub...

Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...

The interest in self-reciprocal polynomials in coding theory originated with Massey (1963, 1964), who has shown tha t whenever a self-reciprocal polynomial is used as a convolutional code-generating polynomial, the resulting code may be decoded backward us well as forward, with the same hardware and the same probabil i ty of decoding error. Let G( D ) = go 4glD 4g~D ~ 4" . . 4g , D ' , where n ...