Maximal Zero Research Articles

The Upper Bound Estimation of Abelian Integral for a Class of Quadratic Reversible System under Small Perturbations

In this article, by using the Riccati equation method, we investigate the maximal values of the isolated zeros of the Abelian integral for a set of quadratic reversible systems (r11) that belong to genus one, while experiencing varying 3rd, 2nd, and 1st-polynomial perturbations. Specifically, we aimed to find the upper bound for the maximal zeros of the system’s limit cycle (a special dynamic behavior in a stable state, characterized by the existence of specific periodic orbits). We know that the Abelian integral is a function of h, so when studying the maximal zeros of the function related to h, we not only consider the highest degree of the relevant function but also take into account the parity of the function and the range of values of h. Then through variable substitution, a smaller upper bound can be obtained: our findings show that the maximal values of the isolated zeros count under varying 3rd, 2nd, and 1st-polynomial perturbations is 12, improving upon previous results where the upper bound was 34 for the 3rd polynomial perturbation and 22 for the 2nd and 1st polynomial perturbations. This study represents an improvement upon previous research.

Flavor symmetric origin of texture zeros in minimal inverse seesaw and impacts on leptogenesis

We study the prediction of maximal zeros of the Dirac mass matrix on neutrino phenomenology and baryon asymmetry of universe (BAU) within the framework of an inverse seesaw ISS (2,3). We try to find the origin of the allowed two zero textures of the Dirac mass matrix from S4 flavor symmetry. ISS (2,3) model contains two pairs of quasi-Dirac particles and one sterile state in the keV scale along with three active neutrinos. The decays of the quasi-Dirac pairs create lepton asymmetry that can be converted to baryon asymmetry of the universe by the sphaleron process. Thus, BAU can be explained in this framework through leptogenesis. We study BAU in all the two zero textures of the Dirac mass matrix. The viabilities of the textures within the framework have been verified with the latest cosmology data on BAU.

Impact of cumulative burden of body mass index and waist circumference on risk of atrial fibrillation: an analysis of 3,700,000 participants who underwent 4-year consecutive annual health examination

Abstract Background There is limited evidence for the significance of the combination of waist circumference (WC), as a surrogate marker of central obesity, with body mass index (BMI) for predicting the risk of atrial fibrillation (AF). Furthermore, the additive value of the burden of BMI and WC cumulated over time on AF risk has not been reported. Purpose We sought to investigate the effect of cumulative burden of BMI, WC, and their combinations on the risk of AF using health check-up data from the Korean National Health Insurance Service. Methods This study included subjects aged >20 years who underwent four times of annual national health check-ups serially during 2009 to 2013, excluding those with a previous history of AF. The 4-year cumulative burden of BMI and WC was represented as burden-score calculated by the summation of BMI score (BMI 18.5–23 kg/m2, score 0; BMI 23–25 kg/m2, score 1; BMI ≥25 kg/m2, score 2) and WC score (WC <90 cm for men or <85 cm for women, score 0; WC ≥90 cm for men or ≥85 cm for women, score 1) at each year of health check-up. Newly developed AF was identified using claims data during a median follow-up of 5.2 years. AF risk was evaluated according to the burden of BMI, WC, and their combinations. A multivariate Cox regression model was used to adjust for baseline differences. Results Of 3,726,172 subjects (mean age 44.5±11.1, men 69.5%) enrolled, 27% had BMI burden-score of zero, while 23% had maximal burden-score of 8. For WC, 71% had zero burden-score and 7% had the highest burden-score of 4. Compared to the zero burden-score, maximal burden-score of BMI mildly increased the risk of AF, whereas the risk of AF predominantly increased in the group of maximal burden-score of WC. The different burdens of BMI in the same WC burden group did not significantly affect the risk of AF. Adjusted HR of each BMI burden-score (BMI burden zero as a reference) ranged from 1.01 to 1.12 in the group with WC burden-score zero, 0.84 to 1.06 in WC burden-score 1, 0.84 to 1.19 in WC burden-score 2, 0.59 to 0.83 in WC burden-score 3, and 0.62 to 1.55 in WC burden-score 4 without statistical significance. In contrast, high WC burden-score further increased the risk of AF even in groups with moderate to high burden of BMI (adjusted HR of maximal WC burden versus zero burden 1.97 [1.49–2.59] in the group with BMI burden-score 4; 1.66 [1.23–2.24] in BMI burden-score 5; 1.49 [1.16–1.91] in BMI burden-score 6; 1.43 [1.18–1.73] in BMI burden-score 7; and 1.49 [1.38–1.60] in BMI burden-score 8). Conclusions The 4-year cumulative burden of WC was a stronger determinant of future AF risk than BMI burden. Particularly in middle-ranged BMI burden groups that include persistently overweight but not obese population, high burden of WC substantially increased the risk of AF. The strategy of active surveillance for AF and comprehensive management of lifestyle and risk factors should focus on high-risk populations determined by the burden of WC. Funding Acknowledgement Type of funding sources: None.

Impact of texture zeros on dark matter and neutrinoless double beta decay in inverse seesaw

We study the impact of maximal zeros of the Dirac mass matrix on neutrino phenomenology and dark matter within the framework of an inverse seesaw ISS (2,3). ISS (2,3) is obtained by adding two right handed neutrinos and three gauge singlets sterile fermions to the standard model leading to an extra sterile state in the keV range. The model is more predictive because of the presence of fewer numbers of right handed neutrinos than the conventional inverse seesaw. Moreover, texture zeros in the structures of the mass matrices involved in the model can reduce the free parameters. We extensively study the effect of different textures of Dirac mass matrix on sterile neutrino dark matter phenomenology. Our study also includes the implications of these texture zero mass matrices on low energy phenomena like neutrinoless double beta decay (0νββ). The zero textures highly constrain the parameter space of the model. Based on the allowed cosmological ranges of the relic abundance, decay rates and dark matter mixing with the active neutrinos, we study the viability of the different textures within the framework.

Maximal zero product subrings and inner ideals of simple rings

Let Q be a (not necessarily unital) simple ring or algebra. A nonempty subset S of Q is said to have zero product if S2=0. We classify all maximal zero product subsets of Q by proving that the map R↦R∩LeftAnn(R) is a bijection from the set of all proper nonzero annihilator right ideals of Q onto the set of all maximal zero product subsets of Q. We also describe the relationship between the maximal zero product subsets of Q and the maximal inner ideals of its associated Lie algebra.

Linear read-once and related Boolean functions

It is known that a positive Boolean function f depending on n variables has at least n+1 extremal points, i.e. minimal ones and maximal zeros. We show that f has exactly n+1 extremal points if and only if it is linear read-once.The class of linear read-once functions is known to be the intersection of the classes of read-once and threshold functions. Generalizing this result we show that the class of linear read-once functions is the intersection of read-once and Chow functions. We also find the set of minimal read-once functions which are not linear read-once and the set of minimal threshold functions which are not linear read-once. In other words, we characterize the class of linear read-once functions by means of minimal forbidden subfunctions within the universe of read-once and the universe of threshold functions.Within the universe of threshold functions the importance of linear read-once functions is due to the fact that they attain the minimum value of the specification number, which is n+1 for functions depending on n variables. In 1995 Anthony et al. conjectured that for all other threshold functions the specification number is strictly greater than n+1. We disprove this conjecture by exhibiting a threshold non-linear read-once function depending on n variables whose specification number is n+1.

Probing maximal zero textures with broken cyclic symmetry in inverse seesaw

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry (Z3) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix (mν) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter ϵ′ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix (ml) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken A4 symmetry group which leads to one of the combinations of ml, mD, MRS and μ to generate effective mν. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on ββ0ν decay parameter |m11| and the sum of the three light neutrino masses (Σimi) are also obtained.

Maximal zero textures in Linear and Inverse seesaw

We investigate Linear and Inverse seesaw mechanisms with maximal zero textures of the constituent matrices subjected to the assumption of non-zero eigenvalues for the neutrino mass matrix $m_\nu$ and charged lepton mass matrix $m_e$. If we restrict to the minimally parametrized non-singular `$m_e$' (i.e., with maximum number of zeros) it gives rise to only 6 possible textures of $m_e$. Non-zero determinant of $m_\nu$ dictates six possible textures of the constituent matrices. We ask in this minimalistic approach, what are the phenomenologically allowed maximum zero textures are possible. It turns out that Inverse seesaw leads to 7 allowed two-zero textures while the Linear seesaw leads to only one. In Inverse seesaw, we show that 2 is the maximum number of independent zeros that can be inserted into $\mu_S$ to obtain all 7 viable two-zero textures of $m_\nu$. On the other hand, in Linear seesaw mechanism, the minimal scheme allows maximum 5 zeros to be accommodated in `$m$' so as to obtain viable effective neutrino mass matrices ($m_\nu$). Interestingly, we find that our minimalistic approach in Inverse seesaw leads to a realization of all the phenomenologically allowed two-zero textures whereas in Linear seesaw only one such texture is viable. Next our numerical analysis shows that none of the two-zero textures give rise to enough CP violation or significant $\delta_{CP}$. Therefore, if $\delta_{CP}=\pi/2$ is established, our minimalistic scheme may still be viable provided we allow more number of parameters in `$m_e$'.

Occam's razor in quark mass matrices

On the standpoint of Occam's Razor approach, we consider the minimum number of parameters in the quark mass matrices needed for the successful CKM mixing and CP violation. We impose three zeros in the down-quark mass matrix with taking the diagonal up-quark mass matrix to reduce the number of free parameters. The three zeros are maximal zeros in order to have a CP violating phase in the quark mass matrix. Then, there remain six real parameters and one CP violating phase, which is the minimal number to reproduce the observed data of the down-quark masses and the CKM parameters. The twenty textures with three zeros are examined. Among them, the thirteen textures are viable for the down-quark mass matrix. As a representative of these textures, we discuss a texture $M_d^{(1)}$ in details. By using the experimental data on $\sin 2\beta$, $\theta_{13}$ and $\theta_{23}$ together with the observed quark masses, the Cabibbo angle is predicted to be close to the experimental data. It is found that this surprising result remains unchanged in all other viable textures. We also investigate the correlations among $|V_{ub}/V_{cb}|$, $\sin 2\beta$ and $J_{CP}$. For all textures, the maximal value of the ratio $|V_{ub}/V_{cb}|$ is $0.09$, which is smaller than the upper-bound of the experimental data, $0.094$. We hope that this prediction will be tested in future experiments.

Maximal zero textures of the inverse seesaw with broken μτ symmetry

The inverse neutrino seesaw, characterised by only one source of lepton number violation at an ultralight $O$(keV) scale and observable new phenomena at TeV energies accessible to the LHC, is considered. Maximal zero textures of the $3\times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $\mu\tau$ symmetry in a specified weak basis. That symmetry ensures the identity of the positions of maximal zeros of the heavy neutrino mass matrix and its inverse. It then suffices to study the maximal zeros of the lighter Dirac mass matrix and those of the inverse of the heavier one since they come in a product. The observed absence of any unmixed neutrino flavour and the assumption of no strictly massless physical neutrino state allow only eight $4$-zero $\times$ $4$-zero, eight $4$-zero $\times$ $6$-zero and eight $6$-zero $\times$ $4$-zero combinations. The additional requirement of leptogenesis is shown to eliminate the last sixteen textures. The surviving eight $4$-zero $\times$ $4$-zero textures are subjected to the most general explicit $\mu\tau$ symmetry breaking terms in the Lagrangian in order to accommodate the nonzero value of $\theta_{13}$ in the observed range. A full diagonalisation is then carried out. On numerical comparison with all extant and relevant neutrino (antineutrino) data, seven of these eight combination textures in five neutrino matrix forms are found to be allowed, leading to five distinct neutrino mass matrices. Two of these permit only a normal (and the other three only an inverted) mass ordering of the light neutrinos.

On Two Sequences of Polynomials Satisfying Certain Recurrence

Bae and Kim displayed a sequence of 4th degree self-reciprocal polynomials whose maximal zeros are related in a very nice and far from obvious way. Kim showed that the auxiliary polynomials in their results are related to Chebyshev polynomials. In this paper, we study two sequences of polynomials satisfying the recurrence of the auxiliary polynomials with generalized initial conditions. We obtain same results with the auxiliary polynomials from a sequence, and some interesting conjectural properties about resultants and discriminants from another sequence.

Morphic and automatic words: maximal blocks and Diophantine approximation

Let w be a morphic word over a finite alphabet �, and letbe a nonempty subset of �. We study the behavior of maximal blocks consisting only of letters fromin w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k'th maximal �-block in w. Then limsupk!1(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a result, we show that the same conclusion holds if (ik, jk) are the starting and ending positions of the k'th maximal zero block, and, more generally, of the k'th maximal x- block, where x is an arbitrary word. This enables us to draw conclusions about the irrationality exponent of automatic and morphic numbers. In particular, we show that the irrationality exponent of automatic (resp., morphic) numbers belonging to a certain class that we define is rational (resp., algebraic).

Asymptotic behavior of the maximal zero of a polynomial orthogonal on a segment with a nonclassical weight

Let {pn(t)}n=0t8 be a system of algebraic polynomials orthonormal on the segment [−1, 1] with a weight p(t); let {xn,ν(p)}ν=1n be zeros of a polynomial pn(t) (xx,ν(p) = cosθn,ν(p); 0 < θn,1(p) < θn,2(p) < ... < θn,n(p) < π). It is known that, for a wide class of weights p(t) containing the Jacobi weight, the quantities θn,1(p) and 1 − xn,1(p) coincide in order with n−1 and n−2, respectively. In the present paper, we prove that, if the weight p(t) has the form p(t) = 4(1 − t2)−1{ln2[(1 + t)/(1 − t)] + π2}−1, then the following asymptotic formulas are valid as n → ∞: $$ \theta _{n,1}^{(p)} = \frac{{\sqrt 2 }} {{n\sqrt {\ln (n + 1)} }}\left[ {1 + {\rm O}\left( {\frac{1} {{\ln (n + 1)}}} \right)} \right],x_{n,1}^{(p)} = 1 - \left( {\frac{1} {{n^2 \ln (n + 1)}}} \right) + O\left( {\frac{1} {{n^2 \ln ^2 (n + 1)}}} \right). $$

Zero subspaces of polynomials on [formula omitted

We provide two examples of complex homogeneous quadratic polynomials P on Banach spaces of the form ℓ 1 ( Γ ) . The first polynomial P has both separable and nonseparable maximal zero subspaces. The second polynomial P has the property that while the index-set Γ is not countable, all zero subspaces of P are separable.

MgB2 Ramp-type Superconducting Thin Film Josephson Junctions

Josephson effects on ramp-type MgB2/Al/AlOx/Nb junctions are demonstrated. The MgB2 thin films were prepared by sequential e-beam evaporation of boron and magnesium on buffered silicon substrate and synthesised by short post-annealing at 700°C. The prepared smooth nanocrystalline films, with maximal zero resistance critical temperature Tco ≈ 36 K, were in situ covered by an SrTiO3 overlayer. Ramp-edge was patterned by ion beam etching through photoresist mask. DC magnetron sputtering of Al (subsequently oxidized) and Nb was applied to complete the junction structure. Current-voltage characteristics and current steps at irradiation of samples by microwaves confirm the presence of weak link effects in the structures.

Finding a maximal zero for some classes of monotone Boolean functions in Post's classification

The Shannon complexity of finding a maximal zero for some classes of monotone Boolean functions in Post's classification is estimated.

Splines with maximal zero sets

Consider a spline s( x) of degree n with L knots of specified multiplicities R 1, …, R L , which satisfies r sign consistent mixed boundary conditions in addition to s ( n) ( a) = 1. Such a spline has at most n + 1 − r + ∑ j = 1 L R j zeros in ( a, b) which fulfill an interlacing condition with the knots if s( x) ≢ = 0 everywhere. Conversely, given a set of n − r + ∑ j = 1 L R j zeros then for any choice η 1 < ··· < η L of the knot locations which fulfills the interlacing condition with the zeros, the unique spline s( x) possessing these knots and zeros and satisfying the boundary conditions is such that s ( n) ( x) vanishes nowhere and changes sign at η j if and only if R j is odd. Moreover there exists a choice of the knot locations, not necessarily unique, which makes ¦s (n)(x)¦ ≡ 1 . In particular, this establishes the existence of monosplines and perfect splines with knots of given multiplicities, satisfying the mixed boundary conditions and possessing a prescribed maximal zero set. An application is given to double-precision quadrature formulas with mixed boundary terms and a certain polynomial extremal problem connected with it.

Optimale Fehlerabsch�tzungen mit dualen Funktionalen bei semilinearen Randwertaufgaben gew�hnlicher Differentialgleichungen

In Shampine [7] it is shown how to obtain variational error bounds for approximate solutions of boundary value problems for semilinear ordinary differential equations. These bounds are depending on a certain constantK, the existence of which is assumed. Our paper aims at practical computation; in order to get applicableL ?-error bounds,K has to be computed explicitly. Using Garding's inequality, we obtainK=K(?) depending on a positive parameter ?. In order to make these bounds efficient,K(?) will be optimized. In application only the maximal zeros of three polynomials have to be computed. Some numerical examples are given to compare the error bounds with the actual errors.