Semidefinite Research Articles

Effect of Smartphone Output Power on the Undetermined Headache among High School Students: Time-Series Study

Background: The undetermined headache, which is not classified as a primary headache, might be a mobile phone associated headache (MPAH). Objective: To investigate the smartphone electromagnetic radiation related to undetermined headaches among high school students. Materials and Methods: One hundred forty-five high school students in the Chiang Mai Province completed a headache diary according to the International Classification of Headache Disorders version 3 beta criteria. It was scored according to the diagnosis algorithm. The smartphone output power (SOP) as measured and recorded by the smartphone application was saved every five minutes and transmitted by email. The completed data included 12,969 entries. The smartphone use, sleep quality, anxiety, and depression were also assessed. Data were analyzed using the Generalized Estimating Equation adjusted for demographic data, smartphone use, and sleep quality, and other. Results: Most students were female 74.7% with a mean age of 17.63±1.01 years (range 16 to 20). The one-year headache prevalence was 92.6% (95% CI 90.8 to 94.1) with undetermined headaches at 18.7% and 16.9% in the first and second phase, respectively. Characteristically, the prevalence of MPAH was higher in the nature of short duration pain, pulsing and tightening, indefinite form of pain, pain occurring in the morning, one side headache at occipital or frontal areas, and low pain severity (p<0.05). The results revealed the strongest effect of SOP at 1.80×10⁻⁵ to 1.99×10⁻⁵ mW range on the undetermined headaches with ORadj 2.32; 95% CI 1.23 to 4.34. Furthermore, the undetermined headaches also had the strongest association with handfree use and internet use (ORadj 1.92; 95% CI 1.11 to 3.29 and ORadj 2.33; 95% CI 1.71 to 3.19, respectively), age, and anxiety (ORadj 1.49; 95% CI 1.26 to 1.76 and ORadj 1.12; 95% CI 1.07 to 1.17, respectively). Conclusion: The undetermined headache associated with SOP, which was a MPAH. These results suggest that an older age for starting smartphone use and utilizing a hand-free device were recommended to prevent chronic headaches. Keywords: Smartphone output power, Undetermined headache, Mobile phone associated headache

Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an (<img src=image/13415329_01.gif>)-type Connection

Jin [1] defined an ( )-type connection on semi-Riemannian manifolds. Semi-symmetric nonmetric connection and non-metric ∅-symmetric connection are two important examples of this connection such that ( ) = (1; 0) and ( ) = (0; 1), respectively. In semi-Riemannian geometry, there are few literatures for the lightlike geometry, so we expose new theories for non-degenerate submanifolds in semi-Riemannian geometry. The goal of this paper is to study a characterization of a (Lie) recurrent lightlike hypersurface M of an indefinite Kaehler manifold with an ( )-type connection when the charateristic vector field is tangnet to M. In the special case that an indefinite Kaehler manifold of constant holomorphic sectional curvature is an indefinite complex space form, we investigate a lightlike hypersurface of an indefinite complex space form with an ( )-type connection when the charateristic vector field is tangnet to M. Moreover, we show that the total space, the complex space form, is characterized by the screen conformal lightlike hypersurface with an ( )-type connection. With a semi-symmetric non-metric connection, we show that an indefinite complex space form is flat.

Estimates for representation numbers of binary quadratic forms and Apollonian circle packings

Fix a primitive, positive definite binary quadratic form g with integer coefficients. We prove asymptotic formulas for sums of the form ∑rg(n)β and ∑rg⁎(n)β, where β≥0 and rg(n), resp. rg⁎(n), denote the number of inequivalent representations, resp. proper inequivalent representations, of n by g. These estimates generalize a previous result by Blomer and Granville (2006) by allowing for non-fundamental discriminants and also clarify some details in the proof of the positive density conjecture for integral Apollonian circle packings by Bourgain and Fuchs (2011).

Transmit beamformer based performance analysis and diversity gains of cell edge user in cooperative MISO-NOMA system

This paper investigates the cell-edge user’s performance in a two-user multiple-input single-output non-orthogonal multiple access (MISO-NOMA) systems using downlink beamformers for optimal power allocation. In particular, power allocation coefficients (PACs) are adjusted through beamformers so that the cell-edge user’s performance is improved in a two-user network scenario. In the proposed model, a cell-center user with strong channel conditions plays a role as an energy harvesting (EH) relay by using simultaneous wireless information and power transfer (SWIPT) protocol to assist the cell-edge user having weak channel conditions. Initially, we formulate the expressions for signal-to-interference-plus-noise ratio (SINR) at the cell-center user and signal-to-noise ratio (SNR) and SINR at the cell-edge user in terms of an indefinite quadratic form (IQF) whilst considering distinct correlation matrices for each link. Next, we achieve exact and approximate closed-form expressions for outage probability of linearly dependent and of distinct beamformers, respectively by using IQF approach. The proposed model achieves diversity gain whereas the analytical expressions are validated by simulation means.

Limiting distribution of eigenvalues in the large sieve matrix

The large sieve inequality is equivalent to the bound \lambda_1 \leq N + Q^2-1 for the largest eigenvalue \lambda_1 of the N \times N matrix A^*A , naturally associated to the positive definite quadratic form arising in the inequality. For arithmetic applications the most interesting range is N \asymp Q^2 . Based on his numerical data Ramaré conjectured that when N \sim \alpha Q^2 as Q \to \infty for some finite positive constant \alpha , the limiting distribution of the eigenvalues of A^*A , scaled by 1/N , exists and is non-degenerate. In this paper we prove this conjecture by establishing the convergence of all moments of the eigenvalues of A^*A as Q\to\infty . Previously only the second moment was known, due to Ramaré. Furthermore, we obtain an explicit description of the moments of the limiting distribution, and establish that they vary continuously with \alpha . Some of the main ingredients in our proof include the large-sieve inequality and results on n -correlations of Farey fractions.

Operators on positive semidefinite inner product spaces

Let U be a semiunitary space; i.e., a complex vector space with scalar product given by a positive semidefinite Hermitian form 〈⋅,⋅〉. If a linear operator A:U→U is bounded (i.e., ‖Au‖⩽c‖u‖ for some c∈R and all u∈U), then the subspace U0:={u∈U|〈u,u〉=0} is invariant, and so A defines the linear operators A0:U0→U0 and A1:U/U0→U/U0.Let A be an indecomposable bounded operator on U such that 0≠U0≠U. Let λ be an eigenvalue of A0. We prove that the algebraic multiplicity of λ in A1 is not less than the geometric multiplicity of λ in A0, and the geometric multiplicity of λ in A1 is not less than the number of Jordan blocks Jt(λ) of each fixed size t×t in the Jordan canonical form of A0.We give canonical forms of selfadjoint and isometric operators on U, and of Hermitian forms on U.For an arbitrary system of semiunitary spaces and linear mappings on/between them, we give an algorithm that reduces their matrices to canonical form. Its special cases are Belitskii's and Littlewood's algorithms for systems of linear operators on vector spaces and unitary spaces, respectively.

On the zeros of Epstein zeta functions near the critical line

Let Q be a positive definite quadratic form with integral coefficients and its discriminant D<0 and let E(s,Q) be the Epstein zeta function associated with Q. Assume that the class number of the quadratic imaginary field Q(D) is bigger than 1. Then we estimate the number of zeros of E(s,Q) in the region ℜs>σT(θ):=1/2+(log⁡T)−θ and T<ℑs<2T, to provide its asymptotic formula for fixed 0<θ<1 conditionally. Moreover, it is unconditional if the class number of Q is 2 or 3 and 0<θ<1/13.

Complex symmetric evolution equations

We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a $$\mathcal {C}$$-selfadjoint operator generates a contraction $$C_0$$-semigroup if and only if it is dissipative. In addition, we examine the abstract Cauchy problem for nonautonomous linear differential equations possessing a complex symmetry. In the unbounded operator framework we isolate the class of complex symmetric, unbounded semigroups and investigate Stone-type theorems adapted to them. On Fock space realization, we characterize all $$\mathcal {C}$$-selfadjoint, unbounded weighted composition semigroups. As a byproduct we prove that the generator of a $$\mathcal {C}$$-selfadjoint, unbounded semigroup is not necessarily $$\mathcal {C}$$-selfadjoint.

On the classification of homogeneous affine tube domains with large automorphism groups in arbitrary dimensions

We classify tube domains in Cn+1 (n≥1) with affinely homogeneous base of their boundary and a.) with positive definite Levi form and b.) with Lorentzian type Levi form and affine isotropy of dimension at least (n−2)(n−3)2.

Galois theoretic study on simultaneous representation of primes by binary quadratic forms

We study intrinsic Galois structure behind theorems by Kaplansky, Brink, and Mortenson on simultaneous representation of primes by binary quadratic forms with different discriminants. This study brings new theorems like theirs also in indefinite quadratic forms.

Quadratic forms with a strong regularity property on the representations of squares

A (positive definite and non-classic integral) quadratic form is called strongly s-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this article, we prove that for any integer k≥2, there are only finitely many isometry classes of strongly s-regular quadratic forms with rank k if the minimum of the nonzero squares that are represented by them is fixed.

On a Zeta Function Associated to a Quadratic Order

For a positive integer N, we derive a Kronecker type limit formula for a Dedekind type zeta function $$\zeta _{\mathcal {O}_{K}(N)}(s;[\mathfrak {a}])$$ associated to a wide ideal class of a quadratic order of conductor N of a quadratic field K. As consequences, we establish a Chowla–Selberg type formula for a modular form for $$\Gamma _{0}(N)$$, give a proof to a classical class number relation of a quadratic field, and find an asymptotic formula for the average value of the number of representations by a primitive positive definite quadratic form of discriminant $$N^{2}d$$ with d fundamental. Furthermore, as an application, we obtain a formula for the Petersson norm of a theta function attached to a class character of the ideal group of conductor N of $$\mathcal {O}_{K}$$.

О КВАДРАТИЧНЫХ ФОРМАХ СО СТАЦИОНАРНОЙ ГИПЕРПЛОСКОСТЬЮ

A critical analysis (with specific numerical examples) of the conclusions following from Onsager’s theory in the classical linear thermodynamics of irreversible processes shown the insufficiency of conditions that guarantee the non-negativity and equality to zero of the entropy production. In order to understand the reasons for such a situation, the article introduces the concept of a quadratic form with a stationary hyperplane and compiles a system of nonlinear equations of a special form, in which a Boolean vector is unknown. Their precise definitions are given. The theorem is formulated and proved as a criterion, the fulfillment of the conditions of which is necessary and sufficient for a quadratic form to be a form with a stationary hyperplane. It is also shown that the quadratic form with a stationary hyperplane as applied to the production of the entropy gives quite correct explanations for the discrepancies that occur in Onsager’s theory. Instead, those explanations do not contradict the second law of thermodynamics. Thus, a quadratic form with a stationary hyperplane can be considered as a completely adequate mathematical model for studying a certain class of issues in the classical linear thermodynamics of irreversible processes. It is shown as well that every quadratic form with a stationary hyperplane is reducible to a perfect square and is a positive semidefinite form. So quadratic forms with a stationary hyperplane can be used in the educational process in the course of algebra when studying the topic “Quadratic forms”.

Bayesian Optimization of Expected Quadratic Loss for Multiresponse Computer Experiments with Internal Noise

Design of systems based on computer simulations is prevalent. An important idea to improve design quality, called robust parameter design (RPD), is to optimize control factors based on the expectation of a loss function so that the design is robust to noise factor variations. When computer simulations are time consuming, optimizing the simulator based on a Gaussian process (GP) emulator for the response is a computationally efficient approach. For this purpose, acquisition functions (AFs) are used to sequentially determine the next design point so that the GP emulator can more accurately locate the optimal setting. Despite this, few articles consider AFs for positive definite quadratic forms such as the expected quadratic loss (EQL) function, which is the standard expected loss function for RPD with nominally-the-best responses. This paper proposes new AFs for optimizing the EQL, analyzes their convergence, and develops quick and accurate methods based on the characteristic function of the EQL to compute them. We apply the AFs to RPD problems with internal noise factors based on a GP model and an initial design tailored for such problems. Numerical results indicate that all four AFs considered have similar performance, and they outperform an optimization approach based on modeling the quadratic loss as a GP and maximin Latin hypercube designs. MATLAB codes for reproducing reported results are given in the online supplement.

A stabilizer-free weak Galerkin finite element method on polytopal meshes

A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous Galerkin finite element methods will simplify formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This new WG method keeps a simple symmetric positive definite form and can work on polygonal/polyhedral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete H1 norm and the L2 norm. Numerical results are presented verifying the theorem.

Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms

Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are further extended to deal with the case of eigenvalue problems defined by positive semi-definite bilinear forms. As an application, the eigenvalue estimation theorems are applied to the error constant estimation for polynomial projections.

Polaron-transformed dissipative Lipkin-Meshkov-Glick model

We investigate the Lipkin-Meshkov-Glick model coupled to a thermal bath. Since the isolated model itself exhibits a quantum phase transition, we explore the critical signatures of the open system. Starting from a system-reservoir interaction written in positive definite form, we find that the position of the critical point remains unchanged, in contrast to the popular mean-field prediction. Technically, we employ the polaron transform to be able to study the full crossover regime from the normal to the symmetry-broken phase, which allows us to investigate the fate of quantum-critical points subject to dissipative environments. The signatures of the phase transition are reflected in observables like stationary mode occupation or waiting-time distributions.

Joint A-hyponormality of operators in semi-Hilbert spaces

The purpose of the paper is to introduce and study a class of multivariable operators on semi-Hilbertian spaces, i.e. spaces generated by positive semidefinite sesquilinear forms. Let and let A be a commuting m-tuple of operators and a positive operator on a complex Hilbert space, respectively. We introduce an A-hyponormal tuple of operators and study some properties of this class of multivariable operators. An m-tuple of operators is said to be A-hyponormal tuple if for each finite collections

Composition law and complex multiplication

Let K be an imaginary quadratic field of discriminant dK, and let n be a nontrivial integral ideal of K in which N is the smallest positive integer. Let QN(dK) be the set of primitive positive definite binary quadratic forms of discriminant dK whose leading coefficients are relatively prime to N. We adopt an equivalence relation ∼n on QN(dK) so that the set of equivalence classes QN(dK)/∼n can be regarded as a group isomorphic to the ray class group of K modulo n. We further establish an explicit isomorphism of QN(dK)/∼n onto Gal(Kn/K) in terms of Fricke invariants, where Kn denotes the ray class field of K modulo n. This would be a certain extension of the classical composition theory of binary quadratic forms, originated and developed by Gauss and Dirichlet.

La nada y el tiempo. La gubernamentalidad temporal del desempleo

Unemployment is not just an economic category but is constituted by governmentality (Foucault, 2010), most evidently by the increase of interventions into the lives of the unemployed through Active Labour Market Policies (ALMP). Furthermore, the International Labour Organization (ILO) definition of unemployment as being without work, available for work and seeking work is a shifting classification which categorises unemployment on multiple temporal horizons, with the passive element of being without work increasingly superseded by the emphasis on seeking work. Through biographical interviews with unemployed in Ireland, spanning from 2012-2018, we trace this transformation of temporality empirically and conclude that governmentality constitutes multiple, contradictory, indefinite forms of time. Particularly, we offer an imaginative reading of two overlapping temporalities: Kairos, waiting, enduring, suffering nothingness in anticipation of transformation by getting a job, and Cronos, not cyclical time, but the devouring of time, where the days and leisure of the unemployed people are deliberately consumed by job-seeking. Ironically, states implement ALMPs in the kairotic hope of transforming their economy, yet these policies do little but make the experience of unemployment even harder to endure.