Introduction: External root resorption is a clinical problem that often cannot be detected clinically. Thus, radiography plays a crucial role in its diagnosis. However, optimal radiographic quality with minimal radiation exposure {2.1 [EN] Verify English word/phrase choice} is an important factor in selecting the appropriate radiographic technique. The aim of this study was the comparison of ac...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

where X and Y are square matrices whose diagonal elements (where i = j) are unity, and whose subdiagonal elements (where i > j) are zero, whilst D is a diagonal matrix, that is, one whose off-diagonal elements (where i ?¿ j) are zero [1]. Where this factorization exists, it is unique [1]. Where it does not exist, there exists another factorization of the form (1) in which the matrices X and Y d...

If r 1, and m and n are each a multiple of (r + 1)2 + r2, then each isomorphic component of Cm ×Cn admits of a vertex partition into (r + 1)2 + r2 perfect r-dominating sets. The result induces a dense packing of Cm × Cn by means of vertexdisjoint subgraphs, each isomorphic to a diagonal array. Areas of applications include efficient resource placement in a diagonal mesh and error-correcting cod...

The exchange of water hydroxyl hydrogen bonds between anions and water oxygens is observed directly with ultrafast 2D IR vibrational echo chemical exchange spectroscopy (CES). The OD hydroxyl stretch of dilute HOD in H(2)O in concentrated (5.5 M) aqueous solutions of sodium tetrafluoroborate (NaBF(4)) displays a spectrum with a broad water-like band (hydroxyl bound to water oxygen) and a resolv...

We are developing a new method using ultrasonic longitudinal and torsional vibration of a hollow-type stepped horn for hole machining. We foresee that the equipment can be simplified and miniaturized. In this paper, ultrasonic vibration sources of a hollow-type stepped horn without a diagonal slits vibration converter and with a diagonal slits vibration converter are used. The longitudinal and ...

For a large class of quantum many-body systems with U(1) symmetry, we prove general inequality that relates the (off-diagonal) long-range order charge gap. system bosons or fermions on lattice in continuum, implies ground state off-diagonal inevitably has vanishing gap, and hence is characterized by nonzero susceptibility. spin system, within magnetization plateau cannot have transverse order.

Background: Detection of women at risk for dystocia will allow physicians to make preparations and treatment decisions that can minimize maternal and neonatal morbidity. We aimed to determine the risk factors for dystocia in nulliparous women. Methods: This case series enrolled 447 nulliparous women who presented with a single pregnancy in the vertex presentation and gestational age of 38-42 we...

Let n ? 4 be an even integer and W the wheel graph with vertices. The distance d i j between any two distinct vertices of is length shortest path connecting . D × symmetric matrix diagonal entries equal to zero off-diagonal In this paper, we find a positive semidefinite L ˜ such that rank ( ) = ? 1 , all row sums zero, one w T 2 + An interlacing property eigenvalues also proved.

Abstract A recent work derived expressions for the induced p -norm of a special class circulant matrices ( n , b ) ∈ ℝ × with diagonal entries equal to and off-diagonal ≥ 0. We provide shorter proofs all results therein using Fourier analysis. The key observation is that matrix diagonalized by DFT matrix. comprise an exact expression ǁ 1 ≤ ∞, where = ), 0 2 − 0; other -norms < upper lower bo...