To reflect the extent of thermolesion of ganglion by testing the change of trigeminal somatosensory-evoked potential (TSEP) before and after ganglion radiofrequency thermocoagulation surgery (GRT), and evaluate long-term clinic effect by follow-up visiting of 1 year.Patients with idiopathic trigeminal neuralgia (TN) in the second division were enrolled between October 2014 and October 2015. The...

In this paper, we mainly study the convergence properties of stochastic gradient descent (SGD) as described in Needell et al. [2]. The function to be minimized with SGD is assumed to be strongly convex. Also, its gradients are assumed to be Lipschitz continuous. First, we discuss the superior bound on convergence (of standard SGD) obtained by Needell et al. [2] as opposed to the previous work o...

Let wk be the minimum degree sum of a path on k vertices in a graph. We prove for normal plane maps that: (1) if w2 = 6, then w3 may be arbitrarily big, (2) if w2 > 6, then either w3 ≤ 18 or there is a ≤ 15-vertex adjacent to two 3-vertices, and (3) if w2 > 7, then w3 ≤ 17.

for various pairs of weight functions w1 : X → R + and w2 : Y → R . Roughly speaking, these weighted estimates are a variant of the usual L estimates which assert that if f avoids the regions where w1 is large, then Tf avoids the regions where w2 is large. If X = Y and one can establish the above type of estimate for many pairs w1, w2, with w1 “looking similar to” w2, then these estimates begin...

Let p be a prime number. Let w2 and w ∗ 2 denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p-adic number ξ satisfies w∗ 2(ξ) ≤ w2(ξ) ≤ w∗ 2(ξ) + 1, with w∗ 2(ξ) = w2(ξ) = 2 for almost all ξ. By means of Schneider’s continued fractions, we give explicit examples of p-adic numbers ξ for which ...

The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer W2,s strings, where the BRST charge is written as QB = Q0+Q1. In this paper, using this method, we reconstruct the nilpotent BRST charges Q0 for the integer W2,s strings and the half-integer W2,s strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the...

Let R −∞,∞ , and let Q ∈ C2 : R → 0,∞ be an even function. In this paper, we consider the exponential-type weights wρ x |x| exp −Q x , ρ > −1/2, x ∈ R, and the orthonormal polynomials pn w2 ρ;x of degree n with respect to wρ x . So, we obtain a certain differential equation of higher order with respect to pn w2 ρ;x and we estimate the higher-order derivatives of pn w2 ρ;x and the coefficients o...

We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans W1, W2 and W1 ∩W2 = {0}, then W1 ⊥W2.