Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 + W2 yields a strict subspace of V and is defined as follows: (Def. 1) The carrier of W1 + W2 = {v + u; v ranges over vectors of V , u ranges over vectors of V : v ∈ W1 ∧ u ∈ W2}. Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 ∩ W2 yields a strict subspace of V and is defined by: (De...

Worker Preferences Firm Preferences w1 : [f1] f2 f3 f4 f5 f6 f7 f8 f1 : [w1] w2 w3 w4 w5 w6 w7 w8 w2 : f1 [f2] f3 f4 f5 f6 f7 f8 f2 : w1 [w2] w3 w4 w5 w6 w7 w8 w3 : f1 f2 [f3] f4 f5 f6 f7 f8 f3 : w1 w2 [w3] w4 w5 w6 w7 w8 w4 : f1 f2 f3 [f4] f5 f6 f7 f8 f4 : w1 w2 w3 [w4] w5 w6 w7 w8 w5 : f1 f2 f3 f4 [f5] f6 f7 f8 f5 : w1 w2 w3 w4 [w5] w6 w7 w8 w6 : f1 f2 f3 f4 f5 [f6] f7 f8 f6 : w1 w2 w3 w4 w5 ...

Previous studies revealed that the recessive allele of the W2 locus generated purple-blue color and high vacuolar pH of flower petals in soybean. The location of W2 gene was reportedly close to simple sequence repeat marker Satt318 in molecular linkage group B2. We used information from the soybean genome to clone a candidate gene for W2. An MYB transcription factor gene belonging to G20 group ...

In classical growth analysis, relative growth rate (RGR) is calculated as RGR = (ln W2 - ln W1)/(t2 - t1), where W1 and W2 are plant dry weights at times t1 and t2. Since RGR is usually calculated using destructive harvests of several individuals, an obvious approach is to substitute W1 and W2 with sample means W1 and W2. Here we demonstrate that this approach yields a biased estimate of RGR wh...

A.L. MANSON, N. CHAPMAN, Y. WEDATILAKE, M. BALIC, H. MARWAY, S.L. SENEVIRATNE and P. HOLLOWAY From the Department of Clinical Immunology, St Mary’s Hospital, Imperial College Healthcare NHS Trust, London W2 1NY, Department of Clinical Pharmacology, St Mary’s Hospital, Imperial College Healthcare NHS Trust, London W2 1PG, Department of Chemical Pathology, St Mary’s Hospital, Imperial College Hea...

The effectiveness of UV and chlorination, used individually and sequentially, was investigated in killing pathogenic microorganisms and inhibiting the formation of disinfection by-products in two different municipal wastewaters for the source water of reclaimed water, which were from a microfilter (W1) and membrane bioreactor (W2) respectively. Heterotrophic plate count (HPC), total bacteria co...

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.