A partial differential equation (PDE) of order m is a relation of the form F (x, u,Du,Du, · · · , Du) = 0. (0.1) Here F is a given function of x ∈ R, ”unknown” function u = u(x), and its derivatives up to order m. We denote Du the set of all the derivatives of u of order k. Using multi-indices l = (l1, · · · , ln), i.e. vectors in R with nonnegative integer components, we can write Du = { Du = ...

A better understanding of the microenvironment in relation to lymph node metastasis is essential for the development of effective immunotherapeutic strategies against cervical cancer. In the present study, we investigated the microenvironment of tumor-draining lymph nodes of cervical cancer patients, by comprehensive flow cytometry-based phenotyping and enumeration of immune-cell subsets in tum...

CCP program 1 simulation(S):2 Init=[[I1|_], [I2|_], ..., [In|_]], 3 run(1,S,Init) || 4 run(2,S,Init) || 5 ... || 6 run(n,S,Init). 7 run(ID, S, [P1, P2, ..., Pn]):8 getTails([P1, ..., Pn],[T1, ..., Tn]), 9 ask(T1=[_|_]) -> skip + 10 ask(T2=[_|_]) -> skip + 11 ... + 12 ask(Tn=[_|_]) -> skip, 13 getLast([P1, ..., Pn],[L1, ..., Ln]), 14 updatePosition(ID,S,[L1,..,Ln],NP), 15 tell(TID=[NP|_]), 16 ru...

The ligands tris[3-(2-pyridyl)pyrazol-1-yl]hydroborate (L1, potentially hexadentate) and bis[3-(2-pyridyl)pyrazol-1-yl]dihydroborate (L2, potentially tetradentate) have been used to prepare ternary lanthanide complexes in which the remaining ligands are dibenzoylmethane anions (dbm). [Eu(L1)(dbm)2] is eight-coordinate, with L1 acting only as a tetradentate chelate (with one potentially bidentat...

Define the Linus sequence Ln for n ≥ 1 as a 0-1 sequence with L1 = 0, and Ln chosen so as to minimize the length of the longest repeated block Ln−2r+1 . . . Ln−r = Ln−r+1 . . . Ln. Define the Sally sequence Sn as the length r of the longest repeated block that was avoided by the choice of Ln. We prove several results about these sequences, such as exponential decay of the frequency of highly pe...

A better understanding of the microenvironment in relation to lymph node metastasis is essential for the development of effective immunotherapeutic strategies against cervical cancer. In the present study, we investigated the microenvironment of tumor-draining lymph nodes of patients with cervical cancer by comprehensive flow cytometry-based phenotyping and enumeration of immune-cell subsets in...

Within this work, a modified preparation of diethyl 4-azidobenzylphosphonate (L1) is presented and the family 4- or 4′-azido-substituted aromatic phosphonate esters increased by three new ligand platforms: diisopropyl (L2), ((4′-azido-[1,1′-biphenyl]-4-yl)methyl)phosphonate (L3), 4-azido-2,3,5,6-tetrafluorobenzylphosphonate (L4), which exhibit an anomalous splitting N3 stretching vibrations. Su...

In this paper, we consider the relationships between the sums of the Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n > 2 Fn = Fn 1 + Fn 2 where F1 = F2 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n > 2 Ln = Ln 1 + Ln 2 where L1 = 1; L2 = 3: The permanent of an ...

A number of results concerning the convergence in distribution of the largest eigenvalue of a large class of random covariance matrices have recently been obtained. In particular, it was shown in Johansson (2000), Johnstone (2001), and El Karoui (2003) that if X is an n×N matrix whose entries are i.i.d standard complex Gaussian and l1 is the largest eigenvalue of X∗X , there exist sequences mn,...

With the previously proposed non-uniform norm called lN -norm, which consists of a sequence of l1-norm or l0-norm elements according to relative magnitude, a novel lN-norm sparse recovery algorithm can be derived by projecting the gradient descent solution to the reconstruction feasible set. In order to gain analytical insights into the performance of this algorithm, in this letter we analyze t...