Tag Archives: 4-ap

It is easy to see that the free constants

It is easy to see that the free constants U1, U2, … correspond to the potentials of a lesser degree, homogeneous in Euler\’s sense. These constants, except for the leading coefficient U0, can be set equal to zero without loss of generality. As a result, we can construct a set of linearly independent basis functions with consistently increasing polynomial degrees.
Listed below are the expressions for symmetric and antisymmetric potentials homogeneous in Euler\’s sense which can serve as spectrographic media; notice that the degree of homogeneity k does not necessarily have to be an integer.
The potentials with even degrees of y, symmetric with respect to z:
The potentials with odd degrees of y, symmetric with respect to z:
The potentials with even degrees of y, antisymmetric with respect to z:
The potentials with odd degrees of y, antisymmetric with respect to z:
Figs. 1–4 show equipotential surfaces of the fields from the list, represented by formulae (9)–(12).
Symmetry or antisymmetry of a function with respect to the corresponding coordinate is fully equivalent to an expansion of the potential only in even or only in odd degrees of a coordinate. This is why expressions (9)–(12) in their ‘expanded’ form, when the y and z coordinates are interchanged, can be used in synthesizing particle optics systems of the required type. However, the OXY plane still remains the main plane where the principal motion of charged particles occurs. Detailed configurations of two-dimensional electrostatic and magnetostatic mirrors as applied to synthesizing 4-ap spectrographs with ideal characteristics have been discussed, for example, in [4,7–10].

We should note that the procedure for generating a quasi-polynomial is, in a sense, inverse to the process of expanding a harmonic function in a Taylor series in the vicinity of the plane of symmetry or antisymmetry by its given behavior along the plane of symmetry or antisymmetry [1,2]. So in this case, for the coefficients of the expansion in Taylor series, we start with the lowest polynomial coefficient and gradually move in a recurrent manner to the polynomial coefficients of all higher degrees. This procedure is, generally speaking, infinite, unless the behavior of the function along the plane of symmetry (or antisymmetry) is in itself a polynomial with respect to two variables. In contrast with this process, the construction of quasi-polynomials starts with the highest coefficient and gradually moves in a recurrent manner to polynomial coefficients of lower degrees, stopping at the lowest term in a finite number of steps. This procedure also differs from the method applied to using the generating function with respect to orthogonal polynomials of general form, for example, the Rodrigues formula for Hermite, Laguerre, Legendre, Chebyshev, Jacobi, Gegenbauer, Sonine, and other polynomials (see Ref. [16]).


This article continues the investigations into spectrographic charged-particle optical structures which can serve as a basis for constructing effective devices with electric as well as magnetic fields. Potential structures of these fields ought to be homogeneous in Euler\’s sense [1,2]. According to our ideology, this property is very important, and a major condition for designing electric and magnetic spectrographs with high-performance characteristics such as resolution, sensitivity, transmission, energy dispersion and others, while the overall dimensions of the field-forming electrodes are rather small, and the device as a whole is compact.
The property of homogeneity is expressed in the following analytical form. A continuous function of three variables, which is the potential U(x, y, z), is homogeneous in Euler\’s sense of k-th order, if the identity
is fulfilled, where k is any real number.
If the function U(x, y, z) is differentiable, then it can be described by a differential equation of first order

br Conclusions The proposed qualitative endoscopic activity score for

The proposed qualitative endoscopic activity score for canine IBD meets the following requirements as described for human endoscopic indices: (1) it is well correlated with the endoscopist\’s overall assessment of abnormal mucosal appearance; (2) the quality of the assessment is consistent when evaluated in a set of patients different than that used for its development; (3) it incorporates mucosal parameters intuitively considered as important by experienced endoscopists; (4) it incorporates mucosal parameters previously shown to be reproducibly collected, and is itself reproducible; and (5) it is simple to calculate. Importantly, this validated endoscopic index should be correlated with clinical indices and laboratory biomarkers of inflammation in future studies (Mary and Modigliani, 1989).

Conflict of interest statement


Porcine tonsils and the nasal cavity can act as a site of colonisation by opportunistic pathogens, including staphylococcal bacteria (Weese et al., 2014). In Belgium, methicillin-resistant Staphylococcus epidermidis (MRSE) has been found to be a major constituent of the methicillin-resistant non-Staphylococcus aureus staphylococci (MRNAS) flora in pig nostrils (Vanderhaeghen et al., 2012).
S. epidermidis colonises the skin and mucous membranes of mammalian species and is acknowledged as an important opportunistic pathogen in humans (Otto, 2009). Approximately 70–95% of the S. epidermidis strains circulating in human hospitals have been estimated to be methicillin-resistant, and most also display resistance to other 4-ap of antimicrobial drugs (Otto, 2009). In staphylococci, methicillin resistance is mediated by acquisition of mecA or mecC genes, located on the mobile genetic element staphylococcal cassette chromosome mec (SCCmec) (García-Álvarez et al., 2011). In some S. epidermidis strains, SCCmec has been found to be associated with the arginine catabolic element (ACME), a genomic island which might contribute to enhanced fitness and an ability to colonise the host (Barbier et al., 2011).
In veterinary medicine, S. epidermidis is one of the main aetiological agents of intra-mammary infections in ruminants (Vanderhaeghen et al., 2014) and can also be involved in various types of infectious disease in companion animals (Kern and Perreten, 2013). The aim of the present study was to investigate the prevalence, genetic diversity, virulence and antimicrobial resistance characteristics of S. epidermidis in pigs, as well as to determine the role that pigs might play as potential reservoirs of zoonotic S. epidermidis for the human population.

Materials and methods


Humans living or working on pig farms have been reported to have an increased risk of colonisation or infection with livestock-associated MRSA (Crombé et al., 2013). Pigs are also a potential reservoir of other staphylococci, including CoNS, such as S. epidermidis, which is one of the most frequent causes of nosocomial infections in humans, especially those associated with indwelling medical devices (Otto, 2009).
In the present study, approximately one-quarter of the healthy pigs tested carried S. epidermidis, with MRSE prevalence of 13.5%. In other published studies, MRSE has been infrequently or not detected in farmed pigs (Zhang et al., 2009; Bhargava and Zhang, 2012). Similarly, in poultry (Zhang et al., 2009; Bhargava and Zhang, 2012) and cattle (Vanderhaeghen et al., 2013) relatively few MRSE isolates have been identified in healthy populations. Conversely, S. epidermidis is one of the main CoNS causing ruminant intramammary infections (Vanderhaeghen et al., 2014), with similar methicillin-resistance rates as reported in the current study (Sampimon et al., 2011; Frey et al., 2013). It has been suggested that the S. epidermidis strains that cause mastitis originate from humans (Watts and Owens, 1989), and some evidence for cis configuration has come from studies, comparing organisms found in milk with strains of S. epidermidis isolated from humans working with those animals (Thorberg et al., 2006; Jaglic et al., 2010).