IntroductionStudies by numerous authors indicate that many bovine chromosomes (BTAs), including BTA3,6,9,14,20, and 23, in particular, bear clusters of quantitative trait loci (QTL) of different milk performance traits. In numerous reports the studies concentrated on BTA6 within 2 regions, in which clusters of genes associated with milk performance traits are located (1). These regions are the fragments in the middle part of BTA6, close to the BM143 marker, and the region close to the casein genes complex (2,3). Previous literature suggests that genes located near BM143 affect 5 milk performance traits, including milk yield (kg), milk protein and fat yield (kg), and milk protein and fat content (%) (1). The region encompassing these genes extends from the FAM13A (family with sequence similarity 13, member A1) to the PPARGC1A (peroxisome proliferator-activated receptor-γ coactivator-1α) genes and spans approximately 6.2 cM. In this range, there are genes whose effects on the performance traits of cattle have already been examined, such as OPN (osteopontin), and genes that may potentially influence these traits, such as FAM13A1, LAP3 (leucine aminopeptidase 3), and HCAP-G (condensin subunit 3) (4-6).Osteopontin (OPN) is a phosphorylated glycoprotein that plays a role in different processes in the organism, for example in cell adhesion, chemotaxis, cell signaling, and the regulation of growth and development of the fetus, as well as in the initiation and maintenance of pregnancy ( 7). The presence of OPN in milk and its high level of expression in mammary epithelial cells may cause proliferation and differentiation of the mammary gland (8). Despite fulfilling so many functions, OPN is treated by most authors as a positional candidate gene for milkperformance traits harboring the QTL region on BTA6 (9,10). Other studied genes do not play such an important role in the organism and, therefore, are considered first of all as positional candidate genes.It was suggested that the FAM13A1, LAP3, and HCAP-G genes may be associated with milk-performance traits such as milk yield and milk composition, mainly due to their location in the analyzed region and due to the fact that the expression levels of these genes were found to be different in the mammary gland (4,(11)(12)(13). Preliminary assessments of the association of these genes with milkperformance traits were reported (5,(11)(12)(13). For instance, the LAP3 gene may affect milk fat and protein yield, the FAM13A1 and LAP3 genes may affect the change in milk protein content, and the LAP3 gene has been associated with milk yield (5,(11)(12)(13).On the basis of the above-mentioned data, this research aimed at determining the allele and genotype frequencies of the single-nucleotide polymorphisms (SNPs) in the FAM13A1, OPN, LAP3, and HCAP-G genes in a herd of Jersey cows, as well as establishing possible associations between the genotypes and the milk-performance traits of the examined herd of cattle.

The scattering process of electromagnetic waves by a conductive half-plane, located between isorefractive media, is investigated. First, the conductive sheet at the interface of isorefractive media is considered. The reflection and transmission coefficients of the plane are evaluated. The diffracted fields by the half-plane are obtained with the aid of a relation between the diffracted and scattered geometrical optics waves. The resultant field expressions are numerically examined.

The uniform asymptotic theory of diffraction is reintroduced in terms of the Fresnel cylinder function for the diffraction problems of cylindrical waves. The transition function of the above theory, which compensates the discontinuities of the diffracted wave, is constructed according to the new function. The scattering problem of waves by a resistive half‐plane is studied by the aid of the improved method. The uniform wave expressions are compared with the ones, obtained by the Fresnel integral at the near and far fields of the edge.

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