Holonomy groups of pseudo-quaternionic-K\"ahlerian manifolds of non-zero scalar curvature

The holonomy group $G$ of a pseudo-quaternionic-K\"ahlerian manifold of signature $(4r,4s)$ with non-zero scalar curvature is contained in \Sp(1)\cdot\Sp(r,s) and it contains \Sp(1). It is proved that either $G$ is irreducible, or $s=r$ and $G$ preserves an isotropic subspace of dimension $4r$, in the last case, there are only two possibilities for the connected component of the identity of such $G$. This gives the classification of possible connected holonomy groups of pseudo-quaternionic-K\"ahlerian manifolds of non-zero scalar curvature.Comment: 7 pages; Dedicated to Dmitri Vladimirovich Alekseevsky at the occasion of his 70th birthda

Automated knowledge capture in 2D and 3D design environments

In Life Cycle Engineering, it is vital that the engineering knowledge for the product is captured throughout its life cycle in a formal and structured manner. This will allow the information to be referred to in the future by engineers who did not work on the original design but are wanting to understand the reasons that certain design decisions were made. In the past, attempts were made to try to capture this knowledge by having the engineer record the knowledge manually during a design session. However, this is not only time-consuming but is also disruptive to the creative process. Therefore, the research presented in this paper is concerned with capturing design knowledge automatically using a traditional 2D design environment and also an immersive 3D design environment. The design knowledge is captured by continuously and non-intrusively logging the user during a design session and then storing this output in a structured eXtensible Markup Language (XML) format. Next, the XML data is analysed and the design processes that are involved can be visualised by the automatic generation of IDEF0 diagrams. Using this captured knowledge, it forms the basis of an interactive online assistance system to aid future users who are carrying out a similar design task

Observation of the spontaneous vortex phase in the weakly ferromagnetic superconductor ErNi2_{2}B2_{2}C: A penetration depth study

The coexistence of weak ferromagnetism and superconductivity in ErNi$_{2}$B$_{2}$C suggests the possibility of a spontaneous vortex phase (SVP) in which vortices appear in the absence of an external field. We report evidence for the long-sought SVP from the in-plane magnetic penetration depth $\Delta \lambda (T)$ of high-quality single crystals of ErNi$_{2}$B$_{2}$C. In addition to expected features at the N\'{e}el temperature $T_{N}$ = 6.0 K and weak ferromagnetic onset at $T_{WFM}=2.3$K, $\Delta \lambda (T)$ rises to a maximum at $T_{m}=0.45$ K before dropping sharply down to $\sim$0.1 K. We assign the 0.45 K-maximum to the proliferation and freezing of spontaneous vortices. A model proposed by Koshelev and Vinokur explains the increasing $\Delta \lambda (T)$ as a consequence of increasing vortex density, and its subsequent decrease below $T_{m}$ as defect pinning suppresses vortex hopping.Comment: 5 pages including figures; added inset to Figure 2; significant revisions to tex

A 2k2k-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$

Antibiofilm forming, antimicrobial activity and some biochemical properties of Vaccinium vitis idaea leaf and berry extracts on Staphylococcus aureus

Infections caused by Staphylococcus genus bacteria remain a relevant problem due to the high percentage of antibio­tic-resistant biofilm-forming strains of isolates of this genus. Herbs are a promising source for many biologically active compounds with antimicrobial properties. The aim of the research was to study the antimicrobial and antibiofilm formation activity of berry and leaf extracts of Vaccinium vitis-idaea L. upon clinical isolates of S. aureus, and the main biochemical properties of these extracts. For the purpose of analysis, we used S. aureus isolated from the mouth cavities and pharynx of human patients suffering from inflammatory diseases. The plants for the study were gathered in Pylypets, Mizhhiria rayon, Zakarpatska oblast (Transcarpathia). From Vaccinium vitis-idaea L., leaf and berry extracts were produced. To determine the chemical properties of the extracts, the following constituents were investigated: total tannin, flavonoids, total phenols, anthocyanins (by spectrophotometric method), and the total amount of vitamin C in berry extract (chromatographically). The antimicrobial activity was studied by diffusion-into-agar method and determination of minimum inhibitory concentrations. The antibiofilm activity of the extracts was tested in standard 96-well microtitration plates. The main chemical composition of ethyl extracts of Vaccinium vitis-idaea L. berries and leaves was identified. The level of tannins in leaf extracts was established to be higher than in fruit extracts (3.50% and 0.26% per 100 g of extract, respectively). It was shown that extracts of V. vitis-idaea berries and leaves demonstrate high antimicrobial activity against clinical isolates of S. aureus. Further it was established that leaf extracts had high ability to destroy the bacterial biofilm of S. aureus. Leaf extracts were also able to destroy the formed biofilm. Even in the 0.01% concentration, leaf extract inhibited the formation of the biofilm by 69.9% and caused the destruction of the formed biofilm by 62.5%. Thereby, the obtained results show good prospects for the use of V. vitis-idaea leaf extracts as an anti-staphylococcal remedy with antibiofilm forming properties

A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations

We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.Comment: 33 pages, no figure

The Entropy of Lagrange-Finsler Spaces and Ricci Flows

We formulate a statistical analogy of regular Lagrange mechanics and Finsler geometry derived from Grisha Perelman's functionals generalized for nonholonomic Ricci flows. There are elaborated explicit constructions when nonholonomically constrained flows of Riemann metrics result in Finsler like configurations, and inversely, and geometric mechanics is modelled on Riemann spaces with preferred nonholonomic frame structure.Comment: latex2e, 20 pages, v3, the variant accepted to Rep. Math. Phy

Ветеринарна медицина і використання лікарських рослин

The article deals with the history of development of veterinary medicine in the Eastern Europe (Austria-Hungary) and Galicia from the Middle Ages to our days. Particular attention is paid to the history of use of plants in veterinary practice. Herbal treatment of animals in the past times was described in Martin Cech's book The book of Horses Treatment (Budapest, 1797). An analysis of modern literature was conducted with the issue of use of plants in veterinary medicine. Basically, it is the use of phytodactyls for feed as an alternative to antibiotics, dyes or other synthetic medicines in pig breeding, poultry farming, fish farming, dairy cattle-breeding and for reducing the bacteriological contamination of food, feed additives and veterinary drugs as well. These actions ensure the ecological safety of livestock products. In modern veterinary plants and their extracts are used as phytodactyls for feed, in particular: Silybum marianum, Echinacea purpurea, Tagetes erecta that increase chickens’ and piglets’ body weight gain, decrease level of diseases and improve organoleptic indicators of carcasses of broiler chickens. Due to the content of various biologically active substances herbal preparations have antimicrobial, immunostimulating, general health improving effect on an animal’s organism. Phytopreparations are used to improve digestion, enhance immunity, growth and reduce morbidity of animals. Phytopreparations are used as bactericidal medications for prevention and treatment of infectious diseases. With prophylactic and curative aim are used phytodactylos, such as “Fitovet”, “Aciprogentin” і “Progentin”, “Species chamomillae SPOFA”. Galega orientalis, Origanum vulgare, species of the genus Philadelphus and other medical plants that contain a huge amount of flavonoids and essential oils. They have bactericidal properties and can be used for prophylactic and treatment of diseases and air disinfections on farms. Unfortunately, we still do not know much about the herbal treatment of animals. The modern veterinarian does not have enough knowledge about the possibilities of using medicinal plants in veterinary medicine.В статті розглянуто історію становлення ветеринарної медицини в Східній Європі (Австро-Угорщині) та Україні, починаючи з Середньовіччя, до наших днів. Особливу увагу приділено історії застосування рослин у ветеринарній практиці. Лікування рослинами тварин в минулому описано з архівної книжки Мартіна Чеха “Книга про лікування коней” (Будапешт, 1797 рік). Проведено аналіз сучасної літератури з питання використання лікарських рослин у ветеринарії. В основному, їх застосовують як фітодобавки до кормів – як альтернативу антибіотикам, барвниками чи іншим синтетичним препаратам у свинарстві, птахівництві, рибництві, молочному скотарстві, а також для зменшення бактеріологічного забруднення продуктів харчування, кормових добавок та ветеринарних препаратів. Це поліпшить екобезпеку продукції тваринництва. Рослинні препарати завдяки вмісту різних біологічно – активних речовин мають антимікробну, імуностимулюючу, загальнозміцнюючу дію на організм тварини. Фітопрепарати використовують для поліпшення травлення, зміцнення імунітету, вони пришвидшують ріст та зменшують захворюваність тварин. Як бактерицидні препарати їх використовують для профілактики та лікування інфекційних захворюваннях. На жаль, ми ще мало знаємо про лікування рослинами тварин і сучасний ветеринар не має достатніх знань про можливості використання лікарських рослин у ветеринарії

Holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature (4,4)(4,4)

Possible holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature $(4,4)$ are classified. Using this, a new proof of the classification of simply connected pseudo-quaternionic-K\"ahlerian symmetric spaces of signature $(4,4)$ is obtained.Comment: 16 page

S-wave/spin-triplet order in superconductors without inversion symmetry: Li2_2Pd3_3B and Li2_2Pt3_3B

We investigate the order parameter of noncentrosymmetric superconductors Li$_2$Pd$_3$B and Li$_2$Pt$_3$B via the behavior of the penetration depth $\lambda(T)$. The low-temperature penetration depth shows BCS-like behavior in Li$_2$Pd$_3$B, while in Li$_2$Pt$_3$B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li$_2$Pd$_3$B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li$_2$Pt$_3$B allows the spin-triplet component to be larger in Li$_2$Pt$_3$B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of $\lambda(T)$. The experimental data are in quantitative agreement with theory.Comment: Phys. Rev. Lett. (in press). More details are include