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Tomasz Łukasz Żynda

Abstract

In this paper we will introduce the concept of weighted reproducing kernel of l 2(ℂ) space, in similiar way as it is done in case of weighted reproducing kernel of Bergman space. We will give an explicit formula for it and prove that it depends analytically on weight. In addition, we will show some theorems about dependance of l 2(ℂ) space on weight.

Open access

Jean-Paul Mavoungou

Abstract

Let F be an endofunctor of a category 𝒞. We prove isomorphism theorems for F-coalgebras under condition that the underlying category 𝒞 is exact; that is, regular with exact sequences. Also, F is not assumed to preserve pullbacks.

Open access

Ekaterina N. Baranova, Inna A. Chaban, Neonila V. Kononenko, Alexander A. Gulevich, Ludmila V. Kurenina and Elena A. Smirnova

Abstract

We investigated how an abiotic factor, i.e. salinity, affects specific intracellular organelles of cells of the root cap. We focused on: 1) amyloplasts, which are specific plastids of the cap that perform important metabolic and sensory functions; and 2) mitochondria, which protect cells from ROS damage by changing their ultrastructure. In our work we studied the ultrastructural changes of these organelles in different areas of the root cap under NaCl and Na2SO4 impact. We showed that the amyloplasts (statoliths) and mitochondria of the columella and the peripheral zone of the cap change their structural organisation in the presence of NaCl. Under action of Na2SO4, in plastids of columella the number of starch grains decreases dramatically, the cells of the peripheral part of the cap do not contain the amyloplasts, and the proplastids that do not store or store a little starch grains, which is attributed to leucoplasts with typical lamellae characteristic for root cortex cells. Thus, Na2SO4 influence has the most significant effect on the plastids of the root cap, and plastids of the cells of the peripheral zone of the cap are subjected to the most significant changes under salinity stress.

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Arzu Cihan, Ayşe Zeynep Azak, Mehmet Ali Güngör and Murat Tosun

Abstract

In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic Fibonacci and negadual-hyperbolic Lucas numbers. Finally, Binet formulas, D’Ocagne, Catalan and Cassini identities are obtained for dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers.

Open access

Dana Piciu, Christina Theresia Dan and Florentina Chirteş

Abstract

In this paper we introduce a new class of residuated lattice: residuated lattice with (C&→) property and we prove that (C&→) ⇔ (C ) + (C∧).Also, we introduce and characterize C , C∨, C∧ and C& → filters in residuated lattices (i.e., we characterize the filters for which the quotient algebra that is constructed via these filters is a residuated lattice with C (C∨ or C∧ or C&→ property). We state and prove some results which establish the relationships between these filters and other filters of residuated lattices: BL filters, MTL filters, divisible filters and, by some examples, we show that these filters are different. Starting from the results of algebras, we present for MTL filters, BL filters and C&→ filters the decomposition conditions.

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Iryna Denega and Yaroslav Zabolotnii

Abstract

In geometric function theory of a complex variable problems on extremal decomposition with free poles on the unit circle are well known. One of such problem is the problem on maximum of the functional

rγ(B0,0)k=1nr(Bk,ak),

where B 0, B 1, B 2,..., Bn, n ≥ 2, are pairwise disjoint domains in ¯𝔺, a 0 = 0, |ak| = 1, k=1,n¯and γ ∈ 2 (0; n], r(B, a) is the inner radius of the domain, B ⊂ ¯𝔺, with respect to a point aB. In the paper we consider a more general problem in which restrictions on the geometry of the location of points ak, k=1,n¯are weakened.

Open access

Baiba Zandersone, Elita Medvedja, Arnolds Jezupovs, Iveta Līduma, Solvita Selderiņa, Sandra Leja, Sintija Sausa and Tatjana Tračevska

Abstract

Colonisation of gastrointestinal tract by extended spectrum beta lactamase (ESBL)-producing Gram-negative bacteria is a source for infections. The present work is a prospective study in Latvia aimed to determine the role of two surgical profile wards in transmission of ESBL-producing bacteria. Differences between hospital wards were not analysed due to low number of patients. We have also determined a correlation between the duration of hospitalisation and risk of ESBL colonisation. Tests for ESBL-producing bacteria were made twice for 136 patients — upon admission and upon discharge from the hospital. Of them, 21 (15.4%) patients already were ESBL-positive at the time of admission and 115 (84.6%) patients were ESBL-negative. Upon discharge from hospital, 45 (33.1%) patients were ESBL-positive, one patient was ESBL-negative, and 25 (18.4%) of ESBL-positive cases had emerged during hospitalisation. In total, 46 (33.8%) from 136 patients were ESBL-positive and ESBL was positive in 51 bacterial isolates. On discharge from hospital, the newly acquired ESBL-positive bacterial isolates were K. pneumoniae (n = 18), E. coli (n = 7) and P. mirabilis (n = 3). The prevalence of ESBL-positive E. coli from all detected E. coli was 7.0% and from all Klebsiella spp. — 88.9% in gut flora. Analysis of patientassociated wound infections did not show correlation between the ESBL-producing gut microbiota and the bacterial species involved in wound infection.

Open access

H. Shojaei, R. Ameri and S. Hoskova-Mayerova

Abstract

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects A and B, the class of all morphisms from A to B denoted by Mor(A, B), admits an algebraic hyperstructures, such as semihypergroup or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semihyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories.

Open access

Jan Kuske and Stefania Petra

Abstract

The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The CS theory shows that any signal/image can be undersampled at a rate dependent on its intrinsic complexity. Moreover, in such undersampling regimes, the signal can be recovered by sparsity promoting convex regularization like 1- or total variation (TV-) minimization. Precise relations between many low complexity measures and the sufficient number of random measurements are known for many sparsity promoting norms. However, a precise estimate of the undersampling rate for the TV seminorm is still lacking. We address this issue by: a) providing dual certificates testing uniqueness of a given cosparse signal with bounded signal values, b) approximating the undersampling rates via the statistical dimension of the TV descent cone and c) showing empirically that the provided rates also hold for tomographic measurements.

Open access

M. Marin, A. Chirilă, L. Codarcea and S. Vlase

Abstract

This study is concerned with the theory of thermoelasticity of type III proposed by Green and Naghdi, which is extended to cover the bodies with dipolar structure. In this context we construct a boundary value problem for a prismatic bar which is subjected to some harmonic in time vibrations. For the oscillations whose amplitudes have the frequency lower than a critical value, we deduce some estimates for describing the spatial behavior.