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Solutions of the time-independent Schrödinger equation by uniformization on the unit circle

Abstract

The idea presented here of a general quantization rule for bound states is mainly based on the Riccati equation which is a result of the transformed, time-independent, one-dimensional Schrödinger equation. The condition imposed on the logarithmic derivative of the ground state function W 0 allows to present the Riccati equation as the unit circle equation with winding number equal to one which, by appropriately chosen transformations, can be converted into the unit circle equation with multiple winding number. As a consequence, a completely new quantization condition, which gives exact results for any quantum number, is obtained.

Open access
Investigation of A Fuzzy Problem by the Fuzzy Laplace Transform

Abstract

This paper is on the solutions of a fuzzy problem with triangular fuzzy number initial values by fuzzy Laplace transform. In this paper, the properties of fuzzy Laplace transform, generalized differentiability and fuzzy arithmetic are used. The example is solved in relation to the studied problem. Conclusions are given.

Open access
A New Approach For Weighted Hardy’s Operator In VELS

Abstract

A considerable number of research has been carried out on the generalized Lebesgue spaces L p(x) and boundedness of different integral operators therein. In this study, a new approach for weighted increasing near the origin and decreasing near infinity exponent function that provides a boundedness of the Hardy’s operator in variable exponent space is given.

Open access
Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Abstract

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Open access
Association of Human Parvovirus B19 Infection with Development and Clinical Course of Myalgic Encephalomyelitis / Chronic Fatigue Syndrome

Abstract

Our aim was to estimate the presence of B19V infection markers, the level of cytokines and time period since the appearance of infection in association with ME/CFS clinical symptoms. In 200 ME/CFS patients and 104 control group individuals the presence of B19V-specific IgG/IgM class antibodies, B19V NS1 gene sequence, mRNA expression, viral load and level of cytokines were determined. B19V-specific IgG-antibodies were found in 70% of ME/CFS patients and 67.4% of controls, IgM-antibodies in 8% of patients and in none of controls, B19V genomic sequences in 29% of patients and 3.8% of controls. 58.6% of positive patients had active and 41.4% had latent/persistent B19V infection. B19V NS1 gene expression was detected in 43% of patients. B19V load varied from < 0.2 copies to median 38.2 copies/µg of DNA. According to the antibody pattern, 36% of patients had a recent, and 43% had sustained B19V infection. Patients with the B19V genomic sequence and NS1 specific antibodies significantly more often had lymphadenopathy and multi-joint pain. Onset of the symptoms corresponded to time of appearance of B19V infection. IL-10 and TNF-levels were higher in patients with elevated B19V load. B19V genome 1 was identified in Latvian ME/CFS patients. The results indicated that at least in some cases B19V infection plays an important role in ME/CFS development

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Colourability and word-representability of near-triangulations

Abstract

A graph G = (V;E) is word-representable if there is a word w over the alphabet V such that x and y alternate in w if and only if the edge (x; y) is in G. It is known [6] that all 3-colourable graphs are word-representable, while among those with a higher chromatic number some are word-representable while others are not.

There has been some recent research on the word-representability of polyomino triangulations. Akrobotu et al. [1] showed that a triangulation of a convex polyomino is word-representable if and only if it is 3-colourable; and Glen and Kitaev [5] extended this result to the case of a rectangular polyomino triangulation when a single domino tile is allowed.

It was shown in [4] that a near-triangulation is 3-colourable if and only if it is internally even. This paper provides a much shorter and more elegant proof of this fact, and also shows that near-triangulations are in fact a generalization of the polyomino triangulations studied in [1] and [5], and so we generalize the results of these two papers, and solve all open problems stated in [5].

Open access
The Deletion-Insertion model applied to the genome rearrangement problem

Abstract

Permutations are frequently used in solving the genome rearrangement problem, whose goal is finding the shortest sequence of mutations transforming one genome into another. We introduce the Deletion-Insertion model (DI) to model small-scale mutations in species with linear chromosomes, such as humans. Applying one restriction to this model, we obtain the transposition model for genome rearrangement, which was shown to be NP-hard in [4]. We use combinatorial reasoning and permutation statistics to develop a polynomial-time algorithm to approximate the minimum number of transpositions required in the transposition model and to analyze the sharpness of several bounds on transpositions between genomes.

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Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done

Abstract

This paper basically completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have enumerated avoiders for all but 14 of them. One of these 14 is conjectured not to have an algebraic generating function. Here, we find the generating function for each of the remaining 13, and it is algebraic in each case.

Open access
EVALD – a Pioneer Application for Automated Essay Scoring in Czech

Abstract

In the paper, we present EVALD applications (Evaluator of Discourse) for automated essay scoring. EVALD is the first tool of this type for Czech. It evaluates texts written by both native and non-native speakers of Czech. We describe first the history and the present in the automatic essay scoring, which is illustrated by examples of systems for other languages, mainly for English. Then we focus on the methodology of creating the EVALD applications and describe datasets used for testing as well as supervised training that EVALD builds on. Furthermore, we analyze in detail a sample of newly acquired language data – texts written by non-native speakers reaching the threshold level of the Czech language acquisition required e.g. for the permanent residence in the Czech Republic – and we focus on linguistic differences between the available text levels. We present the feature set used by EVALD and – based on the analysis – we extend it with new spelling features. Finally, we evaluate the overall performance of various variants of EVALD and provide the analysis of collected results.

Open access
Fast-Track Surgery and Early Rehabilitation for Total Hip Replacement in Hospital of Traumatology and Orthopaedics

Abstract

Due to an ageing population, the necessity for hip replacement has grown, and therefore, new options are being sought, such as the Fast-track principle, to improve patient condition, reduce their hospital stay and enhance the hospital’s ability to treat more patients. The aim of this study was to investigate the effects of same-day patient mobilisation on pain, side effects, complications, duration of hospital stay, and recovery after primary hip replacement, using intermediate-acting local anaesthetics in spinal anaesthesia (SA). A prospective, randomised study was conducted at the Hospital of Traumatology and Orthopaedics. Forty-six patients undergoing total hip replacement were selected and divided into two groups. Spinal anaesthesia was performed in study group (P) with 70 mg plain prilocaine. The control group (B) received 18 mg heavy bupivacaine in SA. On the first postoperative day, pain during movement was 2.00 (P) and 3.33 (B) on the Numeric Pain Rating Scale, the duration of hospital stay in the study group was shorter by ~1 day, and patient self-care was better in the study group. When the Fast-track principle is used with intermediate-acting SA and early rehabilitation, it is possible to reduce post-operative pain during movement, reduce the length of stay and improve patient self-care abilities.

Open access